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Microwave measurement and modeling of the dielectric properties of vegetation

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MICROWAVE MEASUREMENT AND MODELING OF
DIELECTRIC PROPERTIES OF VEGETATION
A Dissertation
Submitted to the College of Graduate Studies and Research
in Partial Fulfillment of the Requirement
for the Degree of Doctor of Philosophy
in the
Department of Electrical Engineering
University of Saskatchewan
by
BIJAY LAL SHRESTHA
Copyright B. L. Shrestha, January 2006, All rights reserved.
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UNIVERSITY OF SASKATCHEWAN
College of Graduate Studies and Research
SUMMARY OF DISSERTATION
Submitted in partial fulfillment
of the requirements for the
DEGREE OF DOCTOR OF PHILOSOPHY
by
Bijay L Shrestha
Department o f Electrical Engineering
University of Saskatchewan
January 2006
Examining Committee:
Dr. G. Schoenau
Dr. S. O. Faried
Dr. H. C. Wood
Dr. D. E. Dodds
Dr. M. DeJong
Dr. V. Meda
Dean/Associate Dean, Dean's Designate, Chair
College of Graduate Studies and Research
Chair of Advisory Committee, Department of
Electrical Engineering
Supervisor, Department of Electrical Engineering
Department of Electrical Engineering
Department of Electrical Engineering
Department of Agricultural and Bioresource
Engineering
External Examiner:
Dr. D. Jayas
Centre for Functional Foods & Nutraceuticals
207 Administration Bldg
University of Manitoba
Winnipeg MB R3T 2N2
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BIOGRAPHICAL
Place of birth
Kathmandu, Nepal
1999 - date
Doctor of Philosophy
Electrical Engineering Department, University of
Saskatchewan, Saskatoon
Lecturer
Department of Electronics and computer engineering,
Tribhuvan University, Kathmandu, Nepal
Master of Science
Electrical Engineering Department, University of
Saskatchewan, Saskatoon, SK
Lecturer
Department of Electronics and computer engineering,
Tribhuvan University, Kathmandu, Nepal
Technical Officer
Nepal Television Cooperation, Kathmandu, Nepal
Bachelor of Engineering
Beijing University of Post and Telecommunication,
Beijing, P. R. China
1996-1999
1994- 1996
1993- 1994
1991 - 1993
1985- 1990
Currently
Senior Design Engineer, Hinz Automation Inc.,
Saskatoon
HONOURS
•
•
•
•
•
Canada NSERC grant for Doctor of Philosophy
Canadian International Development Agency (CIDA) Master of Science scholarship
His Majesty’s Government of Nepal/China undergraduate scholarship
Japan Cooperation International Agency (JICA) audio video training at NHK, Japan
King Birendra Bir Bikram Shah Dev coronation medal
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f
PUBLICATIONS
S. No.
Title of paper
Status
Prediction Of Moisture Content Of Alfalfa Using Density
Independent Functions Of Microwave Dielectric Properties.
Bijay Shrestha, Hugh C Wood, and Shahab Sokhansanj
Journal o f Measurements Science and Technology (England)
Published:
MST 16: 1179 1185,2005
2
Dielectric properties of fresh/frozen Saskatoon berries at
different Pretreatments and Osmotic conditions.
Reddy, L.N., V Meda and B Shrestha.
North Central ASAE/CSAE Intersectional Conference,
Winnipeg
September 26-28,
2004
3
Modeling Of Vegetation Permittivity At Microwave
Frequencies
Bijay Shrestha, Hugh C Wood, and Shahab Sokhansanj
IEEE Transactions on Geoscience and Remote Sensing
in review process
4
A Technique For Microwave Dielectric Measurement Of
Cylindrical Tissues Using Open-Ended Coaxial Probe
Bijay Shrestha, Hugh C Wood, and Shahab Sokhansanj
IEEE Transactions on Instrumentation and Measurement
in review process
5
Determining Moisture Content Of Alfalfa From Microwave
Dielectric Properties Using An Artificial Neural Network
Bijay Shrestha, Hugh C Wood, and Shahab Sokhansanj
IEEE Transactions on Instrumentation and Measurement
in review process
Measurement O f Vegetation Permittivity At Microwave
Frequencies Using Open-Ended Coaxial Probe
Bijay Shrestha, Hugh C Wood, and Shahab Sokhansanj
J. Phys. D: Appl. Phys
in review process
1
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COPYRIGHT
The author has agreed that the Library, University of Saskatchewan, may make
this thesis freely available for inspection. Moreover, the author has agreed that
permission for extensive copying of this thesis for scholarly purposes may be granted by
the professor or professors who supervised the thesis work recorded herein or, in their
absence, by the Head of the Department or the Dean of the College in which the thesis
work was done. It is understood that due recognition will be given to the author of this
thesis and to the University of Saskatchewan in any use of the material in this thesis.
Copying or publication or any other use of the thesis for financial gain without the
approval o f the University of Saskatchewan and the author’s written permission is
prohibited.
Requests for permission to copy or to make any other use of the material in this
thesis in whole or in part should be addressed to.
Head of the Department of Electrical Engineering
University of Saskatchewan, 57 Campus Drive
Saskatoon, Saskatchewan, Canada, S7N 5A9
i
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ACKNOWLEDGMENTS
There are many people the author wishes to thank for all their help. First and
foremost, thanks must go to Dr. Hugh C. Wood, Professor of Electrical Engineering, for
his invaluable suggestions and consistent encouragement through the preparation of this
thesis. The author also wants to take this opportunity to thank Dr. Shahab Sokhansanj,
Professor o f Agriculture and Bio-resource Engineering, for external supervision and
providing lab space to set up the dielectric measurement system at Visual Properties
Laboratory in the Department of Agriculture and Bio-resource Engineering.
It is a pleasure to acknowledge the help of Dr. Bruce Coulman, Assistant Section
Head, Breeding, Curator Forage Germplasm Node, Agriculture and Agri-Food Canada
(AAFC), and Dr. Branka Bari, Program Leader Saskatchewan Herb Research Program,
Department of Plant Sciences, University of Saskatchewan in providing the alfalfa
plants used in this research.
My appreciation also goes to Bill Crerar, Wayne Morley, and Louis Roth from
Department of Agriculture and Bio-resource Engineering, Dave Karaloff from
Department of Electrical Engineering, and Garth wells from Telecommunication
Research Laboratory, Research Drive at Saskatoon for their help.
The financial support provided by the Natural Sciences and Engineering
Research Council (NSERC) is thankfully acknowledged.
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ABSTRACT
Some of the important applications of microwaves in the industrial, scientific and
medical sectors include processing and treatment of various materials, and determining
their physical properties. The dielectric properties of the materials of interest are
paramount irrespective of the applications, hence, a wide range of materials covering
food products, building materials, ores and fuels, and biological materials have been
investigated for their dielectric properties. However, very few studies have been
conducted towards the measurement of dielectric properties of green vegetations,
including commercially important plant crops such as alfalfa. Because of its high
nutritional value, there is a huge demand for this plant and its processed products in
national and international markets, and an investigation into the possibility of applying
microwaves to improve both the net yield and quality of the crop can be beneficial.
Therefore, a dielectric measurement system based upon the probe reflection technique
has been set up to measure dielectric properties of green plants over a frequency range
from 300 MHz to 18 GHz, moisture contents from 12%, wet basis to 79%, wet basis,
and temperatures from -15°C to 30°C. Dielectric properties of chopped alfalfa were
measured with this system over frequency range of 300 MHz to 18 GHz, moisture
content from 11.5%, wet basis, to 73%, wet basis, and density over the range from 139
kg rrf 3 to 716 kg m'3 at 23°C. The system accuracy was found to be ± 6 % and ±10% in
measuring the dielectric constant and loss factor respectively.
Empirical, semi empirical and theoretical models that require only moisture
content and operating frequency were determined to represent the dielectric properties of
both leaves and stems of alfalfa at 22°C. The empirical models fitted the measured
dielectric data extremely well. The root mean square error (RMSE) and the coefficient
of determination (r2) for dielectric constant and loss factor of leaves were 0.89 and 0.99,
and 0.52 and 0.99 respectively. The RMSE and r2 values for dielectric constant and loss
factor of stems were 0.89 and 0.99, and 0.77 and 0.99 respectively. Among semi
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empirical or theoretical models, Power law model showed better performance (RMSE =
1.78, r = 0.96) in modeling dielectric constant of leaves, and Debye-ColeCole model
was more appropriate (RMSE = 1.23, r 2 = 0.95) for the loss factor. For stems, the
Debye-ColeCole models (developed on an assumption that they do not shrink as they
dry) were found to be the best models to calculate the dielectric constant with RMSE =
0.53 and r2 = 0.99, and dielectric loss factor with RMSE = 0.65 and r2 = 0.95.
Density independent functions, DIFs of dielectric properties and artificial neural
networks, ANNs with inputs of dielectric properties were investigated for their ability to
rapidly and reliably predict the moisture content of alfalfa chopped at particle size of
2.87 ± 1 stdev (1.31) mm over the moisture content ranging from 12%, wet basis, to
3
3
73%, wet basis, regardless of its density variation between 139 kg m' and 716 kg m" at
20°C. A DIF, the square root of loss factor over cube root of dielectric constant minus
one produced promising results with standard error of calibration of 0.58% moisture
content, wet basis, and the standard error of performance of 1.54% moisture content, wet
basis, and an ANN with inputs of dielectric properties measured at each of ten
frequencies L01, 1.98, 4.02, 5.96,
8
, 10, 12, 14, 16 and 18 GHz showed better
performance with RMSE of 1.09% moisture content, wet basis, compared to the
standard oven method.
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TABLE OF CONTENTS
COPYRIGHT
i
ACKNOWLEDGEMENTS
ii
ABSTRACT
iii
LIST OF FIGURES
viii
LIST OF TABLES
xvii
LIST OF SYMBOLS AND ABBREVIAIONS
xxi
1. INTRODUCTION............................................................................................................... 1
1.1 Overview....................................................................................................................... 1
1.2 Literature review ...........................................................................................................5
1.3 Research objectives.................................................................................................... 24
2. DIELECTRIC MEASUREMENT SYSTEMS...............................................................27
2.1 Slotted line reflection system.....................................................................................27
2.2 Guided or free space transmission system.................................................................30
2.3 Filled or partially filled cavity resonance systems...................................................32
3. PROBE REFLECTION SYSTEM.................................................................................. 37
3.1 Probe reflection system set up....................................................................................37
3.2 Determining e using an open-ended coaxial probe..................................................40
3.3 System calibration...................................................................................................... 44
3.4 Overall measurement uncertainty.............................................................................. 46
3.5 System accuracy......................................................................................................... 48
3.6 Sample size..................................................................................................................48
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4. MEASUREMENT RESULTS......................................................................................... 56
4.1 Introduction................................................................................................................. 56
4.2 Preliminary experiments............................................................................................. 57
4.2.1 Determining the optimum pressure................................................................ 57
4.2.2 Sensing the sample temperature deviation.................................................... 63
4.2.3 Quantifying the change in the sample moisture content.............................. 64
4.3 The dielectric properties of the alfalfa leaves............................................................65
4.3.1 Frequency dependence.................................................................................... 6 6
4.3.2 Moisture content dependence......................................................................... 72
4.3.3 Bound water dependence.................................................................................75
4.3.4 Temperature dependence.................................................................................77
4.4 The variability, repeatability and the effect of orientation.......................................82
4.5 The dielectric properties of alfalfa stem s.................................................................. 8 8
5. MODELING.................................................................................................................... 114
5.1 Introduction............................................................................................................... 114
5.2 Dry (free) vegetation density....................................................................................115
5.2.1 Nitrogen pycnometer method....................................................................... 115
5.2.2 Vacuum infiltration m ethod......................................................................... 116
5.2.3 Selection of the optimum densities...............................................................118
5.3 The gravimetric and the volumetric moisture contents..........................................119
5.4 The volume fractions of the plant constituents........................................................120
5.5 Dielectric properties of the plant constituents.........................................................123
5.5.1 Free water.......................................................................................................123
5.5.2 Bound water-vegetation............................................................................... 126
5.5.3 Dry vegetation and a ir...................................................................................126
5.6 Modeling the s for the alfalfa leaves....................................................................... 127
5.6.1 Polynomial (Poly).......................................................................................... 128
5.6.2 Power law (PL) model...................................................................................129
5.6.3 Modified Debye - Cole-Cole (DC) model.................................................. 134
5.6.4 Bruggeman models........................................................................................136
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5.6.5 The comparison of the model accuracies.................................................. 140
5.7 Modeling the
e for
alfalfa stems.............................................................................146
5.7.1. Polynomials (Poly)....................................................................................... 147
5.7.2 Power law (PL) model................................................................................... 147
5.7.3 Modified Debye - Cole-Cole (DC) m odel.................................................. 149
5.7.4 Bruggeman models........................................................................................ 149
5.7.5 Comparison o f the model accuracies............................................................159
6
. MOISTURE PREDICTION........................................................................................... 160
6.1 Introduction............................................................................................................... 160
6.2 Moisture prediction using the DIFs......................................................................... 162
6.2.1 Frequency dependence..................................................................................163
6.2.2 Density independence....................................................................................163
6.2.3 Moisture dependence..................................................................................... 166
6.3 Moisture prediction using artificial neural networks.............................................. 171
7. SUMMARY, CONCLUSION AND RECOMMENDATIONS................................. 176
7.1 Summary................................................................................................................... 176
7.2 Conclusions............................................................................................................... 184
7.3 Recommendations.................................................................................................... 186
REFERENCES.................................................................................................................... 188
APPENDIX A ..................................................................................................................... 199
APPENDIX B ......................................................................................................................208
APPENDIX C ......................................................................................................................232
APPENDIX D .....................................................................................................................245
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LIST OF FIGURES
Figure 1.1
Alfalfa
Figure 2.1
(a) Slotted coaxial line reflection system (b) voltage standing
6
wave without (solid line) and with (dashed line) sample
Figure 2.2
Transmission measurement system (b) applicators (i) wave
guide (ii) coaxial line and (iii) a pair of horn antennas
Figure 2.3
28
31
A test material of volume, Vs in a rectangular waveguide
resonant cavity of volume, Vc
33
Figure 3.1
A schematic of the probe reflection system
38
Figure 3.2
A photograph of the probe reflection system
38
Figure 3.3
3.3 HP 85070D Dielectric probe (a) side view (b) probe
aperture
Figure 3.4
39
(a) An open-ended coaxial probe opening into free space (s0),
and (b) its equivalent circuit model
41
Figure 3.5
(a) Directivity and (b) Source match errors
45
Figure 3.6
Error model used for minimizing the systematic errors
45
Figure 3.7
Measured and calculated s of Methanol at 20°C
49
Figure 3.8
The percent relative error of the system determined by
comparing the measured and the calculated e for methanol at
20°C
Figure 3.9
49
The maximum estimated and the observed percent relative error
of the system determined using Eqs. (3.12) and (3.13)
respectively for methanol at 20°C
50
Figure 3.10
Measured and calculated 8 of deionized water at 30°C
50
Figure 3.11
The percent relative error of the system determined by
comparing the measured and the calculated s for deionized
waterat30°C
51
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Figure 3.12
The maximum estimated and the observed percent relative error
of the system determined using Eqs. (3.12) and (3.13)
respectively for deionized water at 30°C
51
Figure 3.13
Measured £ of air at 30°C
52
Figure 3.14
Measured £ of Teflon at 20°C
52
Figure 3.15
The s' o f varying thickness of white bond paper backed by
Copper and Teflon at 300 MFIz
Figure 3.16
The s' o f varying thickness of white bond paper backed by
Copper and Teflon at 1.01 GHz
Figure 3.17
60
Similar e' trends of the alfalfa stems (bulk #2) at various
frequencies
Figure 4.4
59
The e' of the bulks of the alfalfa stems containing 50 stems in
each bulk at various pressures, and at 25°C
Figure 4.3
55
The spectra for the (a) s' and (b) the e" of the alfalfa leaves at
22°C at various pressures and at a moisture content of 73%
Figure 4.2
54
The s' o f varying thickness of white bond paper backed by
Copper and Teflon at 18 GHz
Figure 4.1
54
The s' o f varying thickness of white bond paper backed by
Copper and Teflon at 10.04 GHz
Figure 3.18
53
61
The e of the individual alfalfa stems with different diameters
plotted against the probe pressure (a) and (b) at 0.3 GHz, and
(c) and (d) at 18 GHz, and at 25°C
Figure 4.5
The trends for the temperatures of the leaf sample initially at
5°C subjected to the desired temperature of 30°C
Figure 4.6
64
The frequency dependence of the (a) e' and (b) the e" of the
alfalfa leaves at 22°C with moisture content as the parameter
Figure 4.7
63
6 6
The dielectric spectra of the distilled (0 ppt) , and the saline
water at various salinity, and at 22°C
68
Figure 4.8
The dielectric spectrum of the bound water at 22°C
68
Figure 4.9
The e" of the fluid extracted from the alfalfa leaves at 52 %
moisture content and that of the saline water (15 ppt) at 20°C
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69
Figure 4.10
Cole-Cole diagrams for the distilled water [Kraszewski, 1996],
the saline water at 4 ppt, the leaves at 73% moisture content,
and the bound water [Ulaby and El-Rayes, 1987] at 22°C
Figure 4.11
The Cole-Cole diagrams for the alfalfa leaves at various
moisture contents and at 22°C
Figure 4.12
73
The s' of the fluids extracted from the alfalfa leaves at three
moisture contents and at 22°C
Figure 4.14
71
The e of the alfalfa leaves vs. moisture content (a) s' and (b) s"
with the frequency as parameter at 22°C
Figure 4.13
70
75
The dielectric spectra of the alfalfa leaves for the (a) s' and (b)
the s" at a moisture content of 73 % with the temperature as the
parameter
Figure 4.15
78
The temperature dependence of the s of the saline water at a
concentration of 4 ppt
Figure 4.16
79
The (a) s' and (b) the s" of the alfalfa leaves at 73% moisture
content as a function of temperature with frequency as a
parameter
Figure 4.17
80
The temperature dependence of the free distilled water at
different frequencies
Figure 4.18
81
The means of the (a) s' and (b) the s" of the alfalfa leaves
calculated by measuring the five samples from each of the five
different moisture contents
Figure 4.19
84
The standard errors associated with the variation in measuring
the (a) s' and (b) the s" of the alfalfa leaves from each of the five
different moisture contents at varying frequencies
Figure 4.20
85
The means of the (a) s' and (b) s" of the alfalfa leaves obtained
by repeated measurement of a sample from each of the five
moisture contents at varying frequencies
Figure 4.21
8 6
The standard errors in measuring the (a) the s' and (b) s" due to
the repeated measurement of the same sample from each of the
five moisture contents at varying frequencies
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87
Figure 4.22
The means of the (a) s' and (b) e" of the alfalfa leaves obtained
by measuring the £ of a sample of alfalfa leaves from each of
five moisture content rotating 45° at four positions at varying
89
frequencies
Figure 4.23
The (a) s' and (b) s" for the five materials as a function of
diameters at 0.3 GHz and at 23°C
Figure 4.24
The (a) e' and (b) s" for the five materials as a function of
diameters at 0.48 GHz and at 23°C
Figure 4.25
96
The observed and the reference sSIS for (a) apple, (b) carrot, (c)
cantaloupe, and (d) potato at 23 °C
Figure 4.30
95
The (a) s' and (b) s" for the five materials as a function of
diameters at 18 GHz and at 23°C
Figure 4.29
94
The (a) e' and (b) s" for the five materials as a function of
diameters at 8 GHz and at 23°C
Figure 4.28
93
The (a) s' and (b) s" for the five materials as a function of
diameters at 3.22 GHz and at 23°C
Figure 4.27
92
The (a) s' and (b) e" for the five materials as a function of
diameters at 1.27 GHz and at 23°C
Figure 4.26
91
98
The mean values of the ^(%) for the “tissues” of varying
diameters at a frequency of (a) 0.3, (b) 0.48, (c) 1.27, (d) 3.22,
102
(e) 8 , and (f) 18 GHz
Figure 4.31
The means and the standard deviations of the £(%) for the
“tissues” of varying diameters at different frequencies
Figure 4.32
The ^(%) as a function of the frequency with the diameter as the
103
parameter
Figure 4.33
103
An experimental correction curve to calculate the £,(%) for the
material with varying diameter up to the operating frequency of
8
Figure 4.34
GHz (Y-error bar = ± 1 StDev)
(a) A comparison of and (b) the association between the
calculated and the measured e'sis f°r the apple tissues at 23°C
Figure 4.35
104
(a) A comparison of and (b) the association between the
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105
calculated and the measured e'SIS for the carrot tissues at 23 °C
Figure 4.36
106
(a) A comparison of and (b) the association between the
calculated and the measured e'SIS for the cantaloupe tissues at
23°C
Figure 4.37
107
(a) A comparison of and (b) the association between the
calculated and the measured g'sis f°r the potato tissues at 23°C
Figure 4.38
A comparison of the calculated and the measured e'sis f°r
Teflon at 23°C
Figure 4.39
The (a)
e 1 and
109
(b) the s" of the stems at a moisture content of
79% and at 23°C
Figure 4.40
110
The mean values of (a) the corrected s' and (b) the s" for the
alfalfa stems at 23°C
Figure 4.41
111
The frequency dependence of the (a) s' and (b) the e" of the
alfalfa leaves at 20°C with moisture content as the parameter
Figure 5.1
113
The trends for the volumes of the dry plant parts measured
using the Nitrogen pycnometer
Figure 5.2
108
116
The volume fractions of the constituents of (a) leaves and (b)
stems based upon the shrinking model where Mv = volumetric
moisture content, bw = bound water, bv = bound vegetation, fv
= free vegetation, tv = total vegetation, fw = free water, and a =
air
Figure 5.3
1 2 2
The salinity of the fluid (free saline water) contained in (a) the
leaves and (b) the stems at various moisture contents
Figure 5.4
Comparison of the measured and the calculated (a) s' and (b) the
e" of alfalfa leaves at a moisture content of 73% and at 22°C
Figure 5.5
131
Comparison of the measured and the calculated (a) e ' and (b) the
e" of the alfalfa leaves at a moisture content of 12% and at 22°C
Figure 5.7
130
Comparison of the measured and the calculated (a) s' and (b) the
s" of the alfalfa leaves at a moisture content of 45% and at 22°C
Figure 5.6
125
The association between the measured and the calculated (a) s'
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132
133
and (b) the e " of alfalfa leaves using polynomials
Figure 5.8
The measured and the calculated (a) s' and (b) the e" for the
alfalfa leaves at 22°C using the power law (PL) or Birchak
135
model
Figure 5.9
The measured and the calculated (a) s' and (b) the s" for alfalfa
leaves at 22°C using the Modified Debye - Cole-Cole (DC)
137
model
Figure 5.10
The association between the measured and the calculated values
for ( a ) the
e'
and
(b) the
e"
for the alfalfa leaves at 22°C obtained
141
using the BLD model
Figure 5.11
The association between the measured and the calculated values
for (a) the
e'
and (b) the
s"
for the alfalfa leaves at 22°C obtained
142
using the BLS model
Figure 5.12
The association between the measured and the calculated values
for (a) the e' and (b) the e" for the alfalfa leaves at 22°C obtained
143
using the BLN model
Figure 5.13
The association between the measured and the calculated values
for (a) the
s'
and (b) the
s"
for the alfalfa leaves at 22°C obtained
144
using the BUD model
Figure 5.14
The RMSE, r2, a and b values in fitting the measured
e
of the
alfalfa leaves using the various models
Figure 5.15
145
The association between the measured and the calculated values
for (a) the e' and (b) the e" for the alfalfa stems at 22°C obtained
148
using the Poly model
Figure 5.16
The association between the measured and the calculated values
for (a) the s' and (b) the
e
"
for the alfalfa stems at 22°C obtained
150
using the PL model
Figure 5.17
The association between the measured and the calculated values
for (a) the s' and (b) the s" for the alfalfa stems at 22°C obtained
using the DC model
Figure 5.18
152
The association between the measured and the calculated values
xiii
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for (a) the s' and (b) the e" for the alfalfa stems at 22°C obtained
157
using the BLD model
Figure 5.19
The association between the measured and the calculated values
for (a) the s' and (b) the e" for the alfalfa stems at 22°C obtained
158
using the BUD model
Figure 6.1
The variation in the measurement of (a) the s' and (b) the s"
with density for the particulate alfalfa at different moisture
contents, and at the operating frequency of 9.06 GHz and at
161
20°C
Figure 6.2
The spectra of the DIFs, (a) F2 and (b) F3 for the particulate
164
alfalfa at 20°C
Figure 6.3
The behaviours of the functions (a) F 2 and (b) F3 against the
density at various moisture contents and at 20°C
165
Figure 6.4
The moisture dependence of (a) F2 and (b) Fi at 20°C
167
Figure 6.5
An example of the graphics and the symbols adopted in
calculating the worst case relative errors,
Figure 6 . 6
170
The accuracy of the trained ANNs with varying number of
hidden neurons in predicting the moisture content of the
particulate alfalfa irrespective to its density at 20°C
Figure 6.7
173
The association between the predicted and the reference
(standard oven method) moisture content for particulate alfalfa
174
at 20°C
Figure A1
(a) A longitudinal cross section of the HP85070D dielectric
probe with Teflon jackets, (b) a bottom view of (a) in a sample
200
holder
Figure A2
(a) A sample holder in a temperature bath and (b) a top view of
(a)
201
Figure A3
A photograph of 823 50A PCI GPIB interface card
202
Figure A4
A photograph of a load cell connected to the ring probe holder
203
Figure A5
A photograph of a Corola Messtechnik GMBH Constant
Temperature Circulator (Bath) capable of circulating the waterxiv
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ethylene glycol liquid over the temperature range of -40°C to
+40°C
203
Figure A 6
An automatic network analyzer (ANA) system
204
Figure A7
A shot captured from the ANA display/processor unit - the
reflection coefficients at 201 frequency points ranging over 300
MHz - 18 GHz at a step of 88.5 MHz for distilled water at 24°C
Figure A 8
204
The snapshots of the (a) s' and (b) s", chart and data calculated
from the T shown in Fig. A7 using HP85070D software
205
Figure A9
A photograph of 2 IX Micrologger Data Logger
206
Figure A10
A conditioning circuit
206
Figure A11
A calibration curve to infer the pressure on the probe aperture
from observed voltage in DVM
Figure B1
207
The hollow Aluminum tubes with single sharp edge with the
inner diameters ranging from 1.67 to 6.52 mm (bottom row),
and the Teflon rods with the same range of diameters (upper
209
row)
Figures B2 - B7
The means and the standard deviations of the (a) s' and (b) the
s" of the cylindrical fruit “tissues” at varying diameters at
frequencies of 0.3, 0.48, 1.27, 3.22, 8 , and 18 GHz
Figures B 8 - B ll
210
The (a) s' and (b) s" of the stems vs. diameter atmoisture
contents of 42%, 51%, 62%, and 71% and at 23°C
216
Figures B12- - B16 The spectra for (a) the corrected mean s' and (b) themean s" of
the alfalfa stems at moisture contents of 42%, 51%, 62%, and
71% and at 23°C along with the standard deviation at each of
the
8 8
220
frequencies
Figure Cl
A photograph of a Nitrogen multipycnometer
Figure C2
The dielectric loss factor of the sodium chloride solution at
233
various salinity (ppt), and at operating frequency of 1 GHz and
233
at 22°C
Figures C3 -C 8
The measured and the calculated dielectric spectra for the
xv
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alfalfa leaves at moisture contents of
6 6
%, 45%, 52%, 31%,
23%, and 17%, w.b. based upon the shrinking model
Figures C9
A detailed view of the association between measured and
calculated e' of leaves at 22°C produced by polynomials
Figures D1
D4
246
DIO The behaviour of the DIFs F], F2 , F 3 , F4 , F 5 and F6 against the
density at various moisture contents and at 20°C
Figure D ll
240
The spectra of the DIFs Fi, F4 , F 5 , and F 6 for the particulate
alfalfa at 20°C
Figures D5
234
248
The moisture dependence of the DIFs Fi, F 2 , F 3 , F4 , F 5 and F 6
for the particulate alfalfa at 20°C
xvi
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253
LIST OF TABLES
Table 1.1
Different aspects of vegetation s measurement conducted in the
past
Table 1.2
Modeling of vegetation s investigated in the past
Table 2.1
A general comparison of the microwave dielectric measurement
systems
Table 3.1
Wavelengths in distilled water at 22°C for different operating
frequencies
Table 4.1
The frequencies, the moisture contents and the temperatures at
which the 8 of alfalfa leaves and stems were measured
Table 4.2
The mean difference between the desired and the achieved
sample temperatures
Table 4.3
The sample moisture contents before and after the dielectric
measurement, and the mean of the difference between them
Table 4.4
The relaxation time distribution, Ax, the most probable
relaxation frequency, fr, and the relaxation time, x for the leaves
at different moisture content, and that for the free and the bound
water at 22°C
Table 4.5
The
8
of the supercooled moisture in the vegetation materials
[Torgovnikov, 1993]
Table 4.6
The regression equations and the r values for the ^(%) at
different frequencies
Table 4.7
The statistical data showing the performance of the correction
curve
Table 5.1
Densities of dry plant parts measured using the Nitrogen
pycnometer (kg n f3)
Table 5.2
Densities of dry leaves and stems measured using the vacuum
xvii
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-5
infiltration method (kg m ')
Table 5.3
The optimum densities of the dry leaves and the stems chosen
■y
119
for the modeling (kg n f )
Table 5.4
The means and the standard deviation of the s for the leaves at
the moisture content of 1 2 % and white bond paper
Table 5.5
128
The statistical data showing the performance of the power law
(PL) model in modeling the s of the alfalfa leaves
Table 5.8
136
The Debye - Cole-Cole (DC) model accuracy in calculating the
s of the alfalfa leaves at 22°C
Table 5.10
134
The optimum values for the parameters, b, pa, and pn, based
upon the Debye - Cole-Cole (DC) model
Table 5.9
128
The model accuracy of the polynomial fit for the s' and the e" of
the alfalfa leaves
Table 5.7
127
The values for the coefficients of the polynomials that fitted the
measured s' and the e" of the alfalfa leaves
Table 5.6
118
136
The optimized parameters for the BLD, the BLS, the BLN, and
the BUD models in fitting the measured a for the alfalfa leaves
at various moisture contents and at 22°C
Table 5.11
139
The accuracies of the BLD, the BLS, the BLN, and the BUD
models in fitting the measured s for the alfalfa leaves at various
moisture contents and at 22°C
Table 5.12
Models in ascending and descending order respectively for
146
RMSE and r2 values
Table 5.13
The values for the coefficients of the polynomial in fitting the s'
and the s" of the alfalfa stems at 22°C
Table 5.14
140
147
The model accuracy of the polynomial in fitting the s' and the s"
of the alfalfa stems at 22°C
147
Table 5.15
The values of ‘k ’ for the power law (PL) models
149
Table 5.16
The model accuracy of the PL models in fitting the s' and the s"
of the alfalfa stems at 22°C
Table 5.17
The optimum values for the parameters, b, pa, and pn, based
xviii
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149
upon the Debye - Cole-Cole (DC) model for the alfalfa stems at
22°C
Table 5.18
151
The Debye - Cole-Cole (DC) model accuracy in calculating the
s of the alfalfa stems at 22°C
Table 5.19
The optimum values for the parameters, b, pa, and pn, based
upon the BLD model for the alfalfa stems at 22°C
Table 5.20
153
The optimum values for the parameters, b, pa, and pn, based
upon the BLN model for the alfalfa stems at 22°C
Table 5.22
154
The optimum values for the parameters, b, pa, and pn, based
upon the BLS model for the alfalfa stems at 22°C
Table 5.24
155
The optimum values for the parameters, b, pa, and pn, based
upon the BUD model for the alfalfa stems at 22°C
Table 5.26
156
The RMSE and r2 values in fitting the measured £ of the alfalfa
stems using the various models
Table 6.1
159
The ranges of the SEC and the SEP for the calibration equations
based upon the DIFs
Table 6.2
156
The BUD model accuracy in calculating the £ of the alfalfa
stems at 22°C
Table 5.27
155
The BLS model accuracy in calculating the e o f the alfalfa
stems at 22°C
Table 5.25
154
The BLN model accuracy in calculating the s of the alfalfa
stems at 22°C
Table 5.23
153
The BLD model accuracy in calculating the s of the alfalfa
stems at 22°C
Table 5.21
151
169
The worst case relative errors in percent moisture content,
associated with the calibration equations obtained using the
DIFs and operating at fopt for 11 moisture contents
Table 6.3
The selected frequencies used with the ANNs in predicting the
material moisture content
Table 6.4
171
172
Error statistics in percent moisture content and the training time
for the 20- <X>-1 networks
173
xix
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Table 6.5
Regression analysis of the measured vs. predicted moisture for
174
the 2 0 - <b - 1 networks
Table 7.1
Different aspects of vegetation s measurement conducted in the
past
Table 7.2
178
A general comparison of the microwave dielectric measurement
179
systems
Table 7.3
Frequencies, moisture contents and temperatures at which the s
181
of the plant parts were measured
Tables B1
B6
The means and the standard errors for the variability, the
repeatability and the orientation effect in measuring the s' of the
225
alfalfa leaves at 23°C
Table B7
The means and the standard deviations for the measured
diameters of the alfalfa stems at varying moisture contents and
231
at 23°C
Table D1
The slope, c and the intercept, d, or the magnitude, g, and the
'j
power, p, and the coefficient of determination, r for all DIFs
Table D2
254
The SEC and the SEP for the calibration equations depended
upon the DIFs in predicting the moisture content of the
particulate alfalfa at various frequencies and at 20°C
Tables D3
D8
256
The worst case relative error in percent moisture content, T
associated with the calibration equations obtained using the
DIFs
Table D9
256
The weights and biases to be used in the ANN that predicts
moisture content of chopped alfalfa
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264
LIST OF SYMBOLS AND ABBREVIATIONS
Symbol
Description
A
Attenuation
Aj
Depolarization factors along main axes ( j = 1, 2, or 3) of an
inclusion
B
Boltzmann’s constant
b
Ratio of volume fraction of bound water to volume fraction of
bound vegetation
Cj
Internal electric field concentration of a coaxial line
C0
Fringing field concentration in the surrounding free space
E
Electric field intensity
ed
Directivity error
ef
Frequency tracking error
es
Source match error
f
Frequency
fbwr
Relaxation frequency of bound water
f0
Resonant frequency of an empty cavity
fopt
Optimum frequency
fr
Relaxation frequency
fs
Resonant frequency of an cavity with sample
fSWr
Relaxation frequency of free saline water
Ia
Actual incident signal
Im
Measured incident signal
K
Absolute temperature
ls
Sample length
Mg
Gravimetric moisture content
Mtg
Threshold gravimetric moisture content
xxi
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Mv
Volumetric moisture content
me
Moisture content
Q
Quality factor of a resonant cavity
Qo
Quality factor of an empty resonant cavity
Qs
Quality factor of a resonant cavity with test sample
Ra
Actual reflected signal at measurement plane
Rm
Measured reflected signal at reference plane
r
Radius of a molecular sphere
T
Outer radius of the inner conductor of a coaxial line
r0
Inner radius of the outer conductor of a coaxial line
r2
Coefficient of determination
S
Salinity
Sab
S parameter
T
Temperature
Va
Volume of the air in the plant part,
Vc
Volume of a resonant cavity
Vs
Volume of a test material in a resonant cavity
Va
Volume fraction of air
Vbv
Volume fraction of bound vegetation
Vbw
Volume fraction of bound water
VfV
Volume fraction of free vegetation
Vi
Volume fraction of the i inclusion
Vtv
Total volume fraction of vegetation
VWv
Volume fraction of bound water-vegetation
w.b.
Wet basis
Yex
External admittance
Yin
Internal admittance
Yl
Total admittance
Ym
Measured admittance
Y0
Characteristic admittance
Z
Characteristic impedance of an applicator with test material
xxii
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Zo
Characteristic impedance of an empty applicator
a
Attenuation coefficient o f an applicator with test material
P
Phase change coefficient of an applicator with test material
Po
Phase change coefficient of an empty applicator
r
ra
rm
Actual reflection coefficient
y
Propagation coefficient
To
Propagation coefficient of an empty applicator
ye
Propagation coefficient of an applicator with test material
at
Relaxation time distribution
8
Permittivity or dielectric properties
Ebws
Static permittivity of bound water
£bw°o
Optical permittivity of bound water
Sfv
Permittivity of free vegetation
Eh
Permittivity of host inclusion
Ei
Permittivity of i inclusion
Esw
Permittivity of free saline water
Esws
Static permittivity of free saline water
Eswoo
Optical permittivity o f free saline water
So
Free space dielectric constant
8
Reflection coefficient
Measured reflection coefficient
'
Dielectric constant
"
*
Dielectric loss factor
8
e
/
es
Interfacial permittivity
Static dielectric constant
Optical dielectric constant
no
Intrinsic impedance of air
Xc
Cut-off wavelength
Wavelength in material
^0
Wavelength in free space
xxiii
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Ho
Permeability of air
o
Moisture content (w.b.)
5
Experimental correction coefficient
p
Density
Pa
Density of dry vegetation with air
Pn
Density of dry vegetation without air
Pw
Density of water
Pa/n
Ratio of pa to pn
CJi
Ionic conductivity
X
Relaxation time constant
<K
Number o f hidden neurons
Phase shift
The worst case relative error (% me, w.b.)
K
Viscosity
OJ
Angular frequency
xxiv
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Abbreviation
Description
AAFC
Agriculture and Agri-Food Canada
ANA
Automatic network analyzer
ANN
Artificial neural network
ASAE
American Society for Agricultural and Biological Engineers
BLD
Bruggeman lower limit circular disc model
BLN
Bruggeman lower limit needle model
BLS
Bruggeman lower limit sphere model
BUD
Bruggeman upper limit circular disc model
DC
Debye - Cole-Cole model
DIF
Density independent function
FSP
Fibre saturation point
GPIB
General purpose interface bus
PCI
Peripheral component interconnect standard
PL
Power law model
Poly
Polynomials
ppt
Parts per thousand
PTFE
Polytetrafluoroethylene
RMSE
Root mean square error
SEC
Standard error of calibration
SEP
Standard error of performance
SIS
Sample of infinite size
TE
Transverse electric mode
TEM
Transverse electromagnetic mode
TM
Transverse magnetic mode
XXV
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1. INTRODUCTION
1.1 Overview
Microwaves have been used in many industrial, scientific, medical, and domestic
(ISMD) applications [Thuery, 1992]. The major industrial applications include drying,
vulcanizing, polymerizing, melting, sintering, hardening, cooking and baking, thawing,
blanching, pasteurizing and sterilizing. The quantification of water content in materials,
the study of material molecular structure, soil treatment, germination, and crop
protection are some of the emerging fields in scientific applications. In medical
applications, antitumoral hyperthermia, used alone or in conjunction with conventional
treatment, is an attractive technique. To understand the interaction of microwaves with
matter in these applications, the microwave dielectric properties, or the permittivity, of
the material must be known. The dielectric property is a complex quantity consisting of
two parts namely the dielectric constant (s') and the dielectric loss factor (a"), and is
expressed as s = s' - js '\ These quantities respectively play important roles in
determining the local electric field within the material from the knowledge of the applied
electric field, and the power absorbed by the material, which is dissipated as heat
[Kraszewski, 1996].
Industrial application of microwaves on vegetation or plant crops is a promising
area. These plant crops include commercially important species such as alfalfa and
timothy. Because it has the highest nutritional values of any forage, alfalfa is regarded as
the “queen of forages”. Canadian hay industry has been exporting these crops and their
processed product for years, and in North America, the annual production of forage and
processed products, in particular alfalfa cubes and pellets, is worth over $15 billion
1
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2
annually. Unfortunately, slow and off-line moisture measurement techniques, and
inefficient and destructive conventional drying are still causing a substantial loss in both
the yield and the quality of this commercially important crop.
Moisture content is a critical parameter that affects both the quantity and the
quality of the harvested crop [Sokhansanj et al., 1997]. Therefore, it is desirable to
measure accurately the moisture content of the crop at various stages of production such
as harvesting, baling and storing.
Standing crop has a high moisture content ranging over 70 - 80% by wet basis at
harvest whereas safe storage, when both chemical breakdown and microbial action
cease, occurs at 18 - 20% moisture level. However, by harvesting forage crops at 25 30% moisture content, instead of the 18 - 20% for full field cured forage, the additional
dry matter recovery from the field is about 3 - 5%. For forage worth $120 per tonne, this
can represent an additional $3.60 to $6.00 per tonne. Losses incurred by mechanical
handling on alfalfa leaves, which contain about 70% of the total protein and 90% of the
minerals and vitamins contained within the whole plant, can be minimized by handling
at a relatively high moisture content of about 55%. Baling can be carried out when the
moisture content of the forage falls in the range of 30 - 40% for further drying processes
such as bam drying. The reasons are that the forage dries at a very slow rate once its
moisture content is in this range, and products dried in the bam are sold mostly as
premium forage at about $120 per tonne compared to $60 per tonne for field cured
forage. For example, dry matter losses decreased from 10.9% to 4.5% when the moisture
content of forage was reduced from greater than 25% to less than 20% before they were
stored for 6 months [Rotz and Abrams, 1988].
Successful processes of pelleting and cubing also rely on the moisture content of
alfalfa. The optimum moisture content of forage for pelleting, cubing or wafering is
about 12 - 16% because the crop exhibits varying characteristics at different moisture
contents. For example, moisture content in excess of 18% leads to difficulties in fine
grinding of forage to produce dense stable pellets. Forage exhibits its peak tensile
strength (cohesion) at about 13% moisture content, which is the optimum value for the
production of wafers.
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3
The standard moisture measurement method requires forage samples to be dried
in an oven for 24 h at 103°C [ASAE Standard 2000]. This method is important to
determine the reference moisture content during the analysis phase, but cannot serve as a
good candidate in processes where moisture measurements must be done on-line, when
rapid determination of moisture content is necessary. It is reported that nutrient losses in
alfalfa are as high as 4% of the yield for every day the crop remains in the field
[Wilkinson, 1981]. Therefore a system which can measure the moisture content
accurately and rapidly is needed to enhance the speed of processing, to maximize the
yield, and to maintain the quality of the forage and its processed products.
Drying is another key factor in forage industries to condition the forage to
different moisture contents required for various stages of processing and for storage as
discussed above. The existing methods to achieve this goal include field drying,
mechanical and chemical conditioning, and drying in a bam with heated or unheated air.
Despite these efforts, about 30% of the crop is lost during harvest and storage
[Sokhansanj et al., 1997]. The drawbacks of most of these conventional drying methods
are that they change commercially valuable crop qualities such as the odour and the
colour as well as nutrient content, and are either not energy efficient, or are slow. In
microwave drying, in most cases, the energy couples into the solvent, not the substrate
(energy efficient), drying can be done at low ambient temperatures (nondestmctive),
coupling o f energy tends toward the wetter areas (leveling effects), and the drying time
can be shortened by 50% or more over conventional drying (high processing speed).
Drying with microwaves alone can, however, be very expensive in terms of both
equipment and operating costs [Schifftnann, 1982]. The least efficient portion of a
conventional drying system is near the end, when two-thirds of the time may be spent
removing the last one-third of the water because these methods depend upon the slow
transfer o f heat from the surface of the material to the interior as determined by
differential temperature from a hot outside to a cool inside. Heating with microwaves is,
in effect, bulk heating in which the electromagnetic field interacts with the material as a
whole. A more efficient and economical system is therefore possible with the
implementation of microwave drying at the exit of conventional dryers.
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4
Disinfestation of insects in forages is necessary for exporting these forages to
some markets. For example, Japan, the main importer of forage and processed products,
has imposed plant quarantine regulations according to which the forage must be
specially treated to achieve high mortality rate for insects, particularly Hessian flies. The
common practice has been the application of high temperature but this has some
negative effects on the nutritional value of the crop. Losses in carotene (vitamin A),
xanthophyll (responsible for yellow color in egg yolk), and lysine, an amino-acid
responsible for the growth of animals, have already been reported [Sokhansanj et al.,
1997]. Other methods of disinfestation such as fumigation, visual inspection, and
chemical treatment are time consuming, expensive or hazardous to human or animal
health. Since microwaves have selective heating characteristics depending upon the
material dielectric properties, the knowledge of this quantity for both forage and insects
is the basis for analyzing the insect-to-forage power dissipation ratio. The higher the
ratio the better the chance of implementation of microwave energy to minimize the
adverse effects o f disinfestation methods on the crop.
Microwave remote sensing technology requires knowledge of dielectric
properties of both the vegetation canopy covering the soil and the soil itself in order to
monitor the spatial moisture distribution of the latter, which is an important factor in
agriculture, hydrology and meteorology. The dielectric properties of the vegetation
canopy and the soil link the microwave responses such as the backscattering coefficient
and emmissivity to the scene parameter such as soil moisture content through the
models. Application of the technology in these areas is still in development mainly due
to the lack of knowledge of the dielectric properties of plant parts such as leaves and
stems required to estimate those properties of the vegetation canopy, a vegetation-air
mixture requiring the use of dielectric mixing formulae.
Worldwide, about 28 million hectares of alfalfa are planted with about 12 million
hectares in the US, followed by Canada, Argentina, France, Southern Europe, and parts
of Asia. Therefore, dielectric properties of alfalfa not only may serve in monitoring the
spatial moisture distribution of soil but also in mapping of these crops, monitoring the
plant stress which is determined by its moisture content, and designing the sensor
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5
parameters such as incidence angle, frequency and polarization [Ulaby et al., 1981] for
remote sensing.
Therefore, the aforementioned sectors deserve the exploration of the possibility
of microwave applications, and that in turn requires dielectric properties of the crop of
interest in the microwave frequency band (300 MHz - 300 GHz). Alfalfa has been
chosen as a working material for this research because of its importance to Canadian and
other international forage industries. An image of this crop is shown in Fig. 1.1. Since it
was known that the measurement of dielectric properties for vegetation would be
relatively difficult, some models that would relate these properties to easily measurable
physical quantities such as moisture content were very important. A thorough
investigation was necessary to find out if dielectric properties and the models to estimate
these properties for alfalfa existed in the literature.
1.2 Literature review
A detailed review of the literature and the published data on dielectric properties
of the materials revealed that most of the work has been focused on non vegetative
materials, and only five investigations have been conducted in the last four decades
towards the measurement and modeling of the dielectric properties of vegetation, and
none of those were for alfalfa.
A cavity perturbation technique was used by [Bengtsson and Risman, 1971] to
measure dielectric properties of raw beef and pork, cooked beef, ham and pork liver,
cooked fish, carrots, peas and mashed potatoes and gravies and fats at 3 GHz in the
temperature range of -20°C to 60°C. Samples were prepared by either disintegrating the
test material and injecting into the sample tubes by means of an injection needle, or
cutting out the material at rigid or partially frozen states by using a cork bore. The
measurement accuracy for s' and e" were 5% and 10%, respectively. Better temperature
control is a plus with this method, but sample preparation for materials like moist leaves
could be very challenging, and the dielectric properties can only be measured at a single
frequency.
Researchers [To et al., 1974] used a slotted line technique to measure dielectric
properties of rehydrated non-fat dry milk, beef and turkey at temperatures 25°C, 35°C,
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6
45°C, and 55°C and at frequencies of 300 MHz, 1 GHz and 3 GHz. Measurement
accuracy, and details on sample holders are not given, however, sample size was in the
range of 0.005 kg to 0.007 kg. In this type of dielectric measurement system, sample
preparation is easy for solid and semi-solids, but is extremely difficult for particulate
materials such as grains and chopped plant parts.
Fig. 1.1 Alfalfa.
Dielectric properties of Canadian, Siberian, and Polish wheat were measured by
[Kraszewski et al., 1977] from the changes in attenuation and phase shift of microwaves
(9.4 GHz) as the waves pass through the materials 100 mm thick and held in a Plexiglas
container (0.01 m x 0.15 m x 0.2 m) between hom apertures (.0079 m x 0.0054 m)
placed about 0.15 m apart. Moisture content, temperature, and density of the samples
were in the range of 9.37% to 17.48%, wet basis (= weight of water/weight of moist
material * 100), 5°C to 30°C, and 710 kg m '3 to 790 kg m'3 respectively. No details on
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7
dielectric properties obtained from this free space measurement method is given as this
research was primarily focused on determining relationships between microwave
attenuation and phase shift and density and moisture content of wheat. Moisture content
of wheat was found to be very highly correlated with the electrical parameters with
correlation coefficient of 0.99.
A system based upon an antenna modeling theorem was designed by [Burdette et
al., 1980, 1982] to measure dielectric properties of living tissues such as muscle, kidney,
fat, brain and blood from rats and canines. The measurement accuracy of the system in
measuring pure liquids such as deionized water, methanol, and 0.1 molar saline at 23°C
is reported as 3%. This method has all the advantages of a probe reflection technique.
However, dielectric properties can be measured only up to 10 GHz, and since the outer
diameter of the probe was only 2.16 mm (no data on diameter of inner conductor), the
effective area o f material in contact with the probe is relatively small.
An extensive research on dielectric properties of grains and seeds has been
carried out by different researchers. The dielectric constant for soybeans was measured
at 24°C over the moisture range from 6% to 24%, wet basis, at frequencies 20 MHz, 300
MHz, and 2450 MHz [Nelson, 1985]. Coaxial type sample holders were used in this
transmission method. Later, this technique was used by the same researcher [Nelson,
1987] for other small grains such as spring barley, soft red winter wheat, and winter rye
at moisture content ranging from 8% to 25%, wet basis. Then [Nelson et al., 2000] used
a free space transmission method to measure dielectric properties of hard red winter
wheat at seven frequencies ranging from 11.3 GHz to 18 GHz, at three bulk density
levels from loosely packed to compacted, moisture contents from 10.6% to 19.2%, wet
basis, and at
temperatures between -1°C to 42°C. Grain samples were held in
polyethylene or Styrofoam containers between transmitting and receiving horns
connected to a microwave network analyzer. The dielectric properties were determined
from measurements of both attenuation and phase shift as the microwaves traversed the
grain.
A large coaxial cell was developed by [Chew et al., 1990] to measure the
dielectric properties of Teflon, cement mortar, and tap water at 24°C. The cell was
machined out of a brass block and cut into two halves which were held together by
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8
several screws. The inner diameter of the outer conductor and the outer diameter of the
inner conductor were respectively 499.2 mm and 153.5 mm to allow only TEM waves to
propagate along the cell. Samples were placed between two Teflon plugs located at each
end of the cell. This cell with characteristic impedance of 50 Cl was used to measure
dielectric properties from the S-parameters over the frequency range of 1 MHz to 3
GHz. But, only dielectric properties of water were reported to be comparable to those
obtained from the Klein-Swift formula. Details on system accuracy and dielectric data
are not provided. As with other transmission systems, this cell was more useful for
dielectric measurement of liquids and semi-liquids. Solids must be machined to perfectly
fit into the cell, and granular and vegetative substances are not appropriate for this type
of measurement technique.
Researchers [Raveendranath and Mathew, 1995] investigated the dielectric
properties at microwave frequencies to determine pollution in water collected from
fertilizer, metal and chemical plants, and rivers. Dielectric properties of tap water were
compared with those of organic pollutants such as acetone, methanol and nitrobenzene.
The changes in resonant frequency and Q-factor of a rectangular waveguide cavity when
a capillary tube filled with polluted water was inserted in the cavity were employed to
calculate the dielectric properties of the samples. Dielectric loss factor was found to be
more useful in predicting the concentration of pollution than the dielectric constant.
Although correlation between measured properties and percent concentration of
pollutants was not as accurate as that obtained from chromatographic techniques,
methods based upon dielectric properties were found to be simple, rapid, and less
expensive. No data on dimensions of the apparatus, frequency, and temperature are
given. For the reasons discussed earlier, this type of measurement is more suitable for
materials that could completely fill the tubes, and when a small quantity of a sample
could represent whole material with high confidence.
To explore possibilities in controlling pests in soils, dielectric properties of
insects, nematodes, weed seeds, and plant pathogens, and different types of soil were
measured by [Nelson, 1996]. Based upon principles of microwave energy absorption by
dielectric materials and field experiments, it was concluded that possibility of using
microwaves for mortality and population reduction of the pests was very low except for
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9
insects in very dry soils.
A rapid decay of microwave energy in soils, a lack of
significant differences between the dielectric properties of the pests and soils that
required for selective microwave heating, and very high energy and equipment costs
were the main reasons. However, the susceptibility to control by microwave heating for
pests in soil, in decreasing order, were found to be insects, weed seeds, nematodes,
fungi, and bacteria.
Dielectric properties of pulverized coal and limestone with particle diameters
ranging from 5 pm to 100 pm were measured at 25°C by [Nelson et al., 1996] using an
open-ended coaxial probe technique over the frequency range of 0.2 GHz to 20 GHz.
Moisture contents o f coal and limestone were at 1.4% and 0.14%, respectively. The
dielectric properties of a material were extracted from those measured for the materialair mixture using Landau and Lifshitz, Looyenga dielectric mixing formula. This
formula required the volume fraction of a solid material in the air-material mixture, and
was calculated from the ratio of bulk density of the material to its particle (solid
material) density. The density of the material in the vicinity o f a probe was considered to
be different from bulk density of the whole material in the sample holder. A linear
relation between the cube o f the dielectric constant and bulk density of the material was
found at 11.7 GHz by measuring the dielectric constants of the pulverized material with
known bulk densities contained in an X-band short circuited waveguide. This relation
was then used to estimate the bulk density of the material in the vicinity of the probe
during dielectric measurement from the measured dielectric constant at the same
frequency. The particle density was measured by using a pycnometer. Dielectric
constants of both coal and limestone decreased with increasing frequency between 0.2
GHz and 20 GHz with the limestone showing little dispersion below 3 GHz. The
dielectric loss factors of both coal (0.04) and limestone (0.02) measured by using the
waveguide were comparable to published data, but those obtained from probe system
were erratic and three to ten times greater than those obtained from the waveguide. This
was attributed to low accuracy of the probe system in measuring low loss pulverized
materials.
By measuring dielectric properties of adult rice weevils, a selective heating of
insects for lethal purposes was investigated by [Nelson et al., 1996] at moisture content
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10
of 48.97% over the frequency range of 0.2 GHz to 20 GHz and at temperatures from 10
°C to 65°C with an open-ended coaxial probe technique. Since dimensions of insects (3
to 4 mm in length) were of the same order as the diameter of the probe (3 mm), the bulk
weevils constitute an extremely non-homogeneous mixture for this type of measurement.
Therefore, the effective density of the sample in contact with the open end varied from
the mean sample bulk density. Besides, measured dielectric properties were those of a
mixture of insects and air. Therefore dielectric properties of weevils were determined by
using Landau and Lifshitz, Looyenga dielectric mixing equation and a density correction
curve. Dielectric constant decreased monotonically with frequency, and increased with
temperature. Dielectric loss factors decreased rapidly as frequency increased above 0.2
GHz, reached a minimum in the region between 2 GHz and 3 GHz, and then increased
gradually as frequency continued to increase to 20 GHz. This behaviour was attributed
to the influence of liquid water which has a strong relaxation at 19.6 GHz at 25°C.
Measured data were justified by comparing them with dielectric properties of
mealworms and Colorado potato beetles. This research concluded that the loss factors
for insects at frequencies up to at least 20 GHz had the same degree of selective heating
with respect to the host medium (grain) as that obtained between 10 MHz to 100 MHz.
Low-density fiberglass composites are used in many environments for insulation
purposes. It is important to determine the uniformity with which the resin binder is
applied, the cure state of resin binder, and variations in the glass fiber density for
fiberglass products. These important issues were addressed by [Qaddoumi et al., 1996]
from the measured microwave dielectric properties of the material. The dielectric
properties of fresh and 12-day-old resin binder (indicating a small amount of curing),
resin binder loaded but uncured fiberglass, fiberglass with no resin binder, and curd
fiberglass with three different resin binder levels were measured in the frequency range
from 4 GHz to 18 GHz using a completely filled short-circuited waveguide. This
knowledge of the dielectric properties was then used to distinguish among fiberglass
samples with different resin binder levels using the open-ended waveguide method
because of its suitability for non-contact and on-line uses. A major source of error was
that the fiberglass sample was compressed in the waveguide sample holder, and there
was not good control over pushing out the air between the fibers, and the expansion that
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11
occurred after compression was extremely difficult to take into account. Clearly, this
technique is more suitable for materials that can completely fill the waveguide, and this
excludes, particularly, granular and vegetative samples.
The dielectric properties of low-loss crude oils were measured by [Folgero,
1998], The chemometric modeling uses dielectric properties to determine important
parameters such as density, viscosity, nitrogen, sulphur content and acid number of
petrochemical products. Hence, on-line measurement of dielectric properties is useful in
order to predict changes in these parameters caused by temperature and pressure
variations in the process plant. The system consisted of a 200 mm long coaxial cell
operating from 1 kHz to 6 GHz. The dielectric spectrum was developed by converting
the impedance and S-parameters obtained from reflection-transmission methods through
some algorithms. It was claimed that the deviations between measured values and that
obtained from the Cole-Cole model for crude oils (names not reported) were within
±0.005 at most frequencies. Although, this technique showed high measurement
accuracy, it is not practical for materials such as moist plant materials because of
extreme difficulties in preparing the samples
A two-port transmission technique for dielectric measurement was limited to
only those materials which could be machined to fit into the waveguides. Researchers
[Bois et al., 1999] modified this technique so that liquid and granular materials could be
housed in a waveguide by using two plugs. The presence of the plugs was fully
accounted for in the calculation of dielectric properties of the materials.
Dielectric
properties of cement powder, com oil and antifreeze solutions were measured at X-band
(8.2 GHz - 12.4 GHz), and those of water with salinity of 33 ppm at 19.3°C were
measured at 3 GHz (S-band). Detail on measurement accuracy of the modified system
were not given; however, the difference between predicted and measured values of
dielectric properties for saline water was reported as 1.1%. It is noted that the space
between the plugs within a waveguide needs to be completely filled with a test material.
Therefore, this method can not effectively be used for highly particulate and leafy
materials.
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12
Besides dielectric properties, literature review for both on- and off-line
microwave moisture measurement techniques was also carried out to investigate the
methodology, and the materials this technology was used for.
A free space technique was used by [Trabelsi et al. 1999] to determine bulk
density and moisture content of wheat and corn from dielectric measurements. The
frequency and temperature ranges were same as in [Nelson et al., 2000], The bulk
density of wheat and com ranging from 720 kg m'3 to 880 kg m '3 and 695 kg m '3 and
830 kg nT3 respectively, was determined with an average standard error of performance
•5
-j
(SEP) of 7.8 kg m' and 12.9 kg m' respectively. The moisture content of wheat and
com, ranging from 10.6% to 19.2% and 9% to 19.2%, wet basis, respectively, was
determined at a given temperature independent of density with SEP of less than 0.27%
and 0.46%, respectively.
Using the free space transmission method, moisture contents of a mixture of
Siberian wheat and five varieties of Grana wheat with a thickness (t) of 100 mm and a
density (d) of 750 kg nT3 at 25°C were studied by [Kraszewski et al., 1977] by
measuring attenuation (A) and phase shift (<J>) of microwave signals at 9.4 GHz. Over
the moisture range of 9.37% to 17.48 %, wet basis, each electrical parameter was
linearly related with the moisture content. Each parameter was then expressed in terms
of t, d, mass of water (mw), and two unknown constants. Values for four constants were
determined by measuring A and $ for wheat samples of known t, d, and mw. An
expression for moisture content (= mw) was expressed in terms of A, (J), and the
constants. Some assumptions such as the material being tested was homogeneous in the
macroscopic sense and its electrical parameters were linearly related to the weight of the
water and weight of dry material were made in the final expression. This technique
suffered from density effects on measured moisture content of wheat. Density variation
of 8% and 10% were reported for the wheat varieties at the same moisture content of
12% and 20%, respectively. Some corrections on microwave moisture readings were
still required to minimize the density effect. This technique is instrument dependent and
used for a narrow moisture range near 8%.
Microwave density independent techniques
for prediction
of moisture
measurement of several brands of instant coffee and milk powder mostly at room
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13
temperature were carried out [Rogers, 1987]. The method involved calculation of
dielectric properties from attenuation and phase shift of microwave signal at 10 GHz
obtained by implementing a microwave bridge. The sample was constrained within a
waveguide by two PTFE plugs. Measurements were taken with the sample waveguide
empty except for these two plugs and then with sample in place. The density was varied
by removing the waveguide cell and manually compressing the sample by different
amounts each time. The dielectric properties were measured for over 100 samples of
coffee and milk powders covering the moisture range 2% to 10%, wet basis, (Karl
Fischer titration values). Each powder sample was studied over a range of bulk densities
from loosely packed to compacted, corresponding to bulk density increase of between
approximately 12% and 55% for individual powder samples and up to 260% for a
powder type. The dielectric loss factor over dielectric constant minus one was used as a
density independent function in the prediction of moisture content, and exhibited a
density-dependence much less than that of the dielectric loss alone while retaining the
high moisture sensitivity of the later. Even at the lowest moisture contents investigated,
the ratio was still moisture content sensitive. Details on measurement accuracy were not
reported, however, it was claimed that this technique for predicting the moisture content
of low loss powder food products should be sufficiently insensitive to the bulk density of
the product.
A microwave resonator (47.55 x 22.15 x 203 mm) operating in the H 105 and H 1 0 7
modes at 4.8 GHz and
6
GHz, respectively was used by [Kraszewski et al., 1989] to
measure moisture content of individual soybean seeds at 5°C. Soybean seeds were nearly
spherical in shape, and the ratio of the major and minor diameters was in the range of
1 .2
to 1.36. Major diameters ranged between 6.5 mm and 7.5 mm. A seed was attached to
thin silk threads permitting it to be suspended in the center of the cavity from a
machined circular brass plug that fitted snugly into the 12.62 mm hole milled in the
center of the wider wall at the top of the cavity. The cavity was held between two
waveguide-to-coaxial transitions to connect it to an automatic network analyzer in the
transmission mode. The change in resonant frequency and transmission factor (a
function of S2 1 ) were found to be highly correlated with the water content and dry mass
of the sample. Since the latter two quantities were related to the moisture content of a
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14
material, a calibration equation that related moisture content of soybeans to changes in
those quantities was developed by measuring the quantities for eighteen seeds at each of
six moisture contents ranging over
8
% to 16%. This calibration equation was
independent of mass of the sample. When the system was tested with 55 seeds from the
same lot used in calibration purpose, the mean value of difference between the predicted
and that measured with standard oven method was 0.06% and -0.04% moisture content,
and the SEP was 0.46% and 0.42% moisture content for H 1 0 5 and H 1 0 7 modes
measurements, respectively. In the cavity resonant method, the location, orientation with
respect to the electric field vector, relative permittivity, volume and shape of an object
have effects in change in resonant frequency and transmission factor. In this study, the
first three parameters were fixed for a given moisture content. The change in resonant
frequency and transmission factor were found to be proportional to volume and moisture
content of the seed. The effect of slight variations in seed shape on moisture content was
assumed to be negligible. When the object was very small (10‘3) with respect to the
volume of the cavity, this technique was reported to be independent of variations of
mass.
A dedicated 4.9 GHz homodyne instrumentation system was developed by [King
et al., 1992] to accurately measure the change in wave parameters, the amplitude and
phase due to the presence o f varieties of grains namely com, soybeans, oats, and rice
with hulls between two hom antennas. The homs produced a collimated microwave
beam of diameter 0.134 m on the test samples contained in a sample holder (0.65 m x
0.29 m x 0.13 m inside dimensions). The wave parameters for each sample were the
average of 30 measurements obtained from moving the 0.65 m long sample holder twice
through the beam simulating a moving stream of grains. The wave parameters were
found to be linearly correlated with dry basis weight of grains and the weight of water.
These relations were simultaneously solved for moisture content as a function of these
two weights. Although the samples 60 mm thick were reported to be measured at various
moisture contents below 60% and temperature from -10°C to 70°C, the accuracy in
predicting the moisture content of the grain samples was not given. This technique was
limited to a single frequency, and the search for an optimum frequency of operation for
the problem is not easy.
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15
In order to retain its natural taste and colour of green tea leaves, the drying
procedure is controlled in eight to ten steps according to the moisture content. Thus, the
measurement of moisture in the leaves is necessary to control the drying procedure.
Researchers [Okamura and Ma, 1998] used free space transmission method with a
sample holder slightly different from that usually seen in this method. It was made of a
plastic plate 10 mm thick with relative dielectric constant of 2.55 and loss factor of 0.07.
The inside transverse area of the holder facing to the antennas was 240 mm x 300 mm
with one side fixed, and the other side could be moved free as a piston in order to change
the density o f the sample The system was calibrated at 9.45 GHz to measure the
transmission and reflection coefficients when the sample was placed between the
antennas (58 mm x 80 mm) held apart at a distance of 234.5 mm. These coefficients
were measured for the leaves over moisture contents of 10% to 85%, dry basis, and
densities ranging over 261 kg nT3 to 330 kg m‘3 at room temperature. The dielectric
properties o f leaves were calculated from the measured coefficients. The ratio of the
dielectric constant minus one over the loss factor was used as a moisture predictor
independent of density, and was valid for moisture content prediction in the range below
50%, dry basis. In the range above 50%, dry basis, the moisture content was determined
using another function, the dielectric loss factor divided by the density. The maximum
relative and average errors for moisture prediction compared to the oven moisture
content were 1.675%, dry basis, and 0.629%, dry basis. Although a large amount of
sample was required for each measurement, this method of moisture prediction for
moist green leaves was attractive.
Researchers [Trabelsi et al., 1998a] predicted moisture content of hard red winter
wheat by using a new density independent calibration function. A sample holder of
polyethylene walls of 1 mm thickness, 124 mm wide, 154 mm high providing a sample
104 mm thick was held between two WR-62 homs antennas. The attenuation and phase
shift were measured relative to an empty sample holder between the two antennas by
means of a vector network analyzer set up in the transmission mode. The wave
parameters were measured for 396 wheat samples over wide ranges of moisture content
(10.6 % to 19.6%, wet basis), bulk density (720 kg m'3 to 880 kg m'3), temperature (-1°C
to - 42°C) and frequency (11 GHz - 18 GHz). The dielectric properties calculated from
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16
the wave parameters were normalized to density. When normalized dielectric loss factor
was plotted against normalized dielectric constant, the data points closely followed a
straight line showing a better regression regardless of moisture content and temperature.
The slope of the regression line changed with frequency without change in x-axis
intercept. From the regression line, density was expressed in terms of dielectric
properties, slope, and x-axis intercept, and a new density independent calibration
function was defined as the loss tangent normalized to density. One half of the samples
were used to obtain calibration constants for the function over the moisture content of
interest. A linear relation was obtained when the square root of the calibration function
was plotted against moisture content of the samples determined from standard oven
method. This relation was used as a moisture predictor, and tested with the other half of
the samples. The SEP at two extreme frequencies (11.3 GHz and 18 GHz) were 0.24%
and 0.32%, respectively. This moisture predictor seemed to be very attractive because it
was independent of bulk density, and temperature of the samples could be incorporated
into it. Since dielectric properties were used, this method was also independent of
instruments as long as the properties were measured accurately. The slope and xintercept were determined particularly for hard red winter wheat, this methodology
should therefore be tested for other materials before it could be generalized. The
temperature range was reasonably wide, but the range for moisture content was narrower
than that usually occurring in moist materials. Similar measurement by the same
researchers were also reported in [Trabelsi et al., 1998b], and in [Trabelsi et al., 1998c]
where the working material was com.
In one study conducted by [Kraszewski et al., 1998], moisture content of hard
red winter wheat was predicted from the value of a special function comprised of
dielectric constant and loss factor of the material. Since these functions allowed moisture
content to be measured regardless of variation in material density to some degree, they
were called density independent functions (DIF). A sample holder made of polyethylene
of 0.12 m x 0.15 m vertical cross section with 0.02 m thickness was filled with a layer of
grain of 0.104 m thickness. It was held between two hom antennas, which were
connected to two ports of a vector network analyzer through waveguide-to-coaxial
adapters for use in transmission mode. After calibrating the system with an empty
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17
sample holder, the phase shift and attenuation of microwave signals were measured at
11.3 GHz and 16.8 GHz for 181 samples of wheat with moisture content ranging over
10.6 to 18.2% and bulk density from 720 kg m '3 to 879 kg m '3 at 24°C. The dielectric
constants and loss factors were calculated from measured values of attenuation and
phase of each sample, and were used, in turn, to evaluate the DIFs. Linear regression
lines were obtained by plotting DIF values against moisture content for 181 samples
determined from the standard oven method. Performances of regression lines (or DIFs)
were determined by calculating standard error of calibration (SEC). Based upon the
values of SEC that varied from 0.22% to 0.45% and 0.27% to 0.51% at 11.3 GHz and
16.8 GHz respectively, it was claimed that moisture content of wheat could be
determined independently of bulk density by measuring the dielectric properties, or
wave parameters such as attenuation and phase shift at microwave frequencies. Since the
results were satisfactory for wheat, the DIFs might be useful for similar grain products,
but it must be tested for materials such as moist vegetation, which are different from
wheat in many important aspects such as bulk density and moisture range.
A year later, the same researchers mentioned above [Kraszewski et al., 1999]
conducted microwave measurement of moisture content for a different material, shelled
maize with varying density, and moisture content in the range of 9 % to 19% at 15.2
GHz. The temperature of the samples was also varied from 4°C to 45°C in order to
accommodate temperature into the calibration equation. The instrumentation used in this
study was similar to that used in the previous study except horns and sample holders
were of different sizes, and the latter was made of Styrofoam. The attenuation and phase
shift were measured for 518 maize samples at various moisture contents, densities, and
temperature. These wave parameters were expressed in terms of water mass, dry mass,
and temperature using 259 samples through multi variable regression. From these
equations, moisture content was expressed in terms of wave parameters, and
temperature. When the accuracy of the calibration equation was tested with the
remaining 259 samples, a mean difference of -0.023% moisture content and SEP of
0.449% moisture content were found. It was also observed that the attenuation was
independent o f density for maize. Hence, the moisture content was expressed in terms of
attenuation and temperature without phase. In this case, even better results, a mean
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18
difference of 0.001% moisture content, and SEP of 0.365% moisture content were
found.
The X-band ffee-space transmission method had been used by [Narayanan and
Vu, 2000] in estimating the wet-basis moisture content of powder foods namely, coffee,
coffee creamer, dry milk, flour, salt, and sugar. Since food powders generally lose their
utility and desirable properties, such as flowability and resistance to spoilage, at low
levels of moisture content, typically 3%-7%, special techniques were required to
characterize the moisture content at these low levels. Multiple reflections were more
prevalent in low moisture materials, therefore special precautions were taken in
designing the sample holder. The sample holder thickness was large enough to reduce
reflections from the two interfaces of the sample as well as multiple reflections between
the horn antennas. The transverse dimensions of the sample holder were three times the
antenna aperture to minimize total internal reflections from the four sides of the sample
holder parallel to the sample holder axis, as well as to avoid wave diffraction effects at
the sample holder edges. The sample holder was a Plexiglas container of external
dimensions 0.20 m x 0.15 m in the transverse directions and 0.10 m thickness. The walls
of the container were 4 mm thick. X-band horn antennas of aperture dimensions 57 mm
x 16 mm were used. Samples at various moisture contents were prepared by adding
moisture to the sample oven-dried at 105°C for 8 h. The moisture content before and
after the measurement was found to be within 0.5% on average. Although amplitudes of
microwave signals caused by the sample were measured over 8 GHz - 12, they were
averaged to minimize the errors due to multiple reflections over a bandwidth of 1 GHz
around 10 GHz center frequency for adequate frequency averaging without introducing
dispersive effects The attenuation was expressed in terms of dielectric properties, which
were assumed to be related to moisture content of the materials in both a linear and
nonlinear fashion. The expression for moisture content of each food product was then
formulated using measured attenuation, and product specific fit-constants. Measurement
errors in predicting the moisture content were less than 2% moisture content except for
flour (4.5 %).
In sensing moisture content of cereal grains, Nelson [2000] found that when
attenuation and phase shift measured using a free space transmission method similar to
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19
the one discussed above and normalized to density, they were linearly related with
moisture content of the material. These relations were used to develop a calibration
equation in that moisture content was expressed in terms of these wave parameters and
some other constants. The SEP of the calibration equation was 0.17% moisture content.
So far, measurement of moisture content of materials varied from standard oven
method to classical non-destructive techniques (measurement of electrical properties of
the materials in a sample holder) to modem methods (measurement of dielectric
properties using reflection, resonance, and transmission techniques). Regardless of the
methods used, the measured parameters were not only a function of moisture content but
also depend on bulk density, frequency, and temperature of the material. Since the
theoretical analysis of the interaction of electromagnetic fields with materials is
extremely difficult due to involved complexity, empirical techniques have been
employed. This complexity suggested the artificial neural network (ANN) an attractive
candidate as a solution to this problem. In one study [Bartley et al., 1998], an ANN
comprised of 16 input-, 15 hidden-, and one output neuron with sigmoid activation
function was found to be useful in predicting moisture content of hard red winter wheat
at moisture content in the range from 10.6% to 19.2%, wet basis, and bulk density from
720 kg m 3 to 880 kg m"3 at 24°C. The network was used with amplitude and phase of
transmission coefficients measured at eight microwave frequencies (16 inputs) ranging
from 10 GHz to 18 GHz using the free space transmission technique. A total of 179
samples were used for training and testing, and the trained network predicted moisture
content with a mean absolute error of 0.135% moisture content compared with ovendried measurements. Since this method was simple, comparatively accurate, and no
detailed knowledge of microwave interaction with the material was required, and
because of previous successes in applying this kind of technique to other biologically
based systems, it could be an alternative method of predicting the moisture content of
complex materials.
In an attempt to measure and model the dielectric properties of complex
vegetative materials, only five studies were found. An overview of each work follows,
and they are summarized in Tables 1.1 and 1.2 at the end of this chapter.
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20
Dielectric properties of leaves of grass and com, and needles of taxus cuspidatus
and blue spruce were measured by [Carlson, 1967] using a cavity perturbation technique
operating at 8.5 GHz with the motivation that these properties would provide a basis for
an understanding of the radar scattering from vegetation, and with interest in the
dielectric properties of vegetation for its own sake, because most of the dielectric
measurements at that time were focused on chemical compounds and solutions.
Specimens were cut into rectangular cylinders with typical dimensions of 0.127 mm x
2.44 mm x 1.27 mm. In view of the small size, the approximation that the electric field
in the sample was the same as that outside was reasonable, but the measurement of the
dimensions of the sample was very difficult, and was a major source of error. The
specimen was placed at the center of the cavity with a styrofoam block with their vane
structure parallel to the electrical field. The cavity operating at TEioi mode was made
from a section of X-band waveguide, and one end of which was closed by a shorting
wall and the other end was connected to a microwave network by a wall containing a
small circular opening or iris. The changes in resonant frequency and Q-factor produced
by the specimen were used to calculate the dielectric properties. The dielectric properties
of samples at moisture content up to 65%, wet basis, and temperature in the range from
23°C to 35°C were measured. It was reported that dielectric properties were roughly
proportional to the moisture content, and the values for dielectric constant and loss
factor for the samples at 65% moisture content were found to be 25 and 7, respectively,
which reduced to 1.5 and 0.001 for bone dry specimens. Since the dielectric properties
of the test vegetations were not exactly proportional to that of some equivalent fraction
of water, the dependence on moisture content was accounted for by a dielectric model
consisting of the sum of dry vegetation dielectric constant (1.5) and fractions of
dielectric properties of free water weighted by its volume fraction. The dielectric
properties of the blue spruce needle was somewhat lower than that predicted by the
model, and this was attributed to the hollow cores developed within the specimen as it
dried out resulting in actual volume of matter smaller than the external volume of the
specimen.
Inspired by similar motivation as the one mentioned above Broadhurst [1970]
used a slotted coaxial line reflection method, in which the admittance of a slotted coaxial
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21
transmission line (HP model 805A) with a specimen of the material occupying some of
the space between the lines was measured to calculate the dielectric properties of the
material. These properties were measured for bamboo leaves, tulip leaves, and twigs
from tulip tree branches with moisture content at around 63%, wet basis over the
frequency range from 100 KHz to 4.2 GHz at 23°C. The leaf samples were cut into small
circular shape by using a specially made cookie cutter and were trapped between a ring
snugly fitted near one end of the coax and a transparent polystyrene cap that fitted at the
open end serving the outer surface. The sample pocket thus created was 4 mm deep.
Based upon dielectric measurement of distilled water, a system accuracy of 10% was
reported. Major sources of error were thickness measurement of leaves, and possible air
pockets within the samples although a transparent cap was used. For leaves, in general,
both properties increased with increasing moisture content. Most of the observed
features of the dielectric data on leaves were explained by a model that included separate
cells containing water with large concentrations of ionic impurities. The dielectric
constant with a cell would be constant and close to that of water (~ 80) and loss factor
would be a straight line of slope -1 on the log plot of this property vs. frequency. The
sap within the leaf cells would also reflect the high frequency drop in the dielectric
constant and increase in dielectric loss factor due to the dipolar relaxation of the water
molecules. Interfacial polarization and a Debye-like relaxation were also thought to be
present due to the effect of the cell walls which partially block the flow of ionic charges.
At lower frequencies the dielectric constant would increase, the slope of loss factor
would decrease.
Dielectric properties of grass, needle-shaped leaves of casuarina, and leaves and
wood of rubber were measured by [Tan, 1981] at 9.5 GHz using a device similar to one
used by [Carlson, 1967] at moisture contents between 0% to 75%, wet basis, and at 21
°C. The work was motivated by the necessity of dielectric properties of vegetation to
develop its scattering or propagation model to be used in remote sensing applications.
The orientation o f samples with respect to the electric field exhibited insignificant
influence on dielectric constant, but the loss factor was found to be consistently lower
for vein structures perpendicular to the electric field. This was attributed to a smaller
amount of moisture exposed to the electric fields, since veins might be considered to
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22
contain larger quantities of water than the leaf material. Most of the vegetation, in
general, had similar features of increasing dielectric constant and loss factor with
moisture content, showing the dominant role of water in determining the dielectric
properties of the vegetation. The nature and size of the specimen were considered as the
major difficulties during the measurements. The overall accuracy, verified with pure
distilled water, of the measurements was estimated to be 10% to 15% for both dielectric
properties. Besides, dielectric measurements, six models were also tested for dielectric
properties. Contrary to the model used by [Carlson, 1967], the models used in this work
were based on principles of electromagnetic wave interaction with materials. O f the
model tested for grass, that of Polder and van Santen, and deLoor gave the best results
when the dielectric properties at the interface between the constituents of vegetation
were taken as those of vegetation itself, and depolarization factors along the major axes
of the ellipsoids was (0, 0, 1). The dielectric constant of dry vegetation was assumed to
be 1.5, and the ratio of water density to dry vegetation density was 3. The fit for
dielectric constant was better than that for loss factor. It was concluded that a twocomponent dielectric mixture model for vegetation is an oversimplification, and analysis
on assumed dominant behaviour of the relaxation of water should be checked using a
broad frequency band.
Dielectric properties of leaves and stalks of com and wheat were measured by
[Ulaby and Jedlicka, 1984] using a waveguide transmission system, in which the
magnitude and phase of the field transmission coefficient of the sample (moisture
content up to 80%, wet basis) contained in the sampler holder were measured at 23°C.
Three waveguides were used to cover the frequency range of 1 GHz to 2 GHz, 3.5 GHz
to 6.5 GHz, and 7.5 GHz to 8.5 GHz. The purpose of the dielectric measurement was to
generate dielectric data of vegetation to be used in remote sensing applications, and to
develop dielectric models. Measurement procedure was reported to be not simple
because of shape, size and orientation of the vegetation packed inside the waveguide.
Large variations were observed in response to changes in orientation, particularly with
wheat stalk. The results were found to be reproducible only for chopped vegetation
material packed randomly into the waveguide. The refractive model was used to obtain
the dielectric properties of the vegetation material from the measured dielectric
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23
properties of the air-vegetation mixture. Assuming vegetation was a mixture of 1) dry
vegetation containing air, and free water, 2) dry vegetation, air and water, and 3) dry
vegetation, air, free water, and bound water, three dielectric models were tested, of
which the third model produced the best results. A lack of knowledge in modeling water
contained in a given material was considered as a major problem in modeling.
Dielectric properties of vegetation including leaves and stalks of com, extracted
fluid of com stalk, aspen leaves, and tranks of balsam fir and poplar tree were measured
by [El-Rayes and Ulaby, 1987] using an open-ended coaxial probe reflection technique.
The ranges of frequency (0.2 GHz to 20 GHz), temperature (-32°C to 22°C) and
moisture content (up to 86%, wet basis) considered in this work were higher than others.
Accuracy of the system in measuring dielectric constant and loss factor was 5% and
10%, respectively.
A new dielectric model for com leaves, the Debye-Cole dual­
dispersion dielectric model, was also developed at room temperature. The remarkable
characteristic of this model was the consideration of dielectric properties of bound water
(combined with dry vegetation). The dielectric dispersion properties of the latter was
determined from measurements made for sucrose-water solution of known volume
ratios. It was reported that this model fit the measured data very well.
In summary, a considerable amount of work in the field of dielectric
measurements,
dielectric modeling,
and moisture measurement using
density
independent function for grains have been done in the past years by researchers S. O.
Nelson and others, and as a result, the data and the models for this commodity have been
well documented as the standard [ASAE Standard, 2000], Many other researchers used
various materials of potential commercial value. Surprisingly, only five papers on
dielectric measurements on vegetative materials have been conducted in last 40 years.
Among the works, a relatively more thorough investigation can be found only in one
work by El-Rayes and Ulaby. To my knowledge, there is no work reported yet in which
moisture of these plant materials has been predicted using density independent
functions, and artificial neural networks. The importance of dielectric properties, and
ability to model these properties, and make rapid and reliable measurement of moisture
levels for alfalfa have been discussed in the outset of this chapter. Therefore, this
research was undertaken with the following primary objectives.
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24
1.3 Research objectives
1. To develop a system permitting measurement of 8 over a wide range of important
parameters such as microwave frequency and moisture content, temperature and the
density of the test materials.
2. To generate a database of 8 for alfalfa leaves and stems as a function of frequency,
moisture content and temperature.
3. To model s for both alfalfa leaves and stems.
4. To implement density independent functions (DIFs) of dielectric properties for
moisture measurement of alfalfa using an optimum frequency at room temperature.
5. To design an artificial neural network (ANN) for moisture determination of alfalfa
encompassing various densities over a wide microwave frequency range at room
temperature.
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Reproduced with permission of the copyright owner. Further reproduction
Table 1.1. Different aspects of vegetation s measurement conducted in the past.
Carlson [1967]
Broadhurst.
Tan [1981]
[1970]
El-Rayes and Ulaby
[1984]
[1987]
Guide wave
Probe
Slotted line
Partially
cavity resonance
Reflection
cavity resonance transmission system
system
system
system
Applicator(s)
1
1
1
3
4
Frequency (GHz)
8.5
100 kHz -
9.5
1.1 - 1.9, 3.5 - 6.5,
0.2 - 20
Measurement
Partially
system
filled
filled
Ulaby and Jedlicka
4.2
reflection
system
7 .6 -8 .4
prohibited without perm ission.
MC (% w.b.)
0 -6 5
63
0 -7 5
0 -8 0
0 -8 6
Temp. °C
2 3 -3 5
23
21
23
-32 to 22
s' accuracy (%)
1 0 -2 0
10
10-15
5
5
e" accuracy (%)
1 0 -2 0
10
10-15
5 -3 7
10
Plants/component
Grass,
Bamboo,
Grass,
tulip tree
leaves and wood,
com,
taxus
rubber Leaves and stalks of Leaves and stalks of
com and wheat
com,
com
stalk
cuspidatus, blue
Casuarina needle
fluid, aspen-leaves,
spruce
shaped leaves,
balsam
fir
and
poplar tree tranks
Objective
Microwave
remote sensing
N/A
Microwave
Microwave
remote sensing
sensing
remote
Microwave remote
sensing
Reproduced with permission of the copyright owner. Further reproduction
Table 1.2. Modeling of vegetation e investigated in the past.
Ulaby and Jedlicka
El-Rayes and Ulaby
[1984]
[1987]
6
7
1
-
-
-
-
N/A
Dry vegetation Bulk vegetation with Bound vegetation-water,
Carlson
Broadhurst
[1967]
[1970]
Evaluated
-
-
Proposed
1
Components
Dry
(Total
no.
components)
of vegetation
and
free
Tan [1981]
and
air and water (2)
free water (2)
bulk
water
free
water,
vegetation dispersive
nonresidual
without air, air, and component (3)
water (3)
(2)
prohibited without perm ission.
bulk
vegetation
without air, air, free
water
and
bound
water (4)
“Best model”
Carlson’s
model
N/A
Polder
Ven
and Four-phase refractive Debye’s model
Santen’s model
model
o\
2. DIELECTRIC MEASUREMENT SYSTEMS
Dielectric measurement systems, in general are based upon the interaction of
electromagnetic waves with the test material through transmission and/or reflection or
resonance methods. Because of differences in the applicators used to deliver the
electromagnetic energy to the sample, systems using the same method have emerged
with different names. Both the probe and the slotted line dielectric measurement systems
fall under the reflection method. A suitable system for the test material in hand can be
chosen by referring to the issues presented in the first column of Table 2.1 presented at
the end of this chapter. In an attempt to find the most suitable method to determine the
dielectric properties of alfalfa vegetation, this chapter presents the most common
systems suitable for the dielectric measurement of various materials including
vegetation. The probe reflection method used in this research is described in greater
detail in the following chapter.
2.1 Slotted line reflection system
The £ of a test material is calculated from the admittance measured at a
convenient point along the length of a coaxial air-line with the test material filling some
portion of the line between the conductors as shown in Fig. 2.1. The measured
admittance, Ym is related to the load admittance,
Y ls ,
which is equivalent to the
reflection coefficient measured at the sample boundary (LS), and is used to calculate s as
follows. The relations between the admittances Ym and
Y Ao ,
Y ls , Y ls
and
Y le ,
and
Y le
and
where the subscripts LS, LE and AO respectively stand for the load start, load end
and actual open circuit of the line, are given by [Chew et al., 1990].
27
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28
Y„
Y ls
1
Y le
1
SSI
Y
ao
J
IS
(b)
Fig. 2.1 (a) Slotted coaxial line reflection system (b) voltage standing wave without
(solid line) and with (dashed line) sample.
Y.„ - Y,
Yls + Y0 tanh(y0lm)
(2.1)
° Yo + y l s ^ M 1 o K )
Y1 LS = Y1 eO
y le +
Y so tanh(yels)
( 2 .2 )
Y e o + Y LE t a n h ( y 6l s )
YAO+Y 0tanh[y0(lQ -ls)]
0 Y0 +Y AOtanh[y0(l0 - l s)]
(2.3)
Or, since Y ao = 0
Yle = Y0 tanh[y0(l0 - ls)]
(2.4).
In the above equations, Yo and yo, and Y eo and ye, respectively are the
characteristic admittances and the propagation coefficients of air-and test material-filled
coaxial line, which are given by
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29
Y0 = ------------------------------------------------------------------ (2.5)
60 In
\ T' J
To = j —
c
(2-6)
Y ,„ = i / I y „
(2.7)
T, = VsYo
(2.8),
where r0 and r,, respectively represent the inner radius of the outer conductor and the
outer radius of the inner conductor of the line, and o> and c are respectively the operating
angular frequency and the speed of light in free space.
Using Eqs. (2.2), (2.4), (2.7) and (2.8),
Y
=Y
tanhbo fro ~
)] + Vs tanh(V^y0l s)
l + -^ ta n h [y 0(l0 - l s)]tanh(V^y0l s)
Ve
Since Y ls can be calculated from the measured quantities using Eq. (2.1), Eq. (2.9)
facilitates the calculation of e of the test material. However, Eq. (2.9) can be simplified
in practice by choosing an appropriate operating frequency and the sample thickness
with little increase in error. In [Broadhurst, 1970], f = 4.2 GHz, ls < 0.4 mm, and 10 = 3
mm (found experimentally), which resulted in (l0-ls) < 2.6 mm, and the use of the
approximation tanh(x) ~ x in Eq. (2.9) produced the following relation.
y A -Ij+ e y .l
y ls - Y0 r°Vo
s
i + y' O . - l.)i
(2 . 1 0 )
Elimination of the very small second term in the denominator gave the final simplified
expression for Y ls as
Y ls = Y0[yo(1o - l,)+ e y 0l j
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(2.11)
30
Rearranging Eq. (2.11),
(2 . 12)
The resulting error due to this simplification was reported to be about 7% or less.
2.2 Guided or free space transmission system
A transmission dielectric measurement system is shown in Fig. 2.2 (a), which
may take the form of a guided or a free space transmission system depending upon
whether the applicator used is a coaxial line or a waveguide shown in Fig. 2.2 (b) - (i)
and (ii), or a pair of hom antennas with test material in between as shown in Fig. 2.2 (b)
- (iii). The network analyzer determines the ratios by the magnitudes (m) and the phases
(p) of the transmitted (Tra) and the reference (Ref) signals to produce the transmission
coefficient (T), which is used to calculate e of the test material. The following procedure
is for a guided transmission system, however the same procedure can be used for the
free space transmission system by substituting 1/A,C= 0 since the cutoff wavelength, kc
for the system becomes infinity. In general, these calculations are programmed in a
digital computer to enhance the system speed.
The transmission coefficient is then given by
(2 .1)
where, ls is the sample length, and y and T are respectively the propagation and the
reflection coefficients given by
y = a + jP , and
(2 .2 )
(2.3).
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31
Interface
Digital computer
Processor/Display
Software
IF detector
J i
Ref
•
Tra
Test set
Applicator
RF Source
Network analyzer
(a)
(i)
(iii)
(ii)
(b)
Fig. 2.2
(a) Transmission measurement system (b) applicators (i) wave guide (ii)
coaxial line and (iii) a pair of hom antennas.
In Eq. (2.2) a and P respectively represent the attenuation and the phase change
coefficients of the applicator with test material, and Z and Z0 in Eq. (2.3) are
respectively the characteristic impedances of the applicator with and without the test
material, and are given by
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32
j co(j,0 _ 2ni\0
y
P
K
1+ j
a
+P'
j(flpo = 27tT|0
To
(2.4)
(2.5)
^oPo
where, to, p0, r|o and y0 respectively are the operating angular frequency, air
permeability, air intrinsic impedance, and propagation coefficient of air-filled applicator,
and po is the phase change coefficient of the air-filled applicator given by
271
Po =
1
( 2 . 6)
Since e is related to y as follows
t
=
2 tt % ' ' 2
—£
t
(2.7)
~
A ,
the dielectric properties are given by
' K ' 2 'in ?
(a2-P !)
(2 .8)
\2
(2ap)
(2.9)
and the unknowns a and P are calculated using Eq. (2.1), which is a function of a and p.
T is a measured quantity and other parameters are given by Eqs. (2.2) - (2.6). In
practice, an iterative procedure is required to compute a and P because of their nonlinear
relationships with T [Hallikainen et al., 1985].
2.3 Filled or partially filled cavity resonance systems
When a rectangular waveguide or a cylindrical cavity filled or partially filled
with a test material is used for an applicator as shown in Fig. 2.3 (partially filled) the
resulting system is called the filled or partially filled (perturbation) cavity resonance
system. A detail theoretical analysis is found in [Harrington, 1961]. In the filled cavity
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33
resonance system, the s of the test material is calculated noting the change in the
resonant frequency, and the quality factor of the cavity between when the cavity is
empty and filled with the test material. If f0 and fs, and Q0 and Qs are the resonant
frequencies and the quality factors before and after the cavity is filled with the test
material then s is given by
(2 . 10)
(2 . 11)
z
x
Fig. 2.3
A test material of volume, Vs in a rectangular waveguide resonant cavity of
volume, Vc.
The quality factors are calculated using
(2 . 12)
(2.13)
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34
where f0(3 dB) and fS(3 dB) are respectively the 3 dB frequency bandwidth for the empty and
the filled cavity.
Finding s by filling a cavity with a test material is relatively simple but this is not
practical in many cases for the following reasons:
1. Unavailability of enough test material
2. Lack of homogeneity in filling the cavity with certain test materials
3. High s of the test material, in which case an accurate measurement of f and Q are
difficult due the large frequency shift and/or reduction in the value of Q.
Under these circumstances, a perturbation system could be used. Here the
electric field structure within the cavity is perturbed by the insertion of the test material,
and by knowing the shape of the material, its position in the cavity, and the change it
produces in the resonant frequency and 3 dB bandwidth of the cavity, the s of the test
material is determined. If the sample has a relative permeability of unity, its position in
the cavity is not important since the magnetic field will not be disturbed, and the sample
is usually placed where the electric field is maximum; otherwise it must be placed where
the magnetic field is minimum. For the rectangular waveguide cavity in TEioi mode, this
condition corresponds to a line passing through the center of the cavity parallel to the y
axis (Fig. 2.3). Following the same notations used for filled cavity resonant system, the e
of the test material is given by [Carlson, 1967]
—1 S - i
V
J ____
(2.14)
(2.15),
Qs Qo
where Vs and Vc respectively represent the volumes of the test material and the cavity.
As long as the electric field inside the test material is approximately equal to the
unperturbed field of the cavity, Eqs. (2.14) and (2.15) can be used for test materials of
other shapes.
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35
A general comparison of all the aforementioned microwave dielectric
measurement systems is presented in Table 2.1 including the probe reflection system (to
be described in the following chapter).
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Reproduced with permission of the copyright owner. Further reproduction
Table 2.1. A general comparison of the microwave dielectric measurement systems.
Slotted line
Guided
Free space
Filled cavity
Partially filled
Probe reflection
Reflection
wave
transmission
resonance
cavity resonance
system
system
transmission
system
system
system
system
prohibited without perm ission.
Frequency
Broad band
Banded
Banded
Single
Single
Broad band
Sample size
Moderate
Moderate
Large
Large
Very small
Small
Temperature
Difficult
Difficult
Very easy
Very easy
Very easy
Easy
Low loss material
Very low
Moderate
Moderate
Very high
High
Low
High loss material
Low
Moderate
Moderate
Does not work
Low
High
Sample preparation
Easy
Difficult
Easy
Very difficult
Very difficult
Easy
Most suitable test
Solids, semi­
Solids
Large flat
Solids, semi­
Solids
Solids, semi­
material
solids
sheets
solids, liquids
Meas. e and/or jl
e
e and p
e and p
eor p
£ or p
e
To test material
Destructive
Destructive
N on-destructive
Destructive
Destructive
Non-destructive
Commercial vendors
no
yes
yes
no
no
yes
monitoring/ control
Accuracy for:
solids, liquids
U>
ON
3. PROBE REFLECTION SYSTEM
The probe reflection system, which uses an open-ended coaxial line as a probe to
measure the e of the semi-infmite test material in contact with its aperture has many
advantages over other probe reflection systems. This system is configured by varying the
coaxial line geometry and the position of the test material [Stuchly and Stuchly, 1980]
and the method has been used to measure the e of a wide range of materials such as
fructose solutions [Blackham and Pollard, 1997], ethanol and cheddar cheese [Sheen and
Woodhead, 1999], high water content tissues such as muscle, brain, liver, kidney, low
moisture content tissues such as fat, and blood [Athey et al., 1982] [Burdette et ah,
1980], conifers - Caucasian fir and spruce [Franchois et ah, 1998], ethanol, methanol
and formamide [Ghannouchi and Bosisio, 1989], [Burdette et al., 1982], [Jordan et ah,
1978], Balsam fir and poplar tree trunks, aspen and com leaves, com stalk and its fluid
[El-Rayes and Ulaby, 1987], grapes and sugar solutions [Tulasidas et ah, 1995],
pulverized coal and limestone [Nelson and Bartley,. 1998], fruits and vegetables [Nelson
et ah, 1993], shrimp [Tanaka et ah, 1999] and adult rice weevils [Nelson et ah, 1996].
From the comparative study of the microwave dielectric measurement systems presented
in the previous chapter, the probe reflection system is the most suitable for the broad
band dielectric measurement of the biological substances including vegetation.
3.1 Probe reflection system set up
A probe reflection system was built at the Visual Properties Laboratory in the
Department of Agriculture and Bio-resource Engineering at the University of
Saskatchewan. The photograph and the schematic of the system are respectively shown
37
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38
in Figs. 3.1 and 3.2, and the specifications/sketches of the components are provided in
Appendix A. The network analyzer system consisted of an Hewlett-Packard 851 OB
Dielectric software
Network analyzer System
Interface
Desktop
computer
Open-ended coaxial probe
Load-cell
Test material
Thermocouple
Conditioning circuit
Circulator
Data Logger
Digital volt meter
Laptop computer
Fig. 3.1 A schematic of the probe reflection system.
Fig.3.2 A photograph of the probe reflection system.
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39
network analyzer,
an
HP8341B
synthesized
sweeper
(20
GHz),
an HP
8
515A S-parameter test set (45 MHz - 26 GHz), and an HP 85101B processor/display
unit. An HP 85070D, version D1.0, open-ended coaxial-line shown in Fig. 3.3 was used
as a probe. The network analyzer system was connected via a 82350A PCI GPIB
interface card to a personal computer loaded with HP 85070D software to receive the
phase and the amplitude of the reflection coefficient at the probe/test material interface.
The Virtual Instrument Software Architecture (VISA) software was used to drive the
card. The dielectric properties were measured over the frequency range from 300 MHz
to 18 GHz with 201 frequency points separated by 88.5 MHz.
Grip nut
3.5 mm connector
Inner conductor
Diameter = 0.66 mm
15.5 mm
Ground plane
(Inconel)
19 mm
17.4 mm
Glass
46.7 mm
tat
Xrea = 280 mm'
Outer conductor
Inner Diameter = 3 mm
Outer Diameter = 4.8 mm
(b)
Fig. 3.3 HP 85070D Dielectric probe (a) side view (b) probe aperture.
Since the sample diameter must be greater than 20 mm to simulate a semiinfmite sample surface, and to use with the HP 85070D probe [Product Overview, 2001]
a copper cup with inside diameter of 26.66 mm and depth of 31 mm was constructed to
use as a sample holder. Copper was chosen for better conduction of heat from the
surrounding temperature bath to the sample. As will be explained shortly, the metal
sample holder had no effect on the measurement of the test material s. The sample
holder was snugly inserted into a hole cut in the lid of the aluminum bath. The inlet and
the outlet of the bath were connected to a Corola Messtechnik GMBH Constant
Temperature Circulator with flexible rubber tubing to provide a water-ethylene glycol
jacket around the sample holder, and to maintain the desired sample temperature. The
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40
aluminum bath was wrapped with glass-wool to minimize the heat loss leaving two
small cuts, one on each side for the inlet and the outlet, and one small cut on the top for
the probe to gain access into the sample holder.
Sample temperature was sensed using a Copper-Constantan thermocouple placed
on the sample surface through a 3-mm-diameter and 30 mm long hollow copper tube
attached near to the rim of the sample holder. The thermocouple was connected to a 2 IX
Micrologger Data Logger, which was in turn connected to a laptop computer installed
with PC208W 3.3 Data Acquisition Software for direct sample temperature reading and
the continuous observation of the sample temperature trend. The probe was attached via
a special clamp to one end of a load cell, which was connected to a digital volt meter
(DVM) through a conditioning circuit. The reading on the DVM (milliVolts) was
calibrated against the probe pressure (kilopascal) on the sample. The other end of the
load cell was mounted on a rigid stand through a special clamp. The sample holder and
the aluminum bath with continuous flow of water-ethylene glycol rested on the platform
of a laboratory bench jack, which could be raised as a unit to make firm contact between
the probe and the sample. This method ensured that the phase of the cable connecting
the probe to the network analyzer was unchanged during measurement of e from the one
set in the calibration, thus eliminating any cable phase errors, which otherwise would be
significant [HP Application note].
The probe could be inserted into a custom built hollow Teflon cylinder so that
the whole assembly would provide just enough clearance to insert the probe freely with
a good fit into the sample holder trapping the sample and permitting the probe assembly
to be used as a piston. This assembly was particularly used at the time when the sample
density was required along with the sample s. The sample density was calculated from
the known cross sectional area of the sample holder, and the sample height given by the
difference between the sample holder height and the probe length into the sample holder,
which could be read from the scale etched on the side of the probe assembly.
3.2 Determining s using an open-ended coaxial probe
The major problem in the measurement of the permittivity using an open-ended
coaxial probe is that there exists no analytical relationship between the reflection
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41
coefficient at the probe/test material interface and the permittivity of the test material
contacting the probe. Therefore the success of using the probe depends entirely upon an
accurate probe model that relates the reflection coefficient to the permittivity. A model
was developed as early as 1951 [Levine and Papas, 1951], and now there is a large
number of models ranging from equivalent circuit models to full-wave models that can
be used for samples with infinite thickness and infinite transversal extent. These two
types of models have respectively been categorized into the first and the second stages
of the probe development, and the full wave models that can be used for finite sample
thicknesses belong to the third or the last stage. The model for the HP85070D probe,
which was used in this research falls into the first stage. It is found from the literature
[Stuchly et al., 1982] [De Langhe et al., 1993, 1994] [Poumaropoulos and Misra, 1994]
that the full wave models are accurate but rather involved and computationally very
complex. On the other hand, the equivalent circuit models are less accurate but provide a
closed form expression for s as a function of reflection coefficient that facilitates the
fastest computation [Blackham and Pollard, 1997] and can be used in automatic network
analyzer routines [Gajda and Stuchly, 1983]. Hence the equivalent circuit model is the
most widely used [De Langhe et al., 1994] for sample measurements.
Fig. 3.4 (b) is the equivalent circuit model of the open-ended coaxial probe
shown in Fig. 3.4 (a) opening in free space. The capacitances Q and C0 respectively
represent the electric field concentrations inside the glass-filled part of the coaxial line,
Yex(tt), £())
................................“1
Yi,
„ |B m 4
Y l(co, 8o)
(a)
Fig. 3.4
■
Sample (s)
iCo+Aco
...|Ci
j
L .
(b)
(a) An open-ended coaxial probe opening into free space (s0), and (b) its
equivalent circuit model.
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42
which is independent o f the test material, and the fringing field concentration in the
surrounding free space (s0). In the coaxial line, only the transverse electromagnetic
(TEM) mode is excited, but higher order modes are created at the probe aperture/test
material interface. Because of the axial symmetry of the coaxial line only cp independent
TM higher modes need to be considered, and these modes increase with frequency
resulting in the increase of C0 as C0 + A go2 [Athey et al., 1982],
Furthermore, if these TM modes propagate into free space then the radiation loss
must be incorporated into the model adding a conductance term, which increases with
as
go4
go
[Marcuvitz, 1986], When the operating wavelength is comparable to the line
dimension, or the probe is in contact with the test material with high s, radiation loss is
highly likely. The wavelength in the test material, Xm gradually decreases with the
increase of s according to
(3.1)
y ( l + sec5)
where Xfl is the wavelength in free space and 8 = tan’^s'Vs'). The TM mode may become
a propagating mode if Xm < Xc, the cutoff wavelength of the TM mode. For example, A
for TMoi, the first TM higher order mode, is given by 2.029 (a - b), which is equal to
2.37 mm for the HP 85070D probe. If s of distilled water at 22°C is taken as the upper
limit of £ for the test materials, then from Table 3.1 it can be seen that a TMoi higher
order starts to propagate at 18 GHz for water whereas it does not propagate until the
operating frequency reaches 127 GHz for free space.
Table 3.1 Wavelengths in distilled water (km) at 22°C, and in air (k0) for different
operating frequencies along with the
f (GHz)
e of the
distilled water.
0.3
1
6
12
18
127
e'
79.30
79.10
71.99
56.67
42.41
6.39
e"
1.23
4.09
22.19
34.24
37.21
10.42
X0 (mm)
1000.00
300.00
50.00
25.00
16.67
2.37
Xm (mm)
112.29
33.72
5.83
3.19
2.37
0.77
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43
Referring to Fig. 3.4 (b) the admittance of the line opening in free space is given by
YL(®^o) =
Y i„
+ Yex(<0,So)
(3 -2 )
where,
Yta=j®Ci
(3.3)
Yex(°>>eo) = j ffl(Co + a <d2)+B( o4
(3.4)
and
are respectively the “internal” and the “external” line admittances, and Q, C0, A and B
are the probe geometry dependent model parameters. When the probe is in contact with
the test material of infinite thickness and infinite transversal extent, and of permittivity e
Eq. (3.2) takes the form
Y L(< o ,s )= Y 1„ + Y „ ( a , , s )
(3.5)
The “external” admittance of the probe contacting the test material, Yex(ffl,e) can
be related to that opening in free space using the antenna modeling theorem
[Deschamps, 1962] [Burdette et al., 1980] as follows.
Yex(<», e) = VeYex(co', s0
= VeYex(Veto, e0)
(3.6)
From Eqs. (3.4) and (3.6)
Yex(o>,s) = jcoC0s + jAto3e2 +Boo4s 25
(3.7)
Substitution of Yex (co,e) in Eq. (3.5) results in the probe admittance for the general case
as follows.
YL(«,e) = jcoC; + jooC0e + jAcoV +Boo4e25
The other expression for calculating Y l (co,e) is given by
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(3.8)
44
Yl (cd, s ) = Y '
i+r(co,8j
(3.9)
where Y0 (= 50S) and r(co,s) are respectively the characteristic admittance of the probe
and the reflection coefficient measured at the probe aperture contacting the test material
with permittivity s. This is valid for the perpendicular incidence of TEM mode on an
infinite test material. Substitution of the values of YL (©,£) obtained by measuring
T(a>,e) for the two standard materials of known e using Eq. (3.9) in Eq. (3.8) results in
two complex or four real equations, which are solved in order to determine the model
parameters. This process is generally known as the forward process.
In the inverse process, the Y l (co,e) calculated using Eq. (3.9) from the measured
T(co,e) along with the model parameters determined in the forward process are used to
find the 8 of the test material using Eq. (3.8). An iterative method is used for finding the
value of s that minimizes the error between the value of YL (co,e) obtained using Eq.
(3.9) and the value calculated from the expression on the right-hand side of Eq. (3.8).
The mathematical relations involved in converting the r(co,£) to s are collectively
termed as the e-T model in the subsequent discussion.
The r(co,e) discussed so far is referred to the measurement plane (the probe
aperture/test material interface) and shall be noted as the actual T, Ta whereas the
automatic network analyzer gives r(co,e) seen at the reference plane, the testport/connector interface (SMA 3.5 mm), and shall be noted as the measured T, Tm.
These quantities are not necessarily the same due to the inherent systematic errors of the
measurement system. Therefore the system was calibrated in order to minimize the
errors, and consequently the difference between Tm and I a.
3.3 System calibration
The systematic errors of the automatic network analyzer (ANA) system are
categorized into three groups, the directivity error, e<j, the source match error, es, and the
frequency tracking error, ef.
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45
The directivity error is caused by the direct leakage of the incident signal through
the signal separation devices such as the directional couplers and the bridges, and also
by the reflections from the imperfect connectors and adapters between the signal
separation and the measurement plane. As shown in Fig. 3.5 (a) the measured reflected
signal, Rm at the reference plane (RP) therefore differs from the actual reflected signal,
Ra at the measurement plane (MP) when e<j combines vectorally with Ra.
The source match error arises due to the impedance mismatches at the ANA
system test port and further down the line. As depicted in Fig. 3.5 (b), some of the signal
reflected from the test material reflects off the test port and travels back to the test
material causing the measured incident signal, Im to differ from the actual incident
signal, Ia.
The variation in magnitude and phase flatness as a function of frequency
between the test and the reference signal paths gives rise to the frequency tracking error,
ef.
The analytical model used in this research to calculate Ta using r m was based on
the model given by Hewlett-Packard [User’s manual, 1987], and is shown schematically
in Fig. 3.6.
RP
MP
(a)
(b)
Fig. 3.5 (a) Directivity and (b) Source match errors.
hi
a2
Fig. 3.6 Error model used for minimizing the systematic errors.
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46
Using circuit theory, the error model yields
r „ = ed + T i i ^ -
(3 -1 0 )
r,= ,
(3.11)
l - e sr a
or,
ri" ~ ej ;
l r m Ca) Cs ef
The systematic errors at each frequency of interest were determined by
measuring Tm for three standard materials with known Ta - air (Ta = 1), a short circuit
(Ta = -1), and deionized water at a specific temperature, and substituting them into Eq.
(3.11). The Ta for the deionized water was calculated using Eq. (3.9) where the value of
Yl (co,e) was obtained using Eq. (3.8) with the substitution of e of water calculated using
the Debye model. These errors are stored, and retrieved in the subsequent measurements
to produce Ta from Tmusing the HP 85070D dielectric software.
After calibration, any changes in the cable position and/or the temperature during
the measurement introduce perturbations to the systematic errors that would not be
accounted for by the calibration. These perturbations would result in erroneous Ta, which
would subsequently lead to inaccurate measurement of s. This error was therefore
minimized using an abbreviated calibration procedure known as “refresh cal”
incorporated in the dielectric software in which a single calibration standard (air) was re­
measured under the perturbed system to correct the existing calibration [Blackham,
1992]. This procedure simplified the measurements that must be made at several
different temperatures, or the measurements when the cable must be moved.
3.4 Overall measurement uncertainty
Once the system was calibrated, Ta could be obtained from Tm. However, there
were random errors, and other inherent errors affecting the measurement of Tm (or Ta) as
a result of using the equivalent probe model and the dielectric model to characterize the
permittivity of the water, and due to the residual error and the noise of the network
analyzer. Since the s of the test material was derived from Ta it was necessary to analyze
the effect of these errors on the determination of e . The random errors were minimized
by programming the ANA to measure Tm eight times at each frequency of interest, and
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47
using the average in the subsequent calculations. The effect of other errors was
quantified by estimating the maximum percent uncertainty (sMaxu = AeMax/M %) using
Eq. (3.12) [User’s manual, 1997].
Ae Max
•'MaxU
Id
xl00%
x (u™ + U ™ )
+ — x (u™ + U “ )
+ (je|xNR+n)2 xl00%
(3.12)
where,
sm =
sensitivity for the test material
Sa
=
sensitivity for air
Sw
=
sensitivity for water
u:m =
probe model uncertainty measuring air
=
dielectric model uncertainty measuring air
UP
vJwM
=
probe model uncertainty measuring water
t t DM
=
dielectric model uncertainty measuring water
NR+n
=
ANA residual error plus noise
ttdm
Ua
Uw
observed permittivity of the test material, and
e
|e|
=
Vs'2+e"2
The probe and the dielectric model accuracy were taken as ±3% and ±1%
respectively, and the residual error and noise of the network analyzer were respectively
±5% and ±0.06% resulting in the total network analyzer error of ±5.06% [User’s
manual, 1997], The sensitivity numbers (or data), S are basically the slope of the e-T
model, and were obtained from the 85070D software.
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48
3.5 System accuracy
The system accuracy was determined by measuring s of methanol at 20°C,
deionized water at 30°C, and Teflon, and air at 22°C over the frequency range of 300
MHz to 18 GHz covering the low to high loss materials, and comparing them with the
published data after calibrating the system using distilled water at 20°C, air, and a short
circuit. It is noted that the temperatures of the distilled water used for the verification
and the calibration were different.
For comparison, the s of the methanol and the deionized water at the frequency
of measurement were respectively calculated using the Cole-Cole [Jordan et al., 1978]
and the Debye [Kraszewski, 1996] models, and those for Teflon and air were taken from
[Kraus, 1991].
As shown in Fig. 3.7 the measured and the calculated s for methanol compared
well to each other, and the percent relative error as shown in Fig. 3.8 was found to be
less than ±6% and ±9% for s’ and s”, respectively. Fig. 3.9 depicts the observed percent
relative error given by
+ ( e V . - e " c . J xK>0%
(3.13)
|e C alc|
and that estimated using Eq. (3.12). The system accuracy measuring deionized water at
30°C are shown in Figs. 3.10 to 3.12, and found to be less than ±4% and ±10% for s ’ and
e"
respectively. The e of air at 30°C and Teflon at 20°C are respectively shown in Figs.
3.13 and 3.14. As expected the s' and s" for air are respectively unity and zero, and those
for Teflon agreed well with the reference data [Chew et ah, 1990] [Baker et ah,
1990]. Hence the system relative error (system accuracy) in measuring s' and s'' was
adequately represented by ±6% and ±10% respectively.
3.6 Sample size
Equation (3.9) assumed an infinite test material but that was not the case in a
measurement setup. Therefore the minimal dimensions of the test material both in the
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49
Methanol (20°C)
40
16
30 -
\T -
12
A
+'
A
+
A
A
+
A
+A
>
W 20 - i
t
10 ♦
A
8
*— e1Calc,
s' Meas.
w
e” Calc.
a
e" Meas.
o
0
5
10
15
20
Frequency (GHz)
Fig. 3.7 Measured and calculated e of Methanol at 20°C.
Methanol (20°C)
10
<►«•
8
I<u
T3
o1
6
A £
4
8
-A
A* A
A
A
A A
2
,A
A
0
0
10
15
20
Frequency (GHz)
Fig. 3.8
The percent relative error of the system determined by comparing the
measured and the calculated s for methanol at 20°C.
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50
Methanol (20°C)
10
A
2
8
o
b<D 6
O
i
A
A
A— A - A
4'
£- * A
^ ? i;
2 * :-i
«*> ^
0
T3
5
10
15
*
Maximum
«
Observed
20
Frequency (GHz)
Fig. 3.9 The maximum estimated and the observed percent relative error of the system
determined using Eqs. (3.12) and (3.13) respectively for methanol at 20°C.
Deionized water (30 C)
100
40
+.+*t i
A * *A
$+
75
w
30
50
20 «
25
10
— - e ' Calc.
s' Meas.
+
s"Calc.
a
s" Meas.
"T~
5
10
15
20
Frequency (GHz)
Fig. 3.10 Measured and calculated s of deionized water at 30°C.
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51
Deionized water (30°C)
10
8
Vh
I
*
❖ - *
I\ :
6
CD
>
~g3
4
Pi
2
:
' :A
,A"-W
* * 4
0
5
o
A
A'
•s* \
-
10
15
20
Frequency (GHz)
Fig. 3.11
The percent relative error of the system determined by comparing the
measured and the calculated s for deionized water at 30°C.
Deionized water (30°C)
20
e i6
U
0
g 12
0>
1
8
Pi
4
*
o
*■*
•
Maximum
Observed
*o
0
5
10
15
20
Frequency (GHz)
Fig. 3.12 The maximum estimated and the observed percent relative error of the system
determined using Eqs. (3.12) and (3.13) respectively for deionized water at 30°C.
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52
Air (30 C)
4
3
2
a s'
to
1
0
«0«PQMMOQO*OOOOA
A
a
a
A
A
A
A
A
A
a
A
a
A
O
O
O
O
O
O
O
O
A
O
A
O
O
Meas.
« s" Meas.
-1
5
10
15
20
Frequency (GHz)
Fig. 3.13 Measured e of air at 30°C.
Teflon (20°C)
1.5
"to
a aa
2
a
a
a
a
1
1
0.5
0
0
5
10
15
w
a s'
Meas.
« e" Meas.
20
Frequency (GHz)
Fig. 3.14 Measured s of Teflon at 20°C.
thickness and the transversal extent were investigated in order to simulate an infinite
sample. White bond paper sheets were cut into circular shapes with diameter of 26 mm,
a little less than that of the sample holder. The s' of a varying thickness of the paper
backed with two contrasting materials - Copper and Teflon were measured over the
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53
entire frequency range of interest. As shown in Figs. 3.15 to 3.18 the s' gradually
changed from those of the background materials to that of the paper with the increase in
the paper thickness. The effect of the background materials was negligible when the
paper thickness reached 2.8 mm (28 sheets). As expected, the higher the frequency the
lesser the thickness o f paper required to nullify the effect of the background materials.
Therefore a sample thickness of 2.8 mm and of transversal extent of 26 mm was
sufficient to simulate an infinite sample. In the literature [Langhe et al., 1994] and
[Poumaropoulos and Misra, 1994] the thickness and the transversal extent of the
minimal sample size were found to be approximately twice the inner radius of the outer
conductor. Therefore the thickness estimated for the research agreed well with that
reported, and the transversal extent was more than sufficient. Since the fields in
materials having losses such as vegetation will decay much faster, the minimal sample
size estimated by considering paper, a low loss material, was the worst case scenario.
For convenience, the thickness of the samples in any case were chosen greater than 2.8
mm.
Operating frequency =300 MHz
100
^
-A
* Paper on Copper
0 Paper on Teflon
0
10
20
30
Number of paper sheets
Fig. 3.15 The e' of varying thickness of white bond paper backed by Copper and Teflon
at 300 MHz.
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54
Operating frequency = 1.01 GHz
100
a Paper
w
1 0
on Copper
A
° Paper on Teflon
i
a
o
o
o
o
A oAo * d
o
6
10
6
4
6
A
20
30
Number of paper sheets
Fig. 3.16 The s' of varying thickness of white bond paper backed by Copper and Teflon
at 1.01 GHz.
Operating frequency = 10.04 GHz
100
:
a Paper
-w
10
on Copper
° Paper on Teflon
a
0
o
°
o
°
10
A
o
A
o
A
0
d
6
d
d
20
$
6
30
Number of paper sheets
Fig. 3.17 The s' of varying thickness of white bond paper backed by Copper and Teflon
at 10.04 GHz.
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55
Operating frequency =18 GHz
100
^ Paper on Copper
■to
10
° Paper on Teflon
o
o
Ao a o a f
o
10
.
f
^
a
a
A
a
20
A
a
30
Number of paper sheets
Fig. 3.18 The s' of varying thickness of white bond paper backed by Copper and Teflon
at 18 GHz.
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4. MEASUREMENT RESULTS
4.1 Introduction
Alfalfa (Madicago sativa) at 10% blooming stage was harvested from the
experimental fields of Agriculture and Agri-Food Canada (AAFC), Saskatoon, Canada.
The whole plants were cut into lengths of about 127 mm, and put in air-tight polythene
bags. Some of the samples thus prepared were stored in a cold room at 5°C, and the rest
in a freezer as the plant stayed nearly fresh for only 4-5 days in the cold room. The
leaves were separated from the whole plants manually, and the plant parts, either the
leaves or the stems at various moisture contents, were prepared by drying them in a
computer controlled semi-automated thin layer hot-air dryer starting from the highest to
the lowest moisture contents. The samples thus prepared were put back into the air-tight
polythene bags, and stored at 5°C until used. The same procedure was applied in
preparing the samples from the plants stored in the freezer but only after thawing them at
room temperature for about 2 h, and then storing them at 5°C for 12 h with occasional
shaking to produce a sample with uniform moisture content.
The s of the leaves and the stems of the alfalfa were measured over a broad band
frequency range at various moisture contents and temperatures as shown in Table 4.1.
The dielectric behavior of the alfalfa leaves was analyzed from the point of view of
frequency, the moisture content, the temperature, the salinity, and the bound water
content. Although all the measurements were performed at 201 frequencies, only 33
representative frequencies have been displayed in the subsequent plots.
Measuring the e for vegetation was different from those for the other materials in
the sense that a prior knowledge of the optimum pressure of the probe to be
56
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57
Table 4.1 The frequencies, the moisture contents and the temperatures at which the s of
alfalfa leaves and stems were measured.
Parameters
Frequency (GHz)
Moisture contents (% w.b.)
Temperature (°C)
Plant part
Range
Step
Total measurement points
Leaf
0.3 to 18
0.088
201
Stem
9 9
9 9
9 9
Leaf
12 to 73
5 tol5
9
Stem
42 to 79
8 to ll
5
Leaf
-15 to 30
5 tolO
6
Stem
22
-
1
used onto the test vegetation was required for the measured 8 to be close to the true s of
the vegetation. As for the other materials, the moisture content of the test vegetation
before and after the measurement must be investigated to check for any change in its
moisture content during the measurement. This would help to refer the measured s to the
true moisture content of the test material. Therefore preliminary experiments were
performed to determine the optimum pressure and the change in the moisture content.
Besides, an experiment was also performed to determine any difference between the
temperature acquired by the sample and the system temperature preset at the required
sample temperature.
4.2 Preliminary experiments
4.2.1 Determining the optimum pressure
The system developed during the course of this research for the measurement of
the s of vegetation materials can also be used to measure the 8 of other materials such as
liquids, solids, semi-solids and powered materials, and there is no need to determining
the optimum pressure of the probe onto the test material. To measure the e of liquids,
one has only to make sure that the probe aperture is free from air bubbles, and in the
case of solids only the surface of the material must be smooth for a proper contact
between the sample surface and the probe aperture without any gaps. As the semi-solids
deform to make a good contact with the probe, the measurement is even easier, and for
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58
the powders the measurements can be referred to the material densities. For vegetation,
however an optimum pressure of the probe onto the test material must be determined so
that the natural structure of the vegetation is retained, and at the same time the air is
expelled from the bulk vegetation resulting in the measured e close to the true s of the
natural-state vegetation only.
No clear information on the optimum pressure was available in the literature, and
even if they were present, they would be highly likely to vary depending upon the type
of vegetation. In one study in measuring the e of wood using a two-electrode system
[Torgovnikov, 1993] a pressure o f about 10 ± 2 kPa was suggested. When an experiment
on the alfalfa leaves at 73% moisture content (the most delicate ones) was performed,
the s' increased fairly rapidly with pressure (or with the compactness of the leaves) in the
beginning, and slowed down once the pressure reached approximately 5 kPa as shown in
Fig. 4.1 (a). A sudden increase in the s' was noticed at around 11 kPa indicating the out
flow of fluid from the ruptured leaves, and no significant change in s' was observed
afterwards even for relatively higher pressures. A similar trend was observed for s" as
depicted in Fig. 4.1 (b). Therefore a pressure of 9 ± 1 kPa was chosen as an optimum
pressure to measure the s of the alfalfa leaves throughout the experiment. Although the
pressure applied onto the sample was less than the maximum pressure that could be
applied still retaining the natural integrity of the leaves, attention was paid for unusually
high dielectric values during the measurement to make sure that leaves were intact.
Preliminary experiments in determining the optimum pressure in measuring the s
of the alfalfa stems were also performed. Unlike the leaves, it was necessary to
determine whether the measurements were to be performed on the bulk of the short
stems or a single stem. However, in either case, an optimum pressure, which could be
used for consistent measurement of the s with a minimal disturbance to the plant part
was essential. Alfalfa stems existed in various diameters ranging from 1.89 to 2.58 mm
with the average diameter of 2.29 mm for the fine, and 2.51 to 5.51 mm with the average
diameter of 3.82 mm for the coarse stems [Patil, 1995], and none of them was large
enough to simulate an infinite sample size in using with the dielectric probe, which
induced an additional complication in the measurement of their s. Therefore, either the
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59
kPa
80
o 24.06
O 20.13
a. 17.10
° 11.31
*
m
»
s» *
40
- 10.07
- 8.55
ii i
♦
«i
i i $
♦
♦
♦
+ 7.03
• 6.07
* 5.10
A iSi
x 4.00
_ T - ..
♦ 3.31
10
Frequency (GHz)
15
20
a
1.93
* 0.83
(a)
kPa
80
24.06
>20.13
60
* 17.10
> 11.31
* 10.07
■ 8.55
■7.03
■6.07
c 5.10
♦ ♦
• 4.00
> 3.31
0
5
10
15
20
Frequency (GHz)
* 1.93
> 0.83
(b)
Fig. 4.1
The spectra for the (a) s' and (b) the e" of the alfalfa leaves at 22°C at various
pressures and at a moisture content of 73%.
measurement could be performed on a bulk of the short stems, and the measured s later
corrected to minimize the effect of the air pockets existed between the probe aperture
and the stems, or a single stem placed across the center of probe face could be measured,
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60
and the measured
e
e
compensated through an appropriate correction curve to estimate the
of an infinite sample size.
The first approach was found to be practically not feasible because it was
extremely difficult to achieve a proper contact between the stems and the probe aperture
due to bending, and the variations in the diameters and the softness of the stems. For
example, as shown in Fig. 4.2 none of the s' of the bulk samples except for the bulk #2
Bulk alfalfa stems, 3 cm long, 78% me. (w.b.), 0.3 GHz
Bulk #
*1
60
° 2
Q
45
□
□
□
• 3
A 4
X
X
« 30
x5
15
i
X
# W0
0 J ifi %T T -f ~r
x6
.7
+
r
10
20
15
25
+ 8
-9
kPa
-
Fig. 4.2
10
The s' of the bulks of the alfalfa stems containing 50 stems in each bulk at
various pressures, and at 25°C.
followed the expected general trend and the magnitude of the s' observed for the stems
measured individually (Fig. 4.4 (a)) while all the external parameters such as the
moisture contents, the temperature and the frequency were the same indicating a poor
contact between the probe and the sample. The trends of the
e
were found to be similar
at different frequencies as shown in Fig. 4.3, and therefore the conclusion made on the
trend of the e at a particular frequency can be extended to other frequencies as well.
The second approach was more promising in determining a consistent optimum
pressure of about 7 kPa as shown in Fig. 4.4 for the lower and the upper limits of the
frequency range of interest. As mentioned earlier, the
e
trends for the intermediate
frequencies were similar to those shown in Fig. 4.4.
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61
Bulk alfalfa stems (bulk #2), 3 cm long, 78% me. (w.b.), 25 C
GHz
50
n 0.3
40
• 0.39
0.48
* * X *
CO
30
>
1.01
20
• 2.07
10
6.05
+8
0
10
15
20
- 12.07
25
16.05
Pressure (kPa)
• 18
Fig. 4.3 Similar s' trends of the alfalfa stems (bulk #2) at various frequencies.
Individual alfalfa stems, 3 cm long, 78% m.c., 0.3 GHz
Dia (mm)
60
•
■ 2.15
45 j
a
-w 30
2.01
2.22
2.6
a
*
15
2.8
• 2.9
+ 3.01
0
10
15
Pressure (kPa)
20
25
• 3.09
- 3.28
a 3.68
(a)
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62
Individual alfalfa stems, 3 cm long, 78% m.c., 0.3 GHz
Dia (mm)
60 i
2.01
•
- 2.15
45
-
'
« 30
15
a
2.22
>
2.6
*
2.8
• 2.9
+ 3.01
0
10
15
20
25
Pressure (kPa)
’ 3-09
- 3.28
+ 3.68
(b)
Individual alfalfa stems, 3 cm long, 78% m e., 18 GHz
Dia (mm)
60
» 2.15
45
-w 30
15
2.01
°
a
2.22
*
2.6
*
2.8
• 2.9
Jo i l l 2 !
+ 3.01
o
10
15
Pressure (kPa)
20
25
- 3.09
- 3.28
+ 3.68
(c)
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63
Individual alfalfa stems, 3 cm long, 78% m e., 18 GHz
Dia (mm)
60 ,
»
2.01
» 2.15
45
a
2.22
2.6
% 30
*
2.8
• 2.9
0
J---------------
,
0
5
-~-r
10
+ 3.01
r
15
20
Pressure (kPa)
25
* 3-09
- 3.28
a 3.68
(d)
Fig. 4.4
The £ of the individual alfalfa stems with different diameters plotted against
the probe pressure (a) and (b) at 0.3 GHz, and (c) and (d) at 18 GHz, and at 25°C.
4.2.2 Sensing the sample temperature deviation
The temperature of the sample in contact with the probe aperture must be known
at the time of the measurement so that the measured e could be referred to the correct
temperature. To determine this temperature, preliminary experiments were carried out.
The sample holder was conditioned at a desired temperature, for example, 30°C. Then
sample at 5°C from the storage was placed in it, and the temperatures of the air between
the probe aperture and the sample surface was observed using a Constantine-Copper
thermocouple attached temporarily to the probe face. This assembly was held above the
sample to prevent any heat loss from the sample through conduction. As shown in Fig.
4.5, the temperature of air increased very slowly after about 15 min. When the sample
was slowly brought in contact with the probe aperture at an optimum pressure after 30
min., the observed temperature of the sample surface was very close to the desired
temperature of 30°C. It showed that about 30 min was sufficient to condition a sample at
a desired temperature.
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64
U
i,
H 22
20
"
i
0
10
i- - - - - - - - - - - - - - - - - - - - - - - - -
20
r- - - - - - - - - - - - - - - - - - - - - - - - 1
30
40
Time (min)
Fig. 4.5 The trends for the temperatures of the leaf sample initially at 5°C subjected to
the desired temperature of 30°C.
As shown in Table 4.2 the difference between the desired and the achieved sample
temperatures was found to be about 0.5°C. The sample temperatures were, however,
checked before taking any measurement on the s of the test material during the
experiments.
Table 4.2
The mean difference between the desired and the achieved sample
temperatures.
Temperature (°C)
Observations
Desired
1
2
3
30
Achieved
Difference
29.34
0.66
29.36
0.64
29.63
0.37
Mean Difference
0.55
4.2.3 Quantifying the change in the sample moisture content
To refer the measured 8 to the correct moisture content of the sample, the sample
moisture content at the time of the measurement must be reported. Since there was a
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65
time gap of about 30 min before getting the sample at the desired temperature, and of
about 12 s for the s measurements, it was necessary to check if the sample moisture
content determined following the standards [ASAE Standard, 2000] changed during the
process. As shown in Table 4.3 when the leaf samples at 73% moisture content and at
5°C were measured immediately after the dielectric measurement at 30°C, a mean
difference o f only 0.5% of the moisture content was found.
Since both the moisture content and the desired temperature selected for the
experiment were the upper limits in the corresponding ranges of interest, the change in
the moisture content of any sample at the moisture content and the temperature below
these limits was therefore expected to be not higher than one-half percent of the
moisture content. This fact was further supported by the occasional checks made on the
moisture contents of the samples right after the dielectric measurements during the
experiments.
Table 4.3
The sample moisture contents before and after the dielectric measurement,
and the mean of the difference between them.
Moisture content (%, w. b.)
Observations
1
2
Before dielectric
After dielectric
measurement
measurement
73
3
Difference
Mean
Difference
72.58
0.42
72.44
0.56
72.62
0.38
0.45
4.3 The dielectric properties of the alfalfa leaves
As mentioned in the opening of this chapter, the
e
of the alfalfa leaves were
measured at various moisture contents, temperatures, and frequencies. The measured
data shall be presented in different forms in the following sections as they are analyzed
from the point of view of frequency, moisture content, bound water and temperature.
The parts per thousand (ppt) used in the following sections stands for the degree of
salinity equivalent to a number of grams of Sodium chloride (NaCl) dissolved in one
kilogram of distilled water.
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66
4.3.1 Frequency dependence
The frequency dependence of the e of the alfalfa leaves at 22°C with moisture
content as the parameter is shown in Figs. 4.6 (a) and (b). In the vicinity o f the moisture
Alfalfa leaves, 22°C
me <y/o
50
<> 73
40 --I
° 66
30
Oo
W
■ 58
20 i
10
+ 52
+ + + +++++^
° ° oooitjon
I I * I* XX
S-l ~
o !-
hh^ ;;--.
45
0
"** -*- .
» 31
- r -T~ -r ~ rr ] i
1
0
10
100
* 23
- 17
Frequency (GHz)
- 12
(a)
Alfalfa leaves, 22° C
me 1 7o
<> 73
30 i
° 66
20 1
- 58
to
10
+ 52
" • " ■’/"Oooooo^ 0000000^
+ ++++++4+H>W"+++++H4^ ]
s J g Sft °Wijjflfggl gI
4*
0
0
4.
45
TTfT* * *
1
10
■ 31
100
Frequency (GHz)
* 23
- 17
12
(b)
Fig. 4.6 The frequency dependence of the (a) s' and (b) the s" of the alfalfa leaves at 22
°C with moisture content as the parameter.
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67
content of 23%, the e' of the leaves decreased continuously with frequency, which was
substantially different from the dispersion of the s' of free distilled or saline water shown
in Fig. 4.7 [Stogryn, 1971] but similar to that of bound water, Fig. 4.8 [Ulaby and ElRayes, 1987], Therefore it can be argued that the s' of the leaves below a moisture
content of 23% was dominated by the bound water component. The argument is
justifiable because this particular moisture content was found to be the fiber saturation
point of the alfalfa leaves. Water exists only in the form of bound water in the vegetative
materials at a moisture content below this point, and both the free and the bound water at
a moisture content exceeding this point [Torgovnikov, 1993]. The free and bound water,
and the fiber saturation point shall be described in detail in the next chapter. For the
same reason, the effect of both the bound and the free water on s' of the leaves is
apparent in Fig. 4.6 at moisture contents exceeding 23%. The s' decreased with
increasing frequency at a rate comparable to that of bound water up to the frequency of
approximately 5 GHz, and afterwards similar to that of free water, and as expected the
similarity increased with increasing moisture content. Any sharp decrease in the s' of a
moist material over lower frequency range might therefore be an indication of the
presence of the bound water.
As expected, the s" of the leaves, Fig. 4.6 (b), in general, is similar to that of
bound water at a moisture content below 23% for the entire frequency range. At a
moisture content exceeding 23%, and frequencies up to around 5 GHz, the s" of the
leaves are apparently dominated by those of the free saline water. For example, a
separate experiment on the measurement of the s" of the fluid at 20°C extracted from the
leaves at a moisture content of 52% showed that they were indeed very close to those of
saline water at 15 ppt and at 20°C as shown in Fig. 4.9. Therefore the low frequency
losses observed for s" was attributed mainly to the ionic losses due to the free saline
water present in the leaves, and in part to the losses due to the bound water.
Above 5 GHz, the trends of the s" of the leaves were similar to that of free water
irrespective of its salinity as the ionic losses are negligible, and the relaxation losses are
dominant at higher frequencies. However, a significant difference between the relaxation
frequency of the leaves, approximately ranging over 5 to 8 GHz, and that of free water,
which is 18 GHz, was noticed. This difference was analyzed, in general, by plotting the
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68
Free distilled and saline water, 22°C
100
s' (0 ppt)
s’ (4)
s ' (8) x
80
60
s"(8)
40
20 -
\
s"(4)
-
s" (0)
0 -------(---- r - T —
■
0
--
...
\
e ? ”-
---r-- 1 r -i-,— i--------1----
1
10
100
Frequency (GHz)
Fig. 4.7
The dielectric spectra of the distilled (0 ppt) , and the saline water at various
salinity, and at 22°C [Stogryn, 1971].
Bound water, 22°C
30
24
w
18
12
6
0
1
10
100
Frequency (GHz)
Fig. 4.8
The dielectric spectrum of the bound water at 22°C [Ulaby and El-Rayes,
1998],
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69
180
135 “w
90
Fluid
X
o
X
45
^Xx&33fc& *8®oooo0oHp
Saline water (4 ppt)
0
0
1
10
100
Frequency (GHz)
Fig. 4.9
The e" of the fluid extracted from the alfalfa leaves at 52 % moisture content
and that of the saline water (4 ppt) at 20°C.
Cole-Cole diagrams for the leaves at a moisture content of 73%, the free distilled and
saline water, and the bound water as shown in Fig. 4.10. Only the leaves at 73%
moisture content were considered to make the plot less crowded. The Cole-Cole
diagrams for the leaves at other moisture contents are shown separately in Fig. 4.11. The
position of the center, C l of the circle through the data points for the leaves was found to
be below the abscissa. From the characteristics of the Cole-Cole plot this suggested that
the leaves, as expected, consisted of different molecules with their own relaxation times
distributed around the most probable value unlike the case where the center always lies
on the abscissa for substances consisting of molecules of one relaxation time only, as for
the distilled water (Cd). The relaxation time distribution is characterized by a parameter,
Ax
where \p is the angle formed by the x-axis and the line connecting the center with the
point s' = s ' . The most probable relaxation frequency, fr at which the losses peak was
given by
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70
Saline water (4ppt)
Leaves (73%)
W
^
*
Distilled water
'
^ Bound water
10
Fig. 4.10
Cole-Cole diagrams for the distilled water [Kraszewski, 1996], the saline
water at 4 ppt, the leaves at 73% moisture content, and the bound water [Ulaby and ElRayes, 1987] at 22°C.
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71
30
X
X
20
X
D
CO
Leaf at 73% me
10
58%
66%
20
30
o -
0
0
10
40
50
e
Fig. 4.11
The Cole-Cole diagrams for the alfalfa leaves at various moisture contents
and at 22°C.
(4.2)
where U = yj(e' - e" )2 4- (e")2
and V = ^/(e' - s')2 + (s")2 , and s '
and s i
are
respectively the values for the static and the limiting high frequency s', which are given
by the intersection points of the circle with the abscissa as shown in Fig. 4.10 for the
leaves.
The AT, fr, and the relaxation time, x for the leaves at different moisture content
were calculated using Eqs. (4.1) and (4.2), and are tabulated in Table 4.4 along with that
for the free and the bound water. These values for the leaves should be taken as an
approximation at best because it is usually not possible to obtain sufficiently accurate
Cole-Cole diagrams using experimental data. The fr for the leaves varied from
approximately 5 to 8 GHz depending upon their moisture content, which is in agreement
with the dielectric spectrum presented in Fig. 4.6 (b). As expected, the fr for the leaves
fell in the range between those of the bound and the free water, and are relatively closer
to the fr of the bound water than that for the free water.
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72
Table 4.4 The relaxation time distribution, AT, the most probable relaxation frequency,
fr, and the relaxation time, x for the leaves at different moisture content, and that for the
free and the bound water at 22°C.
Material
AT
x(ps)
fr (GHz)
Bound water
0.5
786
0.20
Leaf (31%)
0.33
30.4
5.23
Leaf (45%)
0.31
20.9
7.61
Leaf (52%)
0.29
26.5
6.02
Leaf (58%)
0.28
21.2
7.51
Leaf (66%)
0.21
18.5
8.62
Leaf (73%)
0.07
20.6
7.71
Water
0.00
9.27
17.16
4.3.2 Moisture content dependence
Water is the ingredient that changes the e of the vegetation the most, and in many
cases dictates them. The values of £ for free water are many times higher than those for
the dry vegetation. Interacting with vegetation in the process of adsorption and capillary
condensation, the water changes its form and hence its own 8, and causes changes in the
£ of the moist vegetation. The free water filling the cell cavities also changes the
character o f the interactions between the moist vegetation and the electromagnetic field.
These changes result in the changes of the £ of the vegetation. The physical factors that
determine the character of the influence of the water on the £ of the vegetation have not
yet been studied theoretically due to the complexity of the problem. Therefore the
influence of the moisture content on the £ of the alfalfa leaves was analyzed from the
macroscopic point of view by measuring the £ at different moisture contents.
Starting with the e" of the alfalfa leaves, they increased exponentially with the
moisture content as depicted in Fig. 4.12 (b) where the solid lines are the exponential fit
to the measured dielectric data. The s" decreased with increasing frequency irrespective
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73
Alfalfa leaves, 22°C
0.3 GHz
40
* 2.51
30
8.09
20
10
0
*
10
20
30
40
50
60
70
80
Moisture content (%, w.b.)
(a)
AHalia leaves, 22°C
0.3 GHz
40
30
8.09
2.51
20
10
0
10
20
30
40
50
60
70
80
Moisture content (%, w.b.)
(b)
Fig. 4.12
The s of the alfalfa leaves vs. moisture content (a) s' and (b) s" with the
frequency as parameter at 22°C.
of the moisture content, and exhibited its maximum value at 8.09 GHz excluding for a
moment the value at 0.3 GHz and decreased at frequencies below or above this
frequency, e.g. at 2.51 GHz and 18 GHz, due to the relaxation losses. A sharp increase
in the s" at 0.3 GHz and at a moisture content above 30% was attributed mainly to the
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74
high electric conductivity of the moist vegetation due to the salt present in it as shown in
Fig. 4.9 and its ability to polarize under the influence of an external electric field. The
electric conductivity of a material depends on the concentration of the dissolved ions and
on their mobility. Hence moisture contents exceeding the fiber saturation point (23%,
w.b.) increased both the quantity of the dissociated ions in the vegetation matrix and
their higher possibilities for the displacement. The vegetation conductivity, o increased,
resulting in a higher e" at low frequencies following the relation
coe0
where a is in Siemens per meter and £o = 8.85 x 10'12 F m"1. The other contributing
factor for higher e" at low frequencies was the loss caused by the bound water as
depicted in Fig. 4.8. As shown in Fig. 4.7 the effect of the conductivity (or salinity) on
the s" of the free water has greatly reduced at a frequency exceeding 3 GHz. This
phenomenon was also reflected in the
e"
of the leaves as both the trend and the
magnitude as shown in Fig. 4.12 (b) at frequencies 2.51, 8.09 and 18 GHz are similar.
The s' of the alfalfa leaves also increased exponentially with the moisture content
as shown in Fig. 4.12 (a) and decreased with increasing frequency for any value of the
moisture content. In general, any change in the moisture content of the leaves
subsequently changed the saline concentration of its fluid. The dielectric spectra for the
s' of the fluids extracted from the alfalfa leaves at the moisture contents of 73%, 58%
and 52%, which are depicted in Fig. 4.13 indicated that the change in the saline
concentration of the fluid with the changing moisture content of the leaves had no
significant effect on its s', and hence on the s' of the leaves. The s' of the fluids at any
frequency decreased with the increasing saline concentration (or decreasing moisture
content), which was similar to that of the free saline water shown in Fig. 4.7.
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75
Extracted fluid of the alfalia leaves, 22°C
100
80
me (%)
60
» 73
40
* 58
20
* 52
0
'T
0.1
1
10
100
Frequency (GHz)
The s' of the fluids extracted from the alfalfa leaves at three moisture contents and at
22°C.
4.3.3 Bound water dependence
Structurally, the free water is assumed to be inside the macro-capillaries that is,
in pores and capillary tubes with a radius exceeding 10'7 m in the plant tissues, and the
bound water resides in the cell walls as chemically or physically bound water
[Torgovnikov, 1993] [Pyper et. al., 1985]. The chemically bound water is the water of
crystallization in which a number of water molecules are bonded to the molecules of
other substances, for example the coordinated water (MgCfr'bHiO), and the physically
bound water exists in two different forms - adsorption and capillary-condensation. The
adsorption water is the water sorbed by the surfaces of the micro-fibrils forming the
intermicrofibrillar interlayers, and is separated into monomolecular and polymolecular
water. The capillary-condensed water occurs in the cell wall pores and is bound to the
vegetation by capillary forces. Definite borders between these fractions of the bound
water are not established, and most likely they are “eroded”, as the transfer from one
fraction to another envelops several layers. Four methods have been suggested to
distinguish the bound water from the free water [Pyper et. al., 1985]. They are (1) the
dynamic dielectric thermal analysis (DDTA), (2) the microwave attenuation analysis
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76
(MAA), (3) the near infrared reflectance analysis (NIRA), and (4) the nuclear magnetic
resonance (NMR). However, this was out of the scope of this research work.
For the analysis of the influence of the different forms of the bound water on the
dielectric properties of the vegetation, three forms of bound water are distinguished,
namely monomolecular, polymolecular, and capillary-condensed, in decreasing bond
energies or increasing reorientational mobility of the molecules resulting in higher
contribution to the s of the vegetation. The s of the bound water is still poorly
understood. Most researchers have drawn their conclusions concerning the e of the
bound water by measuring the e of the oven-dry material and those of the materials with
differing moisture contents, and using them in a dielectric mixing formula. It is reported
that the major error in this formula lies in the fact that the mass of the bound water in the
sample is assumed to be several times less than the mass of the sample itself
[Torgovnikov, 1993]. The estimations of the s of the bound water are therefore largely
qualitative. In this research the s of the bound water was calculated using the Cole-Cole
dispersion equation [Ulaby and El-Rayes, 1987]
e bw - 2 . 9 + -
1+
/
55
p \ 1_A'
(4.4)
0.18
where f is in GHz, and AT = 0.5. This equation is based upon the measurement of the s
of the sucrose-distilled water mixture containing the water only in the bound form, and
fitting the measured data to the Cole-Cole equation to estimate the parameters of the
equation. Since the binding arrangement of the sucrose-water molecules is precisely
known to assure the presence of only bound water in the mixture, and the sucrose is also
a good example of the organic substances present in vegetation, Eq. (4.4) was a
reasonably good choice for estimating the s of the bound water. The real and the
imaginary parts of Eq. (4.4) are already shown plotted in Fig. 4.8. It is noted that this
equation is also free from the ionic conductivity, and hence the low frequency losses are
due to the bound water only. A sharp decrease in the dielectric constant and a small
decrease in the loss factor over the low frequency range, particularly below 5 GHz are
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77
the characteristics of the dielectric spectra of the bound water. However, this type of
frequency response was rarely observed in vegetation because the effect of the salinity
was also present at this frequency range, and what was observed was the combined
spectra of the bound water and the effect of salinity.
4.3.4 Temperature dependence
The temperature acts upon the s of the vegetation as a factor of an external
medium. The dependence of the s of the alfalfa leaves at a moisture content of 73% on
the temperature was analyzed. The temperature considerably affected the e of the alfalfa
leaves as shown in Fig.4.14. To characterize the influence, the equation suggested by
Debye, Eq. (4.5) which correlates the relaxation time, x with the molecular constants
was considered.
x = 4rcr3K/BK
(4.5)
where
r
= radius of the molecular sphere
K
= viscosity
B
= Boltzmann’s constant, and
K = absolute temperature.
Although this equation is considered to be strictly valid only for dilute solutions,
it was considered here for use with the vegetation material to provide a qualitative
estimation of the temperature influence on s. Excluding the ionic losses at lower
frequencies, the increase in the temperature of the vegetation caused a reduction in x ,
and subsequently induced a shift of the maximum value of s" to the region of the higher
frequencies at positive temperatures as shown in Fig. 4.14 (b). The higher temperature
also resulted in a decrease in the viscosity, r| which in turn not only shifted the peak of
the s" but also the whole curve, e" =
cp (f)
to the higher frequencies. The corresponding
change or the decrease in the s' is shown in Fig. 4.14 (a). This phenomenon, as expected,
can be seen more clearly for the free saline water at a concentration of 4 ppt as shown in
Fig. 4.15.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
78
Alfalfa leaves at 73% me
°C
* 30
60
45
• 20
A A
_*A & ,
**
W 30
15
A 10
2*'iS
jp
x£".
□
o
d
a a
<0
° -5
d
0 © O o ooooooaooaocb o (
0
o -15
r r - i T T ------------- 1-------- 1—
1
100
10
Frequency (GHz)
(a)
Alfella leaves at 73% me
m
60
°C
a 30
45
x 20
c 10
30
0
Et
15
0
* -5
A -15
xa
4 l»,
TTTTl
1
'
10
100
Frequency (GHz)
(b)
Fig. 4.14
The dielectric spectra of the alfalfa leaves for the (a) s' and (b) the s" at a
moisture content of 73 % with the temperature as the parameter.
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79
Distilled water at 4 ppt
100
A
80
w
x
A A
A A ^ A,
x x x x xx:
* e' (10)
60
- e"(10)
40
■ s' (20)
□
> £”(20)
20
A
* £' (30)
0
0.1
1
10
100
* £"(30)
Frequency (GHz)
Fig. 4.15 The temperature dependence of the e of the saline water at a concentration of
4 ppt.
The
e of water
changes considerably with the change in the temperature. In most
cases, they exceed those of the cell wall substances [Torgovnikov, 1993]. Therefore it is
fairly reasonable to argue that the observed change in the £ of the vegetation at a
moisture content exceeding the fiber saturation point with temperature was mainly due
to the change in the £ of the contained fluid caused by the changing temperature. As
shown in Fig. 4.15 the e' of distilled water at 4 ppt decreased with increasing positive
temperature up to the frequency of 5 GHz, and increased with the temperature
afterwards. A very similar trend was observed with the alfalfa leaves as shown in Fig.
4.14 (a). In case of the e", except at the low frequencies where the ionic conductivity
dictated the e" of the material, the e" of the leaves at a moisture content of 73% was
found to be affected by the change in the temperature, Fig. 4.14 (b) similar to that for the
distilled water at 4 ppt.
The £ of the leaves at a moisture content of 73% as a function of the temperature
with frequency as the parameter is plotted in Fig. 4.16. The temperature coefficients for
£', k ‘, at positive temperatures showed a great similarity with those of free water
depicted in Fig. 4.17 except at a frequency of 10 GHz over a temperature range of 20 to
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80
Alfalfa, leaves at 73% me
50
40
GHz
—1
30
«—4
20
4—10
to
18
10
0
T
-20
-10
T
0
T
10
20
30
40
Temperature ( ° C )
(a)
AlMa leaves at 73% me
GHz
«_ i
15
4
10
-+— 10
18
5
0
-20
-10
0
10
20
30
40
Temperature ( ° C )
(b)
Fig 4.16
The (a) s' and (b) the s" of the alfalfa leaves at 73% moisture content as a
function of temperature with frequency as a parameter.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
81
Free water at 4 ppt
GHz
s' (1)
100
80
*
i
60
a
A
8-(4)
8- (10)
40
8- (18)
20 i
8"(1)
8 "(4 )
0 40
10
20
30
40
8"(10)
8 "(1 8 )
Temperature ( ° C )
Fig. 4.17 The temperature dependence of free water (4 ppt) at different frequencies.
30°C, where the k ‘, are opposite in signs. Comparison of Fig. 4.16 (b) and Fig. 4.17
reveals that the temperature coefficient for s", k'„ at positive temperatures are similar to
those of distilled water at 4 ppt. The magnitudes of e" for leaves at 1 GHz are
comparable to those of water at 4 ppt due to the ionic conductivity at low frequencies,
and at higher frequencies they are always less than those of free water as the relaxation
losses are dominant at these frequencies, and increase with the quantity of the free water.
At 20°C an e" (18) curve was seen at the top for free water, Fig 4.17 whereas it was
£"(10) for the leaves, Fig. 4.16 (b) because they relax at different frequencies.
An abrupt change of the s of the leaves was noted at a temperature near 0°C, Fig.
4.16. A further increase of the negative temperature affected the s values only slightly.
At negative temperatures, the free water and a part of the bound water turn into ice,
which can not but affect the s of the vegetation. The 8 of ice differs significantly from
those of the free water. The static e' of ice, e'ce srises with decreasing temperature, and at
-0.1°C it is equal to 91.5, at -11°C to 95, at -32°C to 100, and at -66°C to 133 [Auty and
Cole, 1952], The limiting high-frequency e', e'ceoo does not depend on temperature
(down to -66°C) and remains at 3.1. Hence, the change of the 8 of the ice at a frequency
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82
exceeding 1 GHz is comparatively small, and at temperatures from -10 to -20°C the s'
and the e" of the ice are respectively equal to 3.2 and 0.0029 at 3 GHz and 3.17 and
0.0022 at 10 GHz. On the other hand, both the static and the limiting high-frequency e of
the free water, i.e., ews and ewoo respectively increase with decreasing temperature; at
60°C they are respectively equal to 66.7 and 4.2, at 30°C to 76.6 and 5.2, and at 5°C to
85.8 and 5.7 [Kraszewski, 1996]. As a result, the change in the s of free water are very
significant with temperatures at microwave frequencies, and at a temperature of 10°C its
s' and s" are respectively equal to 79.81 and 18.05, and at 20°C to 77.83 and 12.92, at
3.04 GHz, and at 10.39 GHz, they are respectively 52.12 and 38.9 at 10°C and 59.94 and
33.33 at 20°C.
At -15°C, the s' and s" of the leaves varied from 4 to 8 and 0.4 to 2 respectively,
which were higher than those for the ice, particularly the values for the s". This
phenomenon can be explained to some extent as follows. At negative temperatures, the
vegetation consists of the (1) cell wall substance, (2) the air, (3) the ice, and (4) the
nonfreezing-bound moisture. At microwave frequencies, the change of the dielectric
properties of the first three components with a change of the temperature from -5 to 30°C is small [Torgovnikov, 1993]. Therefore, the quantity of the nonfreezing bound
moisture is the main factor determining the change of the s of the moist vegetation at
negative temperatures. However, it is worthwhile noting that vegetation at negative
temperatures may still contain some unfrozen, supercooled moisture, and its £, which are
presented in Table 4.5, are higher than those of ice by many times, and they can
therefore significantly increase the £ of the vegetation at negative temperatures. This
circumstance greatly affected the physical properties of the vegetation and caused a
considerable spread in the data obtained at negative temperatures.
4.4 The variability, repeatability and the effect of
orientation
The variability in the measured values of the £ of the alfalfa leaves were checked
measuring the £ for the five different samples from each lot of the leaves at the moisture
contents of 10, 24, 41, 54 and 75%. The e were measured at 51 frequencies at a step of
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83
Table 4.5 The e of the supercooled moisture in the vegetation materials [Torgovnikov,
1993],
T emperature(°C)
Frequency (GHz)
£
-30
-20
-10
2.4
s'
49
69
79
s"
24.01
42.78
31.6
s'
21
37
54
e"
34.02
44.4
43.2
£'
10.6
17.6
29
e"
21.52
30.8
38.57
£'
6.1
7.0
8.9
E"
7.32
11.62
16.82
5.8
10
30
350 MHz ranging over the entire range of 300 MHz to 18 GHz. The mean values for the
s
are shown plotted in Fig.
4 .1 8 ,
and since the standard errors for the
e'
and the
s"
are too
small to be clearly shown in the plots they are respectively presented in Tables B1 and
B2 (Appendix B) for every other frequency. The standard errors for the
s'
and the
s"
in
any moisture content and any frequency of interest respectively fell in the range of 0.07
to 0.90 and 0.01 to 1.01.
As depicted in Fig. 4.19 the standard errors, in general, increased with the
moisture content, which was attributed to the fact that a small variation in the pressure
during the measurement of the s for the samples at lower moisture contents was not as
significant as it was for the samples at relatively higher moisture content, and decreased
with the increasing frequency for any moisture content.
To check the repeatability of the measurement system for the alfalfa leaves, a
sample at each of the aforementioned moisture contents was prepared, and stored in the
sealed jars at 5°C. A sample from each of the moisture contents was measured four
times. The dielectric measurement system was shut down for 30 min after each
measurement, and the sample was left in the sample holder at 23°C until the four
measurements were completed to make sure that not only the same sample was re-
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84
Alfalfa leaves, 23°C
50
me (%)
40
*x
“ 30
I
•*xx.«***■
*x
♦ 10
o 24
****
*xxxxiexx .
20
A
************,*x
1 0
j
- 54
AAAa a a A a AAa A a a a a a a a a a a a A a a a a a a a a a a a a a a a a a a a a a a
“aooDODaoanaoa DoaDOaoDOQQDonoao a a n o a q a a a 8a o ° a “ n a a a a
* 75
^OOOOOOOOO$OOOOOOOOOOO$OOO$OOOo^oOOOOOOOOOO$O$O^Oo
0
10
0
15
41
20
Frequency (GHz)
(a)
Alfalfa leaves, 23°C 50
w
40
me r/o
30
* 10
o 24
<u 20
10
41
^XXXXXXXXK^^^^KXSXXXXXXXXXXXXXXXXXXXXXXX*
54
0
-10 ®
* 75
5
10
15
20
Frequency (GHz)
(b)
Fig. 4.18
The means of the (a) s' and (b) the s" of the alfalfa leaves calculated by
measuring the five samples from each of the five different moisture contents.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
85
s': Alfalfa leaves, 23°C
1.0
GHz
S-H
O
b(D
03
"O 0.4
§
™ 0.2
-i
o
~
a
o
□
-
A
$
I
°
• 0-30
n 0.65
?
A
D
A
a
i
6.32
i
*
0.0
o
o
0
2.07
60
80
10.21
+ 1 4 ' U
o 18.00
Moisture content (%, w.b.)
(a)
s": Alfalfa leaves, 23°C
1.2 -
GHz
1.0
• 0.30
& 0.8
'd 0.6 c3
§ 0.4 55 0.2 -
° 0.65
a 2.07
- 6.32
*
0.0
20
40
60
80
10.21
+ 14.11
a
Moisture content (%, w.b.)
18.00
(b)
Fig. 4.19
The standard errors associated with the variation in measuring the (a) s' and
(b) the s" of the alfalfa leaves from each of the five different moisture contents at
varying frequencies.
measured but also the orientation of the sample with respective to the probe position was
retained. The means for the repeated measurement of the s' and s" for the leaves at all
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86
Alfalfa leaves, 23°C
50
me (yo
40
CO
o 10
'****:**x.
*xXX,
•**x*xxx:
********x**x
**xxxx:
30
20
10
54
aa*aaaaaaaaaaaaaa
A A A A A A A A A A A A A A A A A A A A a A a AA a A a
0
<* 24
A 41
a
AAAA^
* 75
3«S88g8%888m8888»83833aWae8888m3»W888388888
)
5
10
15
20
Frequency (GHz)
(a)
Alfalfa leaves, 23°C
50
40
me (vo
30
* 10
» 24
20
10
41
************************************************
* 54
0
-10 fr
* 75
5
10
15
20
Frequency (GHz)
(b)
Fig. 4.20
The means of the (a) e' and (b) e" of the alfalfa leaves obtained by repeated
measurement of a sample from each of the five moisture contents at varying frequencies.
the frequencies and the moisture contents are shown plotted in Fig. 4.20, and their
standard errors are respectively presented in Tables B3 and B4 (Appendix B) for every
other frequency along with the corresponding mean values. The general trends of the
standard errors for the repeatedly measured 8 as shown in Fig. 4.21 were similar to those
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87
s': Ahalfa leaves, 23°C
1.0
GHz
U 0.8
§
c3
i
^
• 0.30
0.6
» 0.65
0.4
a 2.07
0.2
- 6.32
*
0.0
r~
o
20
40
60
80
10.21
+ 14.11
a
Moisture content (%, w.b.)
18.00
(a)
s": Alfalfa leaves,23°C
2.0
GHz
O 1.5
fc
<ul
la L0
S-<
» 0.30
° 0.65
a 2.07
§ 0.5
+->
C/3
- 6.32
*
0.0
20
40
60
80
10.21
+ 14.11
a
Moisture content (%, w.b.)
18.00
(b)
Fig. 4.21
The standard errors in measuring the (a) the s' and (b) s" due to the repeated
measurement of the same sample from each of the five moisture contents at varying
frequencies.
found in the analysis of the variability test, and the magnitudes of the errors for the s',
which varied over the range of 0.09 to 0.71 was comparable to, and that for the s", 0.02
to 1.54, was slightly higher than those found in the analysis of the variability. The later
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88
was contributed to the possible change in the conditions of the samples during the
experimentation, which lasted for 4 h. As in the variability analysis the standard errors,
in general, increased with the moisture contents, and decreased with the increasing
frequency
To observe the effect of the orientation on the measured values of the e, a sample
from each of the moisture contents was also measured at four positions rotating the
sample holder containing the sample 45° clockwise at a time about its center coincided
with that of the probe aperture. Unlike a sample of wood, where the fiber directions are
distinctive in certain directions such as radial, longitudinal or tangential depending upon
how they are cut from the trunk, the directions of the veins in the leaves were random in
nature. Form this point of view, a leaf could be considered as a mesh of the veins of
different sizes, and the measured e of the leaves was the mean value of the £ measured
for the veins oriented at different angles to the electric field strength vectors in random
fashion. The observed means and the standard errors for the samples one from each of
the moisture contents were found to be in the range of 0.04 to 1.3, and 0 to 1.61
respectively, which were comparable to those obtained in the repeated measurement of
the sample from the same moisture content; and it also suggested that the measurement
of the s for the leaf-samples was almost independent of the orientation. A slight increase
in the standard errors was attributed partially to the fact that the number of the samples
used here was one less than that used in the repeatability analysis, and the rest to the
sample handling. The mean values for the £ are shown in Fig. 4.22, and the standard
errors for the e' and the e" are respectively presented in Tables B5 and B6 (Appendix B)
along with the mean values at every other frequencies.
4.5 The dielectric properties of alfalfa stems
As discussed in the sub-section 4.2.1, a proper contact between the probe face
and the stems was possible only if the stems were presented individually to the probe
face for the measurement of their e. From experience it was known that once the size of
the material is below the infinite sample size, the
e
of the material would always be
different from those measured for the material of infinite size. Therefore, it was first
necessary to investigate whether the
e
of the undersized sample were indeed different
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89
from those of the infinite sample size, and second if they were then it was necessary to
derive, if possible, an experimental correction coefficient, t which could be used for the
compensation for the 8 of the undersized sample to obtain the 8 of the material having
Alfalfa leaves, 23°C
50
me (u/o
A 10
40
***■
30
***x,
20
10
* 24
■xx***■
***xx::**xxxxx.
**xxxxxx* * * X X X X X X
A 41
- 54
AaAa&AAAAAA
* 75
0
0
5
10
15
20
Frequency (GHz)
(a)
Alfalfa leaves, 23°C
50
me (%
40
A 10
30
o 24
w
41
20
10
0
^XXXXXXXXXXXK^^SXXXXXXXXXXXXXXXXXXXXXXXXXXX
■- 54
aaD u u u u n n p u u u y n n n>,u Mn
* 75
Qp q P q a
UU U
u a o Q q q q q q q q OQ n a o O a a a
10
n
15
20
Frequency (GHz)
(b)
Fig. 4.22 The means of the (a) e' and (b) e" of the alfalfa leaves obtained by measuring
the 8 of a sample of alfalfa leaves from each of five moisture content rotating 45° at four
positions at varying frequencies.
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90
infinite sample size. Since the moisture content and the ionic conductivity of the fruit
tissues were similar to those of the fresh stems of the alfalfa, and the s of the infinite
sample of those tissues were available in the published literature [Nelson et. al., 1993]
for the frequency range o f 200 MHz to 20 GHz, and those tissues were relatively easy to
cut into cylindrical shapes with varying diameters to simulate stem-like structures, the
fresh fruit tissues from the red delicious apple, the cantaloupe, the carrot and the potato
were chosen. Seven hollow aluminum tubes with single sharp edge with the inner
diameters ranging from 1.67 to 6.52 mm as shown in Fig. B1 (Appendix B) were
fabricated to cut the fruit tissues with varying diameters. The inner diameters of the
tubes were so chosen that they would cover the range of the diameters of the fresh
alfalfa stems. To generalize the applicability of the ^ to a certain extent, a set of seven
cylinders made from a contrasting material - Teflon with the diameters equal to the
diameters of the fruit tissues were also included in the measurement.
The s of the cylindrical “tissues” with varying diameters and that of the sample
of infinite size (SIS) of all the five materials were measured, and it was observed that the
s' increased with diameter logarithmically, and the s" showed a little variation around
some mean values. These trends are shown in Figs. 4.23 to 4.28 at six representative
frequencies, that is 0.3, 0.48, 1.27, 3.22, 8 and 18 GHz, where symbol oo represents the
diameter of the SIS. The secondary Y-axis has been used for the clear presentation of the
relatively smaller values for Teflon. Each data point is the mean value of the four
repetitions, and their standard deviations are presented in Fig. B2 to B7 (Appendix B)
along with the means. The s for the cylindrical “tissues”, at this stage, by no means
could be verified, but those for the SIS, eSIS could be compared to the published data
[Nelson et. al., 1993], As shown in Fig. 4.29 the measured 8SiS compared well to the
reference data. The observed deviations of the measured sSiS from the reference values
were attributed to the various factors such as the differences in the moisture contents, the
maturity stages, the selection of the part of the whole fruit especially for the carrot - the
core or the outer layer, and the pressure. The excellent agreement between the observed
and the reference values for Teflon was already discussed in Section 3.5 (Fig. 3.14). The
moisture contents of the apple, the carrot, the cantaloupe and the potato used in this
research were respectively 85, 84, 89, and 77%, and those of the samples used in the
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
91
Operating frequency =0.3 GHz
80
* Apple
° Carrot
ACantaloupe
60
"w 40 ;
X
*
20
1
x Potato
x Teflon
0
0
4
oo
6
Diameter (mm)
(a)
Operating frequency =0.3 GHz
80
4
60 -j
3
2
W 40
1
20 j
$
i
I
0
I
0I
0
* Apple
° Carrot
a Cantaloupe
x Potato
x Teflon
-1
2
4
6
8
00
Diameter (mm)
(b)
Fig. 4.23
The (a) s' and (b) s" for the five materials as a function of diameters at 0.3
GHz and at 23°C.
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92
Operating frequency = 0.48 GHz
5
80
4
60
3
r\
2
-eo 40
20
1
0
° Apple
° Carrot
a Cantaloupe
x Potato
* Teflon
0
4
00
6
Diameter (mm)
(a)
Operating frequency = 0.48 GHz
80
4
60
3
2
« 40
a
¥
X
X
1
L A
20
0
o o
0 4
0
° Apple
0 Carrot
* Cantaloupe
»: Potato
* Teflon
-1
4
00
6
Diameter (mm)
(b)
Fig. 4.24 The (a) e' and (b) e" for the five materials as a function of diameters at 0.48
GHz and at 23°C.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
93
Operating frequency = 1.27 GHz
o
00
5
A
60
A
P
i
&
»
O
A
A
40
A
i
A
r ° ° °
* * * *
20
X
A
»
4
° Apple
A
O
O
^
*
*
^
1
QCarrot
^ Cantaloupe
x Potato
* Teflon
fe
X
0
0
0
2
4
6
8
Diameter (mm)
(a)
Operating frequency =1.27 GHz
80
-4
60
- 3
- 2
40 a
1
X
20
* 1 1 i i s i
§ A A A A O A
i
r
0
;
0
2
4
X
A
- —
6
1---8
■----------- i-------------------------
r 0
° Apple
n Carrot
a Cantaloupe
x Potato
* Teflon
-1
00
Diameter (mm)
(b)
Fig. 4.25
The (a) s' and (b) e" for the five materials as a function of diameters at 1.27
GHz and 23°C.
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94
Operating frequency = 3.22 GHz
80
60
5
j
4
3
w 40 !
- 2
20 i
- 1
0 -!0
4
2
4
6
° Apple
° Carrot
a Cantaloupe
x Potato
x Teflon
-o
oo
8
Diameter (mm)
(a)
Operating frequency = 3.22 GHz
80 i
4
60
3
I
i
2
~w 40
1
20
0
0
Apple
Carrot
Cantaloupe
Potato
Teflon
-
0
4
6
8
00
Diameter (mm)
(b)
Fig. 4.26
The (a) s' and (b) s" for the five materials as a function of diameters at and
3.22 GHz and at 23°C.
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95
Operating frequency = 8 GHz
80 |
5
-4
60 j
a
40 j
2 0
0
-j
A
0 5 1
A §
X
s>- ^ ^ A
A
Q Q O
O X
$I X * *
-J— ....... 1
1
2
4
A
A 9n;
O
^
X
3
?
X
O
X
*
2
i
.r
6
.........-
.
1
* Apple
° Carrot
a Cantaloupe
x Potato
x Teflon
0
oo
8
Diameter (mm)
(a)
Operating frequency =
8
GHz
4
80
3
60
2
*w 40
1
20
0
° Apple
° Carrot
a Cantaloupe
Potato
x Teflon
-1
0
2
4
oo
6
Diameter (mm)
(b)
Fig. 4.27 The (a) s' and (b) s" for the five materials as a function of diameters at
and at 23°C.
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8
GHz
96
Operating frequency = 18 GHz
5
80
4
60
3
~
w 40
X
*
20
*
|
2
X ?
If
| o
1
* Apple
DCarrot
* Cantaloupe
x Potato
* Teflon
0
0
4
6
8
oo
Diameter (mm)
(a)
Operating frequency = 18 GHz
4
80
3
60
2
"to
40
1
20
* <► *
A *
*
A
x
X
X
0
X
* Apple
° Carrot
a Cantaloupe
x Potato
* Teflon
0 0
2
4
6
8
00
Diameter (mm)
(b)
Fig. 4.28
The (a) s' and (b) s" for the five materials as a function of diameters at 18
GHz and at 23°C.
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97
Apple
80
60
— R ef s'sSIS
40
R ef s SIS
Obs e'.SIS
a
X Obs 8 SIS
20
0
0
5
10
15
20
25
Frequency (GHz)
(a)
Carrot
80
60
— R ef 8cSIS
40
. . . R e f s SIS
* Obs SoSIS
x Obs s SIS ?
20
0
0
5
10
15
Frequency (GHz)
20
25
(b)
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98
Cantaloupe
— R ef s'sis
n
. . . R e f s SIS
AObs s SIS
—
0
x Obs e's'is i
T
8
12
16
20
Frequency (GHz)
(c)
Potato
60
— R ef sisis
. . . R e f e sis
40
a Obs
20
X
0
4
8
12
16
s'osis
Obs 8sis
20
Frequency (GHz)
(d)
Fig. 4.29
The observed and the reference eSiS for (a) apple, (b) carrot, (c) cantaloupe,
and (d) potato at 23°C.
reference were 87, 87, 92, and 79% respectively. The other factors were not available in
the reference data.
At a particular frequency, the experimental correction coefficient in percent,
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99
(;(%) required to estimate the
of the material, m using the measured s' of the
cylindrical “tissue” of that material of diameter, d was calculated using Eq. (4.6).
o/„W£sis
5 (%)
£d x l0 0
(4.6)
Cons tan t frequency
and are shown plotted for the fiuit tissues in Figs. 4.30, where the solid lines are the
exponential fit to the mean values of the ^(%). The mean values and the standard
deviations for the <;(%) are shown in Fig. 4.31, and the equations and the r2 values for
the fitted lines are given in Table 4.6.
Table 4.6
The regression equations and the r2 values for the £(%) at different
frequencies.
Representative frequency (GHz)
Regression Eqs.
030
£(%) = 157.15e~°-507d
0.99
0.48
£(%) = 151.143e“0488d
0.99
1.27
£(%) = 134.88e“°'446d
0.97
3.22
£(%) = 172.44e-°'557d
0.99
8.00
£(%) = 115.08e”0424d
0.94
As seen from the Fig. 4.30 or Fig. 4.31 the variation (Stdev) in the £(%)
increased with the frequency, and became very significant at 18 GHz, which was
attributed to the reduced operating wavelength comparable to the sample size, and hence
to the occurrence of the scattering of the microwave energy. Therefore the ^(%) was
limited to an upper frequency of 8 GHz.
When ^(%) was plotted against the frequency with the diameter, d as the
parameter as depicted in Fig. 4.32 using the regression equations presented in Table 4.6,
it was found that they were nearly independent of the operating frequency. Therefore the
^(%) at five representative frequencies were averaged for each diameter, and as shown
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100
o
o
Operating frequency =0.3 GHz
0s
80
* Apple
.60
° Carrot
a
40 -
Cantaloupe
Potato
20
* Teflon
0 ^
+ Mean
1
2
3
4
5
— Expon. (Mean)
Diameter (mm)
(a)
Operating frequency = 0.48 GHz
100
80
♦ Apple
Co' 60
0s
uj* 40
° Carrot
A Cantaloupe
HL
Potato
20
* Teflon
+ Mean
0
2
3
4
— Expon. (Mean)
Diameter (mm)
(b)
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101
Operating frequency = 1.27 GHz
100
^
O'"
**
80 |
♦ Apple
60
a Carrot
40
A
A Cantaloupe
A
Potato
20 S
+ Teflon
* Mean
0
2
0
3
4
5
6
Expon. (Mean)
Diameter (mm)
(c)
Operating frequency = 3.22 GHz
100
C?
o's
up
80
<> Apple
60
° Carrot
a
4 0
Cantaloupe
A
Potato
20
* Teflon
0
+ Mean
0
1
2
3
4
— Expon (Mean)
Diameter (mm)
(d)
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102
Operating frequency = 8 GHz
100
80
° Apple
(S'
60
° Carrot
vu’
4 0
A Cantaloupe
Potato
20
* Teflon
+ Mean
0
2
3
4
5
— Expon. (Mean)
Diameter (mm)
(e)
Operating frequency = 18 GHz
250
200
o Apple
150
° Carrot
0 s-
^
100
O
±
|
='
?
^ Cantaloupe
1
Potato
*
50
* Teflon
0
+ Mean
1
2
3
4
5
6
— Expon. (Mean)
Diameter (mm)
(f)
Fig. 4.30
The mean values of the ^(%) for the “tissues” of varying diameters at a
frequency of (a) 0.3, (b) 0.48, (c) 1.27, (d) 3.22, (e) 8, and (f) 18 GHz.
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103
Y- error bar = 1 StDev
GHz
□ 0.3
250
2 0 0 -i
* *
□ 0.48
150
□ 1.27
100
B 3.22
B8
50
B 18
0
1.67
2.39
3.19
4.05
4.76
5.64
Diameter (mm)
Fig. 4.31
The means and the standard deviations of the ^(%) for the “tissues” of
varying diameters at different frequencies.
80
60
A
Dia (mm)
^2
A
*3
40
■4
*5
20 \
*6
X
*
0
0.1
1
10
Frequency (GHz)
Fig. 4.32 The ^(%) as a function of the frequency with the diameter as the parameter.
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104
in Fig. 4.33, an experimental correction curve was developed fitting a curve to those
mean values in estimating the ^(%) up to the operating frequency of 8 GHz.
80
y = 144.28e
60
0 s-
■0.4826x
R2 = 1
40
20
0 43
4
Diameter (mm)
Fig. 4.33
An experimental correction curve to calculate the £(%) for the material with
varying diameter up to the operating frequency of 8 GHz (Y-error bar = ± 1 StDev).
The applicability of the correction curve was then investigated calculating the
£sis by compensating the e' of the seven fruit tissues from each fruit type. Figures 4.34
to 4.38 show graphically the performance of the correction curve, and the statistical data
are presented in Table 4.7. Since the £'SIS of Teflon was fairly constant at 2.1, the
Table 4.7 The statistical data showing the performance of the correction curve.
Tissues of
RMSE
r2
Apple
0.74
0.99
Carrot
3.5
0.95
Cantaloupe
3.78
0.98
Potato
1.41
0.99
Teflon
0.10
-
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105
Apple
50
j
40
x Calculated
GO
-« 30
20
° Measured
10
0
4
6
8
10
Frequency (GHz)
(a)
Apple
60
« 50
T3
£
S 40
30
30
40
50
60
Calculated s'.
(b)
Fig. 4.34
(a) A comparison of and (b) the association between the calculated and the
measured e'sls for the apple tissues at 23°C.
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106
Carrot
8 0 -i
I
C a lcu la ted
60 i
i
M easu red
40 -
20
° "
0
T
4
6
*
10
Frequency (GHz)
(a)
Carrot
80
% 70
§
;
-
60
C/1
c3
£
50
nn
1
_
_
_
_
_
_
_
_—
‘i
40 4 ----------40
60
80
70
50
C a lcu la ted
s'sis
(b)
.35
(a) A comparison o f and (b) the association between the calculated and the
F ig-4
o
.c. fo r the carrot tissues at 23°C.
m e a s u r e d s sis
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107
Cantaloupe
80
60
x Calculated
40
° Measured
20
0
rL
0
2
4
6
10
8
Frequency (GHz)
(a)
Cantaloupe
80
w
7 0
Iva
S 60
1
50
50
60
70
80
Calculated s'SiS
(b)
Fig. 4.36
(a)
A comparison of and (b) the association between the calculated and the
measured e'sis for the cantaloupe tissues at 23°C.
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108
Potato
80
x Calculated
° Measured
20 i
I
0 I
0
2
4
6
8
10
Frequency (GFlz)
(a)
Potato
80
.a 70
CO
*73
§ 60
C
O
C
03)
2 50
40
40
50
60
70
80
Calculated s'Sis
(b)
Fig. 4.37
(a)
A comparison of and (b) the association between the calculated and the
measured £gls for the potato tissues at 23°C.
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109
Teflon
3.0
2.5
« Calculated
00
-«
2.0
° Measured
1.5
1.0
0
2
4
6
8
10
Frequency (GHz)
Fig. 4.38
A comparison of the calculated and the measured e'SIS for Teflon at 23°C.
association between the calculated and the measured SgIS is expressed in terms of the
means and the standard deviations, which are respectively 2.26 and 0.027 for the
calculated values, and 2.17 and 0.012 for the measured values. A total of 88 frequencies
(data points) ranging over 300 MHz to 8 GHz were used, and the calculated e'SISis the
mean of the s'SIS of the seven cylindrical fruit tissues. The performance of the correction
curve was thus found to be reasonably good. Since the curve was developed using the
materials having contrasting physiochemical properties, it was reasonable to expect the
applicability of the curve to a wide range of other materials as well.
Since the stems lost their cylindrical shapes at lower moisture contents, the
lowest moisture content of 42% was considered for them so that the correction curve
could still be used. Therefore, ten stems with diameters ranging from 1.28 to 3.97 mm at
each moisture content of 42, 51, 62, 71 and 79% were measured for the e. The observed
mean values and the standard deviations for the stems are presented in Table B7
(Appendix B). The logarithmic increase of the s', and the fluctuation of the e" around
some mean value as those observed with the materials used to develop the correction
curve were thus found true with the s of the stems as well. These trends for the stems at
a moisture content of 79% and at 23°C are shown in Fig. 4.39, and those for the rest of
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110
the moisture contents are presented in Figs. B8 to B11 (Appendix B). The s' for the ten
stems from each of the moisture contents were corrected through the correction curve,
and averaged, which are depicted in Fig; 4.40 (a). The mean of the measured s" are
shown plotted in Fig. 4.40 (b). Only 33 frequencies are shown in both Figures for clarity.
Alfalfa stems (79% mc,23°C)
GHz
♦ 0.3
50
40
o
30 -
a a
20
X *
A- A
A,
❖
A
■ (3 •
a
-
X
X
*
n
0.48
a
1.27
x
*
3.22
8
Log. (0.3)
10
Log. (0.48)
0
1
1.5
2
2.5
3
Log. (1.27)
3.5
Log. (3.22)
Diameters (mm)
L°g- (8)
(a)
Alfalfa stems (79% mc,23°C)
50 n
40
GHz
A
A
O
A AQ
O
O 0X °
o
30
cq
1
20
a
*
? '
1*
A
O
O
S ft *
X
X
a
1.27
■■■
x 8
—
r' -'
1
° 0.48
>- 3.22
10 0
a 0.3
1.5
'
T" -----------2
2.5
3.5
Diameter (mm)
(b)
Fig. 4.39 The (a) s' and (b) the e" of the stems at a moisture content of 79% and at
23°C.
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I ll
The complete spectra of the mean s with the standard deviations at each frequency are
presented in Figs. B12 to B16 (Appendix B).
The e of the stems thus obtained using the correction curve at the moisture
contents of 42, 51, 62 and 71% were compared with those of the leaves at the moisture
Alfalfa stems,23°C)
50
me (Vo
40
A 5* ,
30
%
20
10
|
j
* 79
**x
‘ Ai i i i i i AAAAAi ^^- XX **X *
* 71
X X X
° ° " o anoao0aDaDDooD
00 06»” 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0
A A
a
£
° ao oo
a
a
a 62
■ 51
o o
* 42
0
0
4
6
10
Frequency (GHz)
(a)
Alfalfa steins, (23°C)
50
me yVo
40
* 79
30
20
1 0
* 71
* x x x x x x x x x * * * * * * * * * * * * * *
A
\
“I C^ h n ^ ^ ^ A A A A A A A A A A A A A A A A A A A A A A
“ f l OQ
50 . - Q P D o o a a D a a a a o a o a o a n o Q c a a
V° O O O O O O O O O O O O O O O Q O O O O O O O O O O
4
6
62
» 51
a
a
* 42
o
10
Frequency (GHz)
(b)
Fig. 4.40 The mean values of (a) the corrected e' and (b) the s" for the alfalfa stems at
23°C.
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112
contents of 45, 52, 66 and 73%, which did not require any compensation. For this
purpose, Fig. 4.6 is re-plotted as shown in Fig. 4.41 with the appropriate modifications.
The trends of the s' for the stems were found to be similar to those for the leaves as they
gradually decreased with increasing frequency. The magnitudes of the s', however,
exhibited a mixed result. The magnitudes of the s' for the stems at the moisture contents
of 62 and 71% were nearly identical to those of the leaves at the moisture contents of 66
and 73%. The differences in the magnitudes of s' between the stems (at 42%, and 51%)
and leaves (at 45%, and 52%) were larger at the lower frequencies, and were gradually
decreased with increasing frequency. The difference between the s' of stem and leaves at
42% and 45% moisture content respectively, was two at 8 GHz, and it was five for the
stems at 51% moisture content and the leaves at 52% moisture content. On the other
hand, the s" of the stems were found to be very close to those of the leaves in both the
magnitudes and the trends. Since the observed differences could be attributed to the
differences in the moisture contents of the plant parts, the temperature, and the plant
parts themselves, the dielectric properties of the leaves and the stem could be considered
very close to each other. This also suggested that until the dielectric properties of these
plant parts are proved to be significantly different from each other, the applicability of
the experimental correction curve developed in this research shall be of a valuable tool
in the field of the dielectric measurement.
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113
Alfalfa leaves, 20°C
50
40
me (%)
<> 73
'«<*>»<><>*
° 0 Oo
30
o O o o
°
20
++ ++++++ +
10
66
+ 52
+ + + ++
+++++
45
0
4
6
10
Frequency (GHz)
(a)
Alfalfa leaves, 20°C
30
20
|
I
me r/o
« 73
♦
O
° o
°
10
o
+ 52
° 0 ‘> o 0 o o o o o O o o O O O
+++ +++++ +++++++++
4
66
45
6
10
Frequency (GHz)
(b)
Fig. 4.41
The frequency dependence of the (a) s' and (b) the s" of the alfalfa leaves at
20°C with moisture content as the parameter.
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5. MODELING
5.1 Introduction
In general, a plant is a very complicated structure, and many substances are
found to occur in the plant tissues. For example, crude protein, cellulose, hemicelluloses,
pectin, non-structural carbohydrates, lignin, organic acids, lipids, vitamin A and
carotene, and oestrogenic compounds are present in alfalfa plant tissues [Frame et al.,
1998]. The scope of the influence on the dielectric properties of these substances of the
plant material is determined by their own properties, their relative quantities, and the
extent of their mutual interactions with external electromagnetic fields at the molecular
level. In many cases it is impossible to calculate, theoretically, the dielectric properties
of plant tissues with the accuracy required by practice, and it is necessary to rely on
experimentation and measurement. Therefore, a dielectric measurement system was set
up, and used to obtain data on the dielectric properties of the alfalfa plant in this
research. Flowever, the measurement of the dielectric properties is very time consuming,
labourious, and demands extreme care. Computer modeling of the dielectric properties
o f the alfalfa plant making use of the data obtained from the experiments, and assuming
the plant tissues consist of air, free and bound water, and dry vegetation would be a
useful compromise. In such an approach, the factors discussed above such as the
dielectric properties of the constituents, their relative quantities, and their mutual
interactions with the external electromagnetic fields on the molecular level are still
present to some extent. Hence, the methodologies in calculating the dielectric properties
and the volume fractions of the constituents of the plant tissues along with the derivation
of some constant quantities such as the dry (free) vegetation densities, and the
114
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115
conversion of the gravimetric to volumetric moisture content, which were also necessary
for the modeling of the dielectric properties of the vegetation shall be the topics for the
first few sections of this chapter.
5.2 Dry (free) vegetation density
Vegetation is considered as ‘dry’ after subjecting it in a standard hot air oven for
24 h at 103°C [ASAE, 2000]. The densities of the dry vegetation with and without the air
trapped in them were respectively denoted as pa and pn, and were defined as follows.
Dry vegetation weight
Volume o f air + Volume of vegetation
Dry vegetation weight
Total volum e-V olum e of water
\
/
(5.1)
_ Dry vegetation weight ^
Dry vegetation weight
x
Volume o f vegetation
Total volume-Volume of w ater-V olum e of air
/
(5.2)
Two methods, namely nitrogen pycnometer and the vacuum infiltration method, based
upon Archimedes’ principle, were employed to measure the volumes of the dry
vegetation, and appropriate volumes were chosen in order to calculate pa and pn.
5.2.1 Nitrogen pycnometer method
A Multipycnometer from Quantachrome Instruments shown in Fig. Cl
(Appendix C) was used to measure the volumes of the dry leaves and the stems of the
alfalfa in both their whole and powder forms resulting in four categories. The stems
were cut into lengths of about 30 mm. The volume measurements as shown in Fig. 5.1,
were continued until the two successive readings were obtained to within 0.36%
[Pycnometer User’s guide] to assure the minimum movement of the contaminants, if
any, filling or freeing the pores during the pressurization and depressurization processes,
and thus to minimize the error in the volume measurement. Three samples from each
category were taken in order to calculate the means and the standard deviations of the
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116
densities, which are presented in Table 5.1. The densities of leaves and stems in each
case were very close to each other, and differences could be attributed to measurement
error and sample handling.
Nitrogen pycnometer method
5.0
O O O
4.5
° Dry whole leaves
£
a 4.0
O
> 3.5
° Dry leaf powder
□
a
a
□
3.0 -f
2
4
6
8
10
Number of observations
Fig. 5.1 The trends for the volumes of the dry plant parts measured using the Nitrogen
pycnometer.
Table 5.1 Densities of dry plant parts measured using the nitrogen pycnometer
(kg m '3).
Plant parts
Parameters
With air
Without air (powder form)
Dry leaves
Mean
1189
1641
StDev
190
146
Mean
1048
1550
StDev
130
114
Dry stems
5.2.2 Vacuum infiltration method
The volumes of the dry plant parts were determined using the vacuum infiltration
method, which was similar to the method described by [Raskin, 1983]. The whole plant
part was weighed in order in air, in “distilled water”, and again in distilled water after
vacuum infiltration at a pressure of 69 kPa. The volume of the plant parts with air
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117
trapped in it, Vpap was given by Eq. (5.3), and Eq. (5.4) gave the volume of the air in the
plant part, Va to be subtracted from Vpp in order to calculate the volume of the plant part
without air in it, Vpp, Eq. (5.5).
\Yair _ w water
ya = ^ P
EE
(5.3)
pp
y
_
i t j water_______ __ttt- w a te r
inf iltrated pp_______ PP
Vn = V a -V
PP
PP
a
^
^
(5.5)
v
J
The pw and W , respectively stand for the density of the water, and the weight of ‘y’
measured in ‘x ’. The volume of air in the plant part was assumed to be equal to the
volume of the “distilled water” infiltrated into the air spaces in the plant part during the
vacuum infiltration process. The possible swelling of the tissues had no effect in the end
result as the plant parts were always weighed in the water. A 0.05% solution of the
surfactant, Titron X-100 with the distilled water was used to get rid of the air bubbles,
which otherwise would cause a large error in the volume measurements, from the
surface of the plant part. Since the solution was very dilute, and the density of the
surfactant was 1070 kg m'3, the error introduced in assuming the density of the solution
equal to that of the distilled water was negligible. Any loss of the ionic solutes from the
plant part into the solution, which could be detected by measuring the electrical
conductivity of the solution before and after the immersion of the plant part, was not
considered because almost no change in the colour of the solution was noticed. Thus the
accuracy was only limited by the precision of the balance, an Ohaus® Galaxy 160D, with
the precision resolution of 0.1 mg. Fifteen samples each consisting of 20 dry leaves or
stems were used to calculate the densities given in Table 5.2. The variation of the
densities for the dry leaves (or stems) without air was about three times larger than that
for the dry leaves (or stems) with air, which was attributed to the observation that the
infiltration was not consistent and the material had to be weighed in water twice in the
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118
former case comparing to only once in the latter, and consequently a relatively larger
loss of the minute particles from the dry (brittle) material occurred during the
measurement processes. The density variation for the dry stems with or without air was
only about one-third of that for the dry leaves, and which was reasonable because only a
relatively small loss of mass was expected for the stems as they were not as brittle as the
thin dry leaves were.
Table 5.2 Densities of dry leaves and stems measured using the vacuum infiltration
method (kg m 3)
Plant parts
Parameters
With air
Dry leaves
Mean
680
1050
StDev
100
300
Mean
470
800
StDev
30
80
Dry stems
Without air (infiltrated)
5.2.3 Selection of the optimum densities
In the nitrogen pycnometer method, nitrogen gas can penetrate the finest pores
and the crevices approaching 0.1 n m i n a test material [Pycnometer User’s guide] but
there was yet no guarantee that it would penetrate all the pores and the crevices in the
dry plant parts. Hence the measured volumes were regarded as the volumes of the plant
part still with air trapped in them. The plant parts were considered free from such pores
and the crevices, if any, only after grinding them in a precision grinder into powder
forms. The densities of the plant parts calculated by measuring their volumes in the
powder forms were taken as the densities without air. As expected, the densities
increased by about 38% and 48% respectively for leaves and stems comparing to those
calculated using the volumes of the whole plant part (Table 5.1). This also suggested
that the plant parts did have pores and crevices which nitrogen could not penetrate. This
phenomenon was even more justifiable for the relatively bigger water molecules in the
vacuum infiltration method, and hence the values obtained for the densities of the tissues
(without air) in the vacuum infiltration method were not preferable to those obtained in
the nitrogen pycnometer method. Hence, these values presented in Table 5.2 under the
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119
‘without air’ heading were found to be much less than those presented in Table 5.1.
Following the same reasons, however, the use of the water as a displacement fluid was
preferable to nitrogen in measuring the volumes of the plant parts with air trapped in
them. As expected, the values for the densities obtained for the plant parts with air
(Table 5.2) were found to be about 43% and 55% less than those presented in Table 5.1
for leaves and stems respectively. In summary, the values for the densities without air
were chosen from the nitrogen pycnometer method and those with air were from the
vacuum infiltration method as the optimum densities to be used for modeling purposes.
These values are re-tabulated in Tables 5.3.
Table 5.3 The optimum densities of the dry leaves and the stems chosen for the
modeling (kg m '3).
Plant parts
With air (pa)
Without air (pn)
Dry leaves
680
1641
0.4144
Dry stems
470
1550
0.3032
Pa/n
Pa/Pn
5.3 The gravimetric and the volumetric moisture contents
The gravimetric moisture content, Mg and the volumetric moisture content, Mv
are defined as follows.
Weight of water
M = ----------- —------------------Weight of moist material
(5.6)
_ Weight of moist m aterial-W eight of dry material
Weight of moist material
Volume of water
M v = ---------------------------------Volume of moist material
(5.7)
The moisture content of a material unless otherwise mentioned is understood as the
gravimetric moisture content, and is determined following ASAE standards. The
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120
volumetric moisture content Mv, however, is widely used in modeling, and the
expression for calculating the Mv depends upon whether the material shrinks or not as it
dries. In the case o f shrinking, it can be assumed that the shrinkage in the volume of the
tissue is equal to the volume of the water lost, and in the case of not shrinking, a volume
of air equal to that of the water lost can be assumed to penetrate in the tissues resulting
in a constant volume. Hence, for materials that shrink, Eq. (5.8) is used, and Eq. (5.9) for
the materials that do not shrink. The derivations of the equations are respectively
presented in C.l and C.2 (Appendix C).
(5.8)
P;
(5.9)
5.4 The volume fractions of the plant constituents
As discussed earlier, air, vegetation, and water were considered to be the major
constituents of the plant tissues. The number of the constituents, and their states of being
free or bound with other constituents depended upon the moisture content of the tissues.
For the bound form of water and vegetation, a common name - bound water-vegetation
had been chosen, and the volume fraction of the bound water, Vbw and that of the bound
vegetation, Vbv in the bound water-vegetation were assumed to be given by the relation
given in Eq. (5.10) [Ulaby and El-Rayes, 1987].
^
= b = 0.5
Vk„
(5.10)
For the shrinking model, the total volume fraction of the vegetation, vtv is equal
to either the sum of the volume fractions of the bound vegetation, Vbv and the free
vegetation, Vfv, or the bound vegetation volume fraction, Vbv only depending upon
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121
whether the current moisture content, Mg is below or above the fibre saturation point (or
the threshold moisture content, Mtg) as expressed in Eq. (5.11).
(5.11)
The total volume fraction of the vegetation for the not shrinking model equals
Pa/n- The derivations of the total volume fractions for both shrinking and not shrinking
models are respectively presented in C.3 and C.4 (Appendix C) and the calculations of
the Mtg are presented in C.5. As expected the threshold moisture content was almost
independent o f the models, and found to be 0.2335 and 0.2438 respectively for the
leaves and the stems.
The threshold moisture content, Mtg referred to that amount of water which was
just sufficient to put all the vegetation in the plant tissues in the bound form without
freeing any o f them. Free vegetation gradually appears as the moisture content drops
below Mtg, and hence both free and bound vegetation exist in the plant tissues until the
moisture content drops to zero when there will be free vegetation only. Similarly, both
the free and the bound water (bound with vegetation) exists above Mtg because only a
portion of the water changes into bound water forming the bound water-vegetation while
leaving the rest in the free form. And below Mtg, the water exists in the bound form only
as all the water is bound with the vegetation forming bound water-vegetation.
The following expressions were developed to calculate volume fractions of
constituents o f leaves and stems based upon the shrinking model using Eq. (5.10) and
(5.11), and are graphically shown in Fig. 5.2.
For Mg < Mtg:
Volume fraction of the bound water-vegetation
= vwv = Vbw + Vbv = Mv + 2 Vbw = Mv + 2MV= 3MV
Volume fraction of the free vegetation = Vfv = vtv - Vbv = vtv - 2vbw= vtv - 2MV
Volume fraction of the air
= V a = 1 - Vwv - V fv
Volume fraction of the free water
= V sw = 0 .
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122
Leaf - shrinking model
1 .0
g
0.8
_o
tj
& 0.6
■Mv
bw
bv
£ 0.4
o
0.2
fv
tv
0.0
■fw
0
0.2
0.4
0.6
0.8
1
■a
Gravemetric moisture content (Mg)
(a)
Stem - shrinking model
1.0
oG 0.8
*+
0a3
0.6
<u
1 0.4
o
0.2
Mv
bw
bv
fr
\
tv
0.0
■bv
0
0.2
0.4
0.6
0.8
1
■a
Gravemetric moisture content (Mg)
(b)
Fig. 5.2 The volume fractions of the constituents of (a) leaves and (b) stems based upon
the shrinking model where Mv = volumetric moisture content, bw = bound water, bv =
bound vegetation, fv = free vegetation, tv = total vegetation, fw = free water, and a = air.
For M„ > M,tgVolume fraction of the bound water-vegetation
= V wv = Vbw + Vbv
Volume fraction of the free saline water
=1/2
Vbv + Vbv
= vsw= Mv - Vbw = Mv - 1/2 Vbv
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= 3/2 Vbv
123
Volume fraction of the air
= va = 1- vwv - vsw
Volume fraction of the free vegetation
= vvf = 0.
5.5 Dielectric properties of the plant constituents
Since free water, bound water-vegetation, free (dry) vegetation and air were
considered to be the main constituents of plant tissues, determination o f their dielectric
properties to be used in dielectric modeling shall be dealt in the following sub-sections.
5.5.1 Free water
The free water in the plant tissues was found to be contained with some salinity.
Therefore it is interchangeably used with another name - the free saline water, and its e
were calculated using the following expression [Stogryn, 1971] [Klein and Swift, 1977]
[Ulaby et al., 1981.
e . . = e „ - + e”
er
1+ j —
- f r £ iT
2 m °{
<5' 12>
where the parameters £sws, eSw°o, fSWr, and c»j are respectively the static permittivity, the
optical permittivity, the relaxation frequency and the ionic conductivity in Siemens/m,
and e0 is the free space dielectric constant (e0 = 8.85 x 10'12 F/m). Except the optical
permittivity, £sw~ (= 4.9) all the parameters are temperature (T) and salinity (S)
dependent, and were calculated using the following relations [Stogryn, 1971] [Klein and
Swift, 1977],
For 4 ppt < S < 35 ppt, and 0°C < T < 40°C
e„,(T ,S) = 8„.(T,0)a(T,S)
(5.13)
£gws (T,0) = 87.134- 1.949 x 10"'T -1 .2 7 6 x 10"2T 2 + 2.491 x lO ^ T 3
a(T,S) = 1+ 1.163x 10“5T S - 3.656 x KT3S + 3.210x l(T 5S2 -4 .2 3 2 x 10"7S3
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124
For 0 ppt < S <
157
ppt, and
0°C < T < 40°C
f „ „ (T ,s ) = k r S
(5 -1 4 )
f sw
o(T) = ( l.1109 x 1O"1
0 - 3.824 x 10"1
2T + 6.938 x 10"1
4T 2 - 5.096 x 10“ 1
6T 3)“ '
b(T,S) = l + 2.282xl0“5T S -7 .6 3 8 x l0 “4S - 7 .7 5 0 x l0 “6S2 + 1.105xl0"8S3
For 0 ppt < S < 40 ppt, and
0°C < T < 40°C
° i (T, S) = o j (25, S)e“ c
(5.15)
Oj (25, S) = s(0.18252 -1.4619 x 1O’ 3S+ 2.093 x 10~5S2 -1.282 x 10~7S3)
,
J2.03 3 x 10-2 +1.266 x 10"4(25 - T) + 2.464 x 10~6(25 - T )2
c — (25 — TK
r
[ - S[1.849xl0~5 - 2.551xl0”7( 2 5 - T) + 2.551 x lO "8( 2 5 - T f
The salinity of the fluid extracted from the plant tissues was considered as the
salinity of their free water content, and it was estimated comparing the e" of the
extracted fluid with that of the sodium chloride (NaCl) solution of known salinity in part
per thousand (ppt). Since e" was dominated by the ionic losses at frequencies below 5
GFIz, the operating frequency was chosen at 1 GHz for convenience. A hydraulic
pressure, Carver Laboratory Press, was used to extract the fluids. The measured e" of the
NaCl solution at varioussalinities is shown in Fig. C2 (Appendix C).The fluidsalinities
and the moisture contents at which the fluids were extracted areshown plotted in Figs.
5.3 along with the regression line having the form,
S = -28.7 Mg + 34.83 (ppt)
(5.16)
S = -78.11 Mg + 71.34 (ppt)
(5.17)
and
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125
f = 1 GHz, T = 22°C
30
a,
3
20
.B
3tZ)
373 10
0 i
0.4
0.5
0.6
0.7
0.8
0.9
0.8
0.9
Leaf moisture content (% w.b.)
(a)
f = l GHz,T = 22°C
40
3
3
3
30 )
3
3
10
M20
0 -L
0.4
0.5
0.6
0.7
Stem moisture content (% w.b.)
(b)
Fig. 5.3 The salinity of the fluid (free saline water) contained in (a) the leaves and (b)
the stems at various moisture contents.
respectively for the leaves and the stems, which were subsequently used to estimate the
free saline water contained in the plant tissues at any moisture content. The extraction of
the fluids was extremely difficult at lower moisture contents, and was therefore limited
to the moisture content of 50%.
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126
5.5.2 Bound water-vegetation
Another constituent of the plant tissue considered for modeling was the bound
water-vegetation. Unfortunately, the e of this constituent was unknown. Nevertheless the
s of the bound water at 22°C was calculated using the Cole-Cole equation [Ulaby and ElRayes, 1987]
"bw s
e bw - £ bwo. + '
/
1+
(5.18)
f \ 1_A<
f
v
bwr J
with the parameters £bw°° = 2.9, £bWs = 57.9, fbwr = 0.18 GHz, and At = 0.5, and the
operating frequency, f in GHz. The bound water considered in the formulation of Eq.
(5.18) was obtained by combining free distilled water and sucrose in known proportions
so that all the water molecules were bound with the molecules of the sucrose. Because
the sucrose is part of the cellulose, the major constiturent of the plant tissues including
the alfalfa [Frame et al., 1998], Eq. (5.18) was therefore adopted to calculate the
e
of the
bound water-vegetation in this study as well.
5.5.3 Dry vegetation and air
The
e
of relatively dry vegetation were extremely difficult to measure accurately
because of the non-uniform contact between the sample and the probe. Thus,
measurement of e for the leaves was limited to the moisture content of 12%. Since the s
of paper could be measured conveniently, and main constituent of paper is plant material
such as cellulose and lignin, and moisture content varies from 3% to 9%, the s for white
bond paper were therefore measured, and compared with those of vegetation at moisture
content of 12%. The means and the standard deviations of s’ and e" calculated by using
201 data points ranging over 300 MHz to 18 GHz are presented in Table 5.4.
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127
Table 5.4. The means and the standard deviation of the e for the leaves at the moisture
content of 12% and white bond paper.
Parameters
Leaves (12% me)
Paper (3% to 9% me)
£’
8”
8’
8”
Means
2.12
0.49
2.12
0.22
StDev
0.32
0.07
0.13
0.06
The mean of s' for both materials were equal, and the s" of the leaves was higher
than that of the paper, which was attributed to the fact that the leaves contained some
residual moisture. Therefore, the s" of dry vegetation was taken equal to that of the paper
as the best approximation resulting in the s of dry vegetation, £fv = 2.12 - j 0.22.
5.6 Modeling the 8 for the alfalfa leaves
Having the volume fractions and the dielectric properties of the constituents of
the plant tissues, empirical, semi-empirical and theoretical models were investigated
through nonlinear regression method, nonlinear least-squares fitting. The regression
analyses were programmed and executed in Matlab®5.1 running in a Windows-95
operating system. The s of the alfalfa leaves at nine moisture contents and at 22°C were
measured. Each measurement consisted of 201 frequency (data) points ranging over 300
MHz to 18 GHz resulting in 1809 data points in total (N). Although all of the data points
were taken into account for the statistical analysis, such as the root mean square error
(RMSE) and the coefficient of determination (r2), only 33 data points have been used in
the plots showing the measured and the calculated values of the s in order to avoid the
plots from being crowded. The slope and the intercept of the linear regression line
relating the calculated and the measured values of the £ in the x (measured)-y
(calculated) scatter plot are respectively denoted by ‘c’ and ‘d’ as expressed in Eq.
(5.19).
y^cx + d
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(5.19)
128
5.6.1 Polynomial (Poly)
The independent parameters in this model were the frequency, f and the moisture
content, Mg. At first, the equations of the response surfaces expressed in Eqs. (5.20) and
(5.21) were obtained using the built-in full quadratic response surface model (FRSM) in
MatLab®. These equations consisted of the linear, interaction, and quadratic terms, but
they failed to fit the measured data very well.
£ '= a 0 + a ,M g + a 2f + a 12M gf + an M g + a 22f
(5.20)
e"= b 0 + b,M + b 2f + b 12M f + b uM 2 + b 22f 2
(5.21)
Therefore they were modified manually, and the modified polynomials expressed in Eqs.
(5.22) and (5.23), which were obtained after many trials, fit the data exceptionally well.
Thus, use of 1/f term(s) and removable of f2 term proved to be a better choice. The
coefficients of the models, and the statistical data or the model accuracy are respectively
given in Table 5.5, and 5.6.
£—
c o + c r
l
Mg+
V
(5.22)
Mg + (c4 + c 5f)M 3g
C 2 + C3 r-
/
£"=(d0 + d!f)M g+ (d2 + d 3f)Mg + d4 + d 5
(5.23)
M
Table 5.5 The values for the coefficients of the polynomials that fitted the measured £'
and the s" of the alfalfa leaves.
c0=30.64
ci = 2.82
c2 = - 103.06
c3 = 0.97
c4= 176.91
c5 = -2.61
d0= 1.04
di = 0.03
d2 = -•14.97
d3 = 0.23
d4 = 48.07
d5 = 12.56
Table 5.6
The model accuracy of the polynomial fit for the e' and the e" of the alfalfa
leaves.
£
RMSE
r2
c
d
N
£'
0.89
0.99
0.98
0.18
1809
£"
0.52
0.99
0.99
0.06
1809
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129
The performance of the models are also graphically shown in Figs. 5.4 to 5.6 for the
leaves at the extreme moisture contents (73% and 12%) and at one in between (45%),
and those for the rest of the moisture contents are presented in Figs. C3 to C8 (Appendix
C). Fig. 5.7 shows the association between the measured and the calculated s, and Fig.
C9 (Appendix C) presents a detailed view of dielectric constants to show a general idea
of how 201 data points at each of nine moisture contents are distributed depending upon
frequency.
5.6.2 Power law (PL) model
In this semi empirical model, which is also known as the Birchak model, a
certain power of the dielectric values of the constituents of the leaves was weighted by
their corresponding volumes to produce the dielectric values of the leaves raised to the
same power. The general form of the model is given in Eq. (5.24) [Sihvola, 1999]
[Birchak et al., 1974], where v,- and Si are respectively the volume fractions and the £ of
the ith constituent of the material of interest, and n is the total number of the constituents.
The value for the parameter ‘k ’ must be determined so that the model fits the measured
data well. The specific expression of the model used to calculate the s for alfalfa leaves
is given in Eq. (5.25) in which subscripts a, wv, sw, and fV respectively represent air,
bound-water vegetation, free saline water, and free vegetation. The £ and the volume
fractions of the constituents were calculated as discussed earlier.
li
Iv ,
v i=1
■= ( v a £ a
(5.24)
j
+ v wveL + v sw£gW+ v fre£ )k
(5.25)
The values for ‘k’ in fitting the measured e' and the e" were respectively found to
be 0.266 and 0.232. The accuracy of the model for the alfalfa leaves at the moisture
content of 73%, 45%, and 12% are graphically presented in Figs. 5.4 to 5.6, and those
for the rest o f the moisture contents are presented in Figs. C3 to C8 (Appendix C). The
statistical data are tabulated in Table 5.7, and the dependency between the measured and
the calculated £ using the model are shown in Fig. 5.8.
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130
Alfelfa leaf (73% me, 22°C)
Measured
Models:
° Poly
-w 30
a
PL
x Dc
*
X
o BLD
* BLN
5
0
10
15
20
+ BLS
BUD
Frequency (GHz)
(a)
Alfalfa leaf (73% me, 22°C)
60 n
50 *
CO
Measured
Models:
40 X
□ Poly
30
ft PL
20
x Dc
\
Ix Ix |x lx x§ xo x
10
x x
o BLD
0
* BLN
0
5
10
15
Frequency (GHz)
20
+ BLS
■ BUD
(b)
Fig. 5.4 Comparison of the measured and the calculated (a) s' and (b) the s" of alfalfa
leaves at a moisture content of 73% and at 22°C.
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131
Alfalla leaf (45% me, 22°C)
20
Measured
Models:
16
d
12
Poly
* PL
x Dc
8
o BLD
4
* BLN
0
5
10
15
20
+ BLS
* BUD
Frequency (GHz)
(a)
Alfalfa leaf (45% me, 22°C)
15
Measured
Models:
10
Poly
W
PL
5
Dc
BLD
0 1
0
BLN
5
10
15
Frequency (GHz)
20
BLS
BUD
(b)
Fig. 5.5
Comparison of the measured and the calculated (a) s' and (b) the s" of the
alfalfa leaves at a moisture content of 45% and at 22°C.
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132
Alfalfa leaf (12% me,22°C)
13
■+— Measured
Models:
10
° Poly
A PL
7
x Dc
4
o BLD
..._r_.
1
0
10
5
15
Frequency (GHz)
* BLN
20
+ BLS
- BUD
(a)
Alfalfa leaf (12% mc,22°C)
5-
Measured
4
Models:
n Poly
3
& PL
2
x Dc
1
0
<> BLD
A
* BLN
1
+ BLS
Frequency (GHz)
■ BUD
(b)
Fig. 5.6
Comparison of the measured and the calculated (a) e' and (b) the s" of the
alfalfa leaves at a moisture content of 12% and at 22°C.
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133
Alfalia leaves (Model: Poly)
CO
I
40
30
o3 20
O
10
o -!
10
T_-
T"
20
30
40
50
Measured s'
(a)
Alfalia leaves (Model: Poly)
35
=CO 28
& 21
M 14
cd
°
7
10
15
20
25
30
35
Measured e"
(b)
Fig. 5.7 The association between the measured and the calculated (a) s' and (b) the s" of
alfalfa leaves using polynomials.
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134
Table 5.7 The statistical data showing the performance of the Power law (PL) model in
modeling the s of the alfalfa leaves.
s
RMSE
s'
1.78
s"
1.73
c
d
N
0.96
0.94
0.59
1809
0.87
0.95
0.23
1809
5.6.3 Modified Debye - Cole-Cole (DC) model
As mentioned before, the major constituent of the vegetation tissues was the
water both in the free and the bound forms, and hence it was reasonable to assume that
their dielectric properties were dictated by the dielectric properties and the volume
fractions o f these constituents. Also the water contained in the tissues gradually
decreases with decreasing vegetation moisture content, and the dielectric properties of
the vegetation therefore compare well with those of the dry vegetation. Besides, it was
assumed that the water was spatially continuous within the vegetation matrix without
any definite shape, and the dielectric properties of the free and the bound water were
obtained using the modified Debye equation, Eq. (5.12) and Cole-Cole model, Eq. (5.18)
respectively. A semi-empirical model was then developed assuming that the dielectric
properties o f the vegetation tissues were the algebraic sum of those of the water in both
the free and the bound forms, and that of the free vegetation weighted by their respective
volumes as expressed in Eq. (5.26).
O
.
P
SWS
— p
£ = 8 iVV fV +
i+ j
SWOO
~
. f
•
rr
J-
27te f
+
8 bws
e bw ~ + •
f
8 bw°°
^
(5.26)
\ ' - At
1+
/
J
where all the parameters bear the same meaning and the same values as discussed
elsewhere. The ionic conductivity, o, was expressed in terms of the volume fraction of
the free saline water, vsw as shown in Eq. (5.27) because it changes with the moisture
content of the tissues, or the volume fraction of the free saline water.
< b = P + Qvsw
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(5.27)
135
where P and Q were constants to be estimated during the regression, and it is noted that
these parameters had effect only on the s" of the vegetation. The parameters, b, pa, and
pn, were optimized for the model against the measured e of the alfalfa leaves. The
Alfalfa leavess (Model: PL)
50
40
T3
8
=S
o
3
U
0
10
20
30
50
40
Measured s'
(a)
Alfalfa leaves (Model: PL)
60
50
w 40
OJ
43 ^
3
3 20
U 10
T3
0
10
15
20
25
30
35
Measured e"
(b)
Fig. 5.8
The measured and the calculated (a) s' and (b) the e" for the alfalfa leaves at
22°C using the power law (PL) or Birchak model.
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136
optimized parameters are presented in Table 5.8. The accuracy of the model for alfalfa
leaves at the moisture content of 73%, 45%, and 12% are graphically presented in Figs.
5.4 to 5.6, and those for the rest of the moisture contents are presented in Figs. C3 to C8
(Appendix C). The statistical data are tabulated in Table 5.9, and the dependency
between the measured and the calculated e using the model with the optimized
parameters are shown in Fig. 5.9.
5.6.4 Bruggeman models
The Bruggeman models, which are also known as the Polder-Van Santen model,
the de Loor formula, the Bottcher formula, or the effective medium model, are the
theoretical models based upon the interactions of the microwave energy with the host
and the inclusions of a mixture. Unlike the other models, the inclusions of the mixture
Table 5.8 The optimum values for the parameters, b, pa, and pn, based upon the Debye
- Cole-Cole (DC) model.
Table 5.9
Parameters
8'
e"
b
0.47
0.52
Pa
0.30
0.29
Pn
0.87
0.74
P
-
0.87
Q
-
-2.81
The Debye - Cole-Cole (DC) model accuracy in calculating the e of the
alfalfa leaves at 22°C.
£
RMSE
r2
c
d
N
s'
2.17
0.96
0.94
0.94
1809
e"
1.23
0.95
0.83
0.83
1809
are assumed to be random shapes scattering randomly in the host inclusion in random
orientations. The general form of the model in calculating the s of the mixture is given
byEq. (5.28) [Sihvola, 1999],
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137
Alfalia Leaves (Model: DC)
50
CO
40
T3
I
3
U
30
20 i
i
10
0
0
20
10
30
40
50
Measured s'
(a)
Alfalfa Leaves (Model: DC)
40
T3
<D
ta 20
0
10
20
40
30
Measured e"
(b)
Fig. 5.9 The measured and the calculated (a)
e'
and (b) the e" for alfalfa leaves at 22°C
using the Modified Debye - Cole-Cole (DC) model.
/s
^
V^Ej - 8 h)
A;
1
+
^
1
*
A
e = eh + X
3
j=i
Vs
y
-1
X
where,
£h : Permittivity of the host inclusion
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(5.28)
138
£;: Permittivity of the ith inclusion
8*: Interfacial permittivity, the permittivity at the interface between the host and the
inclusion
v ;: Volume fraction of the ith inclusion
A j: Depolarization factors along the main axes ( j = 1, 2, or 3) of the inclusions, and
n:
Number of the inclusions.
Both the shapes of the inclusions and the e* for the vegetation materials were
unknown. Therefore, it was assumed that the shapes of the inclusions were in some
definite geometrical shapes such as spheres, needles, or circular discs so that their A j
were computationally feasible. The A j for spheres, needles, and circular discs are
respectively given by (1/3, 1/3, 1/3), (1/2, 1/2, 0), and (0, 0, 1) [Ulaby et al., 1981].
The study on the dielectric properties of heterogeneous mixtures containing
water showed that value for the 8* for a given mixture falls in between the Sh and the s of
the mixture itself [De Loor, 1963, 1968], that is, £h < e* < 8. Hence a number of
Bruggeman models might be formulated taking the lower or the upper limit of the s* and
assuming one of the shapes described above for the inclusions. In this research, the
following four such models were formulated in modeling the
e
of the vegetation
materials, and air had been chosen as the host, with two inclusions (n = 2), the bound
water-vegetation, and free vegetation or free water depending upon the moisture content
of the vegetation were considered.
1. Bruggeman lower limit circular disc (BLD) model
2. Bruggeman lower limit sphere (BLS) model
3. Bruggeman lower limit needle (BLN) model
4. Bruggeman upper limit circular disc (BUD) model
The Bruggeman lower limit sphere (BLS) model and the Bruggeman lower limit
needle (BLN) model were not considered because no closed forms of the models for the
real and the imaginary parts of the dielectric properties were derivable when the upper
limit of e* was considered. The mathematical forms of the models - BLD, BLS, BLN,
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139
and BUD are respectively shown in Eqs. (5.29) - (5.32), and the optimized parameters
for each model were tabulated in Table 5.10.
f
BLD:
e = Bh + ] £ ^ - ( e i - E h )
i=l
\
(5.29)
2+—
V 8i J
3s,
3Sh+Ei
(5.30)
BLN: £ = eh + X ^ L(£i - £h i 5Sh* ei
(5.31)
BLS: e = s h + ] T ^ ( £ i - s
i=l
i=i
J
I
£ , + £
£h + | X v i(8i _ £ h)
BUD: £ =
J
i=i_________________
3
Table 5.10
V
(5.32)
£j
1/
The optimized parameters for the BLD, the BLS, the BLN, and the BUD
models in fitting the measured s for the alfalfa leaves at various moisture contents and at
22°C.
Parameters
BLD
BLS
BUD
BLN
£'
e"
£'
s"
s'
£"
£'
£"
b
0.70
0.43
1.01
0.19
1.60
0.5
0.55
0.4
Pa
0.71
0.47
-0.29
-0.29
9.88
2.39
0.42
0.30
Pn
1.18
0.61
-0.06
-0.03
2.88
0.82
0.92
0.53
The accuracy of the models are depicted graphically in Figs. 5.4 to 5.7 for the alfalfa
leaves at the moisture contents of 73%, 45% and 12% respectively, and those for the rest
of the moisture contents are presented in Figs. C3 to C8 in Appendix (C). The statistical
data are tabulated in Table 5.11, and the graphical representations of their performances
in associating the measured and the calculated data are shown in Figs. 5.10 to 5.13. It is
noted that the models BLS and BLN did not converge in fitting the measured £ of the
alfalfa leaves, and therefore the parameters given in Table 5.10 are those from the last
iteration.
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140
Table 5.11
The accuracies of the BLD, the BLS, the BLN, and the BUD models in
fitting the measured e for the alfalfa leaves at various moisture contents and at 22°C.
Bruggeman models
BLD
BLS
BLN
BUD
E
RMSE
£'
2.60
e"
..... r2
c
d
N
0.87
0.86
0.54
1809
1.92
0.94
0.88
1.17
1809
s'
3.76
0.94
0.82
2.66
1809
e"
2.40
0.77
0.83
0.46
1809
s'
5.52
0.82
0.61
4.26
1809
E"
3.00
0.74
0.63
1.55
1809
£'
2.00
0.96
0.95
0.44
1809
£"
2.30
0.87
0.86
1.01
1809
5.6.5 The comparison of the model accuracies
In general, the models - Poly, DC, PL, BLD and BUD fitted the measured s of
the alfalfa leaves well. The root mean square error (RMSE), the correlation coefficient
(r ), and the slope, c and the intercept, d of the scatter plot of the measured (x) vs.
calculated (y) e values in the from y = ex + d for all the models are shown plotted in Fig.
5.14. The RMSE in ascending order and the r2 values in descending order for all the
models are tabulated in Table 5.12. From Fig. 5.14 it can be seen that the models, in
general, exhibited better performances in fitting the measured s" values than for s'. The
RMSEs produced by the models in fitting the measured e" were always less than those in
fitting e', and the opposite was true for the r2 values. From Table 5.12, it is evident that
the performances of the polynomials (Poly) were found to be the best for both s' and e".
Although these models are purely empirical, they are still attractive because of their
higher accuracies and the simplicity. The PL models stood next to the Poly in fitting the
measured e', but the DC model for s". In case of Bruggeman’s model, when the
inclusions were assumed to be in circular disc shapes the upper limit for e* that is, the e
of the mixture (whole leaf) rather than the lower limit, that is the Eh, the e of the host
component in the mixture (air), was a better choice in modeling the
e '.
In short, BUD
was better than BLD. The opposite was true in the case of e". Furthermore, the
assumption of continuous spatial distributions of water in vegetation matrix, which
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141
Alfalia Leaves (Model: BLD)
30
20
10
0
0
10
20
30
40
50
Measured s'
(a)
Alfalfa Leaves (Model: BLD)
40
- 30
CO
"O
M
20
3
o
3 io
20
10
30
40
Measureds"
(b)
Fig. 5.10 The association between the measured and the calculated values for (a) the s'
and (b) the e" for the alfalfa leaves at 22°C obtained using the BLD model.
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142
Alfalia Leaves (Model: BLS)
50
-CO 40
.***
£co 30
M20
cd
u
10
1
0
0
10
20
50
40
30
Measured s'
(a)
Alfalfa Leaves (Model: BLS)
30
CO
<D
to
20
3
13 10
O
10
15
20
25
30
Measured s"
(b)
Fig. 5.11
The association between the measured and the calculated values for (a) the s'
and (b) the e" for the alfalfa leaves at 22°C obtained using the BLS model.
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143
Alfalfa Leaves (Model: BLN)
0
10
20
30
40
50
Measured e'
(a)
Alfalfa Leaves (Model: BLN)
40
=CO 30
<D
3 20
=3
JJ
3
^
io
_._T—
10
20
30
40
Measured s"
(b)
Fig. 5.12 The association between the measured and the calculated values for (a) the e'
and (b) the a" for the alfalfa leaves at 22°C obtained using the BLN model.
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144
Alfalia Leaves (Model: BUD)
50
CO
3p
30
u 20
U
10
0
"\
10
'7
20
30
40
50
40
50
Measured s'
(a)
Alfalia Leaves (Model: BUD)
50
40
"to
30
B
a
2 20
S3
u
10
0
10
20
30
Measured e"
(b)
Fig. 5.13 The association between the measured and the calculated values for (a) the s'
and (b) the e" for the alfalfa leaves at 22°C obtained using the BUD model.
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145
Alfalfa leaves (s', 22°C, N = 1809)
6
;
□ RMSE
Poly
PL
DC
BLD
BLS
BLN
BUD
Models
(a)
Alfalfa leaves (s", 22°C, N = 1809)
6 i
B RMSE
Poly
PL
DC
BLD
BLS
BLN
BUD
Models
(b)
Fig. 5.14
The RMSE, r2, c and d values in fitting the measured e of the alfalfa leaves
using the various models.
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146
Table 5.12
Models in ascending and descending order respectively for RMSE and r
2
values.
£
Parameters
Models
RMSE
Poly
PL
BUD
DC
BLD
BLS
BLN
r2
Poly
PL
DC
BUD
BLS
BLD
BLN
RMSE
Poly
DC
PL
BLD
BUD
BLS
BLN
r2
Poly
DC
BLD
PL
BUD
BLS
BLN
s'
s"
could be thought as interconnecting disc shaped water components, was found to be a
realistic assumption because the performance of DC models was next to Poly models in
fitting the e", and was comparable with those of other models in case of s'. The BLS and
the BLN models did not converge, and hence failed to fit the measured s of the alfalfa
leaves. Nevertheless, it suggested that assumptions of spherical or needle shaped
inclusions in the vegetation matrix were unrealistic.
5.7 Modeling the e for alfalfa stems
The explanations given in Section 5.6 in modeling the s for the alfalfa leaves
hold for stems as well except some scatter plots for measured vs. calculated s" were
fitted with nonlinear curves, and their coefficients are shown only in the plots. The
modeling for the s of the alfalfa stems were carried out for the samples at five moisture
contents, that is 42%, 51%, 62%, 71% and 79% only for the reasons given in Section
4.5. The £ for each sample at a particular moisture content was measured at 88
frequencies ranging from 300 MHz to 8 GHz resulting in the total number of the data
points, N = 5 x 88 = 440. The same dielectric models used for alfalfa leaves were used
for the stems.
The assumption of the shrinkage of the material, which was realistic in the case
of the alfalfa leaves, did not work well for the stems. Hence, the stems were assumed not
to be shrunk as they dried, and the dielectric modeling was performed again based upon
a not shrinking model. Once the not shrinking model was chosen, as discussed in C.2
(Appendix C) the moisture content of the samples, Mg can not be greater than 68%. So
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147
the dielectric modeling for the stems was carried out for a reduced number of moisture
contents that is 42%, 51% and 62%. The results thus obtained were difficult to compare
with those obtained with the dielectric models based upon the shrinking model where all
the five moisture contents were used. Therefore the dielectric models based upon the
shrinking model for the s of the stems were repeated again but for the reduced number of
three moisture contents resulting in the total number of the data points, N = 3 x 88 =
264.
5.7.1. Polynomials (Poly)
The polynomials were independent of the shrinking or not shrinking model
because the Mg can be used directly in the polynomials without converting it into Mv.
The coefficients found for the polynomials represented by Eqs. (5.22) and (5.23) and
their accuracies in modeling the s of the alfalfa stems are respectively presented in
Tables 5.13 and 5.14. The association between the measured and the calculated s are
shown in Fig. 5.15.
Table 5.13
The values for the coefficients of the polynomial in fitting the s' and the s"
of the alfalfa stems at 22°C.
c0=-59.63
Cl
= 11.97
c2 = 279.64
c3 = -9.57
C 4=
-188.68
d0= 6.42
dj = -0.30
d2 = -45.57
d3 = 1.77
d4 = 75.14
Table 5.14
The model accuracy of the polynomial in fitting the s' and the s" of the
c5
= -1.81
d5 = 14.61
alfalfa stems at 22°C.
s
RMSE
r2
c
d
N
s'
0.89
0.99
0.99
0.25
440
s"
0.77
0.99
0.99
0.16
440
5.7.2 Power law (PL) model
The parameter ‘k ’ obtained for the power law model expressed in Eq. (5.25) in
fitting the measured s of the stems based upon the shrinking model considering all five
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148
Alfalfa stems (Model: Poly)
50
«
40
I
30
M20
cd
°
10
0
10
20
30
40
50
40
50
Measured s'
(a)
Alfalfa steins (Model: Poly)
50
40
w
'g 30
td
3 20
o
10
i
0
0
10
20
30
Measured s"
(b)
Fig. 5.15 The association between the measured and the calculated values for (a) the s'
and (b) the s" for the alfalfa stems at 22°C obtained using the Poly model.
moisture contents, and those based upon the not shrinking model and the shrinking
model with a reduced number of three moisture contents are given in Table 5.15. The
model accuracies are presented in Table 5.16. The association between the measured and
the calculated s for not shrinking model are shown in Fig. 5.16.
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149
Table 5.15 The values of ‘k ’ for the Power law (PL) models.
Shrinking (5 mcs)
Not Shrinking (3 mcs)
Shrinking (3 mcs)
s'
s"
s'
s"
s'
s"
0.692
0.533
0.032
-0.150
0.866
0.409
Table 5.16
The model accuracy of the PL models in fitting the s' and the f5" of the
alfalfa stems at 22°C.
s
RMSE
r2
c
d
N
Shrinking (5 mcs)
s'
3.80
0.88
1.16
4.18
440
e"
5.22
0.50
0.60
2.44
440
12.95
264
-
264
Not Shrinking (3 mcs)
s'
5.22
0.93
s"
3.61
0.98
1.59
Shrinking (3 mcs)
s'
1.16
0.99
0.85
2.83
264
s"
2.77
0.56
0.95
0.99
264
5.7.3 Modified Debye - Cole-Cole (DC) model
The DC models given in Eqs. (5.26) were used to model the s of the alfalfa
stems. The optimized parameters, b, pa, pn, P and Q for the models are given in Table
5.17, and the model accuracies are shown in Table 5.18. The association between the
measured and the calculated s for not shrinking model are shown in Fig. 5.17.
5.7.4 Bruggeman models
The various forms of the Bruggeman models obtained using Eqs. (5.29) to (5.32)
were used to model the e of the alfalfa stems at 22°C. Both the shrinking and the not
shrinking assumptions were considered for each model, and for the reason mentioned
earlier the models based upon the shrinking assumption were also investigated at the
reduced number of the moisture contents. The optimized parameters and the model
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150
accuracies are tabulated in Tables 5.19 to 5.26. The association between the measured
and the calculated s for BLD and BUD models based upon not shrinking assumption are
shown in Fig. 5.18 and Fig. 5.19 respectively.
Alfalfa stems (not shrinking) (Model: PL)
60
« 45
1
30
JJ
3
13
U 15
10
20
40
30
50
Measured e'
(a)
Alfalfa stems (not shrinking) (Model: PL)
40
w 30
i
•i
y = 0.2006x - 1.6995x+ 4.8343
20
j .0
1
0
10
15
20
Measured s"
(b)
Fig. 5.16 The association between the measured and the calculated values for (a) the s'
and (b) the s" for the alfalfa stems at 22°C obtained using the PL model.
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151
Table 5.17 The optimum values for the parameters, b, pa, and pn, based upon the Debye
- Cole-Cole (DC) model for the alfalfa stems at 22°C.
Parameters
Shrinking (5 mcs)
8
'
8
Not shrinking (3 mcs)
Shrinking (3 mcs)
"
e'
e"
s'
8
"
b
0.47
0.52
0.19
0.45
0.47
1 .1 0
Pa
0.30
0.29
0.22
0.29
0.44
0.69
Pn
0.87
0.74
0.51
0.74
0 .8 8
1.69
P
-
0.87
0.34
-
0.16
Q
-
-2.81
-1.67
-
-2.57
Table 5.18
The Debye - Cole-Cole (DC) model accuracy in calculating the s of the
alfalfa stems at 22°C.
E
RMSE
r2
c
d
N
Shrinking (5 mcs)
s'
2.17
0.96
0.94
0.08
1809
s"
1.23
0.95
0.83
0.30
1809
Not shrinking (3 mcs)
s'
0.53
0.99
1.00
0.05
264
s"
0.65
0.95
0.96
0.27
264
Shrinking (3 mcs)
s'
0.74
0.99
0.98
0.28
264
s"
0.84
0.91
0.93
0.44
264
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152
Alfalfa steins (not shrinking) (Model: DC)
50
CO
40
<D
"S3 30
3 20
KS
U
10
0
T
T
10
20
30
40
50
Measured s'
(a)
Alfalfa stems (not shrinking) (Model: DC)
25
20
CO
<L> 15
c3
3 10
o
5
•••••
C
0
10
15
20
Measureds"
(b)
Fig. 5.17 The association between the measured and the calculated values for (a) the s'
and (b) the s" for the alfalfa stems at 22°C obtained using the DC model.
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153
Table 5.19 The optimum values for the parameters, b, pa, and p„, based upon the BLD
model for the alfalfa stems at 22°C.
Parameters
Shrinking (5 mcs)
e'
8
"
Not shrinking (3 mcs)
8
'
8
"
Shrinking (3 mcs)
e'
e”
b
-394.19
0.19
0.22
0.13
1 .0 0
-634.24
Pa
0.87
0.45
0.34
0.16
1.55
0.48
Pn
-1232.18
0.16
0.54
0.12
1.62
1010.09
Table 5.20 The BLD model accuracy in calculating the s of the alfalfa stems at 22°C.
e
RMSE
r2
c
d
N
Shrinking (5 mcs)
s'
2.54
0.91
0.97
0.82
440
e"
4.85
0.48
0.51
4.55
440
0.07
264
-
264
Not shrinking (3 mcs)
s'
0.52
0.99
s"
1.78
0.77
1.00
Shrinking (3 mcs)
s'
1.03
0.97
0.96
0.77
264
"
3.31
0.63
1.22
3.35
264
8
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154
Table 5.21
The optimum values for the parameters, b, pa, and pn, based upon the BLN
model, for the alfalfa stems at 22°C.
Parameters
Shrinking (5 mcs)
e'
8
Not shrinking (3 mcs)
Shrinking (3 mcs)
'
"
e'
e"
8
0 .8 8
e"
b
-320.05
0.03
-101.86
0.13
0.17
Pa
3677.09
-0.08
0.68
0.33
1719.77
0.74
Pn
-998.07
-0 . 0 1
-1123.57
0.13
1.54
0.17
Table 5.22 The BLN model accuracy in calculating the e of the alfalfa stems at 22°C.
s
RMSE
r2
c
d
N
Shrinking (5 mcs)
s'
5.85
0.95
0.37
12.08
440
e"
6 .1 0
0.14
0.19
9.79
440
Not shrinking (3 mcs)
s'
1.80
0.92
0.95
0.89
264
e"
1.72
0 .6 8
0.82
1.08
264
Shrinking (3 mcs)
e’
3.85
0.87
0.46
8.81
264
s"
2.16
0.48
0.60
2.42
264
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155
Table 5.23
The optimum values for the parameters, b, pa, and pn, based upon the BLS
model, for the alfalfa stems at 22°C.
Parameters
Shrinking (5 mcs)
e'
b
Not shrinking (3 mcs)
e"
-11502.20 1264.05
g'
e"
e'
e"
5.94
-88.42
0.85
-2287.76
Pa
-0.14
-•6848.51
5.53
156.17
-0.44
-1698.68
Pn
-50.04
31.61
1.79
1321.25
-0 . 1 0
-88.04
Table 5.24 The BLS model accuracy in calculating the
£
Shrinking (3 mcs)
RMSE
r2
8
of the alfalfa stems at 22°C.
c
d
N
Shrinking (5 mcs)
£'
9.39
0.07
0.22
16.86
440
s"
1 1 .1 1
0.68
-0.45
1 1 .2 2
440
Not shrinking (3 mcs)
s'
0.93
0.98
0.98
0.39
264
s"
1 .2 2
0.82
0.84
1.08
264
Shrinking (3 mcs)
s'
1.56
0.94
0.91
1.67
264
e"
5.04
0.66
-0.59
9.44
264
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156
Table 5.25 The optimum values for the parameters, b, pa, and pn, based upon the BUD
model for the alfalfa stems at 22°C.
Parameters
Shrinking (5 mcs)
8
'
8
Not shrinking (3 mcs)
"
Shrinking (3 mcs)
e'
e"
s'
s''
b
0.074
0 .2 0
0.14
0.12
0.58
0.14
Pa
0.24
0 .2 2
0.23
0.10
0.61
0.14
Pn
0.32
0.17
0.46
0.12
1.04
0.14
Table 5.26 The BUD model accuracy in calculating the s of the alfalfa stems at 22°C.
£
RMSE
r
d
N
Shrinking (5 mcs)
s'
2.76
0.89
0.92
1 .8 6
440
s"
4.11
0.61
0.67
3.09
440
0.09
264
-
264
Not shrinking (3 mcs)
s'
0.55
0.99
s"
1.72
0.78
0.99
Shrinking (3 mcs)
s'
0.72
0.99
0.98
0.28
264
s"
1 .8 8
0.62
0.78
0.62
264
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157
Alfalfa stems (not shrinking) (Model BLD)
50
to
40
30
I
JcS 20
O
10
0
10
20
30
40
50
Measured e'
(a)
Alfalfa stems (not shrinking) (Model: BLD)
30
CO
24
I3
18
u
6
y= 0.1025x - 0.836x+ 6.7629 ^
12
0
T
T
T
5
10
15
20
Measured s"
(b)
Fig. 5.18 The association between the measured and the calculated values for (a) the s'
and (b) the s" for the alfalfa stems at 22°C obtained using the BLD model.
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158
Alfelfo stems (not shrinking) (Model: BUD)
50
to
40
30
M20
o
10
0
10
20
40
30
50
Measured s'
(a)
Alfalfa stems (not shrinking) (Model: BUD)
30
~w
TJ 20
js
3
3 10
U
y = 0.0998x - 0.7671x+ 6.4415
^
0
5
10
15
20
Measured s"
(b)
Fig. 5.19 The association between the measured and the calculated values for (a) the s'
and (b) the s" for the alfalfa stems at 22°C obtained using the BUD model.
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159
5.7.5 Comparison of the model accuracies
Unlike for leaves, the dielectric models based upon the not shrinking assumption
comparatively, in general, fitted the £ of the stems better than those based upon the
shrinking assumption irrespective o f the number of the moisture contents involved. The
only exception was that the performance of the PL model based upon the shrinking
assumption was better than any other models in fitting the measured s' data. Similar to
the behaviours the models exhibited for the leaves, the performances of the polynomials
(Poly) were the best among the models. The Poly, the PL, the DC and the BUD models
converged for both the full and the reduced number of moisture contents, and for both
the shrinking and the not shrinking models whereas the BLD model did so only when
the not shrinking assumption was made. The BLN and the BLS models did not converge
at all yielding very unrealistic values for the parameters, which can be seen by
comparing these values to the values given in Table 5.3 and Eq. (5.10). The RMSE in
the ascending order and the r2 values in the descending order for the Poly, and all the
models based upon the not shrinking assumption are tabulated in Table 5.27. The BLN
and the BLS models have been excluded from the Table. The association between the
measured and the calculated £ for the models given in Table 5.27 are shown plotted in
Figs. 5.16 to 5.19.
Table 5.27 The RMSE and r2 values in fitting the measured e of the alfalfa stems using
the various models.
£
£'
£"
Parameters
Models based upon not shrinking assumption
RMSE
Poly
BLD
DC
BUD
PL
r2
Poly
DC
BUD
PL
BLD
RMSE
Poly
DC
BUD
BLD
PL
r2
Poly
DC
PL
BUD
BLD
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6. MOISTURE PREDICTION
6.1 Introduction
Besides the moisture content, the dielectric properties of particulate materials are
also dependent on parameters such as density, frequency and temperature [Kraszewsky
et al., 1999], and this is also true for vegetation materials such as chopped alfalfa.
Samples of chopped or particulate alfalfa were prepared cutting the whole plant into
small parts manually. The particle size of the chopped samples containing both the
particles of leaves and stems were determined by following the standard method of
determining and expressing particle size of chopped forage materials by screening
[ASAE, 2000], and was equal to 2.86 mm. The procedures for preparing the samples of
the particulate alfalfa at various moisture contents, and for storing them are the same as
those used for the whole leaves or the stems.
As shown in Fig. 6.1 the dielectric properties of particulate alfalfa increased with
density at any moisture content while the frequency and the temperature were kept
constant at 9.06 GHz and 20°C respectively. Therefore it was not possible to formulate a
direct relationship between the moisture content of such materials and their measured
dielectric properties unless the aforementioned parameters were kept unchanged during
the calibration and the measurement processes. Among the three parameters, the task of
keeping the material density constant was the most tedious and time consuming one.
Hence, from the point of view of the practicability, a method that would eliminate the
effects of the material density was a must in developing microwave moisture sensors so
that the sensors could be operated keeping only the frequency and the temperature
constant. In this context, an emerging method that makes use of some experimentally
160
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161
Particulate alfalfa
25
Compacted
20
15
to
10
+
+
t
i l l
5
Loosely compacted
0
0
20
40
60
80
Moisture content (%, w.b.)
(a)
Particulate alfalfa
25
Compacted
20
15
10
5
I i
0 J
0
20
Loosely compacted
40
60
80
Moisture content (%, w.b.)
(b)
Fig. 6.1
The variation in the measurement of (a) the e' and (b) the s" with density for
the particulate alfalfa at different moisture contents, and at the operating frequency of
9.06 GHz and at 20°C.
determined density independent functions (DIFs) of the measured dielectric properties of
the material [Kraszewsky et al., 1999][Trabelsi and Nelson, 1998] [Meyer and Schilz,
1981] was investigated to see if those functions could successfully be implemented in
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162
determining the moisture contents of the vegetation materials irrespective to their
densities. It is noted that the concept of a density independent function has been
considered as an attractive alternative for an economical and practical on-line
microwave moisture meter, but a theoretical development of these functions has not yet
been explored due to the lack of thorough knowledge of the complicated interaction of
the microwaves and the microscopic constituents of the materials. Looking at the
complexity o f the problem and at the same time having a broad band data on the
dielectric properties of the test material, an artificial neural network (ANN) [Shrestha,
1996] with multiple inputs, which is capable of approximating the complex functions
was chosen as the second approach in the prediction of the moisture content of the
particulate alfalfa.
6.2 Moisture prediction using the DIFs
Six DIFs given in Eqs. (6.1) to (6 .6 ) were considered in this work [Trabelsi and
Nelson, 1998][ Kraszewski et al.,1998].
F, = A -
(6.1)
F2 = TFT—
IT
(6-2)
F3 = -t 4 —
Vs7- !
(6.3)
F
(6.4)
s ' - l
6-1
rr
-W -i
3
40 y ? ( v ? - i)
V[s'
e '+
+ l1 se''
Fe = — r=---- 7— 7
_
Ve7 £'-1
(6 -6 )
Since the DIFs were basically functions of the dielectric properties of the
materials, and those properties were themselves frequency dependent, the dielectric
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163
properties were therefore measured at
2 0 1
frequencies covering a broad frequency band
of 300 MHz to 18 GHz to determine the optimum frequency of operation for
determining the DIFs. The samples at 11 moisture contents, that is 73%, 67.7%, 60%,
54%, 51.5%, 44%, 38%, 30.6%, 24.4%, 19.6%, and 11.5% were prepared, and the
dielectric properties were measured at nine densities for the samples from each moisture
content resulting in a total of 99 moisture-density combinations, or data points to
-5
investigate the DIFs. The density of the vegetation varied from 139 to 716 kg m" , which
corresponded to the density of the loosely compacted sample at 11.5% moisture content
to the density of the compacted sample at 73% moisture content.
6.2.1 Frequency dependence
The spectra of the DIFs, F2 and F 3 , for particulate alfalfa at 11 moisture contents
and at nine densities are shown in Fig. 6.2. Only 33 frequency points covering the entire
frequency range of interest have been plotted to avoid the plots from being over­
crowded. The spectra for the remaining DIFs are presented in Figs. D1 to D4 (Appendix
D). These spectra helped to reveal qualitatively the effectiveness of the functions in
determining the moisture content of the test material. For example, as seen in Fig. 6.2,
the values o f the function F2 evaluated at nine densities per moisture content were more
closely clustered at any frequency than those for the function F 3 . Hence, it gave an
indication of the function F2 being more density independent, and would therefore be
more robust in determining the moisture content of the test material than F 3 . Ideally, at
each frequency the values for a DIF evaluated at different densities per moisture content
would coincide forming the number of clusters equal to the number of the moisture
contents. These spectra also revealed that the degree of clustering varied among the
frequencies, and was, in general, higher within the mid-frequency band.
6.2.2 Density independence
As mentioned above, the DIFs were relatively more independent of the density of
the vegetation material within the mid-frequency band than anywhere else over the
frequency range of interest. A clearer picture of density independence of a DIF can be
presented by plotting its values against density with moisture content being a parameter
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164
me
73.0
Particulate alfalfa
99 samples
Nine samples with
varying densities per
me
67.7
60.0
54.0
AI
■51.5
PL,
44.0
38.0
: 30.6
5
10
15
20
24.4
19.6
Frequency (GHz)
11.5
(a)
me (%)
Particulate alfalfa
- 73.0
10
67.7
8
60.0
■> 54.0
6
- 51.5
4
■ 44.0
2
* 38.0
0
x 30.6
10
Frequency (GHz)
15
20
a 24.4
♦ 19.6
» 11.5
(b)
Fig. 6.2 The spectra of the DIFs, (a) F2 and (b) F3 for the particulate alfalfa at 20°C.
at single frequency as shown in Fig. 6.3. The values of F2 at 10.39 GHz changed mostly
due to the change in moisture content rather than the density of the material as desired.
As seen from the figures, both operating frequency and type of DIF have effects
on density independent moisture measurements. The performances for all DIFs at
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165
frequencies corresponding to minimum SEC, which shall be explained shortly, in
predicting the moisture content at 20°C are given in Figs. D5 to DIO (Appendix D).
me (Vo
Operating frequency = 10.39 GHz
73.0
" 67.7
60.0
- 54.0
3
- 51.5
<N 0
Ph 2
- 44.0
W&OOK
* 38.0
1
^ 30.6
0
0.2
0.4
0.6
0.8
Density(g/cc)
* 24.4
* 19.6
■ 11.5
(a)
me t”/o
Operating frequency = 17.03 GHz
73.0
67.7
10
60.0
8
- 54.0
- 51.5
6
Ph
■ 44.0
4
* 38.0
2
x 30.6
0
0
0.2
0.4
0.6
0.8
Density(g/cc)
* 24.4
<> 19.6
■ 11.5
(b)
Fig. 6.3
The behaviours of the functions (a) F2 and (b) F 3 against the density at a
frequency corresponding to minimum SEC, and at 20°C.
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166
6.2.3 Moisture dependence
In order to implement a density independent function in predicting the moisture
content of the material accurately, its values should only be dependent on the material
moisture content and independent of the material density given a constant operating
frequency and temperature. Some of the functions exhibited a better independence to the
material density if they were used at a particular frequency and temperature as discussed
above. Therefore, it was necessary at this stage to look at their moisture dependence. It
was found that the functions F2 and F 4 increased linearly and the rest of the functions
increased nonlinearly with the moisture content. For example, the moisture dependence
for F2 and F3 are depicted in Fig. 6.4. The moisture dependence for the rest of the
functions at frequencies corresponding to minimum SEC are presented in Fig. D ll
(Appendix D). In order to develop the density independent calibration equations the
functions F 2 and F4 were therefore fitted with linear regression curves and the rest o f the
functions were fitted with nonlinear regression curves of the forms shown in Eqs. (6.7)
and. (6 .8 ) respectively.
where
n
F = an + b
(6.7)
F = gnp
( 6 .8 )
representsthemoisture content of the particulatealfalfa. In general, the
functions werestrongly associated with the moisture content
of thetest material. The
coefficient of determination, r2 along with the slopes, a, the intercept, b, the magnitude,
g and power, p of the regression equations for all the functions are presented in Table D1
(Appendix D). Hence, the density independent calibration equations were obtained from
Eqs. (6.7) and (6 .8 ), and are as follows.
u=
52L^L
(i = 2,4)
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(6.9)
167
Operating frequency = 10.39 GHz
4
3
1
0
20
40
80
60
Moisture content (%, w.b.)
(a)
Operating frequency = 17.03 GHz
8
Ph
I
0
10
20
30
40
50
60
70
80
Moisture content (%, w.b.)
(b)
Fig. 6.4 The moisture dependence of (a) F2 and (b) F3 at a frequency corresponding to
minimum SEC, and at 20°C.
u=
(i = 1, 3, 5, 6 )
§i
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(6.10)
168
The effectiveness of the calibration equation in predicting the moisture content of
the test material using the F values calculated from the measured s were checked at each
of 33 frequencies ranging over 300 MHz to 18 GHz on the basis of the standard error of
calibration (SEC) and the standard error of performance (SEP) which were defined as
follows.
( 6 . 11)
(6.12)
where N (= 99) and n (= 44) are the number of samples, v is the number of variables in
the regression equation, Am, is the difference between the predicted moisture content
and that determined by using the standard oven method for the ith sample, and m is the
bias, which is defined as
(6.13).
All the samples (99) representing 11 moisture contents and nine densities were
used to calculate the SEC, and those samples were divided into two sets, the calibration
set of 55 samples, and the validation set of 44 samples in order to calculate the SEP. In
the latter, the samples in both sets still represented the
11
moisture contents, but the
densities of the samples were so chosen that they were different in the calibration and
the validation processes to observe the robustness of the calibration equations.
The SEC and the SEP in percent moisture content for each of the calibration
equations depended upon the DIFs are tabulated in Table D2 (Appendix D). As
expected, the values for the SEC and the SEP varied with frequency, and the range of
variation over the entire frequency range is presented in Table 6.1 along with the
optimum operating frequency, fopt at which the minimum values for the SEC occurred.
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169
Table 6.1 The ranges of the SEC and the SEP for the calibration equations based upon
the DIFs.
DIFs
SEP (% me)
SEC (% me)
V (GHz)
Min.
Max.
Min.
Max.
Fi
0.79
4.06
1.73
5.75
6.05
f2
0.58
3.93
1.54
5.79
10.39
f3
2.06
5.14
2 .8 6
7.05
2.07
f4
1 .2 0
5.52
2 .6 6
7.76
13.04
f5
0.75
4.07
1 .8 6
5.73
9.06
f6
0.81
4.07
1.89
5.35
9.06
These values showed that not all the density independent functions are equally
effective for developing the calibration equations in order to predict the moisture content
of the test material. Based upon the SEC, the DIFs can therefore be put in the order of
decreasing performance as F2 , F 5 , Fi, F6 , F4 and F3 . Hence the choice of the DIF in
developing the microwave moisture meters depends upon the accuracy sought and the
availability of the microwave source operating at fopt.
Besides the standard errors, the worst case relative errors in percent moisture in
predicting the moisture content of the test material at each of the
11
moisture contents
and at each o f the 33 frequencies using any DIF was also investigated. For example, the
calculation of the worst case relative errors, T at u corresponding to a DIF, F at f GHz
shall be explained referring to the symbols and the graphics adopted in Fig. 6.5.
The values Fh and Fi obtained by measuring the s of the test material at a
moisture content of u have yielded Uh and Ui respectively through the calibration
equation instead of producing the correct value of u. That is,
F. = a a . + b
h
h
and, Fj = au^ +b.
So, F^ - Fj = AF = a(u^ - u j ) = aAu
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170
Operating frequency = f GHz
An
0
Fh
ti*
_ j_
AF
Fi
S
o
•
I
•|
2
8 ..
.
•
e
o
8
8
F = an + b
20
40
Ui u
60
80
Moisture content (%, w.b.)
Fig. 6.5 An example of the graphics and the symbols adopted in calculating the worst
case relative errors, *F.
a =—
AF
or, Au
a
andj'P = — xl00%
u
(6.14)
where Au is considered as the maximum error associated with the calibration equation in
predicting the moisture content, u, and 'F is the maximum (or the worst case ) relative
error expressed in the percent moisture content.
At moisture content, u the data points have been spread due to the residual
density effect. For the non-linear calibration equations obtained for the DIFs Fi, F 3 , F 5
and F6 , the 'F was determined by substituting the Oh and Ui separately in Eq. (6.10), and
finding the corresponding Fh and Fi as no close-form expression was possible for them.
The worst case relative errors, *P associated with the calibration equations
operating at fopt for 11 moisture contents are given in Table 6.2, and those at the rest of
the frequencies are listed in Tables D3 to D 8 (Appendix D).
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171
Table 6.2 The worst case relative errors in percent moisture content, Y associated with
the calibration equations obtained using the DIFs and operating at fopt(GHz) for 11
moisture contents.
Fi
D
foPt ( G H z )
6.05
f2
f3
f4
f5
f6
10.39
2.07
13.04
9.06
9.06
15.7
11.5
9.6
8.7
39.3
6 .0
16.3
19.6
8 .0
3.0
18.2
3.3
3.1
2 .8
24.4
4.6
3.1
9.5
1 1 .1
4.7
3.2
30.6
5.6
2.5
13.0
5.8
3.8
3.5
38.0
4.6
1.5
11.9
6 .8
3.8
3.7
44.0
3.5
1 .8
15.0
5.0
4.3
5.2
51.5
4.7
3.2
7.5
2 .1
3.1
5.5
54.0
1.4
0 .8
9.2
7.5
3.3
3.3
60.0
2.3
1.7
13.1
3.7
0 .6
1.9
67.7
1 .1
1 .2
8 .2
2 .6
1.9
1.7
73.0
4.5
3.3
1 0 .0
6 .8
4.3
4.2
In general, as shown in Table 6.2, all DIFs except F3 provided better results, especially
the results obtained with F2 . Hence, the calibration equations obtained using the DIFs
Fi, F2 , F4 and F6 operating at corresponding fopt could be considered as potential tools for
predicting the moisture content of alfalfa irrespective of its density within the range of
139 kg rrf3 to 716 kg m ' 3 by measuring its dielectric properties at 20°C.
6.3 Moisture prediction using artificial neural networks
A number of artificial neural networks (ANNs) were investigated to predict the
moisture content of the alfalfa nullifying the effect of density at a constant temperature
of 20°C. The dielectric properties, s' and g" at each of ten frequencies shown in Table 6.3
were chosen for each sample as the inputs to the networks resulting in a
2 0
-element
input. The same data set of 99 samples with the moisture contents ranging over 11.5% to
73%, and the densities varying from 139 kg m ' 3 to 716 kg m ' 3 used in the DIFs was used
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172
for the ANNs as well. A total of 6 6 samples out of 99 were used as the training data set,
and the rest (33 samples) plus seven more samples at moisture contents other than those
used in the DIFs, that is a total of 40 samples were used as the test data to test the
performance of the trained networks. To test the robustness of the trained networks, the
test samples were chosen to be different from the training samples either in the densities,
or both the densities and the moisture contents.
Table 6.3. The selected frequencies used with the ANNs in predicting the material
moisture content.
Frequencies (GHz)
1 .0 1
1.98
4.02
5.96
8
10
12
14
16
18
An error back propagation artificial neural network (EBPANN) with the
momentum technique and the adaptive learning rate [Shrestha, 1996] was implemented.
A two-layer network, with tan-sigmoid transfer function in the hidden layer and a linear
transfer function in the output layer, which was a useful structure for the function
approximation or nonlinear regression problems [Neural Network Toolbox, 1998] was
adopted. A suitable number of neurons in the hidden layer was determined by training
the networks for varying numbers of neurons, and observing the prediction error
(RMSE) produced by the networks for the test data set. The training was continued for
each ANN until the error goal, the summed squared error (SSE) reached 0.003 or the
number of the epochs, the total number of training samples, presented to it reached
12000. The RMSEs in percent moisture content produced by the trained networks with
varying number of the hidden neurons, ® when tested with the test data set are shown in
Fig. 6 .6 . And the error statistics of the trained ANNs and the time required to train those
ANNs were presented in Table 6.4, where MAE, MinAE and MaxAE respectively stand
for the mean, minimum and maximum absolute errors. An ANN with five hidden
neurons produced the best results. The association between the predicted and the
measured moisture contents for this network is shown plotted in Fig 6.7.
The slope, c and the intercept, d of the fitted line of the form y = cx + d and r
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173
values for the scattered x-y plot obtained by plotting the moisture predicted by the
network, y vs. the reference moisture content, x are given in Table 6.5.
3
!
£
o'
W
2
°
I
i
i
...•■■©
©
o
j
o
GO
Pi
i
0
4--------------- 1--------------------------------r ------------------------------ r-------------------------------- r-------------------------------1
0
10
20
30
40
50
<h
Fig
6 .6
The accuracy of the trained ANNs with varying number of hidden neurons in
predicting the moisture content of the particulate alfalfa irrespective to its density at
20°C.
Table 6.4 Error statistics in percent moisture content and the training time for the
2 0
- O - l networks.
0
RMSE
MAE
MinAE
MaxAE
Time (s)
2
2.44
1.80
0.08
6.42
60.38
5
1.09
0.83
0 .0 0
2.94
34.45
10
1 .1 0
0.91
0 .0 2
2.63
34.94
15
1.42
1.13
0 .1 1
4.12
17.64
2 0
1.35
1.03
0 .0 1
3.90
59.34
25
1.30
1 .0 1
0.04
2.82
69.95
30
1.24
1.04
0 .1 1
3.08
80.20
35
1.34
1.09
0.05
2.90
91.36
40
1.55
1 .1 1
0 .0 2
5.50
102.09
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174
20-5-1 ANN
80
60
o
s 40
'O
B
_o
2 0
<D
£
0
0
20
40
60
80
Reference me (%, w.b.)
Fig. 6.7
The association between the predicted and the reference (standard oven
method) moisture content for particulate alfalfa at 20°C.
Table 6.5
Regression analysis of the measured vs. predicted moisture for the 20- ® -1
networks.
c
d
r2
2
0.99
1 .1 0
0.984
5
1 .0 0
0 .0 2
0.996
10
1 .0 0
0.33
0.996
15
1 .0 2
0.79
0.995
2 0
1 .0 1
0.06
0.995
25
1 .0 2
0.85
0.996
30
1 .0 0
0.17
0.996
35
1 .0 1
0.48
0.995
40
0.99
0.33
0.990
<J>
In general the trained ANNs predicted the moisture content of the alfalfa irrespective to
its density exceptionally well. In terms of the RMSE, the MAE and the MinAE the
performances of the trained networks with varying hidden neurons were found to be
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175
very close to each other. However, the MaxAEs was found to be more sensitive to the
number of the hidden neurons, and was at around 3% me for the ANNs with the hidden
neurons of 5, 10, 25, 30 and 35, and varied over a range of 3.9 to 6.42% me for the rest
of the networks.
Comparing to the methods discussed earlier using the calibration equations based
upon the DIFs, the use of the ANNs were found to be very straight forward, and the
performances of the trained networks were also exceptionally good. Hence the ANNs
can be considered as a potential tool in the development of the practical microwave
moisture sensors nullifying the effect of the density of the test material.
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7. SUMMARY, CONCLUSION AND
RECOMMENDATIONS
7.1 Summary
Microwaves have been successfully used in many industrial, scientific and
medical (ISM) applications. In the context of Canadian industries, Canadian hay
industries have been exporting hay and processed products to Japan, Taiwan and South
Korea for years. In North America, production of forage and processed products, in
particular alfalfa cubes and pellets, is worth over $15 billion annually. Unfortunately,
problems such as slow and off-line moisture measurement techniques, inefficient and
destructive conventional heating, and the hazard to both crop and human health of
conventional methods of disinfestation are still issues causing a huge loss on both yield
and quality of this commercially important crop. Hence, it was worthwhile to investigate
possibilities of using microwaves to address the aforementioned problems in the hay
industry.
The response of a material to microwaves is paramount in any microwave
processes, and is mostly governed by the dielectric properties (or permittivity) of the
material. Permittivity is a complex quantity consisting of a real part, the dielectric
constant (e') and an imaginary part, the dielectric loss factor (s"), and is usually
expressed as s = e' - je". The value of s' along with knowledge of the applied electric
field is useful in calculating the intensity of local electric field within a material, and that
of e" is used to determine power absorbed by the material, which is dissipated as heat.
Permittivity of a material is generally greatly influenced by various parameters such as
176
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177
moisture content, temperature, density, and operating frequency. Hence, a prior
knowledge of dielectric properties of materials under varying conditions is essential for
any microwave processing of the materials
A detailed review of the literature revealed that the majority of the research has
been focused upon dielectric properties of grain and seeds, stored-grain insects, building
materials, animal tissues, crude oils and polluted water, fruits and vegetables, meats,
woods and textiles, soil and low-density fiberglass composites. Very few investigations
have been conducted towards the measurement of dielectric properties of vegetation in
the last four decades. These are summarized in Tables 7.1, but none of those were for
alfalfa.
A number of different techniques have been implemented to measure the
dielectric properties. These techniques differ in mode of wave propagation (transmission
and/or reflection and resonance) and/or in selection of applicators to deliver
electromagnetic energy to the materials, for example, cavities or antenna pairs. A choice
of a technique has mainly been influenced by the nature of test materials and desired
accuracy. A comparative study of various permittivity measurement techniques is
presented in Table 7.2. A probe reflection technique has been used in measuring the
dielectric properties of a wide variety of materials. Some of these materials include
fructose solutions, ethanol and cheddar cheese, high water content tissues such as
muscle, brain, liver, kidney, low me tissues such as fat, and blood, conifers - Caucasian
fir and spruce, ethanol, methanol and formamide, Balsam fir and poplar tree trunks,
aspen and com leaves, com stalk and its fluid, grapes and sugar solutions, pulverized
coal and limestone, fruits and vegetables, shrimp and adult rice weevils. In particular,
this technique is suitable to measure the dielectric properties of moist green leaves.
A probe reflection system has been set up at the Visual Properties Laboratory in
the Department of Agriculture and Bio-resource engineering at the University of
Saskatchewan. A network analyzer system is used to determine the reflection
coefficients at the probe/material interface by transmitting to and receiving signals at
microwave frequencies from the test material. The network analyzer system consists of a
Hewlett-Packard 8510B network analyzer, an HP8341B synthesized sweeper (20GHz),
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Reproduced with permission of the copyright owner. Further reproduction
Table 7.1 Different aspects of vegetation s measurement conducted in the past.
Carlson [1967]
Broadhurst
Ulaby
Tan [1981]
1970]
Measurement system
Partially
filled
Slotted line
cavity resonance Reflection
Partially
filled
cavity resonance
and
Jedlicka El-Rayes and Ulaby
[1984]
[1987]
Guide wave
Probe
transmission system
system
system
system
system
Applicator(s)
1
1
1
3
4
Frequency (GHz)
8.5
100 (kHz) -
9.5
1.1 - 1.9, 3.5 - 6.5,
0 .2
-
reflection
2 0
7 .6 -8 .4
4.2
prohibited without perm ission.
me (% w.b.)
0 -6 5
63
0 -7 5
0 -8 0
0 - 8 6
Temp. °C
2 3 -3 5
23
21
23
-32 to 22
e' accuracy (%)
1 0 - 2 0
10
10-15
5
5
e" accuracy (%)
1 0 - 2 0
10
10-15
5-37
10
Plants/component
Grass,
Bamboo,
Grass,
tulip tree
leaves and wood
com,
taxus
Objective
mbber Leaves and stalks of Leaves and stalks of
com and wheat
com,
com
stalk
cuspidatus, blue
Casuarina
fluid, aspen-leaves,
spruce
needle-shaped
balsam
leaves,
poplar tree trunks
Microwave
remote sensing
N/A
fir
and
Microwave
Microwave remote
Microwave remote
remote sensing
sensing
sensing
00
Reproduced with permission of the copyright owner. Further reproduction
Table 7.2. A general comparison of the microwave dielectric measurement systems.
Slotted line
Guided
Free space
Filled cavity
Partially filled
Probe reflection
Reflection
wave
transmission
resonance
cavity resonance
system
system
transmission
system
system
system
system
prohibited without perm ission.
Frequency
Broad band
Banded
Banded
Single
Single
Broad band
Sample size
Moderate
Moderate
Large
Large
Very small
Small
Temperature
Difficult
Difficult
Very easy
Very easy
Very easy
Easy
Low loss material
Very low
Moderate
Moderate
Very high
High
Low
High loss material
Low
Moderate
Moderate
Does not work
Low
High
Sample preparation
Easy
Difficult
Easy
Very difficult
Very difficult
Easy
Most suitable test
Solids, semi­
Solids
Large flat
Solids, semi­
Solids
Solids, semi­
material
solids
sheets
solids, liquids
monitoring/ control
Accuracy for:
Meas.
8
and/or |i
and |i
and (a
8
8
To test material
Destructive
Destructive
N on-destructive
Commercial
no
yes
yes
vendors
8
or (i
solids, liquids
s or p.
8
Destructive
Destructive
Non-destructive
no
no
yes
8
180
an HP 8515A S-parameter test set (45MHz - 26 GHz), and an HP 85101B
processor/display unit. An HP 85070D, version D1.0, open-ended coaxial line has been
used as a probe. The analyzer is connected via an 82350A PCI GPIB interface card
driven by using Virtual Instrument Software Architecture (VISA) software to a personal
computer loaded with HP 85070D software that converts the magnitude and phase of the
reflection coefficients to dielectric properties of the material.
The systematic errors of the measurement system originated from directivity, and
source match, and frequency tracking errors, have been minimized by using a three-load
(air, short-circuit and a user defined load) calibration method. Deionized water has been
used as the user defined load. The system accuracy in measuring the dielectric constant
(s') and loss factor (s") has been found to be ± 6 % and ± 1 0 % respectively.
The sample temperature is read and recorded by using an assembly consisting of
a copper-constantan thermocouple, a 21X Micrologger Data Logger, and a laptop
computer loaded with data acquisition software, PC208W 3.3.
The pressure of the probe on a test material during dielectric measurement is
measured with a digital volt meter connected via a conditioning circuit to a load cell,
which holds the probe through a specially fabricated metal ring. A calibration equation
is developed prior to dielectric measurements for converting the volt meter reading
(millivolts) into pressure (kilopascal).
A sample of 2.8 mm thickness and 26 mm in transverse extent was found to be
sufficient to represent an infinite size of a sample for the probe. A copper sample holder
with inside diameter of 27.16 mm, slightly greater than the transverse extent of the
sample, and a depth of 31 mm was fabricated. Since the diameter of the probe (19 mm)
was smaller than that of the probe, it was inserted into a cylindrical Teflon jacket such
that the probe face and the surrounding jacket-rim were coplanar. This provided just
enough clearance to insert the probe freely with a good fit into the sample holder. This
assembly was particularly useful when both dielectric properties and density of a sample
were required. Known physical dimensions of the sample holder along with the length of
the probe in the sample holder, which could be read from the scale etched on it, were
used to calculate sample density.
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181
The sample temperature was controlled dynamically by immersing the sample
holder into a water-ethyleneglycol bath having a continuous circulation of the same fluid
from Corola Messtechnik GMBH, a constant temperature circulator. Both sample holder
with sample in it and bath were raised as a single unit by using a laboratory bench jack
to bring the sample in contact with the fixed probe aperture without disturbing the cable
connecting the probe to the network analyzer, and to maintain an uninterrupted flow of
the fluid. This mechanism greatly minimized measurement errors associated with cable
movements after calibration, and also kept the sample at desired temperature during
measurement.
Samples of alfalfa or Lucerne (Madicago sativa) at 10% blooming stage were
collected from experimental fields of Agriculture and Agri-Food Canada (AAFC),
Saskatoon, Canada. Manually separated leaves and stems were conditioned at various
moisture levels in a computer controlled thin layer hot-air drier before storing them in a
cold-room (5°C) in air-tight polythene bags.
Dielectric properties of leaves and stems were measured and analyzed at various
frequencies, moisture content and temperatures as presented in Table 7.3. Dielectric
properties o f leaves were measured by bringing a stack of leaves in contact with the
probe aperture at an optimum pressure. It was difficult to establish a proper contact
between
Table 7.3
Frequencies, moisture contents and temperatures at which the 8 of the plant
parts were measured.
Parameters
Frequency (GHz)
Moisture contents (% w.b.)
Temperature (°C)
Plant part
Range
Step
Total measurement points
Leaf
0.3 to 18
0.088
201
Stem
9 9
9 9
9 9
Leaf
12 to 73
5 tol5
9
Stem
42 to 79
8 to ll
5
Leaf
-15 to 30
5 tolO
6
Stem
22
-
1
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182
stems and the probe aperture because of bends, and varying hardness and diameters of
the stems. Therefore measurements must be preformed on a single stem, and that again
posed a problem in providing an infinite sample size as discussed earlier because
average diameters for fine and coarse stems were only 2.29 mm and 3.82 mm
respectively. Hence, measured permittivity of a stem was corrected for infinite sample
size by using a correction curve. The curve was essentially a trend of e for known fruit
and vegetative materials cut into stem-like structures at varying diameters.
The fibre saturation point (FSP) for any vegetation bears valuable information on
its dielectric properties because the major constituent, water, exists only in the form of
bound water, and both in free and bound forms at moisture contents below and above the
FSP respectively. A comparison of dielectric properties of alfalfa leaves at various
moisture levels, free water, and bound water over a broad frequency range revealed that
the FSP for alfalfa leaves is at 23% moisture level, wet basis. The e' for leaves at
moisture contents below FSP decreased monotonically with increasing frequency, and
exhibited the mixed trend of both bound and free water at moisture contents exceeding
the FSP. Similarly, the trends of e" below the FSP were similar to that of bound water,
but at moisture contents exceeding FSP and frequency up to 5 GHz the trend was
completely different from that of free/bound water. This was attributed to salinity of the
moisture in the leaves, and hence strong ionic losses at lower frequencies. As expected,
the trend was similar to that of a saline solution at 4 ppt. However, the trend became
similar to that of free distilled water for frequency exceeding 5 GHz, which was
attributed to a change in loss mechanism from low frequency ionic losses to high
frequency relaxation losses. The relaxation frequency at which the value of s" peaks
varied from 5 GHz to 8 GHz for leaves at moisture contents ranging from 31% (w.b.) to
73% (w.b.). These frequencies fell within relaxation frequencies for bound water (0.20
GHz) and free distilled water (18 GHz), being closer to that of the former.
The values of both e' and s" increased with moisture content exponentially.
When frequency was increased, the e' decreased and the s'' first continuously increased
to a peak then gradually decreased irrespective of moisture contents. The magnitudes of
peaks, and frequencies at which they occurred varied with moisture contents.
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183
Since measurement of dielectric properties of vegetation was very time
consuming, laborious, and demands an extreme care, a computer model requiring only a
few easily measurable parameter(s) would be very useful. Natural vegetations are very
complicated materials, for example, alfalfa is composed of crude protein, cellulose,
hemicelluloses, pectin, non-structural carbohydrates, lignin, organic acids, lipids,
vitamin A and carotene, and oestrogenic compounds. As a result, dielectric properties,
relative quantities, distribution, and interactions of each constituent with electromagnetic
fields on the molecular level contribute to the dielectric properties of vegetation. In this
study, however, plant tissues were considered as a mixture of dry vegetation, free and/or
bound water, and air, and empirical, semi-empirical, and theoretical models were
investigated.
As for other materials, knowledge of the water content in vegetation is a key factor
at various stages of its production such as harvesting, baling, storing, pelleting and
cubing of alfalfa. The moisture content of vegetation is not only a function of water
content, but also depends upon its temperature, the measurement frequency and density.
Among these quantities, density is the most difficult to keep constant, or measure,
especially in on-line processes. Therefore a semi-automated density independent
moisture measurement technique has been investigated. The density independent
functions of dielectric properties and artificial neural networks having inputs of
dielectric properties have been implemented in this technique..
Some experiments were run prior to measuring the dielectric properties of materials
so that the later could be measured accurately. These preliminary experiments led to
following results and observations:
1. A sample of 2.8 mm thickness and of 26 mm of transverse extent is sufficient to
simulate an infinite sample for the probe used.
2. Time required to condition samples from storage temperature (5°C) to desired
temperature is about 30 min.
3. Dielectric properties of materials over the frequency range from 300 MHz to 18 GHz
with 201 frequency points separated by 88.5 MHz can be measured in about 12 s.
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184
4. The difference between the moisture contents of a sample before and after measuring
the dielectric properties induced by time lapses occurring in conditioning the sample
to a desired temperature and in measuring the properties is approximately 0.5%
moisture content, wet basis, on average of triplicates.
5. Sample temperature was about 0.5°C less than the temperature set on the circulator
due to heat losses.
6. Pressures of about nine kPa for leaves and seven kPa for stems were optimum in that
a better contact was achieved between the plant parts and probe aperture without
over stressing the former.
7.2 Conclusions
1. A coaxial probe refection system suitable for measuring dielectric properties of
various materials has been set up. The accuracy of the system in measuring the
dielectric constant and loss factor are ±6% and ±10% respectively. This system can
be used to measure dielectric properties of materials over a wide range of frequency,
moisture content, temperature, and density. Pressure of the probe on the test
materials can be read from a dedicated device, which is important for consistent
measurements of dielectric properties in the case of compressible materials, for
example, cake dough and coriander powder. This technique provided a better way
for measuring dielectric properties of not only solids, liquids, and semi liquids, but
also of naturally occurring materials such as green moist leaves, which otherwise
would be difficult due to complications in preparing suitable samples for other
measurement techniques.
2. Dielectric properties of alfalfa leaves were measured over a frequency range from
300 MHz to 18 GHz,, moisture content from 12%, wet basis to 73%, wet basis,
temperature between -15°C to 30°C, and those of stems were measured for frequency
ranging over 300 MHz to 18 GHz and moisture content from 42%, wet basis to 79%,
wet basis at 22°C. Dielectric properties of chopped alfalfa were measured over
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185
frequency range of 300 MHz to 18 GHz, moisture content from 11.5%, wet basis
to73%, and density over the range from 139 kg m '3 to 716 kg m '3 at 23°C.
3. Empirical, semi empirical and theoretical models were investigated to determine the
dielectric properties of both alfalfa leaves and stems at 22°C. Empirical model
developed in this work can be used for modeling dielectric properties of both alfalfa
leaves and stems. The root mean square error (RMSE) and the coefficient of
determination (r2) for dielectric constant and loss factor of leaves are 0.89 and 0.99,
and 0.52 and 0.99 respectively. The RMSE and r2 values for dielectric constant and
loss factor of stems are 0.89 and 0.99, and 0.77 and 0.99 respectively. Only the
moisture content of leaves/stems, and the frequency of interest need to be known. If
semi empirical or theoretical models need to be used then the Power law model
and/or the Debye-ColeCole model can be used. For the dielectric constant of leaves
the Power law model is most suitable (RMSE = 1.78, r2 = 0.96), and for the loss
factor, the Debye-ColeCole model is more accurate (RMSE = 1.23, r2 = 0.95). For
stems, the Debye-ColeCole models (developed on an assumption that they do not
shrink as they dry) can be used to calculate the dielectric constant with RMSE = 0.53
and r2 = 0.99, and dielectric loss factor with RMSE = 0.65 and r2 = 0.95.
4. A density independent function, the square root of loss factor over cube root of
dielectric constant minus one, can be used to determine the moisture content (me) of
alfalfa chopped at particle size of 2.87 ± 1 stdev (1.31) mm according to ASAE
standard over the me ranging from 12%, wet basis (w.b.), to 73%, w.b. regardless of
its density variation between 139 kg m'3 and 716 kg m'3 at 10.39 GHz and at 20°C in
less than 70 ms. The standard error of calibration and the standard error of
performance are 0.58% me (w.b.), and 1.54% me (w.b.) respectively, and the worst
case relative error not exceeding 3.32% me (w.b.) except at lower mcs, e.g. at 11.5%
me (w.b.) is 8.71% me (w.b.) compared to the standard oven method. A linear
relation (r2 = 0.99) to be used to estimate the moisture content from the function
value has a slope and intercept o f 0.0373 and 0.276 respectively.
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186
5. The moisture content of chopped alfalfa described above can be predicted by using
an artificial neural network (ANN) with RMSE of 1.09% me (w.b.) compared to the
standard oven method. The ANN should consist of 20 and 5 neurons with sigmoid
activation functions in the input and hidden layers respectively, and 1 neuron with
linear activation function in the output layer. When dielectric constant and dielectric
loss factor measured at each of ten frequencies (GHz), 1.01, 1.98, 4.02, 5.96, 8, 10,
12, 14, 16 and 18 are input to the ANN after setting its weights and biases to the
values given in Table D9 (Appendix D), the moisture content of the chopped alfalfa
is obtained at the output in percentage wet basis.
7.3 Recommendations
1. Addition of two more inputs to the ANN - one for particle size and the other for
temperature, or train the ANNs with dielectric properties measured at varying
particle size and temperature to accommodate those parameters in predicting the
moisture content of chopped alfalfa at various particle sizes and temperatures.
2. Determine density independent functions on particle size of chopped alfalfa for
moisture prediction.
3. Use density independent function suggested by [Trabelsi et al., 1998a] for moisture
prediction of chopped alfalfa that would include temperature into the calibration
equation, and test the function for a new material as well.
4. Measure the dielectric properties of alfalfa grown at different locations, and at
different stages of growth to see if there are environmental effects.
5. Measure dielectric properties of insects usually found in alfalfa plants such as
Hessian fly, and compare to those of the plants to see if selective heating could be
carried out to disinfect the plants from those insects.
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187
6. Use the models to calculate dielectric properties of other similar vegetations whose
properties are measured using different measurement techniques. For example,
dielectric properties of green tea leaves measured by using the free space
transmission technique [Okumura and Ma, 1998] could be used for this purpose.
This approach would not only help to check the generality of the models one step
further, but also give an assurance of instrument independency of the models in
obtaining the dielectric properties.
7. Develop a model to calculate dielectric properties of alfalfa based upon the physical
characteristics of various substances present in it such as crude protein, organic
acids, and non-structural carbohydrates, and compare to dielectric values obtained in
this research.
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188
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road, St. Joseph, MI 49085-9659, USA.
Athey, T. W., Stuchly, M. A., and Stuchly, S. S., 1982. Measurement of radio frequency
permittivity of biological tissues with an open-ended coaxial line: Part II, IEEE
Transactions on Microwave Theory and Techniques, Vol. MTT-30(1):82 - 86.
Auty, R. P., and Cole, R. H., 1952. Dielectric properties of ice and solid D 2 O, Journal of
Chemical Physics, 20: 1309 - 1314.
Baker J. J., Vanzura, E. J., and Kissick, W. A., 1990. Improved technique for
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199
APPENDIX A
Figures:
A1 - A11
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200
10-
3.58
Sample holder
Probe aperture
0.5
Teflon jacket
27.16
Unit: mm
(b)
Fig. A1
(a) A longitudinal cross section of the HP85070D dielectric probe with Teflon
jackets, (b) a bottom view of (a) in a sample holder.
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201
(a)
Sample holder
Aluminum bath-
A Copper hollow tube
Lid
Unit: mm
(b)
Fig. A2 (a) A sample holder in a temperature bath and (b) a top view of (a).
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Fig. A3 A photograph of 823 50A PCI GPIB interface card.
Specifications
Speed
750KB/S
O/S
Win95/98/NT/2000/Me
Buffers
Built in buffering
I/O Libraries
SICL/VISA
Language support VEE, HP BASIC, & Microsoft
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203
Fig. A4 A photograph of a load cell connected to the ring probe holder.
D ig ita l t h e r m o m e t e r
Motor
Fig. A5
Outlet
A photograph of a Corola Messtechnik GMBH Constant Temperature
Circulator (Bath) capable of circulating the water-ethylene glycol liquid over the
temperature range of -40°C to +40°C.
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204
HP 85101B processor/display
Hewlett-Packard 851 OB network analyzer
HP8341B synthesized sweeper
(20GHz)
HP 8515A S-parameter test set
(45MHz - 26 GHz)
Fig. A6 An automatic network analyzer (ANA) system.
Fig. A7
A shot captured from the ANA display/processor unit - the reflection
coefficients at 201 frequency points ranging over 300 MHz - 18 GHz at a step of 88.5
MHz for distilled water at 24°C.
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205
Wl>i i ,
(a)
(b)
Fig. A8
The snapshots of the (a) s' and (b) s", chart and data calculated from the T
shown in Fig. A7 using HP85070D software.
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206
............. r * ~ . ........................
? ♦ .a •,■■■>,«, -»& a a -J *
............................................ ^
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a
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Fig. A9 A photograph o f 21X Micrologger Data Logger.
C3
R3
VR1
R E S -V A R
C4
10uF
RES
CAP
Fig. A10 A conditioning circuit.
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207
DVM Calibration Curve
30 i
24
'S'
EC
& 18
B
3Xfl
12 B
Oh
o- '
&'
O' "
6
o ■"
0 -----------------T--------------- .--------0
100
200
300
400
500
600
Voltage (mV)
Fig. A ll
A calibration curve to infer the pressure on the probe aperture from observed
voltage in DVM.
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208
APPENDIX B
Figures:
B 1 -B 1 6
Tables:
B 1 -B 7
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Fig. B1
The hollow Aluminum tubes with single sharp edge with the inner diameters
ranging from 1.67 to 6.52 mm (bottom row), and the Teflon rods with the same range of
diameters (upper row).
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210
f= 0.3 GHz, 23°C, Y-errorbar = 1 StDev
80 i
pg
□ Apple
□ Carrot
□ Cantaloupe
E3Potato
H Teflon
1.67
2.39
3.19
4.05
4.76
5.64
6.52
00
Diameter (mm)
(a)
f= 0.3 GHz, 23°C, Y-errorbar = 1 StDev
□ Apple
□ Carrot
□ Cantaloupe
J ><
0 Potato
H Teflon
1.67 2.39
3.19
4
4.76
5.64
6.52
®
Diameter (mm)
(b)
Fig. B2
The means and the standard deviations of the (a) s' and (b) the s" of the
cylindrical fruit “tissues” at varying diameters at a frequency of 0.3 GHz.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
211
f = 0.48 GHz, 23°C, Y-error bar = 1 StDev
□ Apple
□ Carrot
□ Cantaloupe
W 40
E3Potato
S3Teflon
1.67 2.39
3
3.19
4.05
4.76
5.64
6.52
oo
Diameter (mm)
(a)
f = 0.48 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
40
fi*
X
<
:X
X
X
20
X
X
X
X
1.67 2.39
3.19
□ Carrot
□ Cantaloupe
0 Potato
H Teflon
I
4.05
4.76
5.64
6.52
°°
Diameter (mm)
(b)
Fig. B3
The means and the standard deviations of (a) the s' and (b) the s" of the
cylindrical fruit “tissues” at varying diameters at a frequency of 0.48 GHz.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
212
f= 1.27 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
<
<
<
<
<
<
<
<
<
<
<
<
<■_
"w 40
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<
<
1.67
2.39
3.19
4.05
4.76
E Carrot
□ Cantaloupe
0 Potato
X
5.64
6.52
HTeflon
°°
Diameter (mm)
(a)
f= 1.27 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
□ Carrot
□ Cantaloupe
40
20
0
\
1.67
3C
y^
n
3
E Potato
r
!
f
>
r
r
r
ft
r 1
2.39
3.19
4.05
4.76
r
i
5.64
<
<
r
6.52
X*
r
. X
. X
■ X
BTeflon
ti
oo
Diameter (mm)
(b)
Fig. B4
The means and the standard deviations of (a) the e' and (b) the e" of the
cylindrical ftuit “tissues” at varying diameters at a frequency of 1.27 GHz.
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213
f = 3.22 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
□ Carrot
□ Cantaloupe
to 40
E3 Potato
20
H Teflon
0
1.67
2.39
3.19
4.05
4.76
5.64
6.52
°o
Diameter (mm)
(a)
f = 3.22 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
□ Carrot
□ Cantaloupe
40
0 Potato
20
H Teflon
0
1.67
2.39
3.19
4.05
4.76
5.64
6.52
oo
Diameter (mm)
(b)
Fig. B5
The means and the standard deviations of (a) the s' and (b) the s" of the
cylindrical fruit “tissues” at varying diameters at a frequency of 3.22 GHz.
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214
f = 8 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
0 Carrot
□ Cantaloupe
W 40
0 Potato
20
H Teflon
0
1.67
2.39
3.19
4.05
4.76
5.64
6.52
°o
Diameter (mm)
(a)
f = 8 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
0 Carrot
□ Cantaloupe
=w 40
X
M Potato
X
X
a Teflon
X
20
x
0
1.67
2.39
3.19
4.05
4.76
5.64
6.52
oo
Diameter (mm)
(b)
Fig. B6
The means and the standard deviations of (a) the s' and (b) the e" of the
cylindrical fruit “tissues” at varying diameters at a frequency of 8 GHz.
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215
f= 18 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
H Carrot
□ Cantaloupe
“w 40
0 Potato
X
20
X
X
X
53 Teflon
X
0
1.67
2.39
3.19
4.05
4.76
5.64
6.52
Diameter (mm)
(a)
f= 18 GHz, 23°C, Y-error bar = 1 StDev
80
□ Apple
60
□ Carrot
□ Cantaloupe
40
0 Potato
20
S3 Teflon
1.67
2.39
3.19
4.05
4.76
5.64
6.52
00
Diameter (mm)
(b)
Fig. B7
The means and the standard deviations of (a) the s' and (b) the s" o f the
cylindrical fruit “tissues” at varying diameters at a frequency of 18 GHz.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
216
Alfalfa stems (42% me, 23 °C)
GHz
0.3
50
0.48
40
1.27
30
3.22
20 H
8
CO
'8 8
I* s S
*
10-j
AAA
Log. (0.3)
xx*
Log. (0.48)
0 41
1.5
2
2.5
3.5
Log. (1.27)
Log. (3.22)
Diameters (mm)
Log. (8)
(a)
Alfalfa stems (42% me, 23°C)
50
GHz
* 0.3
40
« 0.48
30
a
20
10
1.27
> 3.22
X8
88
0
1
1.5
2
2.5
3
3.5
Diameter (mm)
(b)
Fig. B8 The (a) s' and (b) s" of the stems vs. diameter at moisture content of 42% and at
23°C.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
217
Alfalfa stems (51% me, 23°C)
GHz
0.3
25
A «
AA o
o#
0.48
&A‘ *
** *
3.22
A A
20
aa
15
A A
10
* X
1.27
8
5
Log. (0.3)
0
Log. (0.48)
1.5
2
2.5
3
Log. (1.27)
3.5
Log. (3.22)
Diameter (mm)
Log. (8)
(a)
Alfalfa stems (51% me, 23 °C)
50
GHz
o 0.3
40
D 0.48
30
a
20
* 3.22
$0
10
1.27
*8
t
$
0
1.5
2
2.5
3
3.5
Diameter (mm)
(b)
Fig. B9 The (a) s' and (b) s" of the stems vs. diameter at moisture contents of 51% and
at 23°C.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
218
Alfalfa stems (62% mc,23°C)
GHz
0.3
50 j
0.48
40 j
1.27
30 i
3.22
20
*
x*%** *
8
Log. (0.3)
10
Log. (0.48)
0
1
1.5
2
2.5
3
Log. (1.27)
3.5
Log. (3.22)
Diameters (mm)
Log. (8)
(a)
Alfalfa stems (62% mc,23°C)
50
GHz
o 0.3
40
c 0.48
30
* 1.27
CO
20
* 3.22
x8
* I
10
0
1.5
2
2.5
3
3.5
Diameter (mm)
(b)
Fig. B10 The (a) s' and (b) e" of the stems vs. diameter at moisture contents of 62% and
at 23°C.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
219
Alfalfa stems (71% mc,23°C)
GHz
0.3
50
0.48
40
1.27
30
a o1
$
%'
f"
20
3.22
8
10
Log. (0.3)
0
Log (0.48)
1.5
2
2.5
3
3.5
Log (1.27)
4
Log (3.22)
Diameters (mm)
Log (8)
(a)
Alfalfa stems (71% mc,23°C) 50
40
GHz
♦ 0.3
30
n 0.48
*
Oa
a 1.27
»**
3.22
%8
20
I
10
*
0
1.5
2
2.5
3
3.5
Diameter (mm)
(b)
Fig. B11 The (a) s' and (b) s" of the stems vs. diameter at moisture contents of 71% and
at 23°C.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
220
Alfalfa stem (42% me, 23 °C)
Y- error bar = + /- 1 StDev
50
40
30
20
10
0
4
6
10
Frequency (GHz)
(a)
Alfalfa stems (42% me, 23°C)
Y-error bar = +/- 1 StDev
50
40
30
CO
20
10
^^^yba&n»YVMWi*«fw^irjryrM
iw>iM
'M
m
rtwmrri«»rt>0i%
.ODCa^OPCPCO<3OflPQflOOOaftffM
Bflft«ttiaBq
0 -t
0
4
6
10
Frequency (GHz)
(b)
Fig. B12
The spectra for (a) the corrected mean e' and (b) the mean s" of the alfalfa
stems at a moisture content of 42% and at 23°C along with the standard deviation at each
of the 88 frequencies.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
221
Alfalfa stem (51 % me, 23°C)
Y- error bar = +/- 1 StDev
50
40
30
CO
20
10
0
4
6
8
10
Frequency (GHz)
(a)
Alfalfa stems (51% mc,23°C)
Y-error bar = +/- 1 StDev
50 i
40
s
CO
30
20
0
"I- - - - - - - - - - - - - - - - - - - - - -
I......................
0
2
—
r
----------------- r ------------------------ r ------------------------
4
6
8
10
Frequency (GHz)
(b)
Fig. B13
The spectra for (a) the corrected mean s' and (b) the mean s" of the alfalfa
stems at a moisture content of 51%and at 23°C along with the standard deviation at each
of the 88 frequencies.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
222
Alfalfa stem (62% mc,23°C)
Y- error bar = +/- 1 StDev
50 :
0
I ------------------------- ,---------------------- r --------------------- n--------------------------n----------------------■
0
2
4
6
8
10
Frequency (GFIz)
(a)
Alfalfa stems (62% mc,23°C)
Y-error bar = +/- 1 StDev
50
40
w
30
0 ----------------1-------------- 1---------------- i--------------- 1------------0
2
4
6
8
.
10
Frequency (GHz)
(b)
Fig. B14
The spectra for (a) The corrected mean e' and (b) the mean e" of the alfalfa
stems at a moisture content of 62%and at 23°C along with the standard deviation at each
of the 88 frequencies.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
223
Alfalfa stem (71 % me, 23°C) >
Y- error bar = +/- 1 StDev
40
30
CO
20 -
0
2
4
6
8
10
Frequency (GHz)
(a)
Alfalfa stems (71% mc,23°C)
Y-error bar = +/- 1 StDev
0 “I---------------r...
0
2
i
4
T
6
8
i
10
Frequency (GHz)
(b)
Fig. B15
The spectra for (a) The corrected mean e' and (b) the mean s" of the alfalfa
stems at a moisture content of 71%and at 23°C along with the standard deviation at each
of the 88 frequencies.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited without perm ission.
224
Alfalfa stem (79% me, 23 °C)
Y- error bar = +/- 1 StDev
50 i
CO
20 10 -i
i
0
2
4
6
8
10
Frequency (GHz)
(a)
Alfalfa stems (79% mc,23°C)
Y-error bar = +/- 1 StDev
50
1
40 I o
30
-i
......
i
-I
■■©
■■■©....
lMMy-
Qa° ^ tocOfl^®OO<tocOOOOOOflOQOCOflOOOOO«OOpC0flO<»flOO»tfWOO6OO<»aooflocoOOOOOOefl0000
20
10
0
0
2
4
6
8
10
Frequency (GHz)
(b)
Fig. B16
The spectra for (a) The corrected mean e' and (b) the mean s" of the alfalfa
stems at a moisture content of 79%and at 23°C along with the standard deviation at each
of the 88 frequencies.
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
225
Table B1
The means and the standard errors for the variability in measuring the s' of
the alfalfa leaves at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
1.72
2.56
1.52
0.11
0.13
5.35
4.59
0.46
0.40
21.87 0.76
17.67 0.54
44.05 0.90
35.65 0.71
1.50
1.48
1.39
1.39
1.47
1.43
1.37
1.40
1.35
0.13
0.12
0.12
0.13
0.13
0.12
4.53
4.41
4.23
4.25
4.33
4.17
16.60 0.47
15.94 0.44
15.42 0.41
15.20 0.37
14.96 0.36
14.30 0.34
1.26
1.25
1.26
1.19
1.22
0.11
0.11
0.11
0.11
0.10
4.08
4.07
3.95
3.86
3.80
3.79
3.79
3.72
3.67
33.30
31.80
30.68
29.66
28.85
27.73
26.41
1.33
0.12
0.11
0.11
0.11
0.37
0.34
0.33
0.32
0.30
0.29
0.28
0.26
0.26
11.85 0.48
9.85 0.33
9.29 0.29
8.82 0.26
8.46 0.23
8.46 0.22
8.44 0.21
7.87 0.19
7.57 0.17
7.29 0.17
7.17 0.15
0.25
0.25
0.24
0.23
0.22
0.22
6.91
6.56
6.42
6.44
6.24
6.05
0.15
0.14
0.14
0.12
1.28
1.31
1.36
1.34
1.28
1.23
1.11
1.23
1.20
0.10
0.10
0.10
0.10
0.11
0.11
0.10
0.07
0.11
3.69
3.64
3.70
3.72
3.66
3.54
3.53
3.61
3.62
0.22
0.20
0.19
6.09
5.96
5.78
0.23
0.21
0.21
0.21
0.21
0.21
5.90
5.92
5.65
5.46
5.45
5.41
0.14
0.13
0.13
0.13
0.13
0.13
0.13
0.12
0.11
2.42
3.13
3.84
4.55
5.26
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
16.58
17.29
18.00
0.12
0.14
13.85
13.34
12.92
12.43
11.79
11.52
11.45
11.20
11.01
11.04
10.77
10.49
10.60
10.54
10.13
9.82
9.71
9.67
0.33
0.31
0.30
0.29
0.27
0.25
0.25
0.25
0.26
0.27
0.27
0.28
0.27
0.27
0.28
0.28
0.27
0.28
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
0.68
0.67
0.67
0.66
0.67
0.65
0.65
25.24 0.66
24.21 0.65
23.04 0.67
22.05 0.60
21.44 0.60
20.78
20.20
20.05
19.77
19.06
18.51
18.10
17.61
17.21
16.87
16.55
15.76
0.60
0.58
0.57
0.57
0.57
0.56
0.52
0.50
0.49
0.48
0.40
0.43
226
Table B2
The means and the standard errors for the variability in measuring the s" of
the alfalfa leaves at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
1.72
2.42
3.13
3.84
-0.49
-0.22
-0.11
-0.02
0.00
-0.01
0.01
0.08
0.11
0.02
0.03
0.02
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.33
0.34
0.49
0.65
0.69
0.69
0.76
0.84
0.81
0.94
4.46
1.98
1.76
2.17
2.36
2.26
2.50
2.63
2.70
2.72
0.81
0.31
0.24
0.23
0.22
0.20
0.19
0.20
0.19
11.42
5.56
4.51
4.56
4.63
4.55
4.80
4.97
5.21
42.19 0.97
18.20 0.43
14.01 0.33
12.88 0.24
12.60 0.25
12.34 0.23
12.67 0.22
13.13 0.24
0.02
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.81
0.86
0.81
0.79
0.18
0.17
0.17
0.16
0.16
0.16
0.15
0.13
0.14
0.14
0.13
0.12
0.12
0.11
0.11
0.11
0.12
5.36
5.37
5.40
5.24
5.10
5.08
4.95
4.51
4.46
4.81
4.88
4.78
4.84
4.73
4.55
4.58
4.66
1.01
0.73
0.53
0.42
0.39
0.36
0.35
0.36
0.35
0.34
0.32
0.31
0.30
0.30
0.30
0.29
0.27
13.76
13.59
13.09
12.88
12.89
12.75
12.51
12.50
12.40
12.33
12.56
12.70
12.42
12.05
12.15
11.78
4.55
5.26
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
16.58
17.29
18.00
0.13
0.08
0.11
0.11
0.05
0.06
0.06
0.06
0.06
0.07
0.06
0.05
0.01
0.02
0.09
0.09
0.07
0.01
0.01
0.02
0.04
0.10
0.03
0.81
0.81
0.72
0.68
0.70
0.70
0.67
0.61
0.57
0.61
0.62
0.70
0.13
0.12
0.12
0.11
0.11
0.11
0.12
0.11
0.11
0.11
0.11
0.10
0.10
0.11
0.10
0.10
0.09
0.09
0.09
0.08
0.07
0.07
0.07
0.07
0.08
0.07
2.71
2.74
2.68
2.61
2.68
2.62
2.28
2.24
2.53
2.57
2.42
2.43
2.39
2.28
2.30
2.39
0.27
0.29
0.27
0.26
0.25
0.25
0.25
0.25
0.26
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
13.64 0.25
13.74 0.28
0.31
0.32
0.33
0.35
0.42
0.43
0.40
0.43
0.50
0.51
0.51
0.53
0.56
0.58
0.59
0.59
227
Table B3 The means and the standard errors for the repeatability in measuring the s' of
the alfalfa leaves at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
1.72
2.57
1.86
1.84
2.42
3.13
3.84
1.81
1.72
1.72
3.95
3.35
3.15
3.05
2.94
2.84
0.25
0.20
0.19
0.18
0.17
12.44
9.78
9.14
8.87
8.55
4.55
5.26
1.80
0.17
0.17
0.15
0.14
0.14
0.13
0.13
0.12
0.12
0.13
0.12
0.11
0.12
8.19
7.94
22.15 0.67
18.00 0.54
16.92 0.51
16.18 0.51
15.63 0.50
15.50 0.50
15.38 0.50
45.39 0.53
36.11 0.46
33.82 0.45
32.29 0.48
31.28 0.50
30.64 0.58
29.84 0.62
14.57
13.98
13.40
13.11
12.60
11.95
11.72
11.74
11.44
11.18
11.20
10.92
10.60
10.76
10.70
10.24
0.50
0.50
0.49
0.49
0.49
0.47
0.45
0.45
0.46
0.45
28.48
27.19
26.10
25.14
23.97
22.87
22.34
21.74
21.04
20.87
9.96
9.89
9.81
0.49
0.50
0.54
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
16.58
17.29
18.00
1.75
1.68
1.67
1.65
1.59
1.56
1.52
1.53
1.47
1.50
1.53
1.55
1.58
1.59
1.52
1.44
1.44
1.51
1.51
0.27
0.32
0.27
0.26
0.26
0.23
0.19
0.21
0.22
0.19
0.20
0.20
0.21
0.20
0.17
0.19
0.20
0.19
0.15
0.15
0.17
0.18
0.20
0.21
0.18
0.18
2.78
2.73
2.71
2.59
2.58
2.55
2.48
2.43
2.35
2.35
2.42
2.38
2.26
2.24
2.32
2.33
2.32
2.34
2.34
2.35
7.74
7.53
7.29
6.98
6.78
6.65
6.41
6.18
5.98
5.80
5.74
0.12
0.12
0.11
0.11
0.10
5.79
5.77
5.71
0.09
0.10
0.12
5.42
5.70
5.58
5.39
5.33
0.68
0.51
0.45
0.41
0.38
0.36
0.35
0.32
0.29
0.27
0.26
0.24
0.23
0.21
0.21
0.20
0.19
0.18
0.17
0.16
0.16
0.17
0.16
0.16
0.16
0.16
0.47
0.46
0.46
0.47
0.49
0.49
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
0.64
0.66
0.65
0.67
0.69
0.67
0.66
0.68
0.67
0.70
20.57 0.71
19.64 0.68
18.99 0.66
18.74 0.68
18.24 0.70
17.62 0.68
17.15 0.66
16.97 0.65
16.21 0.66
228
Table B4 The means and the standard errors for the repeatability in measuring the e" of
the alfalfa leaves at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
1.72
2.42
3.13
3.84
-0.35 0.19
-0.11 0.21
-0.01 0.17
0.07 0.11
0.10 0.08
0.09 0.11
0.11 0.11
0.19 0.08
0.20 0.07
0.23 0.07
0.17 0.08
0.21 0.06
0.51
0.73
0.67
5.12
3.47
2.94
0.66
0.28
0.23
0.22
0.22
0.21
11.61
5.13
4.22
4.54
4.72
4.57
1.54
0.50
0.34
0.21
0.22
0.20
0.20
0.19
0.19
0.19
0.18
0.17
4.85
5.18
5.41
5.46
5.40
0.21
0.20
0.18
0.19
0.18
0.19
0.17
0.17
0.16
0.17
0.16
0.16
0.17
0.16
0.14
0.15
0.14
5.16
4.68
4.65
5.13
5.15
36.29
16.31
12.89
12.20
12.09
12.13
12.77
13.22
13.71
13.86
13.98
13.87
13.39
13.30
13.59
13.49
13.09
0.13
0.12
0.13
0.12
0.12
0.12
4.96
5.02
4.91
4.73
4.80
4.75
0.17
0.17
0.18
0.18
0.19
0.20
4.55
5.26
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
16.58
17.29
18.00
0.53
0.50
0.59
0.61
0.59
0.54
0.59
0.54
0.22
0.15
0.16
0.07
0.08
0.08
0.53
0.53
0.54
0.55
0.15
0.14
0.14
0.15
0.14
0.14
0.12
0.09
0.12
0.12
0.19
0.06
0.06
0.06
0.04
0.03
0.48
0.46
0.46
0.42
0.38
0.05
0.05
0.05
0.04
0.37
0.35
0.33
0.35
0.36
0.36
0.06
0.08
0.08
0.10
0.08
0.06
0.06
0.06
0.05
0.06
0.06
0.06
0.06
0.06
0.06
0.05
0.05
0.05
0.04
0.04
0.07
0.06
0.04
0.04
0.05
0.05
0.05
0.05
2.60
2.53
2.65
2.72
2.78
2.86
2.96
2.98
3.02
3.01
2.92
2.71
2.65
2.62
2.50
2.43
2.42
2.33
2.34
2.48
2.50
2.42
2.53
5.47
5.33
5.19
5.24
0.28
0.26
0.22
0.16
0.16
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1.44
0.54
0.38
0.26
0.22
0.23
0.23
0.24
0.27
0.31
0.30
0.32
0.34
0.38
0.47
0.48
0.42
13.17 0.44
13.33 0.53
13.25 0.55
13.35 0.54
13.53 0.56
13.25 0.56
12.91 0.56
12.90 0.59
12.68 0.60
229
Table B5
The means and the standard errors of the s' obtained by measuring the
samples of alfalfa leaves at four orientations separated by 45° and at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
1.72
2.42
3.13
3.84
4.55
5.26
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
2.38
1.75
1.77
1.74
1.68
1.71
1.79
1.73
1.67
1.78
1.62
1.61
0.07
0.09
0.09
0.08
0.08
0.08
4.56
4.11
0.14
0.12
3.89
3.77
3.65
3.52
3.44
3.39
3.36
3.19
3.18
0.11
0.11
0.11
0.08
10.98
8.60
8.11
7.90
7.58
7.26
1.30
1.00
0.92
0.87
0.85
0.83
1.56
1.58
5.63
0.08
1.65
1.65
1.54
1.56
1.61
1.65
1.62
1.57
1.48
0.07
0.07
0.06
0.06
0.07
0.07
0.06
0.07
0.07
0.07
0.07
21.65 0.57
17.82 0.45
16.78 0.41
16.21 0.34
15.71 0.31
15.33 0.34
15.08 0.34
14.57 0.26
14.12 0.23
13.60 0.21
13.20 0.21
12.72 0.19
12.12 0.17
44.43
35.68
33.33
31.67
30.56
29.86
28.91
27.51
26.18
25.06
24.09
6.01
5.84
0.25
0.19
0.17
0.15
0.14
0.15
0.15
0.13
0.12
0.11
0.11
0.10
0.09
16.58
17.29
18.00
1.51
1.53
1.48
0.06
0.13
0.04
5.45
5.32
5.11
5.06
5.09
5.14
5.12
5.04
4.88
4.80
4.80
4.78
0.08
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.06
0.06
0.06
0.06
11.79 0.18
11.67 0.19
11.49 0.16
11.33 0.14
11.35 0.14
11.09 0.13
10.87 0.13
10.99 0.13
10.99 0.13
10.66 0.13
10.33 0.14
10.19 0.14
10.13 0.07
16.29
15.90
15.78
15.10
0.31
0.29
0.30
0.26
0.08
0.08
0.08
0.07
0.08
0.07
3.11
3.08
3.00
2.90
2.91
2.96
2.87
2.78
2.83
2.90
2.88
2.86
2.88
2.86
2.76
0.07
0.09
0.10
0.09
0.08
0.08
0.09
0.07
0.06
0.06
0.08
0.06
0.06
0.08
0.08
0.08
0.09
0.09
0.08
0.14
7.08
6.93
6.74
6.60
6.20
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0.77
0.74
0.70
0.66
0.62
22.87 0.58
21.72 0.55
21.20 0.52
20.61 0.49
19.85 0.46
19.63 0.44
19.28 0.41
18.30 0.38
17.65 0.37
17.47 0.35
17.01 0.32
230
Table B6
The means and the standard errors of the s" obtained by measuring the
samples of alfalfa leaves at four orientations separated by 45° and at 23°C.
Moisture content (%, w.b.)
10
24
41
54
75
f (GHz)
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
Mean StdEr
0.30
1.01
-0.45
-0.21
0.03
0.03
-0.12 0.03
0.02 0.02
0.07 0.01
0.03 0.02
0.03 0.02
0.10 0.02
0.10 0.02
0.64
0.90
0.83
0.69
0.66
0.76
0.80
0.77
0.73
0.11
0.19
0.15
0.06
0.04
4.05
2.88
2.46
2.18
2.12
2.24
2.31
2.35
2.40
0.15
0.10
0.08
0.07
0.07
0.07
0.07
0.07
0.08
10.80
5.62
4.59
4.42
4.46
4.47
4.67
4.84
5.07
0.25
0.15
0.15
0.01
0.01
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.76
0.74
0.72
0.70
0.73
0.72
0.65
0.63
0.63
0.50
0.49
0.53
0.04
2.56
2.54
2.54
2.54
2.44
2.31
2.26
2.20
2.04
0.07
0.07
0.08
0.08
0.08
0.08
0.07
0.06
0.06
0.06
0.06
0.06
5.19
5.21
5.25
5.04
4.89
4.87
4.74
4.31
4.16
4.40
4.50
4.47
0.19
0.19
0.20
0.21
0.17
0.19
0.24
0.21
0.17
0.01
0.01
0.06
0.06
0.01
0.49
0.47
0.50
0.54
0.05
0.05
4.51
4.38
4.21
4.28
4.22
0.16
0.16
0.15
0.14
0.24
1.72
2.42
3.13
3.84
4.55
5.26
5.96
6.67
7.38
8.09
8.80
9.50
10.21
10.92
11.63
12.34
13.04
13.75
14.46
15.17
15.88
16.58
17.29
18.00
0.15
0.13
0.10
0.12
0.14
0.11
0.17
0.18
0.09
0.05
0.09
0.22
0.24
0.13
0.51
0.06
0.05
0.03
0.04
0.05
0.04
0.03
0.03
0.03
0.02
0.04
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.04
2.00
1.96
1.89
1.88
1.97
2.03
1.97
2.08
0.05
0.06
0.06
0.86
0.19
0.15
0.21
0.24
0.20
0.22
0.24
0.22
0.22
0.20
0.20
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38.37 1.61
16.78 1.11
13.15
12.47
12.35
12.39
12.94
13.27
13.76
13.94
14.01
13.87
13.39
13.32
13.66
13.48
12.98
13.09
13.30
13.13
0.77
0.64
0.59
0.58
0.59
0.57
0.57
0.57
0.58
0.59
0.56
0.56
0.55
0.55
0.54
0.55
0.54
0.52
13.09 0.51
13.20 0.51
12.92 0.51
12.56 0.49
12.65 0.49
12.39 0.48
231
Table B7
The means and the standard deviations for the measured diameters (mm) -
runl to run 3 of the alfalfa stems at varying moisture contents and at 23°C.
Stem no.
1
2
3
Run 1
Run 2
Run 3
1.57
1.53
1.53
1.88
1.82
1.93
Mean
1.54
1.63
1.57
1.5
1.57
StDev
0.02
0.07
Run 1
Run 2
Run 3
1.79
1.58
1.74
1.64
1.82
1.72
Mean
StDev
1.70
0.11
Run 1
Run 2
Run 3
Mean
StDev
Run 1
Run 2
Run 3
Mean
7
79%
8
9
10
2.85
2.98
2.87
3.24
3.3
3.22
3.3
3.34
3.81
3.85
3.63
3.64
2.90
0.13 0.08 0.16 0.07
Moisture icontent = 71%
3.25
3.48
0.04
0.28
3.71
0.12
2.32
2.23
2.38
1.73
0.09
2.09
2.15
2.02
2.09
0.07
2.67 2.75
2.6
2.76
2.63 2.72
2.31 2.63 2.74
0.08 0.04 0.02
Moisture icontent =
2.8
2.83
2.88
2.84
0.04
62%
2.9
3.21
2.83
2.98
0.20
3.37
3.32
3.36
3.35
0.03
3.97
3.76
3.86
3.86
0.11
1.96
1.98
1.95
1.94
0.02
2.06
1.99
2.03
2.03
0.04
2.17
2.16
2.01
2.11
0.09
2.14 2.34
2.2
2.21 2.29 2.32
2.08 2.27 2.29
2.16 2.23 2.32
0.07 0.08 0.03
Moisture content =
2.57
2.48
2.55
2.53
0.05
51%
2.64
2.82
2.65
2.70
0.10
2.89
2.61
2.67
2.72
3.32
3.26
3.29
3.29
0.15
0.03
1.74
1.65
1.88
1.76
0.12
2.33
2.26
2.28
2.29
0.04
2.53
2.41
2.31
2.42
2.8
2.77
2.91
2.83
2.96
2.71
2.92
2.86
2.96
2.84
StDev
1.24
1.28
1.31
1.28
0.04
0.13
Run 1
Run 2
Run 3
Mean
StDev
1.69
1.7
1.64
1.68
0.03
1.89
1.84
1.78
1.84
2.17
2.18
2.25
2.20
0.04
0.11 0.18 0.10 0.07
Moisture content = 42%
2.34 2.6
2.66 2.71
2.55 2.62 2.52 2.89
2.39 2.6
2.67 2.88
2.43 2.61 2.62 2.83
0.11 0.01 0.08 0.10
2.86
2.89
0.06
2.95
2.85
3.47
3.09
0.33
2.98
3.09
2.97
3.01
0.07
3.14
2.99
3.15
3.09
0.09
0.06
1.88
0.06
5
6
Moisture content =
2.28 2.47 2.97
2.24 2.63 2.69
2.49 2.54 2.7
2.34 2.55 2.79
4
2.64
2.55
2.9
2.70
2.6
2.76
2.78
2.71
3.24
2.42
3.22
2.96
0.47
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APPENDIX C
Figures:
Cl - C9
Derivations:
C l -C5
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233
Fig. Cl A photograph of a Nitrogen multipycnometer.
NaCl solution (f = 1 GHz, T = 22°C)
150
100
y = 2.541x+ 12.789
50
r2 = 0.99
0
10
20
30
40
50
60
Salinity(ppt)
Fig. C2
The dielectric loss factor of the Sodium Chloride solution at various salinity
(ppt), and at operating frequency of 1 GHz and at 22°C.
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234
Alfalfa leaf (66% me, 22°C)
40
■Measured
35
Models:
30
Poly
« 25
PL
20
Dc
xX
15
BLD
10
BLN
0
5
10
15
20
BLS
BUD
Frequency (GHz)
(a)
Alfalfa leaf (66% me, 22°C)
50
■Measured
40
Models:
Poly
w
PL
Dc
BLD
0 45*
0
BLN
5
15
10
Frequency (GHz)
20
BLS
BUD
(b)
Fig. C3
Comparison of the measured and the calculated (a) s' and the (b) s" alfalfa
leaves at moisture content of 66%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model)
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235
Alfalfa leaf (58% me,22°C)
31
Measured
27
Models:
23
n Poly
19
» PL
15
* Dc
11
* BLD
7
* BLN
0
5
10
15
20
+ BLS
- BUD
Frequency (GHz)
(a)
Alfalfa leaf (58% me, 22°C)
25
Measured
20
Models:
° Poly
15
A PL
10
* Dc
5
o BLD
0
* BLN
0
5
15
10
Frequency (GHz)
20
+ BLS
- BUD
(b)
Fig. C4
Comparison of the measured and the calculated (a) s' and the (b) e" alfalfa
leaves at moisture content of 58%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model)
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236
Alfalfa leaf (52% me,22°C)
25
Measured
20
Models:
Poly
15
PL
Dc
10
BLD
5
BLN
5
10
15
20
BLS
BUD
Frequency (GHz)
(a)
Alfelfa leaf (52% me,22°C)
20
Measured
15
Models:
Poly
10
PL
Dc
5
BLD
0
BLN
0
5
10
15
Frequency (GHz)
20
BLS
BUD
(b)
Fig. C5
Comparison of the measured and the calculated (a) s' and the (b) s" alfalfa
leaves at moisture content of 52%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model)
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237
Alfalfa leaf (31 % me, 22°C)
15
13
11
9
7
5
3
1
Measured
Models:
° Poly
* PL
x Dc
o BLD
T
5
10
* BLN
20
15
+ BLS
* BUD
Frequency (GHz)
(a)
Alfalfa leaf (31 % me, 22°C)
6
4.
-j.
Measured
4* 4*
-P
+ Hr
Models:
o p0iy
1
-4
10
15
20
& PL
x Dc
o BLD
-9
x BLN
-14
+ BLS
Frequency (GHz)
- BUD
(b)
Fig. C6
Comparison of the measured and the calculated (a) s' and the (b) s" alfalfa
leaves at moisture content of 31%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model)
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238
Alfalfa leaf (23% me, 22°C)
14
Measured
11
Models:
° Poly
w
8
* PL
5
x Dc
o BLD
2
* BLN
0
5
15
10
Frequency (GHz)
20
+ BLS
- BUD
(a)
Alfalfa leaf (23% me, 22°C)
5
Measured
4
Models:
° Poly
3
* PL
w 2
x Dc
1
* BLD
0
* BLN
1
+ BLS
Frequency (GHz)
■ BUD
(b)
Fig. C7
Comparison of the measured and the calculated (a) s' and the (b) s" alfalfa
leaves at moisture content of 23%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model)
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239
Alfalfa leaf (17% me,22°C)
Measured
Models:
n
P o ly
a PL
* X j;
j,
+ + + •*•
$ ¥ *
x Dc
m m & ±
□a o a □ o
*
* BLD
n st v
* BLN
5
10
15
Frequency (GHz)
20
+ BLS
- BUD
(a)
Alfalfa leaf (17% mc,22°C)
5H
Measured
4
Models:
o Poly
A PL
CO
* %
x
Dc
o BLD
* BLN
+ BLS
Frequency (GHz)
- BUD
(b)
Fig. C8
Comparison of the measured and the calculated (a) s' and the (b) e" alfalfa
leaves at moisture content of 17%, and at 20°C. (Poly = Polynomial, PL = Power law
model, DC = Debye-ColeCole model, BLD = Bruggeman lower limit disc model, BLN
= Bruggeman lower limit needle model, BLS = Bruggeman lower limit sphere model,
BUD = Bruggeman upper limit disc model).
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240
Alfalfa leaves (Model: Poly)
300 MHz
50
-to 40
l
300 MHz
BcS 30
M
ca 20
me (%)
X 73%
300 MHz
18 GHz
66%
■ 58%
18 GHz
U 10
18 GHz
0
20
10
40
30
50
Measured e'
(a)
Alfalfa leaves (Model: Poly)
300 MHz
20
300 MHz +
w 15
\
/
me (%)
+ 52%
y
T3
I3
o
"3
U
10
5
18 GHz
18 GHz
18 GHz
300 GHz
■ 31%
18 GHz
0
5
^ 45%
10
15
20
Measured s'
(b)
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241
Alfalfa leaves (Model: Poly)
7
6
W 5
I 4
o 3
U 2
1
0
300 MHz
300 MHz /
300 GHz /
me (7 o
* 23%
18 G1
- 17%
18 GHz
x 12%
18 GHz
"I”
3
2
4
Measured s'
(c)
Fig. C9
A detailed view of the association between measured and calculated s' of
leaves at 22°C produced by polynomials.
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242
C l. Expression for calculating the Mv for the materials those shrink as they dry.
As discussed in the main text the shrinkage in the material is equal to the volume
of the water lost during drying, and hence the absolute volumes of the dry material and
the air are independent of the moisture content, or they remained unchanged.
M
Water wt.
= ----------------------------------------------
Total wt. of the moist material
_
Water wt.
Water wt + Dry material wt.
Water volume
Water volum e+pa(Total volum e-W ater volume)
M„
Mv + P a ( l - M v)
M„
°r,M =
g
(Cl)
Pa
C.2 Expression for calculating the Mv for the materials those do not shrink as they dry.
In this expression it is assumed that the air fdls up the pores and the crevices
once occupied by the water as the material losses water as it dries resulting in the
constant volumes of the dry material and the material as a whole.
Water wt.
M = ----------:----------------------------Total wt. of the moist material
_
Water wt.
Water wt + Dry material wt.
Water volume
Water volum e+pn(Dry material volume without air)
Dividing the numerator and the denominator by the total volume,
M
M g = *------M v+PnW
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(C 2 )
243
where, vv = dry material volume fraction without air.
The dry material wt. at any stage of the moist material consisting of the dry
material, air and water, w is equal to the dry materia wt. at a stage of the material when
it is completely dry consisting of only dry material and the air, Wd, that is,
W = Wd
or, Vv*pn = l*pa
or, pn*vv = pa.
(C3)
Using Eqs. (C2) and (C3),
Mv+Pa
M„Pa
Mv=
(C 4)
1-M „
Unlike the shrinking model there is an upper limit for the Mg that can be used
with this model, and is equal to (l + pa ) _1 = (l + 0.47 ) ” 1 = 0.68 or (6 8 %)
C.3
Derivation of the total volume fraction of the vegetation, vtv in the plant tissues
assuming the shrinking model, i.e.
^
= P a/ „ ( l - M v ).
Derivation:
1Pn
Water volume
Total volume
Pa_
Pn
Total volum e-W ater volume
Total volume
From definition of pa, and p n
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244
Vegetation volume
f Total volum e-W ater volume
Total volum e-W ater volume
Total volume
Vegetation volume
Total volume
= Total volume fraction of vegetarion
0T>V« = P a / n ( l - M v)
C.4
(C5)
Derivation o f the total volume fraction of the vegetation, vtv in the plant tissues
assuming the not shrinking model.
Derivation:
Total vegetation weight = Vegetation volume fraction x pn = Total volume (= unity) x pa
Hence, Vegetation volume fraction = p^ pn for all the moisture contents.
C.5 Estimation o f the Mtg for the leaves and the stems.
At the volumetric threshold moisture content, Mtv, the vtv and the Mv in Eq.
(5.11) can respectively be substituted by 2*Vbw= 2*Mtv and Mtv resulting in
(C 6 )
Substituting the values of pa/n for the leaves and the stems from Table 5.3 in Eq. (C 6 ),
and using Eqs. (5.8) and (5.9), the Mtg for the leaves and the stems were calculated to be
0.2335 and 0.2438 respectively.
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245
APPENDIX D
Figures:
D l-D ll
Tables:
D1-D9
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246
me i ”/o
Particulate alfalfa
73.0%
2.0
67.7%
60.0%
1.5
54.0%
- 51.5%
ft 1-0
0.5
- s • -i I I S 1 I : I
- 44.0%
j i t i t 1 1N 1II 1t 1I 1H 1H
* 38.0%
M S M
I I 8 II I i i I ft > 1
0.0
10
15
x 30.6%
2 0
- 24.4%
<> 19.6%
Frequency (GHz)
■ 11.5%
Fig. D1 The spectrum of the DIF Fi for the particulate alfalfa at 20°C.
me r/o
Particulate alfalfa
73.0%
2.0
67.7%
60.0%
1.5
54.0%
■II ■ ■
III I a I I
MN M
| | | 4 x4 ix M«A N
II ! i
■ 8 » I ■H I I B I ■
I ! ! ■
■> ■
If!:
ft 1.0
0.5
51.5%
44.0%
38.0%
30.6%
0.0
5
10
Frequency (GHz)
15
20
24.4%
19.6%
11.5%
Fig. D2 The spectrum of the DIF F4 for the particulate alfalfa at 20°C.
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247
me (%)
73.0%
Particulate alfalfaa
67.7%
60.0%
54.0%
I 1 I 5 3*1
I f j I If i
S I ! I al lb
0
■
2 *»*
1I
j ll fl
I I
e b ..Sa1
I1
i
I
10
* ■
I 1
1 1
|1 I§
VB
0 -------
15
2 0
- 51.5%
- 44.0%
* 38.0%
x 30.6%
* 24.4%
* 19.6%
Frequency (GHz)
- 11.5%
Fig. D3 The spectrum of the DIF F 5 for the particulate alfalfa at 20°C.
me
Particulate alfalfa
- 73.0%
‘ 67.7%
1.2
60.0%
54.0%
0.8
- 51.5%
M nhm m yj
■i ■ ■ S 1 i ! i
I ■ 1 ■ • ■ • i 1
I I
1 m
1 t 1 ■
g g
X X X
X
X
X
* 44.0%
* 38.0%
X
Hlliiiii
10
Frequency (GHz)
15
X
20
30.6%
* 24.4%
« 19.6%
° 11.5%
Fig. D4 The spectrum of the DIF F 6 for the particulate alfalfa at 20°C.
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248
Operating frequency =6.05 GHz
73.0
67.7
60.0
1.5
-• 54.0
1
- 51.5
- 44.0
0.5
* 38.0
x 30.6
0
0
0.2
0.4
0.6
* 24.4
0.8
* 19.6
Density(g/cc)
Fig. D5
■ 11.5
The behaviour of the function Fi against the density at a frequency
corresponding to minimum SEC, and at 20°C.
me K/0)
73.0
Operating frequency = 10.39 GHz
67.7
60.0
54.0
3
£
2 i
- 51.5
■ 44.0
%U4v" <
WtiKX*
» 38.0
1
x 30.6
0
0.2
0.4
Density(g/cc)
Fig. D6
0.6
0.8
a 24.4
o 19.6
» 11.5
The behaviour of the function F 2 against the density at a frequency
corresponding to minimum SEC, and at 20°C.
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249
me {vo)
73.0
Operating frequency =2.07 GHz
67.7
60.0
6
54.0
4
- 51.5
- 44.0
2
* 38.0
x 30.6
0
0.2
0.4
0.6
* 24.4
0.8
* 19.6
Density(g/cc)
Fig. D7
» 11.5
The behaviour of the function F 3 against the density at a frequency
corresponding to minimum SEC, and at 20°C.
me t /oj
73.0
Operating frequency = 13.04 GHz
67.7
60.0
2
» 54.0
1.5
Hh
- 51.5
1
1
- 44.0
0.5
* 38.0
x 30.6
0
0.2
0.4
0.6
0.8
Density(g/cc)
Fig. D 8
- 24.4
« 19.6
= 11.5
The behaviour of the function F4 against the density at a frequency
corresponding to minimum SEC, and at 20°C.
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250
me r/o)
73.0
Operating frequency =9.06 GHz
67.7
60.0
0.75
- 54.0
0.5
- 51.5
- 44.0
0.25
* 38.0
x 30.6
0
0.2
0.4
0.6
* 24.4
0.8
* 19.6
Density(g/cc)
Fig. D9
- 11.5
The behaviour of the function F 5 against the density at a frequency
corresponding to minimum SEC, and at 20°C.
me
Operating frequency = 9.06 GHz
170
73.0
- 67.7
60.0
1
54.0
0.75
£
- 51.5
0.5
• 44.0
0.25
* 38.0
x 30.6
0
0.2
0.4
0.6
0.8
Density(g/cc)
Fig. D10
* 24.4
♦ 19.6
° 11.5
The behaviour o f the function F6 against the density at a frequency
corresponding to minimum SEC, and at 20°C.
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251
Operating frequency = 6.05 GHz
1.5
1
P-4
0.5
__!
0
20
40
80
60
Moisture content (%, w.b.)
(a)
Operating frequency = 10.39 GHz
.
2
,
I
1
1
1
*
, 0-
- ©'
©
0
20
40
60
Moisture content (%, w.b.)
(b)
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80
252
Operating frequency =2.07 GHz
6
4
i t
2
I
0
40
20
60
80
60
80
Moisture content (%, w.b.)
(c)
Operating frequency = 13.04 GHz
1.5
1
0.5
0
20
40
Moisture content (%, w.b.)
(d)
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253
Operating frequency =9.06 GHz
0.15 0.1 j
0.05
0
0
20
40
60
80
60
80
Moisture content (%, w.b.)
(e)
Operating frequency = 9.06 GHz
1
0.75
£
0.5
0.25
0
20
40
Moisture content (%, w.b.)
(f)
Fig. D ll
The moisture dependence of (a) Fj (b) F2 (c) F 3 (d) F4 (e) F 5 and (f) F 6 at a
frequency corresponding to minimum SEC for the particulate alfalfa at 20°C.
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254
Table D1
The slope, c and the intercept, d, or the magnitude, g, and the power, p, and
the coefficient of determination, r2 for all DIFs.
Freq.
Fi
f2
f3
(GHz)
gxlO'1
P
r2
c
d
r2
0.30
0.57
0.74
0.004
0.008
0.010
1.899
1.687
1.629
0.925
0.991
0.995
0.068
0.264
0.315
0.041
0.035
0.033
1.01
1.27
1.54
1.80
0.010
0.014
1.613
0.971
0.994
0.996
0.992
0.293
0.033
0.031
0.030
0.031
0.936
0.974
0.981
0.971
2.07
2.25
2.51
2.78
3.04
0.013
0.016
0.017
0.013
0.015
0.014
0.014
0.012
0.012
0.017
0.015
1.525
1.484
1.513
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
0.014
0.012
0.011
1.551
1.500
1.483
1.552
1.508
1.530
1.526
1.565
1.570
1.543
1.586
1.600
0.012
0.011
0.010
0.008
0.007
1.581
1.620
1.658
1.721
1.739
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
0.007
0.005
0.007
0.005
0.005
0.005
0.006
0.005
0.004
1.745
1.829
1.749
1.822
1.833
1.851
1.799
1.875
3.31
3.57
3.75
4.02
18.00
1.876
0.994
0.997
0.998
0.996
0.996
0.992
0.994
0.992
0.995
0.995
0.994
0.996
0.996
0.996
0.995
0.995
0.996
0.994
0.989
0.993
0.994
0.994
0.992
0.992
0.986
0.992
0.379
0.413
0.384
0.396
0.419
0.399
0.395
0.398
0.407
0.412
0.395
0.405
0.386
0.365
0.351
0.380
0.350
0.345
0.339
0.273
0.291
0.295
0.260
0.296
0.230
0.229
0.265
0.213
0.215
0.030
0.030
0.031
0.030
0.031
0.031
0.030
0.031
0.031
0.032
0.032
0.033
0.032
0.034
0.034
0.035
0.036
0.037
0.037
0.038
0.037
0.039
0.039
0.038
0.040
0.040
0.979
0.968
0.965
0.967
0.966
0.974
0.972
0.962
0.970
0.978
0.968
0.978
0.985
0.979
0.983
0.978
0.993
0.994
0.994
0.995
gxlO"1
0.001
0.005
0.009
0.010
0.013
0.020
0.021
0.019
0.017
0.020
0.016
0.021
0.021
0.020
0.016
0.020
0.019
0.015
0.011
0.019
0.021
0.011
0.012
0.997
0.994
0.997
0.998
0.996
0.995
0.996
0.992
0.011
0.007
0.007
0.007
0.010
0.013
0.005
0.011
0.004
0.993
0.009
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P
v2
2.535
2.183
2.029
1.974
0.793
0.960
0.976
0.966
0.984
1.907
1.804
1.781
1.806
1.841
1.794
1.848
1.787
1.781
1.795
1.856
1.807
1.819
1.872
1.960
1.829
1.814
1.979
1.961
1.971
2.087
2.091
2.105
2.014
1.946
2.194
1.978
2.227
2.044
0.987
0.989
0.985
0.989
0.989
0.988
0.989
0.990
0.991
0.986
0.988
0.987
0.986
0.985
0.988
0.984
0.982
0.980
0.987
0.981
0.978
0.978
0.983
0.978
0.976
0.977
0.918
0.981
255
Table D1 contd.
Freq.
(GHz)
f4
c
d
f5
r2
gxlO-1
p
f6
r
2
0.30 0.108
0.57 0.203
0.74 0.214
1.01 0.228
1.27 0.251
1.54 0.274
1.80 0.279
2.07 0.268
2.25 0.266
2.51 0.277
2.78 0.241
3.04 0.262
0.020
0.018
0.017
0.907
0.925
0.930
0.001
0.001
0.001
1.774
1.568
1.547
0.016
0.015
0.015
0.015
0.015
0.015
0.015
0.016
0.015
1.419
1.410
0.991
0.991
0.233
0.238
0.251
0.015
0.015
0.016
0.016
0.015
0.017
0.016
0.016
0.001
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.001
0.002
0.002
1.525
1.457
1.402
1.412
1.469
1.401
1.476
1.515
1.446
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
0.917
0.913
0.909
0.918
0.910
0.919
0.906
0.897
0.911
0.932
0.919
0.992
0.988
0.981
0.992
0.989
0.984
0.992
0.988
0.989
0.987
1.447
1.443
1.440
1.531
1.462
1.494
0.991
0.993
0.994
0.994
0.263
0.243
0.234
0.016
0.017
0.018
0.019
0.019
0.019
0.019
0.020
0.020
1.524
1.582
1.629
1.701
1.719
1.760
1.729
1.762
1.750
1.732
1.735
1.908
1.788
0.997
0.997
0.997
0.181
0.188
0.195
0.188
0.189
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.266
0.280
0.242
0.252
0.272
0.166
15.08 0.153
16.05 0.146
17.03 0.120
18.00 0.147
0.021
0.021
0.022
0.021
0.935
0.938
0.940
0.942
0.931
0.935
0.952
0.953
0.971
0.984
0.989
0.985
0.986
0.990
0.988
0.988
0.970
0.980
0.992
0.001
0.001
0.001
0.001
0.001
0.951
0.976
0.993
0.995
0.998
0.997
0.994
0.995
0.996
0.996
0.991
0.994
0.981
0.994
g x lO 1
p
r2
0.004
0.008
0.007
1.807
1.594
0.946
0.977
1.607
0.012
0.011
0.016
1.471
1.478
1.393
1.406
1.405
1.408
1.497
1.448
1.444
0.983
0.988
0.983
0.993
0.015
0.015
0.015
0.011
0.013
0.013
0.014
0.015
0.013
0.014
0.013
0.010
0.011
0.012
0.011
0.008
0.007
0.005
0.006
0.005
0.005
0.006
0.005
0.004
0.005
0.003
0.005
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1.435
1.428
1.443
1.514
0.991
0.988
0.991
0.989
0.985
0.989
0.992
0.991
0.991
0.994
0.994
0.994
1.497
1.487
1.504
1.600
1.630
1.713
1.702
1.757
1.737
1.697
1.733
1.795
1.757
1.862
1.772
0.993
0.996
0.997
0.996
0.997
0.998
0.996
0.994
0.995
0.996
0.997
0.995
0.995
0.983
0.995
1.433
1.406
256
Table D2 The SEC and the SEP for the calibration equations depended upon the DIFs
in predicting the moisture content of the particulate alfalfa at various frequencies and at
20°C.
Freq.
F,
f2
f3
SEC
SEP
SEC
SEP
SEC
SEP
(GHz)
(% me)
(% me)
(% me)
(% me)
(% me))
(% me)
0.3
0.57
0.74
1.01
1.27
1.54
1.8
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18
4.06
2.07
1.67
1.97
1.62
1.56
1.80
1.98
1.56
1.86
1.92
1.91
1.63
1.29
1.50
1.36
1.09
1.09
1.21
0.90
0.79
0.89
1.35
1.11
1.46
1.78
1.50
1.71
1.80
1.67
1.91
2.09
1.86
5.75
3.01
2.53
2.76
2.92
2.64
3.08
3.49
3.17
3.26
3.24
3.39
2.87
2.97
2.92
2.64
2.60
2.51
2.59
2.23
1.79
1.78
2.01
1.73
1.92
2.29
2.04
2.38
2.38
2.24
3.25
3.22
2.67
3.93
2.27
2.27
2.93
2.78
2.90
3.04
3.21
3.05
3.01
3.14
3.07
2.69
2.68
2.75
2.53
2.18
2.24
2.31
1.91
1.50
1.20
0.85
0.87
0.58
0.95
0.81
0.83
1.09
1.07
1.25
1.57
1.04
5.79
3.85
3.73
4.13
3.86
3.84
4.27
4.67
4.21
4.40
4.70
4.53
4.28
3.86
3.81
3.92
3.81
3.51
3.57
3.32
2.75
2.27
2.01
1.84
1.70
1.97
1.54
1.88
1.94
1.80
3.47
2.84
2.12
5.14
3.87
3.17
2.99
2.69
2.50
2.12
2.06
2.41
2.12
2.15
2.06
2.22
2.34
2.41
2.31
2.29
2.36
2.57
2.45
2.85
3.15
3.43
3.01
3.40
3.35
3.43
3.48
3.27
3.43
3.62
3.74
3.42
7.05
5.21
4.68
3.67
3.43
3.19
3.49
3.24
2.88
3.25
2.86
3.24
3.17
3.07
2.95
3.23
3.34
3.29
3.10
3.47
3.79
3.75
3.85
4.05
4.13
4.16
4.16
4.09
4.69
4.15
4.69
4.43
4.45
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257
Table D2 contd.
Freq.
f4
f5
f6
SEC
SEP
SEC
SEP
SEC
SEP
(GHz)
(% me)
(% me)
(% me)
(% me)
(% me)
(% me)
0.3
0.57
0.74
1.01
1.27
1.54
1.8
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18
4.81
4.40
4.10
4.86
5.34
5.01
5.30
5.45
5.04
5.27
5.52
5.00
4.83
4.91
4.83
4.56
4.38
4.42
4.46
3.93
3.39
2.63
1.95
2.05
1.43
1.82
1.23
1.20
1.23
1.40
1.25
1.52
1.37
6.66
5.97
6.78
6.66
6.55
7.40
7.38
7.51
7.10
6.74
7.76
7.22
6.90
7.08
6.87
6.68
6.83
6.09
6.02
5.79
5.05
4.55
3.98
3.61
3.44
3.40
3.19
3.28
2.85
2.97
4.07
3.32
2.66
4.07
2.62
2.29
2.57
2.81
2.76
2.74
3.22
2.83
3.08
3.20
3.15
2.80
2.84
2.68
2.34
2.15
2.17
2.13
1.81
1.27
1.01
1.12
0.75
0.99
1.46
1.15
1.35
1.37
1.15
1.56
2.04
1.37
5.73
3.56
3.54
4.27
4.20
4.33
5.01
4.91
4.79
4.39
4.52
4.78
4.39
4.15
4.20
4.00
4.00
3.54
4.08
3.39
2.64
2.25
2.07
1.91
2.09
2.28
1.86
2.25
2.06
2.06
3.04
2.74
2.35
4.07
2.47
2.12
2.92
2.63
2.75
2.92
3.47
2.93
2.92
3.26
2.92
2.75
2.66
2.53
2.24
2.11
2.16
2.15
1.86
1.35
0.92
0.97
0.81
1.17
1.38
1.11
1.31
1.27
1.29
1.66
1.87
1.40
5.35
3.54
3.56
4.40
4.31
4.25
4.86
5.12
4.69
4.31
4.61
4.48
4.28
4.25
4.62
4.00
4.00
3.62
3.68
3.36
2.64
2.32
2.15
1.92
1.89
2.34
1.91
2.03
2.12
2.03
2.96
2.78
2.36
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258
Table D3
The worst case relative error in percent moisture content, T associated with
the calibration equation obtained using the DIF Fi.
GHz
11.5
19.6 24.4
Moisture content (%, w.b.)
30.6
51.5
38.0
44.0
54.0
0.30
0.57
0.74
1.01
1.27
1.54
23.9
12.2
9.3
59.1
13.2
16.6
29.9
11.7
6.3
25.4
9.1
26.3
16.1
21.4
10.0
32.4
4.0
10.2
21.5
8.0
20.0
4.5
4.1
7.3
7.3
5.8
5.8
6.4
5.8
9.1
6.2
8.8
9.0
22.1
11.4
11.1
9.8
11.3
1.80
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
4.7
9.6
25.3
9.5
16.1
10.6
29.8
4.9
10.9
8.8
4.0
18.1
5.4
25.9
20.1
9.7
6.7
15.6
11.6
9.8
9.4
13.1
9.4
10.5
14.2
11.3
11.9
8.0
9.9
11.8
4.6
7.5
5.6
10.0
7.8
9.2
6.5
10.3
16.0
6.3
4.8
9.1
6.1
6.5
6.1
7.9
3.7
5.7
5.6
5.7
6.1
4.6
4.6
6.1
5.2
5.8
4.8
6.4
4.9
3.7
5.1
5.0
2.3
1.8
18.5
8.1
6.6
17.6
11.0
9.3
8.5
8.2
3.8
6.8
7.6
7.2
7.8
5.0
6.7
4.9
5.6
6.7
5.2
1.6
4.1
3.7
5.9
5.6
2.8
3.0
4.3
4.7
2.8
4.2
3.3
5.2
3.3
2.6
3.0
2.7
3.4
1.1
2.3
1.0
1.2
6.6
6.2
5.6
5.4
6.1
7.4
2.7
3.0
4.6
5.3
7.2
7.7
8.1
7.5
5.4
3.5
5.2
5.1
4.9
4.8
3.8
8.8
4.6
7.6
5.8
4.8
4.1
9.2
7.9
7.2
3.9
3.7
2.6
3.0
5.0
2.7
2.5
1.4
2.9
2.4
0.7
2.0
3.5
5.6
8.0
9.2
7.2
6.5
5.4
4.2
7.2
4.7
4.5
5.0
4.4
21.3
15.1
5.6
3.6
5.7
8.8
8.9
8.3
11.1
10.5
11.8
6.5
9.6
6.7
6.9
5.1
4.4
5.1
3.7
4.1
4.7
3.2
7.7
7.7
7.2
9.4
7.3
8.3
9.7
7.2
9.7
10.1
5.2
13.9
8.8
13.5
7.6
13.1
15.6
7.2
12.3
12.5
18.4
16.8
15.0
11.0
10.4
9.2
8.2
7.5
7.2
8.2
2.5
1.4
3.4
6.0
5.6
8.7
6.2
8.2
4.4
9.5
4.7
7.3
9.4
5.7
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60.0
67.7
73.0
24.3
12.1
7.5
4.0
6.9
7.8
4.8
11.5
6.6
5.2
5.3
12.2
7.7
4.3
9.7
2.7
10.6
15.4
8.3
6.3
14.3
5.9
4.0
9.9
12.0
8.2
9.5
10.0
10.3
6.8
6.0
7.2
4.3
8.2
2.6
3.3
2.6
3.6
3.9
3.3
2.9
2.3
2.4
2.9
4.2
8.4
8.1
6.6
11.8
6.2
5.9
10.7
13.8
14.7
5.0
3.6
5.1
6.0
2.5
1.1
5.0
6.4
2.7
7.0
2.5
7.2
8.9
8.9
7.2
8.0
4.5
5.2
8.1
8.5
6.2
2.1
6.8
3.5
6.4
6.9
6.1
10.8
4.2
4.9
6.9
4.1
4.5
2.1
3.4
4.2
4.8
4.5
6.2
5.0
5.3
7.6
9.6
13.1
4.1
259
Table D4 The worst case relative error in percent moisture content, T associated with
the calibration equation obtained using the DIF F2 .
GHz
0.30
0.57
0.74
1.01
1.27
1.54
1.80
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
11.5
19.6
24.4
21.9
21.6
3.9
7.3
2.7
21.8
4.2
7.2
9.3
48.8
11.6
9.4
42.4
8.8
10.0
9.4
22.6
15.0
26.9
16.6
13.0
11.2
17.7
13.6
6.8
9.1
13.1
9.9
7.7
14.7
18.6
12.9
14.0
8.5
11.3
7.8
7.9
8.5
13.0
15.5
22.8
6.4
17.3
10.4
3.2
12.9
8.7
9.9
10.0
11.1
5.0
11.2
3.3
3.0
3.4
2.7
6.4
6.6
9.6
8.9
7.4
5.0
15.7
16.7
12.5
4.9
12.2
8.7
12.9
6.0
Moisture content (%, w.b.)
51.5
54.0
30.6
38.0
44.0
6.3
3.6
3.1
3.2
4.0
3.7
4.1
3.7
3.2
10.6
2.6
2.3
6.3
7.4
9.3
9.1
9.8
11.9
14.4
18.7
25.0
7.3
6.2
8.2
7.1
10.4
11.3
10.6
10.1
10.6
11.7
11.2
6.6
8.6
13.0
2.8
2.6
2.9
1.8
12.0
7.6
8.7
7.5
8.8
6.9
11.0
8.7
14.6
18.6
17.6
28.0
17.8
11.1
12.3
21.4
3.1
11.6
10.1
2.1
2.2
1.9
7.8
6.5
5.7
9.6
8.9
9.0
9.4
9.0
5.8
3.1
2.9
3.1
3.6
1.5
1.3
2.3
1.0
0.3
0.4
8.3
5.6
7.6
7.4
3.4
13.7
11.3
14.3
13.7
18.8
13.2
13.6
13.9
14.7
7.4
11.0
11.0
11.3
13.8
10.0
11.2
13.5
12.9
11.2
2.3
7.5
5.9
6.7
10.5
5.9
1.8
1.5
3.0
2.5
3.4
2.2
1.2
1.3
0.9
1.0
0.8
1.0
4.2
3.9
3.0
1.8
3.6
2.5
1.5
2.9
2.3
1.7
2.1
2.3
3.1
3.2
2.3
8.8
5.7
5.3
4.8
3.0
1.2
1.8
3.4
1.8
1.0
1.4
1.2
1.9
2.4
1.4
2.4
1.6
16.6
8.5
13.2
12.8
6.2
8.4
6.7
3.2
4.6
3.9
3.2
5.4
2.1
3.6
7.7
3.0
3.5
7.3
7.1
17.8
12.9
15.9
15.9
8.2
13.7
14.6
12.2
6.2
4.3
3.0
3.1
0.8
4.1
3.8
0.6
8.6
3.9
5.0
9.4
5.2
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60.0
67.7
73.0
17.9
2.5
4.2
9.6
13.2
9.3
11.8
8.6
15.4
13.6
8.9
13.5
11.0
14.2
11.9
20.0
12.5
14.5
11.3
12.5
13.0
12.9
3.7
4.6
7.7
15.3
7.6
3.9
8.9
18.8
19.4
10.6
9.5
10.8
8.6
9.1
8.9
17.1
18.1
3.5
19.1
20.6
12.6
12.2
10.9
7.0
6.9
6.2
5.2
12.9
4.6
4.8
4.1
1.9
0.8
1.7
4.5
3.6
4.9
2.7
6.5
10.7
1.9
4.4
8.7
8.8
4.4
3.8
1.7
3.5
1.5
1.2
4.3
3.3
3.6
6.6
2.8
7.9
2.6
2.9
2.8
10.2
6.1
15.9
14.4
12.2
7.5
4.9
5.3
3.1
3.3
1.9
5.9
4.1
5.9
5.8
5.9
4.3
8.0
260
Table D5
The worst case relative error in percent moisture content, 'P associated with
the calibration equation obtained using the DIF F 3 .
GHz
0.30
0.57
0.74
1.01
1.27
1.54
1.80
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
11.5
19.6
24.4
153.0
64.0
16.1
67.5
41.5
25.0
20.1
11.7
9.3
11.4
31.9
21.8
11.4
18.3
18.2
14.0
22.8
22.4
17.2
4.9
10.1
6.4
13.8
25.1
13.8
39.3
16.1
28.8
18.1
17.5
12.7
11.6
13.1
25.8
17.7
13.8
33.0
13.0
13.5
21.0
19.9
22.1
19.2
36.3
24.8
20.8
51.8
45.9
20.1
106.7
14.4
20.8
16.1
19.2
11.7
17.3
15.3
20.1
14.2
20.3
18.6
22.0
12.1
13.7
9.8
14.1
11.4
16.5
17.4
18.6
26.4
16.2
3.9
9.5
8.6
7.1
4.0
7.1
8.2
7.3
10.3
7.0
7.3
6.7
8.4
7.8
4.7
6.5
11.7
13.1
11.4
10.2
13.7
6.7
13.1
8.0
5.4
9.2
10.8
Moisture content (%, w.b.)
30.6
44.0
38.0
51.5
54.0
60.0
67.7
73.0
15.5
9.2
12.0
10.0
14.8
12.6
12.8
13.6
17.1
15.9
11.3
13.9
11.8
12.1
37.9
20.4
10.1
23.5
28.7
15.5
11.6
10.6
18.3
8.9
27.8
12.4
8.8
13.8
20.1
19.0
13.9
13.0
14.4
15.0
13.2
15.4
11.9
9.6
6.3
11.3
11.0
11.0
6.0
12.6
11.7
12.6
8.3
7.3
12.2
9.0
16.7
13.1
15.8
7.4
15.0
5.8
10.3
4.2
8.7
12.3
12.7
12.4
11.6
7.9
8.3
8.2
13.1
13.0
12.6
15.7
12.3
16.0
7.5
4.7
7.8
6.8
10.1
11.9
8.7
7.7
16.1
14.0
16.8
5.0
6.6
16.0
9.8
16.8
14.0
14.4
14.6
15.8
12.5
10.7
12.3
14.5
7.1
16.3
12.8
13.7
12.6
20.6
18.3
15.2
13.7
13.3
5.9
9.2
7.7
11.5
16.9
13.9
14.5
18.1
13.0
13.1
13.3
15.0
10.4
12.5
10.8
13.2
8.1
13.0
11.1
12.8
15.1
13.6
10.6
12.4
11.5
13.5
11.6
10.6
10.3
22.0
11.9
11.5
14.8
4.7
4.9
7.3
6.6
13.8
15.5
10.6
9.9
18.7
19.8
7.5
13.2
7.2
5.8
9.2
9.9
12.6
9.9
8.7
12.1
10.0
12.5
12.5
12.8
10.8
11.6
13.3
14.6
18.3
15.4
14.1
12.9
18.7
15.6
14.7
16.4
11.6
13.5
13.6
11.7
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
13.1
14.3
15.8
8.5
14.0
7.8
8.9
15.3
12.2
8.5
11.4
8.1
15.9
14.6
20.5
10.3
11.5
18.9
21.3
21.4
24.1
11.9
16.2
13.1
18.4
12.1
4.3
12.7
6.3
8.2
3.3
4.7
4.9
5.1
4.2
9.1
3.9
4.8
5.2
5.7
11.0
13.0
14.5
15.9
14.3
12.1
11.1
10.0
13.2
10.4
9.7
10.8
12.2
14.2
13.9
12.2
12.8
12.1
14.7
14.0
16.7
13.5
10.6
16.8
15.4
19.1
19.9
10.8
8.9
8.7
9.9
12.8
13.2
16.9
7.8
13.9
19.9
14.4
15.3
22.9
24.9
15.1
26.2
22.8
25.3
261
Table D 6
The worst case relative error in percent moisture content, ¥ associated with
the calibration equation obtained using the DIF F4.
GHz
11.5
19.6
24.4
0.30
0.57
0.74
1.01
180.6
67.6
66.8
73.7
64.0
23.9
11.7
6.6
12.4
15.4
1.27
1.54
1.80
2.07
2.25
2.51
58.3
14.3
26.0
24.0
7.2
17.9
18.1
7.1
17.4
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
37.3
15.5
23.0
12.1
43.5
31.5
16.1
11.6
22.2
10.5
8.3
22.0
21.2
6.2
13.9
23.7
4.9
11.6
5.6
29.7
23.7
6.0
3.2
6.4
10.0
19.3
7.9
Moisture content (%, w.b.)
30.6
44.0
51.5
54.0
38.0
3.0
7.0
6.7
4.1
5.8
3.9
9.2
19.1
22.9
2.8
18.9
21.8
11.0
15.6
3.1
2.6
6.8
14.6
16.0
16.6
20.1
16.5
15.8
16.4
16.5
16.1
15.2
13.2
19.2
14.2
13.0
3.8
13.1
14.1
13.1
9.3
5.7
4.7
5.0
6.6
11.8
6.2
2.1
6.4
4.5
3.3
6.6
10.7
13.4
6.8
3.8
4.7
3.2
2.7
8.3
1.2
11.1
3.3
3.3
4.1
5.8
5.4
5.9
7.6
6.2
5.8
7.1
5.1
19.8
5.2
9.0
9.2
11.4
9.2
7.4
8.6
5.6
5.9
2.2
5.1
7.4
4.8
5.9
6.4
6.3
5.4
20.6
29.2
20.6
4.4
22.0
16.0
24.0
22.0
20.9
29.0
33.2
9.8
20.4
18.3
9.7
20.7
18.0
20.0
22.6
24.9
22.7
24.7
25.8
27.1
22.3
25.5
26.2
21.1
24.0
16.5
19.8
25.7
34.3
30.1
41.4
43.4
32.8
30.6
29.5
31.4
31.2
29.0
20.5
27.8
19.2
30.6
25.4
28.6
24.3
33.4
20.9
22.8
23.7
27.8
24.9
15.4
32.4
31.0
23.5
22.6
27.1
16.5
13.5
7.2
5.4
4.1
16.6
10.3
11.1
4.2
6.2
24.7
19.3
13.8
4.8
5.3
3.9
5.0
3.3
6.2
6.2
4.9
7.0
4.9
2.1
6.1
1.8
4.2
3.5
4.5
6.7
7.5
5.9
6.4
18.7
16.2
9.8
10.6
4.5
7.3
6.4
1.5
3.7
1.4
2.2
3.8
2.8
4.0
4.2
5.5
10.2
4.6
3.8
5.2
2.4
15.8
15.1
18.3
12.6
15.4
24.8
16.8
15.0
24.6
22.8
15.9
21.4
23.1
18.7
14.6
7.6
15.8
16.2
12.3
4.5
4.2
3.2
4.5
4.4
6.8
4.9
5.0
5.0
4.0
2.6
73.0
16.9
12.1
21.3
28.5
9.5
13.5
11.2
12.3
3.1
8.5
67.7
31.3
27.5
10.5
14.1
3.0
14.9
15.2
17.1
23.2
19.4
17.4
23.4
17.3
8.5
18.1
19.2
16.5
10.0
13.2
16.1
60.0
5.7
4.1
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11.6
22.1
16.8
20.9
21.6
22.9
20.7
21.3
21.0
20.8
15.2
36.9
33.0
33.4
22.0
35.5
33.6
20.1
19.4
32.0
19.7
29.8
32.2
15.9
18.0
17.6
14.7
11.2
28.5
15.2
6.6
19.6
5.8
7.5
3.7
4.3
2.5
2.6
1.5
2.8
4.2
16.7
11.3
11.2
11.5
8.1
6.8
7.7
9.0
7.0
3.1
2.0
6.9
13.0
262
Table D7 The worst case relative error in percent moisture content, T associated with
the calibration equation obtained using the DIF F 5 .
GHz
0.30
0.57
0.74
1.01
1.27
1.54
1.80
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
Moisture content (%, w.b.)
30.6
38.0 44.0
51.5
54.0
6.6
16.3
9.9
27.8
23.1
60.0
67.7
73.0
24.3
15.0
8.4
10.9
6.8
12.1
9.9
4.2
16.2
14.1
5.3
20.4
14.3
9.5
22.9
14.6
8.8
15.8
21.1
21.5
14.6
10.6
11.4
8.8
16.6
13.5
7.9
15.6
18.4
13.0
13.7
15.7
15.3
12.1
11.6
13.0
10.1
10.0
8.5
6.1
12.6
15.0
7.1
12.9
13.2
23.7
24.9
14.6
14.2
13.3
12.3
11.0
12.6
21.8
13.0
10.0
4.5
6.5
0.9
0.6
2.9
5.8
4.3
7.8
10.2
11.7
6.3
3.8
8.9
10.5
8.3
1.3
4.1
1.9
3.5
5.6
5.1
5.1
4.8
4.0
9.7
3.2
4.6
6.0
6.7
4.3
4.3
3.0
7.2
6.0
11.5
19.6
24.4
22.6
52.1
6.2
13.2
43.3
4.2
18.2
5.9
6.9
3.8
3.4
5.6
5.9
9.5
6.5
14.0
9.5
3.0
3.4
3.8
9.3
9.7
15.1
13.4
13.7
14.3
9.0
14.5
10.4
7.6
10.1
8.0
9.3
7.9
7.0
6.5
2.6
1.0
3.0
3.1
3.7
5.9
6.9
10.9
8.7
10.0
9.0
5.5
6.5
7.1
7.5
6.0
4.7
5.0
4.3
3.7
6.9
11.0
14.2
10.2
10.7
9.6
9.0
6.9
6.9
10.2
7.8
8.8
10.7
10.0
3.7
11.5
9.1
6.4
10.4
15.4
3.1
5.7
4.4
7.4
5.2
7.0
9.0
7.3
14.7
8.0
7.2
8.0
7.1
3.9
3.4
4.7
4.4
3.6
2.4
6.5
2.3
5.2
8.8
5.4
1.0
3.6
2.6
2.6
1.4
44.0
15.3
25.9
31.6
15.6
24.6
7.7
25.6
14.3
3.4
5.1
17.9
17.0
19.5
4.0
14.2
13.6
8.9
6.3
16.3
9.0
7.1
20.0
14.0
7.4
36.4
15.4
14.5
28.6
16.1
18.8
17.2
5.4
12.3
13.8
6.2
4.7
2.6
2.8
3.1
1.7
2.3
3.4
3.1
3.8
3.0
4.8
3.9
2.5
1.6
3.1
1.6
1.9
2.2
7.6
5.4
9.7
7.6
8.2
7.1
9.0
9.3
6.8
6.2
4.0
8.6
7.3
2.6
22.3
8.0
13.2
27.3
20.2
12.7
12.2
20.0
15.4
13.8
30.2
19.7
21.1
26.6
22.9
18.2
15.8
16.9
11.7
10.5
6.2
17.9
19.5
16.9
15.4
12.6
5.9
3.2
2.8
2.6
3.2
3.8
4.8
2.9
3.2
3.7
3.2
1.4
1.1
2.9
4.3
2.2
2.9
4.3
6.2
9.9
6.2
3.1
1.5
1.4
3.3
1.5
3.7
4.7
5.3
13.8
11.2
6.9
3.5
4.5
3.3
4.4
2.4
5.2
1.9
9.1
3.8
6.3
6.5
6.8
8.0
7.4
6.1
8.5
4.4
2.3
4.4
3.3
3.0
2.5
5.0
5.6
3.1
3.7
8.6
3.4
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4.0
6.2
10.3
6.0
6.8
4.8
7.9
10.6
6.6
263
Table D8
The worst case relative error in percent moisture content, lP associated with
the calibration equation obtained using the DIF F6.
GHz
0.30
0.57
0.74
1.01
1.27
1.54
1.80
2.07
2.25
2.51
2.78
3.04
3.31
3.57
3.75
4.02
4.28
4.55
4.81
5.08
6.05
7.03
8.09
9.06
10.39
11.01
12.07
13.04
14.02
15.08
16.05
17.03
18.00
11.5
19.6
24.4
15.5
53.0
45.3
17.1
41.0
15.0
5.5
10.1
15.7
24.5
29.6
24.4
12.1
18.6
20.0
42.7
15.5
15.5
17.3
13.3
6.8
12.1
3.2
5.9
6.7
10.3
9.0
8.3
8.9
9.6
2.1
3.6
11.0
9.8
8.4
8.0
9.2
3.4
17.1
8.1
12.9
16.4
3.1
20.9
12.8
10.5
10.0
8.0
8.3
7.6
10.2
12.1
6.2
8.9
7.3
10.8
2.8
5.8
2.2
8.1
9.6
7.5
5.9
15.3
7.1
25.0
9.0
5.0
4.7
11.4
13.0
4.4
7.3
15.1
7.6
19.1
4.0
12.8
22.3
6.9
15.7
10.5
Moisture content (%, w.b.)
30.6
51.5
54.0
38.0
44.0
6.5
3.2
4.2
5.0
3.4
3.7
4.0
3.5
2.4
3.8
3.9
5.3
7.0
5.5
5.6
4.0
3.3
3.2
4.5
2.4
3.3
3.5
3.5
2.8
3.6
3.4
2.1
1.5
3.6
2.6
2.5
2.1
1.9
3.4
3.5
3.1
3.6
3.6
6.7
3.6
4.6
5.6
5.5
1.0
2.3
1.0
2.9
0.5
1.8
1.9
8.4
4.6
2.6
14.7
7.9
5.7
6.0
7.7
10.8
10.6
6.8
8.3
6.2
3.7
8.2
8.4
8.2
9.7
12.1
9.7
9.4
5.5
6.6
8.0
5.8
5.9
3.8
3.0
4.8
2.9
2.6
4.4
3.7
4.0
1.6
3.2
1.6
5.1
2.9
4.0
2.3
4.3
6.7
5.1
5.2
10.0
6.2
5.0
8.7
7.1
5.3
5.2
2.2
1.1
1.3
4.0
5.2
2.2
2.0
4.3
2.8
3.8
2.8
1.6
4.4
4.7
26.9
13.7
7.5
19.6
7.8
14.9
19.7
14.4
15.0
12.0
12.7
9.2
17.4
8.0
12.5
14.4
10.4
11.7
8.7
6.7
5.3
4.2
3.0
5.5
4.5
2.8
2.2
4.6
8.4
3.9
6.7
4.6
8.0
60.0
67.7
73.0
29.1
5.7
7.6
13.7
16.7
19.2
24.1
9.1
6.5
14.1
20.8
22.2.
25.9
12.9
14.9
16.7
16.0
23.4
22.9
18.5
17.8
19.6
14.4
18.2
17.7
15.1
14.3
5.6
11.5
20.8
12.2
13.1
13.6
17.7
8.3
6.0
12.8
5.6
12.8
5.9
14.5
13.7
15.3
23.9
14.7
14.1
3.6
3.3
3.3
4.5
3.9
6.8
2.0
5.8
3.3
5.7
8.8
4.0
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14.8
16.0
14.1
6.9
11.4
14.9
7.8
6.7
6.1
3.7
0.6
1.9
3.6
5.8
5.2
6.5
4.3
3.8
5.8
3.2
11.3
15.5
14.1
20.5
15.3
13.5
16.5
28.9
13.7
13.4
16.6
14.9
11.7
11.6
9.1
10.2
10.0
9.3
10.7
8.0
4.1
1.6
3.9
1.7
3.5
5.7
4.8
5.4
6.0
4.3
9.8
4.7
4.6
12.5
13.3
5.4
11.1
7.2
8.6
10.5
10.6
8.4
8.1
5.7
4.2
7.8
3.0
4.5
8.7
6.9
8.1
9.7
10.9
6.7
264
Table D9 The weights and biases to be used in the ANN that predicts moisture content
of chopped alfalfa’.
wl
w2
bi
-0.0792
0.0191
0.048
-0.0086
-0.0656
-0.7374
-2.354
-0.0390
0.0229
-0.0019
0.0452
-0.0021
0.2994
0.4922
-0.0553
-0.0042
0.0658
0.0211
-0.0679
-0.6224
-2.0654
-0.0252
0.0332
-0.0149
0.0579
0.0152
0.2693
-0.4227
-0.0679
-0.0504
0.0883
0.0400
-0.0434
0.2671
-0.9139
-0.0274
0.0180
0.0187
0.0497
0.0473
-0.0602
-0.0363
0.0820
0.0573
-0.0143
-0.0375
0.0373
-0.0050
0.0206
0.0097
-0.0206
-0.0615
0.0983
0.0135
-0.0358
-0.0163
0.0262
0.0269
0.0725
0.0146
0.0026
-0.0090
0.0643
0.0247
-0.0154
-0.0317
0.0230
0.0127
0.0467
0.0034
-0.0183
0.0038
0.0954
-0.034
0.0279
-0.0122
-0.0273
-0.0237
0.0432
0.0079
0.0112
-0.0391
0.1154
-0.0255
0.0371
-0.0403
-0.0013
-0.0098
0.0467
0.0326
-0.0280
0.0024
0.0824
-0.0584
-0.0251
-0.0498
0.0180
0.0026
0.0580
0.0438
0.0000
0.0412
0.1256
0.0375
0.0131
-0.0231
0.0508
0.0047
0.0208
0.0103
b2
! First column of wl represents the weights connecting 20 inputs, from top to bottom, to
the first neuron of hidden layer; second column of w l represents the weights connecting
20 inputs to the second neuron of hidden layer, and so on; w2 represents the weights
connecting five hidden neurons to an output neuron; b l and b2 represent biases for the
hidden and output neuron.
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