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Complex antenna pattern measurements using infrared imaging and microwave holography

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Complex Antenna P attern M easurem ents
using
Infrared Imaging and Microwave Holography
by
John E. Will
B.A., Physics, State University of New York a t Geneseo, 1983
B.S.E.E., Clarkson College of Technology, 1983
M.S.E.E., Syracuse University, 1990
A Thesis subm itted to the
Faculty of the Graduate School of the
University of Colorado in p artial fulfillment
of the requirem ents for the degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
1996
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UMI Number: 9623704
Copyright 1996 by
Will, John E.
All rights reserved.
UMI Microform 9623704
Copyright 1996, by UMI Company. All rights reserved.
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© Copyright by John E. Will 1996
All Rights Reserved
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i
This Dissertation for the Doctor of Philosophy degree by
John E. Will
has been approved for the
Departm ent of
Electrical and Computer Engineering
by
/
/ J /'Z r z .^
John D. Nor^ard
Ronald M. Sega
/
M ark Robinson
MaVek Grabowski
Alan Mickelson
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Will, John E. (Ph.D., Electrical and Computer Engineering)
Complex A ntenna P attern M easurem ents using Infrared Imaging and
Microwave Holography
Thesis directed by Professor John D. Norgard
Infrared (IR) thermographic m easurem ents of microwave fields have
been previously developed for the purpose of mapping radiating field
intensity patterns and for mapping surface currents induced in conductors by
radiating fields. A single therm al image provides a rapid m easurem ent of
the field m agnitude over a surface, with the effective num ber of probe
locations lim ited only by the pixel resolution of the imaging camera. This
thesis research focused on investigating some methods of also determ in in gthe relative phase of the field by thermographic measurements.
One method of determining the relative phase of the field a t each
thermographic pixel location is a “Plane-to-Plane” (PTP) Fourier iterative
technique. Field m agnitude m easurem ents are made over two planes, both
in the radiating near-field of the antenna under test, and separated by only a
few wavelengths.
Starting with an estim ate of the field phase, Fourier
processing techniques are used to iteratively “propagate” between the planes
to determine the unique phase distribution a t each plane.
The PTP
processing technique is described and comparisons are then made between
the sim ulated results and results from m easured IR thermograms of the field
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of a 36 element patch array antenna operating at 4 GHz using the UCCS
Therm al Camera. Agreement between the simulations and m easured data
results is very good, with the simulations indicating th a t a therm al
m easurem ent dynamic range of about 30 dB is necessary to accurately
reconstruct the field phase information.
A second, completely independent, method related to classical optical
holography is also described. This holographic technique uses the known
m agnitude and phase of a second, reference source, field to back out the
m agnitude and phase of the desired field from the interference patterns
between the fields. Simulation results of this technique are shown which
indicate excellent phase reconstruction from thermographic measurements
having only a 20 dB dynamic range, given well known reference field data.
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ACKNOWLEDGMENTS
There are several individuals th a t I wish to thank for their support
during this thesis research. Foremost of these is my wife, Barbara, and my
sons David and Daniel (10 and 8). Barbara h ad to suffer with my gloomy
moods, put up with periodically stressful times, and let prepared dinners go
un-eaten, without truly understanding my joy found in a well-solved
equation or a well-executed subroutine.
My sons were great, constantly
asking if I had "gotten my Doctor yet," wishing me well, offering to help, and
being very empathetic about the stress surrounding each of the various
exams and presentations.
I wish to than k the National Institute of Standards and Technology
(NIST) in Boulder, CO. Their interest and support in my thesis research
topic allowed me to stay focused and committed to my research.
Katie
MacReynolds provided me with desperately needed near-field antenna
calibration data from which I could compare my results with confidence. Dr.
Carl Stubenrauch was my catalyst. We shared and discussed ideas on all
aspects of my research, he cross-checked my codes and proof-read my reports,
and we have become good friends.
I could not have asked for a better
research partner.
I would also like to thank Dr. A.T. Adams, now retired, from Syracuse
University, who was my M aster's thesis advisor and instructor for many of
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my EM classes in my M aster's program a t Syracuse. Because of his support
and enthusiasm towards me, my M aster's program experience was very
enjoyable; thus, encouraging me to continue with a Ph.D.
There is also one individual th a t I wish to th an k th a t I have never
met, Dr. G. Junkin of the University of Sheffield. After seeing a reference to
a paper by Dr. Junkin related to my research, I sent him an email asking for
more information. He responded back w ithin ju st a few hours, attaching a
complete paper (text and figures) to his message. A few days later he sent
some additional related papers of his th a t were about to be published th at
were very helpful in my research. I sincerely appreciate his help, and hope
th a t one day I will be able to m eet him to th an k him in person.
I would also like to th an k my advisor, Dr. John Norgard, for
suggesting this topic and introducing me to the people at NIST. His support
and encouragement throughout my entire Ph.D. program have been very
valuable.
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TABLE OF CONTENTS
CHAPTER 1: INTRODUCTION.................................................................... 1
1.1
E x te n sio n
of
H a rd w ire
T ech n iq u e s
to
T h erm o g ra p h ic
M e a s u re m e n ts ..........................................................................................................2
1.2 S p e c ia l T h erm o g ra p h ic S c r e e n s ................................................................. 4
1.3 H o lo g ra p h ic T e c h n iq u e s................................................................................ 5
CHAPTER 2: IR MAGNITUDE MEASUREMENTS OF RADIATING
FIELDS..............................................................................................................7
2.1 In tro d u c tio n to IR M a g n itu d e M e a s u re m e n ts.........................................7
2.2 T h e rm a l C o n v e c tio n ......................................................................................10
2.3 T h e rm a l C o n d u ctio n .....................................................................................13
2.4 T h e rm a l R a d ia tio n ........................................................................................13
2.5 T h e rm a l P a p e r T em p era tu re fro m In c id e n t F ie ld s.............................14
2.6 UCCS C a m e ra ................................................................................................. 19
CHAPTER 3: MEASUREMENT SETUP AND PROCEDURE................22
3.1 B a sic M ea su re m e n t S e tu p ............................................................................22
3.2 M ea su re m e n t P ro c e d u re ..............................................................................26
3.3 C onversion o f A G A 780 O u tp u t to E -F ield D a t a ...................................28
3.4 O ff-A xis Illu m in a tio n ................................................................................... 30
CHAPTER 4: PLANE-TO-PLANE (PTP) PHASE RETRIEVAL
32
4.1 In tro d u c tio n o f P T P T e c h n iq u e ...............................................................32
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4.2 P la n a r N ear-F ield to F ar-F ield T ra n sfo rm a tio n s...............................35
4.3 P lane-to-P lane (PTP) P h a se R e trie v a l R e s u lts .................................... 41
4.3.1 Sim ulations................................................................................................. 41
4.3.2 IR Thermogram Results............................................................................. 45
4.4 F u tu re W o r k .....................................................................................................48
CHAPTER 5: HOLOGRAPHY..................................................................... 50
5.1 In tro d u c tio n to H o lo g ra p h ic T e c h n iq u e ................................................ 50
5.2 D e te rm in in g th e R eferen ce A n te n n a F ie ld .............................................55
5.3 C lassical H o lo g ra p h ic Im a g e R e c o n s tr u c tio n ..................................... 60
5.3.1 Theory o f Classical Holographic Image Reconstruction........................60
5.3.2 Sim ulation o f Classical Holographic Image Reconstruction............... 62
5.4 Im p ro ved H olo g ra p h ic Im a g e R e c o n stru c tio n ..................................... 64
5.4.1 Theory o f Improved Holographic Image Reconstruction.......................64
5.4.2 Sim ulation o f Improved Holographic Image Reconstruction............... 66
5.5 F u tu re H o lo g ra p h ic W o rk ...........................................................................68
CHAPTER 6: SUMMARY............................................................................. 70
BIBLIOGRAPHY...........................................................................................72
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TABLE OF FIGURES
Figure 1 - Geometry of E-Field Incident on a M aterial....................................... 8
Figure 2 - Close-up IR Image of an Array Showing the Distortion from Rising
Warmed A ir.......................................................................................................12
Figure 3 - Tem perature Rise in Teledeltos Paper v.s. Einc............................... 16
Figure 4 - Comparison of Normalized E-Field D ata Using Sm ith's E quationl8
Figure 5 - Comparison of Normalized E-Field D ata Using Polynomial Fit
(Equation 13).................................................................................................... 19
Figure 6 - Photograph of IR M easurement Setup...............................................23
Figure 7 - Close up of Thermal Camera with Aiming Laser and M irrors...... 25
Figure 8 - Comparison of IR M easured E-Field to Expected Levels................30
Figure 9 - Schematic of PTP Measurement S etup..............................................33
Figure 10 - Plane-to-Plane (PTP) Phase Retrieval Process...............................34
Figure 11 - Exterior Field Regions of a Radiating A n te n n a.............................37
Figure 12 - PTP Generated Far-Field from NIST M agnitude D a ta ................42
Figure 13 - PTP Results Using NIST Magnitude D ata Truncated to 20 dB
Dynamic R ange................................................................................................43
Figure 14 - PTP Results from Simulated 30 dB Dynamic Range D a ta .......... 45
Figure 15 - PTP Results for AGA 780 Therm ogram s........................................ 46
Figure 16 - Overlay of Convergence Error Metrics for Various PTP Runs ....48
Figure 17 - Typical Setup to Produce a Classical Optical Hologram...............51
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Figure 18 - Setup to Produce a Microwave Hologram...................................... 52
Figure 19 - Schematic of the Setup for the Holographic M easurem ents
53
Figure 20 - Example of the Construction of a Microwave Hologram..............55
Figure 21 - Setup for Determining Tilted Plane Configuration...................... 57
Figure 22 - Contour Plots of the Magnitude of the Field of the Reference
Antenna, (a) Computed horn NIST Near-Field Data, (b) From IR
Thermogram M easurem ents...........................................................................59
Figure 23- Sim ulated Classical Hologram Reconstruction Comparison with
True F a r Field for 36 by 36 Element A rray ................................................. 63
Figure 24 - Sim ulated Classical Hologram Reconstruction Comparison with
True F ar Field for 6 by 6 Element A rray ..................................................... 64
Figure 25 - AUT Far-Field Computed from Sim ulated Hologram s................. 68
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1
CHAPTER 1: INTRODUCTION
There continues to be significant interest in the development of new
near-field m easurem ent techniques for the purpose of determ ining the farfield radiation patterns of antennas.
The current practice today is to
carefully position a hard-w ired field probe to several well known locations
about a surface around the antenna-under-test (AUT) while recording the
m agnitude and relative phase of each measurement [1].
Many different
techniques have been developed for accurate probe positioning and
minimization of the num ber of probe location m easurem ents required;
however, all these techniques are time intensive due to the large num ber of
probe m easurem ent locations required [2],
Thermographic
m easurem ents
of microwave
fields
have
been
developed for the purpose of m apping radiating field intensity patterns [3, 4,
5, 6, 7, 8, 9, 10] and m apping surface currents induced in conductors by
radiating fields [11, 12, 13, 14, 15].
A resistive sheet positioned in a
radiating field will absorb energy in proportion to the strength of the
radiating field, resulting in a tem perature rise in the sheet.
A therm al
'picture' is then taken of the h eat p attern on the resistive sheet. Each pixel
of this therm al picture then represents a m easurem ent of the intensity
(magnitude) of the field at the pixel location on the resistive sheet. A single
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2
therm al image, therefore, provides a rapid m easurem ent of the field
magnitude over a surface; with the effective num ber of probe locations
limited only by the pixel resolution of the imaging camera.
The
problem
with
this
previous
thermographic
m easurem ent
technique is th a t only the m agnitude of the field is measured. In order to
obtain a far-field p attern from near-field antenna measurements, relative
phase information is also required [1,2]. The m ain purpose of this work is to
develop and evaluate several techniques for obtaining the necessary phase
information from thermographic measurements.
Several potential methods of obtaining phase from magnitude only
thermographic m easurements are considered. These methods are grouped
into those th a t were developed originally for hardw ired measurements, the
development of special thermographic screens, and microwave holographic
techniques. These are discussed separately below.
1.1
E x ten sio n
of
H a rd w ire
T ech n iq u es
to
T h erm o g ra p h ic
M ea su rem en ts
Direct m easurement of phase information in standard hard-wired
near-field antenna m easurem ent ranges requires the use of expensive vector
m easurem ent equipment and suffers from inaccurate measurements,
particularly at the higher frequencies, due to errors such as mechanical
positioning of the probe antenna and tem perature induced cable length
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3
changes. As a result, several algorithms have been proposed in recent years
to
retrieve
phase
measurements.
information
from
phase-less
(magnitude
only)
Comparison of some of the practical algorithms and an
overview of the m athem atical basis of phase retrieval can be found in [16,
17].
Two closely related error-reduction type techniques, known as the
Gerchberg-Saxton
[18]
and the
Input-O utput [17] methods,
require
magnitude m easurem ents in both the near field and in the far field; thus,
they are not practical for the therm al imaging technique (which requires
high power levels), and, therefore, were not further investigated in this thesis
research.
An iterative Fourier technique known as the Miseli algorithm [19]
requires two far-field m easurem ents with the antenna beam "defocused".
This technique, therefore, is also impractical for consideration with a therm al
imaging technique.
Another technique, known as Plane-to-Plane (PTP) Phase Retrieval
[20, 21, 22] was specifically developed for near-field measurements of
antennas.
A closely related phase retrieval algorithm [23] has been
successfully implemented by Yaccarino and Rahmat-Samii a t the University
of California at Los Angeles (UCLA) with a bi-polar planar hard-wired near­
field m easurem ent system using magnitude only data m easured over two
planes separated by only 2.560
a.
[24].
Further modifications and
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4
improvements to this technique have been carried out by Rahmat-Samii, et.
al. [25] and Junkin et. al. at the University of Sheffield, UK. [26, 27, 28].
The question of the uniqueness of the solution obtained via a plane-to-plane
phase retrieval algorithm has been addressed by several authors, most
notably Isem ia, Leone, and Pierri [22, 29, 30 ].
One form of this Plane-to-Plane phase retrieval technique was applied
to a set of therm ally acquired m agnitude data as p art of this research work,
and is discussed in more detail in Chapter 3.
1.2 S p e c ia l T h erm o g ra p h ic Screens
The concept of using a special therm al screen with built-in tuned
dipoles to determine the m agnitude and phase of a radiating field was also
reviewed as p a rt of this thesis research. The idea behind this concept, which
is being pursued by Mission Research Corporation (MRC), is th a t a m atrix of
dipoles, tuned to the frequency of measurement, is built into the resistive
sheet used to therm ally measure the radiating field at each location for
which m easured data is desired [31]. Typically, in near-field m easurements,
the m easurem ent spacing is slightly less th an 0.5 X, and the planar area to
be m easured is a few 10's cf X; thus, literally thousands of dipoles built into
the screen would be required. The m agnitude and phase of the radiating
field of the AUT is then determined from a series of m agnitude only therm al
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5
m easurem ents made with the dipoles radiating at a known power level and
relative phase.
This technique was not pursued under this thesis research for two
reasons. First, another group (MRC) is currently pursuing this technique,
and, second, it appears th a t the required therm al screen(s) would be very
difficult and expensive to build and would also have lim ited utility.
1.3 H olo g ra p h ic T echniques
Microwave
holography
techniques
appear
well
suited
to
the
determination of the complete (complex) field data from thermographic
measurements.
In general, the term hologram m eans an interference pattern.
In
particular, hologram means a very special interference pattern from which it
is possible to reconstruct the complete complex image.
Holography was first introduced in 1948 at optical frequencies by
Gabor [32]; while
at
microwave frequencies,
holography
was first
demonstrated by Dooley in 1965 [33]. In microwave holography, as applied
in this thesis research to therm al imaging of radiating RF fields, two
antennas are set up to irradiate a resistive sheet from which the therm al
image is to be recorded. One antenna is the antenna under test (AUT) and
the second antenna is a well known reference (REF) antenna.
The two
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6
antennas are set to radiate at the same frequency, so th at a static
interference pattern is generated on the therm al paper. The relative phase
difference of the fields from the two antennas a t each location over the
therm al paper produces either constructive or destructive interference.
Two options for reconstructing the complex field data from this
microwave hologram were considered in this thesis research.
The first
method is analogous to an optical hologram read-out. In this method, the
hologram is processed by direct multiplication of each d ata point by a
normalized reference wave, which is sim ilar to re-illum inating an optical
hologram with its reference wave. The result is then three "images", viz. an
amplitude modulated version of the reference wave, the desired complex
image, and a phase-shifted complex conjugate of the desired image. Viewing
of this image is then lim ited to the region of the desired image only.
A second processing method results from the realization th a t the
hologram can be processed exactly, th a t is, with the additional knowledge of
the m agnitude of the field of the AUT, the other images can be removed in
the final data.
The m agnitude and phase of the field of the reference
antenna are well known and the magnitude of the field of the AUT can be
m easured by the IR imaging technique directly; thus, the hologram data can
be presented as an equation with a single unknown, the phase of the AUT
field.
These two holographic processing methods and th eir results are
discussed in detail in C hapter 4.
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7
CHAPTER 2: IR MAGNITUDE MEASUREMENTS OF RADIATING
FIELDS
2.1 In tro d u c tio n to IR M a g n itu d e M ea su rem en ts
The quality of the results of phase retrieval and holographic
techniques depends a great deal on the quality of the magnitude data
m easurements. This chapter discusses the background and process used to
collect the IR therm al m easurem ents of the m agnitude of a radiating field.
The basic principle involved in IR m easurem ents of the magnitude of a
radiating field is th a t a lossy m aterial positioned in the field will heat as it
absorbs power from the field. Since the absorbed power is related to the
strength of the field, the tem perature rise in the m aterial can be m easured
and then related to the field strength.
For a thin, low-loss m aterial, the fields in the m aterial can be
approximated as constant; thus, the power absorbed per square m eter in the
m aterial is adequately described by [34]:
P abs
=
+
W
where h is a vector normal to the surface of the lossy m aterial, d is the
thickness of the lossy m aterial, co is the radian frequency, a is the real p art of
the m aterial conductivity, s" is the im aginary p a rt of the complex permitivity
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of the material, |i" is the im aginary p art of the complex perm iability of the
m aterial, and the t subscripts on the field quantities imply the tangential
components.
In this thesis research, Teledeltos paper was used as the lossy
m aterial.
The m aterial properties of this paper are d = 80 pm, o'' = 8
siemens/m, e" = 0, and p" = 0. Thus, for the Teledeltos paper, the absorbed
power can be described by:
)[% ¥*
(2>
Z 0
Consider the illustration of a propagating electric field incident on a
sheet of therm al paper shown in Figure 1. As a result of the discontinuity
between the wave impedance in the m aterial to the wave impedance in the
surrounding air, there are reflecting waves at both boundaries of the
m aterial in addition to the transm itted waves.
The total electric field in the
inc
absorbing m aterial can be described
as the summation of the positive
inc
z=0
z=d
traveling wave transm itted from the
incident wave through the m aterial
Figure 1 - Geometry of E-Field
Incident on a M aterial
boundary and the negative traveling
wave resulting from a reflection of
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the transm itted wave off the back side of the absorbing material.
Mathematically, this is represented as:
E2 = EXe~r* +EZe~r'-z
where
y 2
=
h +_ 2 _ =a
V jo e 2
(3)
2 +jp 2.
The square of this electric field is therefore:
E \ = \E; |V2c- + \E2\2e2a'-: + 2 R e{£;£;
(4)
Using this result in equation 2 and integrating, the total absorbed
power per square m eter in the Teledeltos paper is:
Pabs = —
4
] 5 l ( e^ _
- l)+A Re{£*£2--^ -W -l)}
(5)
Through the application of boundary conditions, E~_ and E2 can be
determined from the original tangential incident electric field, E~rc as:
e;
e;
r +i
i - r 2p2
+ -rp2(r + i)
=e .
i - r 2p2
=e ,
where, for norm al incidence, P = e~r'-d, T = (j]2 —770)/(772 + 77o)’
(6)
"H2
intrinsic wave impedance in the material.
V=. 'G
JW
+ jCO S
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(7)
10
Due to energy conservation, in equilibrium, this absorbed power m ust
be balanced by the power lost through therm al convection and therm al
radiation as described below.
2.2 T h e rm a l C onvection
Convection is the loss of h eat to the m aterial surrounding the therm al
paper. Previous therm al imaging work [5, 6, 7, 14, 34, 35] has shown that
convection is adequately described by Newton’s law of cooling:
q = M(Ts - T a)
(8)
where q is the heat in W atts, h is the convection h e at transfer coefficient in
W/m2K, A is the surface area in m2, Ts is the surface tem perature in K, and Ta
is the am bient tem perature in K.
In general, this convective h eat loss occurs on all six sides of a block of
m aterial. The edges of the thin resistive paper used for these tests, however,
have a negligible surface area; thus, convective losses from the edges of the
paper were ignored. Additionally, the therm al paper was mounted on two
layers of artist's poster board (total thickness of 1.0 cm). The poster board,
therefore, represents a thick, EM transparent, therm ally insulative layer
(low convection h eat transfer coefficient) between the paper and the
radiating antenna. Thus, convection off the back side of the resistive paper
was reduced to a negligible value. Convective h e at loss was then essentially
lim ited to the front side of the therm al paper.
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11
The h eat transfer coefficient, h, is dependent on environmental factors
such as the movement of air around the therm al paper (the capacity of the
surrounding air to remove heat from the therm al paper); however, in this
thesis research, since all therm al m easurem ents were performed in the
enclosed anechoic chamber, a fixed value of h=0.93 as determined by Metzger
[34] was used.
In future work it may be possible to m easure certain
environm ental factors to determine an accurate value of h a t the time of the
therm al m easurement, and then use this value to balance the therm al paper
heating equation. It is anticipated th a t some form of real-time determination
of h such as this will be required in order to transfer the therm al
m easurem ent technology from the
(controlled) laboratory to a field
m easurem ent system.
A second problem with therm al convection is that, as the heat in the
therm al paper is transferred to the surrounding air, the air decreases in
density and, therefore, begins to rise. With the therm al paper oriented
vertically, the rising, warmed, air tends to convect heat back into cooler areas
of the therm al paper; thus, distorting the upper portion of the therm al image.
This distortion can be clearly seen in Figure 2, which shows a close up
therm al image of the radiating field from an array. The contour lines around
the perim eter of the array in this image should be fairly rectangular, but as
can be seen, the contour lines are deformed on the upper edge of the image.
It may be possible to reduce or remove the effects of this distortion by data
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12
processing. In addition, a modification of the screen with cells or baffles to
reduce or eliminate air currents along the face of the screen may be possible.
This is an area also left for future research. In this thesis work, distortion
from rising, warmed air was eliminated by orienting the therm al screen
horizontally as described in the test set-up section (Section 3.1).
10
20
PWlMBMni
30
40
50
60
Figure 2 - Close-up IR Image of an A rray Showing the
D istortion from Rising W armed Air
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13
2.3 T h e rm a l C onduction
Conduction is the flow of h eat within a m aterial from hotter regions to
cooler regions resulting in a "defocusing" of the therm al picture. The effect of
conduction can be seen in the comparison of therm al m easurements to either
hard-w ired m easurements or calculations as
warmer than
expected
minimums (nulls) and cooler th an expected maximums [10, 36]. Thermal
conduction is described mathem atically by Fourier's law of h eat conduction:
qx = -kA ^
ex
(9)
where qx is the heat flow in the x direction in W atts, k is the therm al
conductivity of the m aterial in W/mK, A is the cross-sectional surface area in
m2 and T is the tem perature in K.
Metzger [34] mentions th a t it may be possible to use therm al transport
finite differencing methods to remove the therm al conduction distortions
from the m easurement data.
Other work, however, has shown that, in
general, for low electrical conductivity therm al paper such as used in the
measurements in this research, the therm al conductivity, k, is also low [11].
2.4 T h e rm a l R a d ia tio n
The Stefan-Boltzman law states th a t the total hemispherical emissive
power of a blackbody is related to the tem perature of the blackbody by [37]:
q = (JbA T
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(10)
14
where q is in watts, cn> is the Stefan-Boltzman constant (5.669E-8 W/m2K4), A
is the surface area in m2, and T is the surface tem perature in K.
The net power radiated by a gray body surrounded by several other
gray bodies at different tem peratures is extremely complicated and,
therefore, difficult to accurately compute for a test set-up like th a t used
during this thesis research. A reasonably accurate first order approximation
can be made, however, for a gray body with emissivity Sir (the Teledeltos
paper), radiating into a larger body (the anechoic chamber) m aintained at a
uniform ambient tem perature, Ta.
Using this approximation, the net
radiated power is given by:
q = e,r<rbA ( T ; - T ; )
( 11)
2.5 T h e rm a l P a p e r T em p era tu re fro m In c id e n t F ields
The final (therm al equilibrium) tem perature of a sheet of Teledeltos
paper in an EM field is then the result of a balance between the EM power
absorbed by the paper and the power lost due to therm al convection and
therm al radiation. Equations 8 and 11 therefore, can be combined as:
^
- £ ) +Mjr. - T.)
02 )
where Pabs is given by equations 5 and 6.
R ather than attem pting to find a closed form solution to the above
equations for Einc in terms of the therm al paper surface tem perature, a three
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15
step process was performed. First, the above equations and constants were
programmed into MATLAB and using the built in MAPLE symbolic solver,
an array of surface tem perature values were then calculated for an array of
Einc values.
This data was then fit (via a built in least squares type
polynomial fit function) to a 2nd order polynomial in surface tem perature.
The MATLAB code MET2.M listed in Appendix A was used to perform these
steps.
Using this code, the best least-squares 2nd order polynomial fit for the
Teledeltos paper is:
3.1x10~5(£,“.) + 3.5x1CT3(£ mc) - 0.302 = AT
(13)
where AT = Ts - Ta is the tem perature rise in Kelvins above ambient.
Figure 3 shows a comparison of this polynomial (equation 13) to the
computation of equation 12 (including equations 5 and 6). As shown in this
figure, the fit is quite good with the exception of the lowest tem perature
values. The disagreement in the curves at the low tem perature values is,
however, partially offset by the lim itations of the UCCS AGA 780 therm al
camera when set to the 10 degree therm al range (discussed in the next
section). If the AGA 780 were used on a sm aller therm al range setting, such
as 2 degrees, or a therm al camera with a greater dynamic range were used,
then a different process of converting tem perature rise to incident E-field
values would be necessary. For example, equations 5, 6, and 12 could be
programed into an iterative minimization routine th a t uses the polynominal
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16
derived values (equation 13) as a starting point to provide a more accurate
computation of tlie incident E-field from a m easured tem perature rise.
Overlay o f M etzger's Equation (solid) with Polynom ial Fit (d ash ed )
4 -
Q.
100
300
200
400
500
600
F igure 3 - T em perature Rise in Teledeltos P aper v.s.
Einc
It should be stated that, at the sta rt of this thesis research, the
following 2nd order polynomial taken from Sm ith’s M asters Thesis [38] was
used to convert tem perature rise to E-field values:
b + (b2 +4aAT)V2'
2a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(14)
where a=3.703E-7, b=2.192E-4, AT is the difference in the pixel tem perature
from the ambient background tem perature in Kelvins, and S is a scaling
constant. The results from this equation do not agree very well with the
expected results derived above.
This, by itself, would not necessarily be
serious; however, another problem was discovered. Two sets of thermograms
were taken of an antenna radiating a t two different power levels; one a t a
power level such th a t the maximum tem perature was near the full scale
reading of the therm al camera (about 10 degrees above ambient), and one at
a power level such th a t the maximum tem perature was at only about one
th ird of the full scale reading of the therm al camera.
When these
thermograms were processed into incident E-field levels using equation 14
and then normalized, the agreement between them was very poor, except
near the maximum value, as illustrated in Figure 4. This clearly illustrates
th a t equation 14 is a poor representation of the tem perature rise from an
incident field for the range of field values used during this thesis research.
When these same thermograms were re-processed using the roots of equation
13, however, the agreement was quite good (given the differences in the
m easurem ent dynamic range between the two thermograms) as shown in
Figure 5.
Equation 13, therefore, was used to convert thermogram
tem peratures to E-field values throughout this thesis research work.
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18
Comparison of Normalized E-Field Data Using Smith's Equation
0.9
0.8
T3
-
0.7
0.6
1 0.5
U-
£ 0.4
0.3
0.2
0.1
40
50
60
70
x-pixels
Figure 4 - Com parison of Normalized E-Field D ata Using
Sm ith's Equation
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19
Comparison of Normalized E-Field Data Using New Polynomial
1
0.9
0.8
-o 0.7
0.6
0.5
=5 0.4
2 0.3
0.2
0.1
0
10
20
30
40
50
60
70
80
x-pixels
Figure 5 - Com parison o f N orm alized E-Field D ata Using
Polynomial Fit (Equation 13)
2.6 UCCS C am era
The current UCCS therm al camera is an AGA Thermovision® 780.
This particular therm al camera provides an analog output to an external 8
bit digitizer to produce a m atrix of therm al intensity pixels [39].
These
therm al intensity levels are in Isotherm al Units (IU) which are related to a
blackbody tem perature by the non-linear relationship:
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20
where I is the Isotherm al U nit Value, T is the absolute tem perature in
degrees K, and A, B, and C are constants associated with the sensor type and
lens aperture setting. For example, for the long wave sensor (8-12 pm): A =
552855, B= 2994, and C=0.975 with an aperture setting of f=1.8 [40].
The controls of the therm al camera allow full scale therm al range to be
set as either 2, 5, 10, 20, 50, 100, 200, 500, or 1000 IUs with an analog
vernier adjustm ent for the setting of the IU of the center of the therm al
range. From the 8 bit digitizer, there are 256 linear intensity levels across
the full scale of the cam era output in IUs. For sm all changes in IUs (<10),
near room tem perature, the conversion to blackbody tem perature (equation
15) is nearly linear.
The conversion from blackbody tem perature to the
strength of the square of the electric field is also approximately a linear
conversion for small tem perature changes as discussed in the section above.
There are, therefore, roughly 256 linear levels in the m easurem ent of the
magnitude of the electric field using the UCCS therm al camera. Assuming
the best of circumstances, i.e., a barely saturated therm al image, this results
in 101ogio(256), or about 24 dB of dynamic range [measured as the difference
in the full scale level (256 levels) to the sm allest detectable change (1 level)].
In addition, m easurem ents made with the UCCS therm al camera on a
therm ally stable object indicate variations of about ± 2 intensity levels for
m easurements of identical tem peratures after using a 15 fram e average. The
actual, realizable, dynamic range for therm al m easurem ents of the electric
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21
field strength, therefore, were reduced to about 20 dB of dynamic range and
S/N for most measurements.
An IBM/XT personal computer is interfaced to the external digitizer
connected to the AGA 780 therm al camera and is used to retrieve and store
the digital pixel intensity levels.
An existing compiled PASCAL program
called GETDAT.EXE w as used to collect IR images from the external
digitizer and store them on a PC disk. This program perm itted a maximum
of 15 frames of IR data to be captured at one time. The full 15 frames of data
capture was used for each scene of data collected in this thesis research.
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22
CHAPTER 3: MEASUREMENT SETUP AND PROCEDURE
3.1 B a sic M ea su rem en t S e tu p
A photograph of the setup used in this thesis research for both the
Plane-to-Plane (PTP) and holographic m easurements (to be discussed in
detail below) is shown in Figure 6. The 36 element patch array antenna used
as the AUT is shown at the top of the photograph.
This antenna was
supplied by the N ational Institue of Standards and Technology (NIST),
Boulder, CO. Complete calibration data in the form of standard planar near­
field scan data was also supplied by NIST.
Centered, directly below the
array antenna is the therm al paper, with its backing of therm al insulator
(poster board), oriented horizontally and sitting on a wooden perim eter
frame. Also, above the therm al paper near the top right h an d side of the
photograph, is shown the 4 GHz Standard Gain Horn used as a reference
antenna during the holographic data measurements. This reference horn,
and complete calibration data for the horn, were also supplied by NIST. Well
below the therm al paper (almost 3 meters below) is the AGA 780 therm al
imaging camera.
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23
Figure 6 - Photograph o f IR M easurem ent Setup
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24
The AGA 780 therm al imaging camera requires liquid nitrogen to cool
the therm al detector; thus, the camera m ust be positioned within ju st a few
degrees of level.
In order to view the therm al paper hanging above the
camera, an IR m irror was used to re-direct the camera view in the vertical
direction.
The m irror used was a 127 mm by 102 mm gold coated first-
surface m irror obtained from Edm und Scientific. In addition, a second, lower
quality, first-surface mirror of the same size was mounted adjacent to the
first m irror such th a t the total mirror surface was 254 mm by 102 mm. This
second m irror was only used to aid in the alignm ent and aiming of the
therm al camera. A leveling laser was attached to the top of the camera and
aimed into the second mirror with the laser beam parallel to the camera
optical path. A bubble level built into the leveling laser was used to level the
therm al camera. Then, a small patch of reflective m aterial was temporarily
attached to the therm al paper at the location of the laser spot. The mirror
tilt angle was then adjusted such th at the laser fight reflecting off of the
patch on the therm al paper returned into the laser aperture. In this way, a
nearly perfect perpendicular view of the therm al paper was ensured. Figure
7 is a photograph showing a close-up view of the therm al camera with the
mirrors and laser attached.
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25
Figure 7 - Close up of Therm al Cam era w ith Aiming Laser and
M irrors
In plan ar near-field antenna measurements, it is desirable to measure
the m agnitude and phase of the field over a planar m atrix with spacings of
slightly less th an one h a lf wavelength, and to cover the entire region of non­
zero field amplitude. Obviously, the size of this region varies with antenna
design; however, a good rule-of-thumb estim ate for many antennas is twice
the size of the antenna aperture [41], Using the widest angle lens available
at UCCS for the AGA 780 camera, one with a 20° field of view, and
positioning the camera at about 3 meters from the therm al paper, the image
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26
area was a little larger th an twice the array area (the array area is 38 cm by
38 cm whereas the IR image area was about 94 cm by 115 cm). Given the
dynamic range lim itations of the AGA 780 camera (about 20 dB), this field-ofview was quite sufficient; however a larger field-of-view (about 180 cm 180
cm) would be more desirable for this array antenna, if a camera with a
greater dynamic range were used.
3.2 M ea su rem en t P rocedure
The following m easurem ent procedure was used for all of the IR
thermograms collected for this thesis research. The IU therm al range dial
was set to 10.
This was selected as a balance between achievable
tem perature rise in the therm al paper at acceptable RF power levels for the
array (less than about 50 watts) and minimization of the risk of introducing
data errors from therm al drift in the equipment or the ambient environment.
The IU therm al level vernier dial was then set such th a t the ambient
background tem perature registered ju st above zero on the 8-bit digitizer
output.
These settings were then locked in and no further camera
adjustm ents were made for the entire m easurem ent set.
RF power was then applied with the amplitude adjusted such th a t the
greatest tem perature rise for the entire m easurem ent set did not exceed the
maximum m easurable tem perature rise (10 IUs above ambient).
For the
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27
data processed by tbe Plane-to-Plane technique, a m easurem ent set was the
amplitude m easurem ents of the array fields at the two chosen plane
distances.
For the data processed holographically, a m easurem ent set
consisted of six amplitude measurements; the array alone, the reference horn
alone, and the two antennas radiating simultaneously with relative phase
shifts between them of 0, 90, 180, and 270 degrees. The selection of RF
power level was, therefore, an iterative process, since it was also desirable
from a dynamic range stand-point to ensure th a t the greatest tem perature
rise of the measurement set was very nearly full scale, and for the
holographic measurements th a t the peak amplitudes from the two antennas
separately were approximately equal.
Once the RF power level was selected and applied, the therm al paper
was illum inated for approximately 10 m inutes to ensure th a t therm al
stability had been reached in the paper.
This was further confirmed by
m arking the peak therm al amplitude (using one of the cameras two
isotherm al m arker controls) and verifying th a t the peak therm al amplitude
rem ained unchanged after an additional 1 m inute of RF illumination. Once
the image was considered therm ally stable, 15 frames of the image (the
maximum allowable by the GETDAT.EXE program) were captured and
stored in a file. This therm al data was then converted to E-field m agnitude
data as discussed in the next section.
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28
3.3 C onversion o f A G A 780 O u tp u t to E -F ield D a ta
The raw IU therm al data captured and saved by the GETDAT.EXE
program was then processed into E-field levels by three MATLAB programs
listed in Appendix A; IR_AV_C.M, TQTEMP.M, and TEMP2E3.M.
The first program, IR_AV_C.M, reads in a raw IU data file and
displays the stored header information about the file.
The header
information includes date and time, therm al level and therm al range
settings, am bient tem perature, RF power level, IR lens used, num ber of data
fields per frame, total num ber of fields in the file, and 4 comment lines. The
program then asks for the fram es th at should be averaged together. For this
work, all 15 frames (the maximum) were averaged together for each file. The
program then reads the appropriate fields and assembles them into frames
and averages the frames together, storing the data in the 116x64 element
m atrix variable 'frame'. A contour plot of the final averaged frame data is
then displayed.
The MATLAB program TOTEMP.M was then used to convert the
averaged frame data, which h as levels from 0 to 255 digitizer units, to
tem perature in degrees C. This code uses the IU to blackbody conversion
equation (equation 15) modified to include emissivity of the therm al paper
and atmospheric attenuation as described in the AGA m anual [40]. The code
stores the data converted to tem perature in the m atrix 'tframe' and then
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29
displays the maximum and minimum tem perature of the image and a
contour plot of the entire image.
This tem perature was then converted to E-field levels by the MATLAB
function TEMP2E3.M, which finds the positive root of equation 13. This
equation relates the E-field to a rise in paper tem perature above the ambient
tem perature. Since it is quite difficult to determine the exact setting of the
therm al level of the UCCS AGA 780 therm al camera, the baseline or ambient
tem perature was determined from the minimum tem perature value of each
image, rath er th an from an independent ambient tem perature measurement.
In practice, it was determined th a t a choice of ambient tem perature about
0.3°C above the minimum tem perature of the image was best. An example of
the comparison between the E-field determined from an IR thermogram
m easurem ent
and
the
expected
result
based
on
NIST
near-field
measurements of the array is shown in Figure 8. As shown in this figure,
agreement between the curves is quite good down to about 18 dB to 20 dB
below the peak, as expected from the particulars of the AGA 780 camera
discussed in Chapter 2.
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30
Comparison of Expected (*) to Measured (+) E-Field at 45.1 cm
i f -15
-20
-25
100
-100
x-position (cm)
Figure 8 - Comparison of IR M easured E-Field to Expected
Levels
3.4 O ff-Axis Illu m in a tio n
A current literature search of previous work on thermographic
mapping of EM fields shows only parallel and normal incidence of the field
on the therm al paper.
The holographic techniques used in this thesis
research required th at at least one of the antennas produce a field of
illumination at an oblique angle to the therm al paper. The effect of this
angular illumination on the power absorbed by the therm al paper was
discussed by Metzger [34]. This effect in a thin therm al screen, such as the
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31
Teledeltos paper used in this thesis research, for tangetial E-Fields, however,
is negligable.
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32
CHAPTER 4: PLANE-TO-PLANE (PTP) PHASE RETRIEVAL
4.1 In tro d u c tio n o f P T P T ech n iq u e
The setup used for the plane-to-plane (PTP) phase retrieval technique
is shown in Figure 9 and the phase retrieval process is illustrated in Figure
10. First, various variables and constants are defined and an estim ate of the
magnitude and phase of the aperture field is made. This estim ate is then
"propagated" to m easurem ent plane 1 by Fourier transform ation techniques,
the details of which are described in the next section (section 4.2).
The
convergence error is then calculated, defined as:
<16)
where M is the m easured m agnitude data and IAI is the calculated
magnitude data a t each pixel location in the plane of interest. The calculated
magnitude is then replaced with the m easured m agnitude with the
calculated phase retained. This complex data is then propagated by Fourier
techniques back to the original aperture plane.
All data outside of the
antenna aperture is then truncated and the truncated data propagated to the
second m easurem ent plane. Again, the convergence error is calculated and
the calculated m agnitude data replaced with the m easured m agnitude at
plane 2 with the calculated phase retained, and th is data is then propagated
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33
back to the aperture plane. At this point in the process, the change in the
convergence error from the previous iteration is checked, and if the change in
convergence error is less th an a set tolerance, the iterations are halted. If,
however, the change in convergence error is still sufficiently large, the above
iteration is repeated, starting with a truncation of data outside the antenna
aperture. The MATLAB code PTPLOOP.M th a t implements this algorithm is
also listed in Appendix A.
T h erm a
Paper
Source
AUT
Camera
Plane 2
Plane 1
Ap e r t u re
Plane
Figure 9 - Schem atic of PTP M easurem ent Setup
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34
Initialize Variables
including Complex
Aperture Estimate
Truncate Data outside
Aperture Plane
Propagate to Plane 1
Plane 1
Measured
Magnitude
Calculate Convergence
Error
i
j
Impose Measurer-’
Magnitude
Back-Propagate to
Aperture
Okay
Truncate Data outside
Aperture Plane
Check# of
Iterations
Exceeded
Propagate to Plane 2
END
Plane 2
Measured
Magnitude
Calculate Convergence
Error
Impose Measured
Magnitude
No
Check
Convergence
Yes
Back-Propagate to
Aperture
Figure 10 - Plane-to-Plane (PTP) Phase R etrieval Process
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35
Junkin has recently suggested [27] th a t a "phase change acceleration
procedure" be imposed between iterations.
This procedure reduces the
possibility of PTP algorithm stagnation due to a local minimum, which is an
increasing problem with decreasing scan plane separation. In this research,
the scan plane separation used was over 1.5 wavelengths, or about 0.066 D2/a
(the scan plane separation used by Junkin was 0.0033 D2/X); thus the utility
of incorporating the phase change acceleration procedure may be minimal.
In addition, Junkin and Trueba [28] have also suggested a center-of-gravity
type algorithm to help in the alignment of the two planes of measurements,
which becomes more critical with increasing antenna operating frequency.
Both of these algorithm modifications should be looked a t in future research
as improvements to the PTP algorithm developed for this research.
4.2 P la n a r N ear-F ield to F ar-F ield T ra n sfo rm a tio n s
The PTP algorithm discussed above is based on planar near-field to
far-field transform ations which are the result of the pioneering work of
Kerns and his development of the plane-wave scattering m atrix theory [42,
43, 44, 45, 46]. The planar near-field m easurem ent was the first of the near­
field techniques to be developed, verified, and implemented as an operational
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36
method of obtaining antenna param eters. An excellent review of the history
of near-field antenna m easurements is given by Yaghjian in [47].
The fields exterior to a radiating antenna are typically divided into
three regions, as illustrated in Figure 11. The specific transitions from one
region to the next are not sharply defined, and vary based on the antenna
type and the acceptable uncertainty in the use of the data. Very dose to the
antenna, i.e., within about one wavelength, is the region called the reactive
near-field or sometimes the evanescent region. In this region, the imaginary
portion of the complex Poynting vector, which is typically proportional to the
inverse of the radial distance to the power of 3 or greater, is not negligible. It
is this region th a t contributes to the reactive p a rt of the antenna input
impedance, and is, therefore, why this region is called the reactive near-field.
Beyond about one wavelength and out to, typically, a radial distance of about
2 D2/X is a region called the radiating near-field, or sometimes the Fresnel
region. In this region, the electric and magnetic fields are propagating, but
do not yet exhibit the hWr dependence characteristic of the far-field. This
region is where the near-field measurements in this thesis research were
made. Finally, the far-field region, sometimes called the Fraunhofer region
is th a t volume th a t extends from a radial distance of about 2 D2/X from the
antenna out to in fin ity
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37
Reactive
Near-Fieli
Radiating
Near-Field
or
Fresnel Region
Far-Field
or
Fraunhofer Region
- I 'D I X
F igure 11 - E xterior Field Regions o f a R adiating A ntenna
The basic idea of near-field to far-field transform ations is that: 1) the
far-field region is th at region where the radiating field phase front is locally
very nearly planar, 2) energy leaving an antenna always propagates in a
straight line in a uniform medium, 3) near-field m easurem ents of the
m agnitude and phase determine the phase front of the radiating energy and
this can he transform ed into an angular spectrum of plane waves, 4) this
angular spectrum of plane waves is equivalent to the antenna far-field
p attern [48].
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38
Using the concept of superposition, the field at a distance, z = di, in
front of a radiating antenna is a combination of a series of plane waves
(analogous to the idea th a t a time domain waveform is the superposition of a
combination of frequency spectral signals).
Mathematically, this can be
w ritten as [49]:
co
BXx,y,z = dt) = \ \ n k , , k y)-S(kx,k>) e ^ e ‘u-" t>»dkxdkr
(17)
-c o
where Bo is the output of a probe at position (x,y,z), T(k) is the plane-wave
spectrum (which is equivalent to the far-field pattern of the AUT), S(k) is the
vector receive p attern of the probe antenna (set to unity for the therm al
paper), and y = [(2:t/?i)2-(kx2 + ky2)]°'° is the wavenumber in the z direction (kz
is often used in the literature instead of y).
A slight re-arrangem ent of
equation 17 with a replacement of D(kx, ky) = T(kx, ky) • S(kx, ky) gives:
Be(x,y,z = d1)= ] \ e ^ D ( k x,ky) e ^ y)dkxdky
(18)
-c o
This integral equation is the same as an Inverse Fourier Transform with the
added multiplication of an ei7d term. The Fourier Transform pair to equation
19 is:
D(kx, k ) = ~
47C ~ A—coi/
1 \B 0(x,y,z = dx)e'KkxX+k’y)dxcfy
(19)
where A is a m easurem ent insertion loss correction constant used to
determine the absolute gain of the AUT.
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39
Equations 18 and 19 provide the m eans for transform ing from phase
front (near-field) measurements to th e angular spectrum (which is an
equivalent representation of the AUT far-field) and back.
Since these
equations are integral equations, they imply th a t m easurem ents m ust be
made over a continuous (non-discrete) surface. It turns out, however, th at
since the angular spectrum is band-limited, near-field d ata sampling can be
performed at intervals of 7J2 in x and y and the Discrete Fourier Transform
(DFT) used with no loss of generality [41, 50].
Since a discrete Fourier Transform can be used, standard Fast Fourier
Transform (FFT) routines can be used to transform complex near-field data
to the far field, or an inverse FFT (IFFT) used to transform from the far field
in to the near field. In the MATLAB code PTPLOOP.M listed in Appendix A,
the transform ations involve only a single line of code, such as for the
aperture field (distance = 0) to the far-field and back to the m easurem ent
plane 1:
El = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(1))
.* evan));
In this code line, the complex aperture field matrix, Eap is first propagated to
the far field by a two-dimensional FFT. The FFTSHIFT function is then
imposed to re-arrange the FFT output into the correct quadrants (FFT
algorithms result in an output in which quadrants 1 and 3 are swapped and
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40
2 and 4 are swapped). Since the input data to the Fourier Transform (Eap) is
complex., the opposing quadrant data are not necessarily identical and the
entire output m atrix is valid. This data then represents the far field of the
antenna. To back-transform to m easurement plane i, the complex far-field
data is m ultiplied by ei’/d, where d is the distance from the antenna aperture
to m easurem ent plane 1, an FFTUNSFT function performed to swap the data
quadrants in preparation for the inverse FFT, and then the inverse FFT
performed. In addition, the data m atrix is m ultiplied by the m atrix EVAN
ju st prior to the FFTUNSFT operation. The elements in the m atrix EVAN
are one everywhere y is pure real, and are 0 otherwise. This multiplication,
therefore, performs a band-limiting operation th a t perm its a discrete Fourier
Transform operation with near-field data collected a t spacings of up to
[41, 47].
a /2
Planar near-field, far-field transform ations using a modem
complex, m atrix-oriented language such as MATLAB are, therefore, quite
simple to implement and reasonably efficient (a complete loop of the code
PTPLOOP.M, which includes 4 FFT-IFFT operations as well as convergence
error calculations and m agnitude replacements for a non-power-of-2 57x57
element data m atrix on a 486DX2-100 is performed in about 4 seconds).
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41
4.3 P lane-to-P lane (PTP) P h a se R e trie v a l R e su lts
This section discusses the results of the PTP algorithm performed on
both sim ulated and actual IR m easured magnitude data.
The two
m easurem ent planes selected for the 36 element patch array antenna were at
a distance of 32.4 cm and 45.0 cm. Since the array operates at a frequency of
4 GHz, these distances were approximately 4.3 X and
6
X.
The exact
distances were arbitrary, with the goal of being well outside the reactive
near-field and of having a plane separation of greater than one wavelength,
b ut not so far apart as to result in a large difference in peak therm al paper
tem peratures.
4.3.1 Simulations
Before processing the therm al m easured data, a set of simulations
were performed. First, the array antenna was m easured by the National
Institute of Standards and Technology (NIST) in their standard near-field
antenna test range. The data provided by NIST on the array consisted of a
57x57 element m atrix of field m agnitude and phase data spaced 3.175 cm
apart (about 0.4 A.) in a plane 38.1 cm in front of the array. The near-field to
far-field FFT processing methods discussed above were then used to compute
the m agnitude and phase of the array fields a t the two m easurem ent planes
selected for the IR therm al m easurem ents (32.4 cm and 45.0 cm).
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The
42
m agnitudes of these data were then used as an initial simulation of the
capabilities of the PTP algorithm.
Figure
12
is an overlay of the far-field pattern of the array as
determined by the PTP algorithm (dashed *) and from the original NIST
complex data (solid +). As the figure illustrates, the agreement between the
PTP determined far-field pattern and the array's "real" far-field pattern is
excellent.
Comparison of Nist Far-Field (+) to Iterative from Nist M agnitudes (’) E-Plane
-10
dB
-15
-20
-25
-30
-35
<-
-100
-50
50
100
Degrees
Figure 12 - PTP G enerated Far-Field from NIST
M agnitude D ata
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43
The PTP algorithm was then re-run with the NIST magnitude data
truncated at amplitudes 20 dB below the peak as an estimate of the dynamic
range of the UCCS AGA 780 therm al camera. The result of this simulation is
shown in Figure 13. As illustrated in this figure, the PTP algorithm was only
able to reconstruct the antenna main-lobe and provide an indication of the
location of the first two side-lobes (but not the correct amplitudes for the sidelobes).
Comparison of Nist rar-Field (+) to Iterative from Nisi Mag Reduced to 20 dB Range (*) E-Plane
-10
dB
-15
-20
-25
-30
-35
-100
-50
50
100
D egrees
Figure 13 - PTP Results Using NIST M agnitude Data
T runcated to 20 dB Dynamic Range
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44
Obviously, the results above from the simulations of AGA 780 type
dynamic range are only m arginally useful; however, modem
1 2
-bit digitizing
therm al cameras such as Rome Laboratories AGEMA 900 should have at
least a 30 dB RF dynamic range [51].
The results of th e PTP algorithm
applied to data with a 30 dB dynamic range are substantially better than for
data with only a 20 dB dynamic range, as shown in the sim ulation results of
Figure 14. As shown in these sim ulation results, data from thermograms
collected with a camera such as the AGEMA 900 should be adequate for the
PTP algorithm to faithfully reproduce the far-field pattern of antennas such
as the array tested in this research. Future work will show the validity of
this simulation and additional work will focus on investigating the utility of
the algorithm for other antenna styles, particularly those with lower sidelobes.
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45
Comparison of Nist Far-Fieid (+) to Iterative from Nist Mag Reduced to 3 0 dB Range (*) E-Plane
-10
-
dB
-15
-20
-25
-30 >-
-100
-50
50
100
D egrees
Figure 14 - PTP Results from Sim ulated 30 dB Dynamic
Range D ata
4.3.2 IR Thermogram Results
Actual thermograms were then taken at these m easurement planes.
Direct comparison of the field m agnitudes from the thermograms to the
expected values based on the NIST m easured data confirmed that the
therm al m easurem ents from the AGA 780 camera resulted in about 18 db 20 dB of usable dynamic range. The MATLAB code PTPLOOP.M was then
slightly modified to account for the pixel spacing in the thermograms (this
version, PTPLPTHM.M is also included in Appendix A). The result of the
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46
PTP algorithm on this data is shown in Figure 15. As can be seen, the result
of processing th e AGA 780 thermograms is very encouraging as it is
approximately the same as the
2 0
dB dynamic range simulation.
Com parison of Nist Far-Field (+) to Iterative Plane-to-Plane (*) E-Plane
-10
-15
dB
-20
-25
-30
-35
-40 •-100
-50
50
100
Degrees
F igure 15 - PTP Results for AGA 780 Therm ogram s
Another useful measure of the success of the PTP algorithm is a plot of
the convergence error metric. Figure 16 shows an overlay of the convergence
error metric of the PTP algorithm for the four cases discussed above (full
range simulation, 30dB dynamic range simulation, 20dB dynamic range
simulation, and AGA 780 thermogram data). Several observations can be
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47
made from this figure. First, th e convergence metric settles to a stable value
for each case in less than 40 iterations, which represents only 2-3 minutes of
processing time on a 486DX2-100 processor for these m atrix sizes. Secondly,
the convergence metric stays stable for m any iterations (all runs were taken
out for 200 iterations and all rem ained stable). Thirdly, it appears th a t the
value of the convergence metric is a usable m easure of how well the
algorithm was able to re-construct the AUT far-field pattern.
Since in actual practice, the AUT p attern will be unknown to the user
(or the user would not be trying to m easure it), the convergence metric may
be very useful in determining the reliability of the PTP algorithm results.
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48
Comparison of Plane-to-Plane Iteration Convergence
IR Thermal Data
2 0 dB Range Simulation
30 dB Range Simulation
"Full11Range Simulation
100
150
200
Number of Iterations
Figure 16 - Overlay of Convergence E rro r M etrics for
Various PTP Runs
4.4 F u tu re W ork
In summary, the PTP algorithm appears very well suited to the
reconstruction of the far-field pattern from thermographic measurements on
2 near-field planes.
pursued.
Additional research in the PTP technique should be
First, a camera with greater dynamic range, such as Rome
Laboratories AGEMA 900 should be used to verify the results of the 30 dB
dynamic range simulation shown in this work (an improved tem perature rise
to E-Field conversion algorithm may be necessary for processing data from a
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49
higher dynamic range camera). In addition, the phase change acceleration
and center-of-gravity concepts proposed by Junkin should be investigated for
incorporation into the PTP algorithm developed here [27, 28]. Furtherm ore,
several antenna styles with different side-lobe amplitudes should be
m easured in order to build confidence in this technique.
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50
CHAPTER 5: HOLOGRAPHY
5.1 In tro d u c tio n to H o lo g ra p h ic T ech n iq u e
Microwave
holography
techniques
appear
well
suited
to
the
determination of the complete (complex) field data from thermographic
measurements. In general, a review of the literature shows th a t the term
microwave holography is often used to m ean data containing phase
information.
The classical (optical) hologram, however, is a magnitude
pattern created by th e constructive and destructive interference of two
signals. Upon re-illum ination of this hologram interference pattern with one
of the signals used to create it, the complete 3-dimensional, or complex,
second signal is retrieved. Holography, in this thesis research, refers to this
classical description of holography, which has not previously been applied to
IR images of EM fields.
A typical setup for creating a classical optical hologram is shown in
Figure 17. A beam of coherent light (typically from a laser) is split into two
beam paths. One beam directly illum inates a photographic plate, while the
other illum inates the photographic plate after reflecting off of the object for
which the holographic image is desired.
Since the original beam was a
coherent light source, the amplitude of the light a t the photographic plate is
modulated by constructive or destructive interference between the two light
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51
beams due to the difference in their p ath lengths. It is im portant to note th at
the hologram is not like a standard photograph; when the hologram is reillum inated by the reference wave, the reference wave signal is modulated by
the interference pattern of the hologram, and the result is a reconstruction in
3 dimensions of an image of the original object (discribed in the next section).
Object
t0 b e ( ^
Imaged
Object Beam
LASER
Reference Beam
Beam
Splitter
Photographic
Plate
Figure 17 - Typical Setup to Produce a Classical
O ptical Hologram
The setup for producing the microwave holograms in this thesis
research, as shown in Figure 18, is very sim ilar to the classical hologram
setup discussed above.
Two antennas are set up to irradiate a sheet of
therm al paper from which the therm al image is to be recorded. One antenna
is the antenna under test (AUT) and the second antenna is a well known
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52
reference (REF) antenna. The two antennas radiate a signal split from the
same source, so th a t a static interference pattern is generated on the therm al
paper. The relative phase difference of the fields from the two antennas at
each location over the therm al paper produces an interference pattern.
AUT
Source
IR Camera
Thermal
Paper
Ref
P hase - 1
Figure 18 - Setup to Produce a M icrowave Hologram
For this thesis research, the AUT was a 36 element patch array
antenna designed for operation at 4 GHz (previously described), and the
reference antenna was a WR-187 waveguide standard gain horn (SGH)
designed for operation over 3.95 GHz to 5.85 GHz. A schematic showing the
layout of this setup is given in Figure 19. As shown in this figure, the AUT
was centered over the therm al paper with the direction of propagation from
the AUT normal to the surface of the therm al paper. The reference antenna
was angled so th at the direction of propagation was at a 60 degree angle to
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53
the normal of the therm al paper. The E-Fields from both antennas were in
the same direction and tangential to the therm al paper surface.
38 cm
PATCH ANTENNA
(AUT)
24.2 cm
45.1 cm
E-FIELD
DIRECTION
POSTER BOARD
23.5 cm
THERMAL PAPER
Figure 19 - Schem atic of th e Setup for th e H olographic
M easurem ents
Examples of therm al images collected with this setup are shown in
Figure 20.
The four images in this figure are false color images of the
tem perature distribution in the therm al paper (which can be related to the
m agnitude of the electric field as previously discussed). In all four of these
images, the top of the image is the edge closest to the reference antenna. The
top left image is of the AUT antenna radiating alone (no radiation from the
reference antenna).
The top right image is of the reference antenna
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54
radiating alone (the effect of tilting the reference antenna is clearly seen in
the oblong shaped pattern of the field m agnitude in this image). The bottom
two images are the interference p attern holograms (both antennas radiating).
The difference between the two holograms is th a t an additional 180 degree
phase shift was inserted into the reference antenna feed line for the image on
the right. Notice th a t the peak tem perature on the left hand hologram occurs
around pixel 32 on the vertical axis, whereas this same location in the right
h an d hologram is a local minima; thus, it can be seen th a t a 180 degree
phase shift of the reference signal converts constructive interference points to
destructive interference points and vice-versa, as expected.
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55
Figure 20 - Example of the Construction of a Microwave Hologram
5.2 D e term in in g the R eference A n te n n a F ield
Processing these microwave holograms requires knowledge of the
m agnitude and phase of the fields of the reference antenna at the locations of
th e thermogram pixels. There are, at least, two methods for obta in in g this
data; hard-wired vector m easurem ents of the fields at the locations of
interest, or computation from a standard near-field scan.
This section
discusses one method of computing the desired reference field data from
standard planar near-field scan data.
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56
Consider the configuration illustrated in Figure 21. Using the Fourier
transform ation techniques discussed in section 3.2, the complex planar n ear­
field data of an antenna can be readily calculated on any other near-field
plane parallel to the aperture of the antenna (the region of accurate
calculation was shown by Lewis and Newell [52] to typically extend from
about r = X to r = 2D2IX). Calculation of the complex planar near-field data
on a plane tilted with respect to the antenna aperture plane can be
accomplished by picking off the appropriate rows (or columns) from a series
of aperture parallel planes.
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57
Planes
Calculation
Plane
Interest
0-1)
AY =
Figure 21 - Setup for D eterm ining T ilted Plane Configuration
This is illustrated in Figure 21. The height of the lower edge of the
aperture from the plane of interest, hi, the length of the aperture, l x, and the
angle between the aperture plane and the plane of interest, 0 , are specified.
The distance di, which is the distance from the plane of interest to the center
of the aperture along the plane parallel to the aperature is then determined
from:
h
smd?
/
2
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(20)
58
The distance from the aperture to the aperture parallel plane (plane of
calculation) th a t intersects with the plane of interest for the row th a t
coincides with di is then found from:
RfA) = dx tan(0)
(21)
Since the location of di is at the center of the aperture, the original
p lan ar near-field
scan extends
d(rovs = \) = dx- Ay((«+ 1)/ 2 )
from
d{row = ri) = dx + Ay((« +1)/2), where n is the num ber of near-field
to
scan rows
and Ay is the spacing between rows (typically slightly less th an 7J2).
Thus, for each row in the original near-field data, the row distance,
d(row), as defined above, is determined and the complete near-field at this
row distance is computed.
From this data, only the row in the plane of
interest is saved. This is repeated for all rows in the original data until a
complete m atrix of data of the same size as the original near-field data
m atrix is obtained for the plane of interest.
Since the plane of interest is tilted from the original aperture-parallel
data, the distance between rows of data in the computed plane of interest has
also been changed. The row spacing in this tilted plane of interest data is
then found from:
AY =
cos#
(22)
The final step in determining the reference field data is an
interpolation of the tilted plane of interest data to the specific pixel locations
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59
of the hologram. Two separate two-dimensional interpolations are required;
one for the field magnitude, the other for the field phase.
The MATLAB program TILT.M, listed in the Appendix, is an
implementation of the algorithm described above.
This code determines,
from a NIST supplied near-field scan, the complex near-fields of the SGH
reference antenna in the configuration used in this thesis research (60 degree
H-Field tilt). A contour plot of the computed m agnitudes of the fields of the
reference antenna is shown in Figure 22a. Figure 22b is a contour plot of the
fields of the reference antenna as determined from a m easured IR
thermogram. Comparison of these plots shows good agreement, although in
the thermogram m easurements, the reference antenna also had a slight EField tilt which is clearly seen in the contour plot.
Com putaa Magntuda of TXad SGH
IRTharmogram Ma*surad Magntuda ofTdtad SGH
-20
•20
-50
•40
•20
0
20
-50
60
-60
■20
0
20
40
60
Figure 22 - C ontour Plots of th e M agnitude of th e Field of the
Reference A ntenna, (a) Computed from NIST Near-Field Data, (b)
From IR Therm ogram M easurements.
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60
5.3 C lassical H olo g ra p h ic Im a g e R ec o n stru c tio n
5.3.1 Theory o f Classical Holosravhic Im ase Reconstruction
Consider the two waves incident on the conductive sheet of therm al
paper from which the therm al cam era obtains its image. One wave, Sa, is
from the Antenna Under Test (AUT) for which the antenna p attern data is
desired.
The other wave, Sr, is from a second, reference, antenna.
The
conductive sheet was shown above to h eat in proportion to the square of the
m agnitude of the electric field incident on the sheet. Therefore, IE t 12, where
Et = E a + E r is the sum of the complex electric field from the AUT and the
complex electric field from the reference antenna, is of interest in this
holographic work. Thus:
(23)
then:
|£,|2 = (£ . + £,X £ . + e J
= f a + E, t E- * E ')
(24)
thus:
(25)
where the * indicates the complex conjugate.
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61
In classical (optical) holography, after producing the hologram, it is
illum inated by a read-out wave, E 0, in order to see the stored complex image.
M athematically, the reconstructed data (image), I, is:
I = \Ea\2Ea +\Er\2E Q+EaE'rE0 +E'aErE0
(26)
Normally (in optical holography) the read-out wave is identical to the
reference wave used to generate the holographic interference pattern;
however, since the therm al image hologram can be "read" by computer, the
readout wave can be chosen to be:
thus:
!= m
. + E r+ ^
N '
N
+E E .
N
(28)
this can be further reduced to:
f\F
1=
I2
Er +Ea + E ’ae12*
(29)
where <j>is phase of the reference field relative to the AUT wave.
The three terms of equation 29 above represent three optical images.
The first term is an amplitude scaled version of the reference field, the
second term is the desired complex field of the AUT, and the third term is a
phase shifted complex conjugate of the AUT field.
With appropriate
positioning of the AUT and reference antennas, these three "images" from the
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62
hologram reconstruction are spatially separated.
To obtain the desired
image, E a, the “viewing" of the reconstructed hologram is restricted to the
area of the desired image, ju st as is done in optical holography.
5.3.2 Sim ulation o f Classical Holographic Image Reconstruction
A series of computer simulations of th is classical holographic
reconstruction technique for various antennas and set-ups (relative positions
of the AUT, REF and therm al screen) were performed [53, 54]. Figure 23
shows an example of one these simulations displayed next to the true farfield plot for a 36 by 36 element array antenna.
In this simulation, the
reference antenna is located a t the upper left com er of the plot. Comparing
the two plots, shows th a t the center of the holographic reconstruction image
(the antenna far-field m ain lobe and first side lobe) is a good representation
of the true far field data for this antenna. Also clearly seen in the upper left
and lower right portions of the hologram are the corruption due to the other
image term s of equation 29.
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63
Tn>* Fw*R*W of 32x32 0 *m «nt Array
S«nul**d Hologram Far-FtoW of 32x32 Bamont Array
04
m
02
3*
0
£
0
•02
-02
■04
-0 4
-0.5
• 0.6
•0.8
•0.8
Figure 23- Sim ulated Classical H ologram R econstruction
Com parison w ith True F ar Field for 36 by 36 Elem ent A rray
Another simulation is shown in Figure 24. This simulation is for a
by
6
6
element array antenna such as the one used for the AUT during this
thesis research. This antenna has a much broader far-field m ain beam than
the 36 by 36 element antenna discussed above. As a result, very little of the
classical hologram contains un-corrupted data (only the first contour line of
the far-field pattern appears sim ilar to the true far-field contour plot). Thus,
these simulations show that, although in some cases this technique may be
useful, classical holographic viewing will not be practical for all antenna
types.
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64
Tnw Far-Ficld o f 6x6 Efenwtf A m y
Sim ultftd Hotegr*n FwFwW o f 6x6 0*m w « Array
0.6
Q.6
04
02
2
0
-02
•0 4
•0.6
-0.8
F ig u re 24 - S im u la te d C lassical H o lo g ram R e c o n s tru c tio n
C o m p ariso n w ith T ru e F a r F ie ld fo r
6
by
6
E le m e n t A rra y
5.4 Im p ro ved H o lo g ra p h ic Im a g e R eco n stru ctio n
5.4.1 Theory oflm vroved Holosravhic Imase Reconstruction
With computerized data collection and processing, however, the
holographic technique is not limited to a single m easurem ent of IEt 12. Given
the hologram equation derived above:
|Et\z = |Ea\2 +\Er\z +EaE m
r +ElEr
(30)
This equation can be re-arranged and written as:
!-£/!
~1^1
E,\\E.
~ l^ rl
_
= e**'-*') +
_
=
2 cos(4>a - <j>r)
(31)
Thus, the difference in phase between the AUT and reference antenna is:
cos"1
hEX-- \ E\ z - \ E ^
2\E1E„
= <f>a -<f,r =A0
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(32)
65
Unfortunately, because of the inverse cosine function, this equation will
produce answers only in the region of 0 to tc for the phase difference, rather
th an the desired range of -it to it. This ambiguity, however, can be elim inated
by processing a second hologram where a phase shift has been inserted into
the reference antenna feed line.
One method for elim inating this phase
ambiguity is discussed below [55].
Re-arranging the terms in the hologram equation (equation 30), and
defining an interm ediate term, H, gives:
H = |£ ,f - |£„|! - | £
,|2
= £„£,' + E:E,
(33)
writing E a and E r in term s of th eir real and imaginary components, this
becomes:
h
=( e : + j e ' x e : -
j e :)+( e
:-
je% e
: +j e d
m
carrying out the multiplication and combining term s results in:
H = 2(.E;Era + E irE'a)
(35)
Two holograms, differing only by the phase of the reference antenna
field, result in:
H(X)=2{E'rmE : +E ‘rmE'a)
H(2)=2(Err(2)E :+ E !ri2)E ‘)
(36)
Re-arranging these two equations and solving for the unknown AUT
field components results in:
Er =
*
~
2{ E ^ E ^ - E ^ E ^ )
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(3 7 )
66
and
Ei=-
(38)
The procedure for determining the AUT phase is then as follows. Step
1, collect a thermogram with the AUT radiating alone (this gives the
m agnitude of the AUT, Ea). Step 2 , collect a therm ogram with the reference
antenna radiating alone (this gives the magnitude of the reference antenna,
Er).
Step 3, collect a holographic thermogram by radiating from both
antennas. Step 4, collect a second holographic therm ogram by inserting a
phase shift in the reference antena feed line. Step 5, compute the phase of
the reference antenna at the pixel locations of the thermograms using
standard m agnitude and phase near-field scan data as discussed in section
5.2 above.
Step
6
, compute H(p and H® by subtracting the squared
magnitudes of the reference and AUT fields from each of the holograms.
Step 7, compute the complex components of the AUT field from equations 37
and 38 above.
5.4.2 Sim ulation of Improved Holosravhic Imase Reconstruction
Four m agnitude input data sets (AUT alone, reference antenna alone,
and the
2
holograms) were computed from the NIST calibration data for
these antennas.
The m agnitude data was then truncated at amplitudes
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67
below 20 dB down from the peak m agnitude of each data set to sim ulate the
dynamic range of the UCCS AGA 780 therm al camera as discussed above.
This sim ulated data was then processed as described above for the improved
holographic image reconstruction technique.
Figure 25 shows a comparison of the AUT far field pattern computed
from this sim ulated holographic data to the pattern obtained from the NIST
calibration data for the AUT. As can be seen in the figure, the reconstruction
capability of the holographic technique is excellent; however, the logistics of
determining the position and angle of the reference antenna, such th at the
phase of the reference antenna field can be accurately computed, are non­
trivial.
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68
Comparison of NIST Far-Field (*) with Holographic Far-Field (+), Simulated 20 dB Range H-Plane
-10
dB -15
-20
-25
-30
-35
-100
-50
0
50
100
D egrees
Figure 25 - AUT Far-Field Computed from Sim ulated
Holograms
5.5 F u tu re H o lo g ra p h ic Work
The results of the simulation of the improved holographic image
reconstrction are very encouraging. Even with the "measurement" dynamic
range limited to 20 dB in the simulations, this holographic technique appears
able to accurately reconstruct the AUT far-field pattern.
Thermographic
m easurem ents are needed to confirm the results of the simulation. Extreme
care m ust be taken, however, in the positioning of the reference antenna.
Small positioning errors th a t are normally unim portant in m agnitude
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
m easurem ents can be very im portant to these holographic m easurem ents
since significant phase errors are introduced with position errors of only a
fraction of a wavelength.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
CHAPTER 6: SUMMARY
Two basic techniques for extending m agnitude only IE, thermographic
m easurements to the complex near-field m easurem ents of tr ansm itting
antennas were investigated in this thesis research, a Fourier interative
Plane-to-Plane (PTP) technique and a holographic technique.
Simulations of the PTP technique were performed for various dynamic
ranges of the m agnitude data. These simulations showed th at the technique
produced a good representation of the the AUT far-field pattern for
magnitude data with a 30 dB or greater dynamic range (a range th a t should
be possible with modem therm al cameras). For m agnitude data with a 20 dB
dynamic
range,
the
PTP
technique
simulation
produced
a
good
representation of only the main lobe of the AUT. IR thermograms of the field
magnitude were then made using the UCCS AGA 780 therm al camera. The
PTP technique processed results from these thermograms, which had a
dynamic range of approximately 20 dB, were in agreement with the
simulation results.
An error metric was also defined for the PTP technique th a t appears
useful in determining the quality of the PTP processing results. Additional
m easurements of other AUT types should be performed to confirm the utility
of the error metric in determining the accuracy of the PTP results.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
Additionally, the phase change acceleraction and center-of-gravity data
alignment concepts recently proposed by Junkin should be investigated for
incorporation into the PTP algorithm.
A second, independent, method of determining phase information of a
field from IR therm al m easurem ents was also developed. This technique is
based on an extension of classical holography. This holographic technique
was shown by simulation to be less reliant on the dynamic range of the
magnitude data from the thermograms than the PTP technique for an
accurate reconstruction of an AUT far-field pattern. The trade-off is th at
four therm al m easurem ents and a priori knowledge of the phase distribution
of the reference antenna at the m easurem ent locations are necessary.
Thermogram holographic measurements are needed to confirm the results of
these simulations.
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72
BIBLIOGRA PHY
[1]
G.E. Evans, "Antenna M easurem ent Techniques", Artech House, 1990.
[2]
Special Issue on Near-Field Scanning Techniques, IEEE Transactions
on Antennas and Propagation, Vol 36, No 6, June 1988.
[3]
L.G. Gregoris and K. Iizuka, "Thermography in Microwave
Holography", Applied Optics, Vol 14, No. 7, pp. 1487-1489, July 1975.
[4]
R.M. Sega and J.D. Norgard, "An Infrared M easurement Technique for
the Assessment of Electromagnetic Coupling", IE EE Transactions on
Nuclear Science, Vol. NS-32, No. 6, pp. 4330-4332, December 1985.
[5]
R.M. Sega and J.D. Norgard, "Infrared M easurements of Scattering
and Electromagnetic Penetration Through Apertures", IEEE
Transactions on Nuclear Science, Vol. NS-33, No. 6, pp. 1658-1663,
Dec. 1986.
[6]
R.M. Sega and J.D. Norgard, "Expansion of an Infrared Detection
Technique using Conductive Mesh in Microwave Shielding
Applications", SPIE Vol. 819 Infrared Technology XII. pp. 213-219,
1987.
[7]
J.D. Norgard and R.M. Sega, "Microwave Fields Determined from
Thermal Patterns", SPIE Vol. 780 Thermosense IX. pp. 156-163, 1987.
[8]
R.M. Sega, J.D. Norgard, and G.J. Genello, "Measured Internal
Coupled Electromagnetic Fields Related to Cavity and Aperture
Resonance", IEEE Transactions on Nuclear Science, Vol NS-34, No. 6,
pp. 1502-1507, Dec. 1987.
[9]
J.D. Norgard, R.M. Sega, M. Harrison, A. Pesta, and M. Seifert, "
Scattering Effects of Electric and Magnetic Field Probes", IEEE
Transactions on Nuclear Science, Vol. 36, No. 6. pp. 2050-2057, Dec
1989.
[10] J.D. Norgard, D.C. Fromme, and R.M. Sega, "Correlation of Infrared
M easurem ent Results of Coupled Fields in Long Cylinders with a Dual
Series Solution", IE E E Transactions on Nuclear Science, Vol. 37, No. 6,
pp. 2138-2143, Dec. 1990.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
[11]
R.M Sega, V.M. M artin, D.B. Warcnuth, and R.W. Burton, "Infrared
Application to the Detection of Induced Surface Currents", SPIE, Vol.
304, Modern U tilization o f Tnfrared Technology VII. pp. 84-91, 1981.
[12]
J.P. Jackson and R.W. Burton, "Surface C urrent Detection by Infrared
Inspection", Proceedings: IEEE Region 5 Conference and Exposition,
pp. 175-178, May 1982.
[13]
R.M. Sega, C.V. Stewart, and R.W. Burton, "Induced Surface Currents
Obtained Through Infrared Techniques Correlated with Known Values
for Simple Shapes", Proceedings: IE E E Region 5 Conference and
Exposition, pp. 179-181, May 1982.
[14]
V.M. M artin, C.V. Stewart, and R.W. Burton, "An Optimized
Conductive Coating for Thermographic M easurem ent of Microwave
Induced Surface Currents", Proceedings: IE E E Region 5 Conference
and Exposition, pp. 182-185, May 1982.
[15] R.M. Sega, "Infrared Detection of Microwave Induced Surface Currents
on F lat Plates", RADC-TR-82-308, 1982.
[16] L.S. Taylor, "The Phase Retrieval Problem", IEEE Transactions on
Antennas and Propagation, Vol. 29, pp. 386-391, March 1981.
[17] J.R. Fienup, Applied Optics, Vol. 21, pp. 2758-2769, August 1982.
[18] R.W. Gerchberg and W.O. Saxton, Optik, Vol. 35, pp. 237-246, 1972.
[19] D.L. Misell, "A Method for the Solution of the Phase Problem in
Electron Microscopy", Journal o f Physics D, Applied Physics, Vol. 6,
pp. L6-L9, 1973.
[20] V.Yu.Ivanov, V.P.Sivokon, and M.A.Vorontsov, "Phase Retrieval from
a Set of Intensity Measurements: Theory and Experiment", Journal of
the Optical Society of America, Vol. 9, No. 9, pg. 1515-1524, Sept. 1992.
[21] T. Isem ia, G. Leone, and R. Pierri, "New Approach to Antenna Testing
from N ear Field Phaseless Data: The Cylindrical Scanning", IEE
Proceedings, Vol. 139, Pt. H, pp. 363-368, August 1989.
[22] O.M.Bucci, G.D’Elia, G.Leone, and R.Pierri, "Far-field Pattern
Determination from the Near-field Amplitude on Two Surfaces", IEEE
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
Transactions on Antennas and Propagation, Vol 38, No. 11, pg 17721779, Nov. 1990.
[23]
A.P. Anderson and S. Sali, "Diagnostics, P art I: Error Reduction
Techniques", IE E Proceedings, Vol. 132, Pt. H., pp. 291-298, August
1985.
[24]
R.G. Yaccarino and Y. Rahmat-Samii, "Phaseless Near-Field
M easurements Using the UCLA Bi-Polar P lanar Near-Field
M easurement System", 16th A nnual Antenna Measurement
Techniques Association Symposium, pp. 255-260, October 1994.
[25]
R.G. Yaccarino and Y. Rahmat-Samii, "Phaseless Bi-polar Near-field
Measurements: A Squared Amplitude Interpolation / Iterative Fourier
Algorithm", 1995 Antenna Measurements Techniques Association 17th
Meeting and Symposium, Williamsburg, pgs 195-200, Nov 13-17, 1995.
[26]
C.A.E. Rizzo, G. Junkin, and A.P. Anderson, "Near-field/Far-field
Phase Retrieval M easurem ents of a Prototype of the AMSU-B SpaceBorne Radiometer Antenna a t 94 GHz", 1995 Antenna Measurements
Techniques Association 17th Meeting and Symposium, Williamsburg,
pgs 385-389, Nov 13-17, 1995.
[27]
G.Junkin, A.P.Anderson, C.A.E.Rizzo, W.J.Hall, C.J.Prior, and
C.Parini, "Near-field/Far-field Phase Retrieval M easurement of a
Prototype of the Microwave Sounding Unit Antenna AMSU-B at 94
GHz", ESTEC Conference on M illimeter Wave Technology and
Applications, Noordwijk, N etherlands, 1995.
[28]
G.Trueba, G.Junkin, "A Numerical Beam Alignment Procedure for
Planar Near-field Phase Retrieval", Electronics Letters, 1995.
[29]
T.Isemia, G.Leone, R.Pierri, "Phaseless Near-field Techniques:
Uniqueness Conditions and A ttainm ent of the Solution", Journal of
Electromagnetic Waves and Applications, Vol. 8, No. 7, pg. 889-908,
1994.
[30]
R.Barakat and G.Newsam, "Algorithms for Reconstruction of Partially
Known, Band-limited Fourier-transform Pairs from Noisy Data",
Journal of the Optical Society o f America, Vol. 2, No. 11, pg. 20272039, 1985.
[31]
Telephone conversations between J.D. Norgard and W. Kent of MRC,
Dayton, Ohio.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
[32]
D. Gabor, "A New Microscopic Principle", Nature, Vol 161, pp. 777-778,
May 1948.
[33]
R.P. Dooley, "X-Band Holography", Proceedings o f the IEEE, Vol 53, p.
1733, Nov. 1965.
[34] D.W. Metzger, "Quantification of the Thermographic Mapping of
Microwave Fields", Ph.D. Thesis for the University of Colorado,
Colorado Springs, 1991.
[35]
G.D. Wetlaufer, "Optimization of Thin-Screen M aterial Used in
Infrared Detection of Microwave Induced Surface Currents a t 2-3
GHz", MSEE Thesis, University of Colorado, Colorado Springs, 1985.
[36]
W.C. Diss, "Techniques for M easuring Microwave Interference Using
Infrared Detection and Computer Aided Analysis", MSEE Thesis,
University of Colorado, Colorado Springs, 1984.
[37]
R. Segal and J. Howel, "Thermal Radiation H eat Transfer", McGrawHill, 1972.
[38] M.D. Smith, "Infrared Detection of Electromagnetic Penetration
Through Narrow Slots in a Ground Plane", MSEE Thesis, University
of Colorado, Colorado Springs, 1990.
[39]
D. Fredal, R.M. Sega, J.D. Norgard, and P.E. Bussey, "Hardware and
Software Advancement for Infrared (IR) Detection of Microwave
Fields", SPIE Vol. 781, Infrared Image Processing and E n h ancem en t.
pp. 160-167, 1987.
[40]
AGA Thermovsion® 780 Operation M anual, AGA Infrared Systems
AB, 1979.
[41]
A.C. Newell, "Planar Near-field A ntenna Measurements", N ational
Institute of Standards and Technology, Electromagnetic Fields
Division N ear Field Course Notes, March 1994.
[42]
D.M. Kerns, "Analytical Techniques for the Correction of Near-field
A ntenna M easurements Made with an Arbitrary but Known
M easuring Antenna", Abstracts o f URSI-IRE Meeting, Washington,
DC, pp. 6-7, April-May 1963.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
[43]
D.M. Kerns, "Plane-wave Scattering-m atrix Theory of A ntennas and
A ntenna-antenna Interactions", National Bureau of Standards,
Monograph 162, Ju n e 1981.
[44] D.M. Kerns, "Scattering M atrix Description and Near-field
M easurements of Electroacoustic Transducers", Journal o f the Acoustic
Society of America, Vol. 57, pp. 497-507, Feb. 1975.
[45]
D.M. Kerns, "Correction of Near-field Antenna M easurem ents Made
with an Arbitrary but Known M easuring Antenna", Electronic Letters,
Vol. 6, pp. 346-347, May 1970.
[46] R.C. Baird, A.C. Newell, P.F. Wacker, and D.M. Kerns, "Recent
Experimental Results in Near-field Antenna Measurements",
Electronic Letters, Vol. 6, pp. 349-351, May 1970.
[47]
A.D. Yaghjian, "An Overview of Near-field Antenna Measurements",
IE EE Transactions on Antennas and Propagation, Vol. AP-34, No. 1,
pp. 30-45, Jan. 1986.
[48] D. Slater, "Near-Field Antenna Measurements", Artech House, 1991.
[49] J.J. Lee, E.M. Ferren, D.P. Woollen, and K.M. Lee, "Near-field Probe
Used as a Diagnostic Tool to Locate Defective Elements in an Array
Antenna", IE E E Transactions on Antennas and Propagation, Vol. 36,
No. 6, pp. 884-889, June 1988.
[50] A.D. Yaghjian, "Efficient Computation of Antenna Coupling and Fields
Within the Near-field Region", IE E E Transactions on Antennas and
Propagation, Vol. AP-30, No. 1, Ja n 1982.
[51] Private conversations with Mike Siefert of Rome Laboratory RL/ERST
about capabilities of th eir AGEMA 900 Thermal Camera.
[52] R. Lewis and A. Newell, "An Efficient and Accurate Method for
Calculating and Representing Power Density in the Near-Zone of
Microwave Antennas", National B ureau of Standards, NBSIR 85-3036,
December 1985.
[53] C. Stubenrauch, "Holographic Antenna M easurements using Infrared
Imaging", Presented a t the NIST Antenna and M aterials Metrology
Group Seminar, May 18, 1995.
[54] Private communications with C. Stubenrauch, NIST, Boulder, CO.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
[55]
Derivation originally suggested by R. Cormack, NIST, Boulder, CO.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-l
APPENDIX A: MATLAB CODES
M E T 2.M ..................................................................................................................... 2
IR_AV_C.M................................................................................................................4
TO TEM P.M ............................................................................................................... 7
TEM P2E3.M ..............................................................................................................8
P T P L O O P.M .............................................................................................................9
PT PLPTH M .M ....................................................................................................... 11
TILT.M ..................................................................................................................... 13
FIL E R D .M ...............................................................................................................15
FFTU N SFT.M .........................................................................................................16
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A-2
MET2.M
% Met2.m - Program to determine the temperature to E-field curve
%
using the equations derived in Metzger's PhD Thesis.
%
% John E. Will 1/29/9S
% First initialize a bunch of stuff
clear i;
clear pi;
% thermal conductivity
h=0.93 ;
% emissivity of paper
epsilonir=0.96;
% boltzmann constant
boltzmann=5.7e-8;
ambtemp=23+273;
% ambient temo in oK
eps0=8.854e-12;
mu0=4e-7*pi;
% freq in Hz
freq = 4e9;
epsrdiel=lO;
% relative permitivity of paper
sigma=8;
% paper conductivity
d=80e-6;
% paper thickness
% Now use the above values to generate some useful other stuff
etaair= (muO/epsO) ~ .5
omega=2 *pi *freq;
gammadiel=(i*omega*sqrt(muO*epsO*epsrdiel)*sqrt(1+sigma/(i*omega*epsO*epsrdiel))
) ;
alpha=real(gammadiel);
beta=imag(gammadiel);
etadiel=(sort(muO/(epsO*epsrdiel+sigma/(i*omega)) ) ) ;
p=(exp(-gammadiel*d));
gamma=((etadiel-etaair)/ (etadiel+etaair));
% Now we find E+ and E- and power/sqm from the Einc
lp=0 ;
for it=10:10:900
lp=lp+l
einca(Ip)=it;
eir.c=it;
e2plus=(einc*(gamma+1)/ (1-(gamma~2)* (p^2)));
e2minus=(einc*(-gamma*pA2)* (gamma+1)/ (1-(gammaA2)* (p^2)));
powerabspersqm=(sigma./(4.*alpha).*((abs(e2minus).~2).*(exp(2.*alpha.*d)-1)(abs(e2plus).~2 ) .*(exp(-2.*alpha.*d)1))+sigma./(2,*beta).*real(e2plus.*conj(e2minus).* i .*(exp(-2.* i .*beta.*d)-1)));
powerincpersqm=einc.~2/3 77;
% Now we find the surface temp
eb=epsilonir*boltzmann;
reman=powerabspersqm+h* amb temp+eb *ambtemp^ 4;
x=solve('eb*TsA4+h*Ts=reman', 1T s ');
(eval(x(l,:)}-273);
(eval (x (2, :) )-273) ;
surf temp (lp) = (eval (x (3 , :)) -273)
(eval (x (4, :) )-273) ;
% the third root above is the one we want to save
end ;
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A-3
% now
'surftemp'
is an array of surface temperature inCfor
% einc in V/m as saved in array ’e i n c a 1
an
% so now try fiting a 2nd order polynomial to this data
ambtemp=ambtemp-273;
thermp=polyfit(einca,(surftemp-ambtemp),2)
% thermp should now be a 3 element array with the coefficients for
% thermp(1)*Einc~2 + thermp(2)*Einc + thermp(3) = Temp rise above ambient
% with Temp rise in C and Einc in V/m
% This can then be turned around using the MATLAB function ROOTS
%
(see TEMP2E3.M code)
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A-4
IR_AV_C.M
% THIS CODE REQUIRES THE FULL VERSION OF MATLAB ################£#######
% John E. Will June 1995
clear
elf
fid=-l;
while fid==-l
fnme=input('Filename for processing? ','s'),fid=fopen(fnme);
if fid==-l
di s p (['********** File not found, try again...'])
end
end
% now read in the header field
A=fread(fid,[116,64],'u i n t 8 ');
(same total size as all fields)
% print out the header info and decide what to do next
% note current code doesn't give you many options, future
% versions could include frame selection, averaging, etc.
nmflds=A(2,1); % this location contains a code for fields/frame
if nmflds==0 nmflds=4;end; % 0 implies 4 fields per frame
if nmflds==255 nmflds=2;end; % 255 implies 2 fields per frame
% I intend to also have a file type with only 1 field per frame
%A(1,1) is the total number of fields stored in file, thus the
%number of frames is fields/(num fields per frame) from above
nmframes=A(1,1)/nmflds;
dis p ( [' '] )
disp(['This file, ',fnme,', contains ',int2str(nmframes),' frames of data.'])
%month is A(3,l); day is A(4,l); year is A(5,l) and A(6,l)-two byte val
%hour is A (7,1); min is A(8,l); shot number is 2 bytes A(9,l) and A(10,l)
d isp(['recorded on
',int2str(A(3,1)),'/', int2str(A(4,1)), '/',int2str((256*A(6,1))+A(5,1)) ,. . .
' at ',int2str(A(7,1)),':’,int2str(A(8,1)),' and is shot number
',int2str((256 *A (10,1))+A(9,l))])
%next is frequency of illumination saved as 2 byte base, 2 byte exponent
%base is in (11,1) and (12,1); exponent in (13,1) and (14,1)
freq=((256*A(12,1))+A (11,1)) * 10" ( (256*A (14,1) )+A (13 ,1) ) ;
disp(['Frequency of illumation was ',num2str(freq),' Hz'])
% Thermal range and level are in A(15,l) and A(16,l)
thermlevl=A(16,1);thermrange=A(15,1);
disp(['The Thermal Range Setting was ',int2str(thermrange),'
Level of 1,...
int2str(thermlevl)])
with Thermal
% Ambient Temperature is next, again 2 byte base and exponent
% base is (17,1) and (18,1); exponent is (19,1) and (20,1)
ambtemp=((256*A(18,1))+A(17,l)) * 1 0 " ( (256*A(20,1))+ A (19,1));
disp(['The ambient temperature was ',num2str(ambtemp),' degrees C'])
% Radiating power level is next 2 byte base and exponent
% base is (21,1) and (22,1); exponent is (23,1) and (24,1)
powerlev=((256* A (22,1))+ A (21,1)) * 1 0"((256*A(24,1))+ A (23,1));
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-5
disp(['The RF radiating power level was 1,num2str(powerlev),' dBm'])
% Next is the IR Camera Lens (this will be needed to get correct cal curve)
% Location is A(25,l)
% 1
- is LW f/1.8 7deg
% 2
- is LW f/1.8 20deg (wide angle)
% 3
- is LW f/1.8 3.5deg (telephoto)
% 4
- is SW f/1.8 7deg
1ensnum=A(25,1);
if lensnum==l
lenstype=(['LW f/1.8 7deg']);
elseif lensnum==2
lenstype= ([1LW f/1.8 20 deg (wide angle)']),elseif lensnum==3
lenstype= ([' LW f/1.8 3.5deg (telephoto)']),elseif lensnum==4
lenstype=(['SW f/1.8 7deg']);
end
disp(['The lens used for this datafile was the ',lenstype])
%next is the number of lines per field in location A(26,l)
%- I'm not sure what this means, but one note said
%"Typically 64 lines/field, but others can be created"
%so I'll not currently worry about displaying this
% Now, all that's left is 5 lines of comments as follows:
% Line 1 - A (1,9) through A (80,9)
% Line 2- A(l,10) through A(80,10)
% Line 3- A(l,ll) through A(80,ll)
% Line 4- A(l,12) through A(80,12)
% Line 5- A (1,13) through A(80,13)
dis p (['File comments a r e : '])
for jj =9:13
ii=l;
cmt = ’-';
while (A(ii,jj) < 128) & (ii < 80)
cmt=[cmt A (i i,j j )];
ii=ii+l ,end
disp(setstr(cmt))
end
%********** a l l the rest of the first field of datafile is junk
( 2S2TOS) * * * * * * * * * * *
% I would then follow this with a check of any possible changes
%in case the file data is wrong (even allow a re-write of corrected info)
framenum=input(['Range of frames to be averaged [start, stop]? ']);
while ((max(framenum) > nmframes) | (min(framenum) < 1))
dis p (['********Invalid number.
Input for this file must be between 1 and
',int2str(nmframes)])
framenum=input(['Range of frames to be averaged [start, stop]? '])
end
fseek(fid,(29696*(framenum(1)-1))+7424,'bof');
Fl = zeros(116,64);F2=zeros (116,64);
for ii=framenum(1):framenum(2)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-6
% now fieldl
Al=fread(fid,[116,64],’uint8’);
% now field2
Bl=fread(fid,[116,64],'uint8');
%now field3
Cl=fread(fid,[116,64],'uint8');
% now field4
Dl=fread(fid,[116,64],'uint81);
% now we need to generate the real frame from the 4 fields
% and adjust so that 0 is min temp, 255 is max temp
% the first two fields are averaged together to get the odd scan lines
% while the last two are averaged to get the even scan lines
F1=F1+(255-((Al+Bl)/2));
F2=F2+(255-((Cl+Dl)/2));
end
% now create the final full frame
% BUT WE HAVE A LITTLE PROBLEM, seems as though the UCCS camera is
% not giving us good even/odd scan lines, but are really the same set
% so instead o f :
% frame (1:116,1:2:127) =Fl/ (framenum(2) -framenum(l) +1) ,% frame(1:116,2:2:128)=F2/(framenum(2)-framenum(1)+1);
% we will do the following:
frame(1:116,1:64)=((F1+F2)/2)/ (framenum(2)-framenum(1)+1);
% set up variables for plotting the full frame with the
% full version of MATLAB (the Student edition
% is limited in matrix and array size.
X =1:64;
% put this back in if camera is fixed ---->
y = l :116;
x=l:128;
% now let's plot
hold off
contour(frame);
%surfc(x,y,frame);
title(fnme);
%shading flat;
%colormap hot,-colorbar;
v i e w (90,90)
% this sets the appropriate angle for viewing plot
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TO TEM P.M
%code to convert a frame of raw or averaged IR data intorealtemperature
% assumes the ir data is in an array called frame
% first need to get some additional info
ambtemp = input('Ambient temperature in degrees C(usually about
20) ');
do = input('Distance from screen to camera in meters (use 1 if unknown) ')
eps = input('Emissivity of thermal emitter (Teledeltos is .93) ');
L0 = input('Thermal Level Setting ');
Tr = input('Thermal Range Setting ');
% the next constants assume we are using the AGA 780 LW sensor
% at an aperature of f=l.8
A=552855;
B=2994;
C = .975 ;
% now calculate the atmospheric attenuation effect coeff.
tau = e x p (-0.008*(sqrt(do)-1));
% now we get the temperature in isothermal units
IA = A/(C*exp(B/(ambtemp+273.15))-1) ;
10 = ((frame./256)-0.5).*Tr;
1 0 = ((L0+I0),/(tau*eps)) - (( (1/(eps*tau) )-1) *IA)
% then convert to temperature degrees K
tframe = B./log(((A./I0)+ 1)./C);
% now to degrees C
tframe = tframe-273.15;
maxt=max(max(tframe))
mint=min(min(tframe))
%colormap(jet);surf(tframe);colorbar
contour (tframe) ,-view (90, 90) ;text (140, 5, ['max temp = ' num2str (maxt) ' C •] )
t e x t (140,50,['min temp = ' num2str(mint) ' C'])
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-8
TEM P2E3.M
function [E]=temp2e3(tem,base)
% TEMP2E - Function to convert to magnitude of E based on a polynomial fit
%
to the results of Metzger's equation.
[E]=TEMP2E3(tem,base) where
%
E is the
returned E field matrix, tem is the temperature matrix
%
from the
thermal camera, and base is the base-line temperature
%
at which
(and below) E is assumed zero, base, for this version
%
is typically min(min(tem)), since the typical 0.3degree offset
%
from the min temperature has been included in the roots below.
%
%
John E. Will Jan 1996 for Ph.D. Research
% now determine delta Temperature from temp and base
deltaT=(tem>base). * (tem-base);
%the first part assures deltaT only positive, and zero below base
% now get Einc from polynomial minimization
% For this version, the zeroth polynomial coefficient has been
%set to zero, thus the 0.3 degree rise above min temp normally
%used is not necessary. Use E=temp2e3(file,min(min(file)))
for it=l:size(deltaT,l)
for it2=l:size(deltaT,2)
etmp=roots([3.le-5 .0035 (-deltaT(it,it2) )]) ;
E(it,it2)=etmp(etmp>-le-17);
%picks positive root only
end;
end;
%Thaaat1s i t .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-9
P TP LO O P .M
%PTPLOOP.M Program to iteratively find the phase from 2 planes of
%
magnitude only data using Fourier Transform Propagation.
%
Requires the function FFTUNSFT.M which reverses the effect
%
of the MATLAB provided FFTSHIFT.M function in order to properly
%
account for non-power-of-2 sized matrices.
%
%
%
%
This particular version is hard-coded for the processing of
magnitude only NIST near-field data on the 36 element array
operated at 4 G H z .
%
%
%
Final output is complex matrix 'farap' which is the array
far-field data.
%
% John E. Will - December 23, 1995
% first set up some constants that will be read in later versions
ncol = 57;
nrow = 57;
delx = 3.175;
dely = 3.175;
AOB= 15.18;
AOB = 10~(AOB/20);
freq = 4;
c = 29.979;
% now calculate some other constants
fk = 2*pi*freq/c;
c3 = delx*dely/(4*pi*pi*A0B)
cx = 2*pi/(delx*ncol) ,cy = 2*pi/(dely*nrow) ;
% now generate the ksqr matrix and gama
fk x = (1:ncol);
fkx=fkx- ( (ncol+1) /2)
fkx=fkx * cx;
fky=(1:nrow);
fky=fky-{(nrow+1)/2),fky=fky * cy;
for Ll=l:ncol;
for L2=l:nrow;
fsqr(Ll,L2)=fkx(Llp2 + fky(L2)"2;
end;
end;
gama = sqrt(fk^2 - fsqr);
evan = imag(gama)==0;
% evan will be 1 for gama real, 0 for gama imag
%
% NOW we can set up the data for looping
load at3S_l
% complex data at 3 8.1 cm
load at72_0
% complex data at 72.0 cm
Ml = abs(at38_l);
%magnitude of measurement plane 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-10
dist (1)=38.1;
M2 = abs(at72_0);
dist (2)=72.0;
%distance from antenna plane to meas
%magnitude of measurement plane 2
%distance from antenna plane to meas
plane 1
plane 2
kk=l;
% now open a couple of files to store my measure of convergence
plotting)
fidl=fopen{'mdl','w');
fid2=fopen('md2','w');
(for later
%first we need an estimate of the aperature plane
Eap=zeros(nrow,ncol);
la=round(((ncol+1)/2)-(38/(2*delx))),ra=round(((ncol+1)/2)+(38/(2*delx)));
ua=round(((nrow+1)/2)+(38/(2*dely))),da=round(((nrow+1)/2)-(38/(2*dely))),Eap(la:ra,da:ua)=ones(size(Eap(la:ra,da:ua)));
% left,right,up,and down aperature location - set all aperature to ones
ap = Eap-=0;
% ap should be 1 1s only inside aperature. Used to truncate data outside
cnv=1000;
perr=0;
while ((kk < 201) & (cnv > 0.000001))
% truncate outside of aperature
Eap = Eap .* a p ;
% aperature to plane 1
El = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(1)) .* evan));
% calculate convergence error
errl = sum(sum((abs(El)-Ml) .~2)) / (sum(sum(Ml.^2))) ;
% now replace magnitude with measured
El = (Ml .* cos(angle(El))) + (i*Ml .* sin(angle(El)));
% now back to aperature
Eap = ifft2(fftunsft(fftshift(fft2(El)) .* exp(-i*gama*dist(1)) .* evan));
% truncate outside of aperature
Eap = Eap .* a p ;
% aperature to plane 2
E2 = ifft2(fftunsft(fftshift(fft2(Eap)) .* e x p (i*gama*dist(2)) .* evan));
% calculate convergence error
err2 = sum(sum( (abs(E2)-M2) .~2)) / (sum(sum(M2.~2)));
% now replace magnitude with measured
E2 = (M2 .* cos (angle (E2) ) ) + (i*M2 .* sin (angle (E2))) ,% now back to aperature
Eap = ifft2(fftunsft(fftshift(fft2(E2)) .* exp(-i*gama*dist(2)) .* evan));
fprintf(1,'%s %g %s %g %s %g\n','loop number = ',kk,'
’,errl) ,fprintf(fidl,'%g\n',errl);
fprintf(fid2,'%g\n',err2);
err2 = 1,err2,1
cnv=abs (perr-err2) ,perr=err2 ;
kk=kk+l;
end;
fclose(fidl);fclose(fid2);
farap=(fftshift(fft2(Eap))) * c3 .* evan;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
errl =
A -ll
P TP LP TH M .M
%PTPLPTHM.M Program to iteratively find the complex results
%
from 2 planes of Thermally measured data collected 12/19/95.
%
Adjust initialization parameters and file names for other data.
%
%
%
%
Requires the function FFTUNSFT.M which reverses the effect
of the MATLAB provided function FFTSHIFT.M in order to properly
account for non=power-of-2 sized matrices.
%
%
%
Final output is complex matrix 1farap'
complex far-field data.
which is the AUT
%
% John E. Will - December 28, 1995
% first set up some constants that will be read in later
ncol = 116;
nrow = 64;
delx = 1.0;
dely = 1.49;
AOB= 0;
AOB = 10"(AOB/20);
freq = 4;
c = 29.979;
% now calculate some other constants
fk = 2*pi*freq/c;
c3 = delx*dely/(4*pi*pi*AOB);
cx = 2*pi/(delx*ncol);
cy = 2*pi/(dely*nrow),% now generate the ksqr matrix and gama
f kx=(1:ncol);
fkx=fkx-((ncol+1)/2);
fkx=fkx * cx;
fky=(1:nrow);
fky=fky-((nrow+1)/2);
fky-fky * cy;
for Ll=l:ncol;
for L2=l:nrow;
fsqr(Ll,L2)=fkx(Ll)"2 + fky(L2)~2;
end;
end;
gama = sqrt(fkA2 - fsqr);
evan = imag(gama)==0;
% evan will be 1 for gama real,
0 for gama imag
% NOW we can set up the data for looping
load c:\ir\decl9\decl9_27.e
% thermal magnitude data at 32.4 cm
load c:\ir\decl9\decl9_29.e
% thermal magnitude data at 45.0 cm
Ml = decl9_27;
%magnitude of measurement
d ist(1)=32.4;
%distance from antenna
M2 = decl9_29; %magnitude of measurement
d ist(2)=45.0;
%distance from antenna
plane
plane
plane
plane
1
to meas plane 1
2
to meas olane 2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-12
kk= 1 ;
% now open a couple of files to store my measure of convergence
plotting)
fidl=fopen('mdl1, 'w') ;
fid2 = fopen('md21, 'w') ;
(for later
%first we need an estimate of the aperature plane (38cm x 38cm)
Eap=zeros(ncol,nrow);
la=round(((ncol+1)/2)-(38/(2*delx)));
ra=round(((ncol+1)/2)+(38/(2*delx))),ua=round(((nrow+1)/2)+(38/(2*dely)));
da=round(((nrow+1)/2)-(38/(2*dely)));
Eap(la:ra,da:ua)=ones(size(Eap(la:ra,da:ua))),% left,right,up,and down aperature location - set all aperature to zero
ap = Eap-=0;
% ap should be l's only inside aperature. Used to truncate data outside
cnv=1000;
perr=0;
while ((kk < 201) & (cnv > 0.000001))
% truncate data outside of aperature
Eap = Eap .* a p ;
% aperature to plane 1
El = ifft2 (fftunsft (fftshift (fft2 (Eap) ) .* exp (i*gama*dist (1)) .* evan)) ,% calculate convergence error
errl = sum(sum((abs(El)-Ml).^2)) / (sum(sum(Ml.A2 ) ));
% now replace magnitude with measured
El = (Ml .* cos (angle (El) ) ) + (i*Ml .* sin (angle (El) )) ;
% now back to aperature
Eap = ifft2(fftunsft(fftshift(fft2(El)) .* exp(-i*gama*dist(1)) .* evan));
% truncate outside of aperature
Eap = Eap .* ap ;
% aperature to plane 2
E2 = ifft2(fftunsft(fftshift(fft2(Eap)) .* exp(i*gama*dist(2)) .* evan));
% calculate convergence error
err2 = sum(sum((abs(E2)-M2).A2)) / (sum(sum(M2.A2)));
% now replace magnitude with measured
E2 = (M2 .* cos(angle(E2))) + (i*M2 .* sin(angle(E2)));
% now back to aperature
Eap = ifft2(fftunsft(fftshift(fft2(E2)) .* exp(-i*gama*dist(2)) .* evan));
fprintf(1,'%s %g %s %g %s %g\n','loop number = ',kk,'
',errl);
fprintf(fidl,1%g\n',errl);
fprintf (fid2, '%g\n',err2);
err2 = ',err2,'
cnv=abs(perr-err2);
perr=err2 ,kk=kk+l;
end;
fclose (fidl) ;fclose (fid2) ,farap=(fftshift(fft2(Eap))) * c3 .* evan;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
errl =
A-13
TIL T.M
% TILTH - Program to compute the complex fields of an Antenna on a tilted
%
near-field H-plane from the complex far-field data. This version
%
is currently hard-coded
for the SGH used for thesis work.
%
%
%
%
%
Input file is farsgh.mat and Output is:
result - matrix of complex tilted plane data at
wantx,wanty - arrays of 'result' point spacings
which should agree with Dec20_2x data files.
%
%
-John E. Will
Feb 1996
% first set up some constants that will be read in later
ncol = 57;
nrow = 57;
delx = 3.175;
dely = 3.175;
AOB= 14.8 8;
AOB = i(T(A03/20);
freq = 4;
C = 29.979;
lambda=c/f req;
% First, compute the original, measured data, spacings about zero center
rowpos=((1:nrow)- ( (nrow+1)/2))*dely;
colpos=((1:ncol)- ( (ncol+1)/2))*delx;
% now calculate some other constants
fk = 2*pi*freq/c;
c3 = delx*dely/(4*pi*pi*A0B);
cx = 2*pi/(delx*ncol);
cy = 2*pi/(dely*nrow);
% now generate the ksqr matrix and gama
fkx = (1:ncol);
fkx=fkx-((ncol+1)/2);
fkx=fkx * cx;
fky=(1:nrow);
fky=fky-((nrow+1)/2) ;
fky=fky * cy;
% Pre-allocate for faster processing
fsqr=zeros (ncol,nrow) ,for Ll=l:n c o l ;
for L2=l:nrow;
fsqr(L1,L2)=fkx(Ll)"2 + fky(L2)"2;
end;
end;
gama = sart(fk^2 - fsqr) ,evan = imag (gama) ==0 ,% evan will be 1 for gama real, 0 for gama imag
load farsgh
% load the complex far-field data for the Standard Gain Horn
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-14
% now for each row calcuate the distance and then the data
% this is setup now for the Dec20_2X files
hl=23.5;
%height of lowest edge, cm
ang=60;
%antenna tilt angle in degrees
ang=ang*2*pi/3 6 0 ; %convert to radians
11=22.75;
%length of horn edge along the angle axis, cm (Wide side)
d l = (11/2)+(hl/sin(ang));
%length of triangle side from horn center, cm
% now pre-allocate the tilted plane matrix
tiltplane=zeros(ncol,nrow);
for row=1:nrow
% compute the distance each row is from the aperture
rowdist= (dl+rowpos (row) )*tan (ang) ,% compute the complex near-field matrix at this rowdist
plane=ifft2(fftunsft((farsgh/c3) .* exp(i*gama*rowdist) .* evan));
% now pick off the row of interest and save for later
tiltplane(row,:)=plane(row,:);
end;
% tiltplane now contains the tilted plane complex near-field data,
% BUT, the point spacing has changed.
So now we compute the new
% point spacings.
tilty=rowpos;
tiltx=colpos/cos(ang);
% Now we'll need to do some 2-D interpolation to get data at the points
%
of interest for the holographic processing.
wantv=(-51:54)*.86;
wantx=(-32:31)*1.72;
% need to do the magnitude and phase seperately
magresult=interp2(tilty,tiltx,abs(tiltplane),wanty,wantx,'cubic');
pharesult=ir.terp2 (tilty, tiltx, angle (tiltplane) ,wanty,wantx, 'cubic ') ,% now combine
result=magresult.*exp (i*pharesult) ,V = 0 .001:.1:1.001;
contour(wanty,-wantx,magresult/max(max(magresult)), V);axis('equal')
title('Computed SGH Reference Magnitude for 60 degree Tilt')
% this should overlay very well with
%hold on;
%load c:\ir\dec20\dec20_28.e2
% contour(wanty, -wantx,dec20_28'/max(max(dec20_28)) ,V , ':');axis('equal')
%hold off;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-15
F ILE R D .M
function [DATA] = filerd(filename)
%File to read NIST fortran binary antenna data files
% Written by John E. Will 7/27/95
(for use by inverse)
% This is a code fragment, so I've hard set some stuff
fid=fopen(filename) ,if fid == -1
disp(['Did not find file'])
stop
end
% I've hard-coded the data array length to be 57 points here
npoints=57;
% now read header line
A=fread(fid,112,'char');
% now the data
for ii = l:npoints
DATAmagtii, :) = fread (fid, npoints, 'float')' ,DATApha(ii,:) = fread (fid, npoints, 'float')',junk = freaa(fid,2,'float');
% takes care of extra bits at end of each chunk
end
fclose(fid);
% Now, DATAmag is in like volts, DATApha is in degrees - so to convert:
i = sqrt (-1) ;
DATArad = DATApha .* pi / 18 0;
DATA = (DATAmag .* cos(DATArad)) + (i*(DATAmag .* sin(DATArad)));
% so now DATA is a (57x57) complex array of the file data
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A-16
F F T U N SF T.M
function y = fftunsft(x)
%FFTUNSHIFT Move zeroth lag to edge of spectrum.
%
Un-Shift F F T . For vectors FFTSHIFT(X) returns a vector with the
%
left and right halves swapped.
For matrices, FFTSHIFT(X) swaps
%
the first and third quadrants and the second and fourth quadrants.
%
FFTSHIFT is useful for FFT processing, moving the zeroth lag to
%
the center of the spectrum.
%
%
%
%
J.E. Will 9-19-95
Un-does the fftshift function originally written by:
J.N. Little 6-23-86
Copyright (c) 1984-94 by The MathWorks, Inc.
[m, n] = size (x) ;
ml = l:floor(m/2);
m2 = floor(m/2)+1 :m;
nl = l:floor(n/2);
n2 = floor(n/2+1):n;
% Note: can remove the first two cases when null handling is fixed,
if m == 1
y = [x(n2) x(nl)];
elseif n == 1
y = [x (m2) ; x (ml) ] ,else
y = [x(m2,n2) x(m2,nl); x(ml,n2) x(ml,nl)],end
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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