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Macroscopic roughness determination of conductive surfaces by microwave speckle contrast measurements

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Macroscopic Roughness Determination o f
Conductive Surfaces by Microwave Speckle
Contrast Measurements
by
Douglas Andrew Oursler
A dissertation submitted to The Johns Hopkins University
in conformity with the requirements f o r the degree o f
D octor o f Philosophy
Baltimore, Maryland
1996
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UMI Number: 9617587
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To my Kris Ann...my life.
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ABSTRACT
Techniques for the non-contact determination o f large scale surface roughness,
on the order o f millimeters, are greatly needed in the field o f Nondestructive
Evaluation. The ability to detect metallic surface irregularities is an important tool for
both corrosion location and on-line process control. Traditional methods such as
mechanical profilometers are typically time consuming and impractical in cases where
the surfaces are covered and/or can not be touched.
Microwave speckle contrast measurements can be used to perform remote
determination o f macroscopic roughness on conductive surfaces. This procedure is
non-contact and can be accomplished through windows o f certain dielectric materials.
The technique is wavelength unspecific and can be used over a large range o f surface
roughnesses. The frequency o f the electromagnetic irradiation is typically chosen so
that its wavelength is roughly four times the maximum root-mean-squared (RMS)
surface variation. The microwaves are focused onto a surface and are scattered upon
reflection. A receiver, placed at some distance in the diffuse reflection, is used to
make the necessary measurements o f speckle contrast or sharpness.
In this work 60 GHz (A,=5 mm) microwaves are used in a non-imaging speckle
configuration to examine the surface roughness o f conductively coated sandpaper. A
variety o f different grit sandpapers, 80 to 16, are painted with silver electrode paint
and are used as roughness standards. The speckle contrast measured by the receiving
horn is well predicted by equations developed in this work. Using these equations and
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the measurement o f the real and imaginary parts o f the speckle field, the RMS surface
roughness (out-of-plane dimension) and the surface roughness correlation length (in­
plan dimension) may be calculated.
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my advisor, Dr. James W agner
for his direction, support and enthusiasm. I consider m yself lucky to work with such a
renowned engineer and scientist. Though this work was never directly funded he
permitted me to follow an interesting idea. I offer him my congratulation (and
condolences) on his appointment to the position o f department chair.
I would also like to thank Dr. Robert Green, whom I consider the patriarch o f
the Materials Science and Engineering Department at Johns Hopkins. His continuing
effort with the Center for Nondestructive Evaluation is greatly appreciated and
enjoyed.
I am very grateful to Dr. Michael Ehrlich for his friendship and assistance,
especially when I first came back to Johns Hopkins for graduate school. I credit him
with my early computer knowledge. He is an excellent resource for the department and
is always willing to lend a helping hand.
I would like to thank Dr. James Spicer who has always been a great resource
on theoretical topics. W ithout his help my work on EMATs would not have been
possible.
I would also like to thank J. Scott Steckenrider, R. Scott Lillard, Robert Hubert
and Kirsten Green, all ex-graduate students. I remember them all fondly. Special
thanks go to the members o f Jim Wagner's optics group. Todd Murray and Johanna
Bernstein have been very helpful as well as John Champion who assisted me in the
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acquisition o f important equipment.
I would like to thank Eric Schlecht and Jim Sowers o f Lockheed-M artin for
loaning us the V-band bolometer with which all the data was taken. I also recognize
Dr. Roger W estgate for lending us his department's surplus o f old waveguide
consonants.
The staff members in the Materials Science department have been great during
my graduate career. Debbie Harris and Debbie Manley, the ladies upstairs have kept
CNDE running smoothly for years. I would especially like to thank Marge Weaver,
Janet Lamerti and Linda Eckhart who are the keystones o f the department. W ithout
these ladies the department would cease to function.
I am very grateful to my mother for her continual encouragement during my
pursuit o f higher education.
Above all else I thank my wife Kris Ann who has supported me greatly with
her friendship, love and affection.
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TABLE OF CONTENTS
ABSTRACT
iii
ACKNOWLEDGEMENTS
v
TABLE OF CONTENTS
vii
LIST OF FIGURES
ix
LIST OF TABLES
xii
1.
INTRODUCTION
1
2.
BACKGROUND
2.1
Surface Roughness Measurements
2.2
Non-Contact Methods o f Roughness Determination
2.3
Process Control in the Molten Alloy Spray Forming
2
3
4
SCATTERING OF ELECTROMAGNETIC WAVES
3.1
Background
3.2
Optical Speckle
7
8
3.
4.
5.
6.
7.
THEORETICAL DEVELOPMENT OF SPECKLE CONTRAST
4.1
Formulation
4.2
Calculating the Speckle Field Contrasts
4.3
Back-Calculating the Roughness Dimensions
EXPERIMENTAL APPARATUS
5.1
Introduction
5.2
Determining the Real and Imaginary Parts o f the Electric Field
5.3
Verification of Surface Roughness by Laser Triangulation
Profilometer
RESULTS
6.1
Laser Triangulation Profilometer Results
6.2
Predicted Behaviors
6.3
Experimental Results
6.4
Surface Roughness and Correlation Length Back-Calculation
DISCUSSION
7.1
Laser Triangulation Profilometer
7.2
Predicted Behaviors
7.3
Experimental Contrast M easurement and Back-Calculation o f
Dimensions
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14
21
25
27
30
33
36
38
45
64
67
67
68
8.
CONCLUSIONS
70
APPENDICES
A
A .l
PREVIOUS WORK
"Microwave Speckle Contrast for Surface Roughness Measurement"
72
B
B .l
B.2
DERIVATIONS
Derivation o f Equations 18, 19, 20 and 21
Derivation o f Equation 34.
81
85
C
C .l
C.2
LISTINGS OF IMPORTANT PROGRAMS
Labview Programs
M aple Program
88
131
D
D .l
D.2
D.3
EQUIPMENT
Equipment and W iring
Focusing the Parabolic Antenna
Diode Detector versus Bolometer
134
137
140
E
E .l
LASER TRIANGULATION PROFILOMETER
Specifications
142
REFERENCES
143
VITA
145
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LIST OF FIGURES
Figure 1
The molten alloy spray forming chamber.
Figure 2
The imaging and non-imaging arrangements for optical speckle.
Figure 3
The specular and diffuse reflections from a rough surface.
Figure 4
An arrangement to produce a speckle pattern in transmission
through a random phase grating.
Figure 5
The arrangement to produce a speckle pattern in reflection as
used in the microwave experiments, (3 is the angle o f incidence.
Figure 6
The microwave apparatus used to measure the real and imaginary
parts o f the electric field in the speckle pattern.
Figure 7
The laser triangulation profilometer is used to verify surface
roughness.
Figure 8
The RMS roughness and correlation length versus grit from
Table 1 as detected by the laser triangulation profilometer.
Figure 9
The real and imaginary electric field contrasts versus surface
roughness, crh.
Figure 10
The real and imaginary electric field contrasts versus surface
correlation length, a.
Figure 11
The real and imaginary electric field contrasts versus angle o f
incidence, p.
Figure 12
The real and imaginary electric field contrasts versus illumination
spot size, co.
Figure 13
The real and imaginary electric field contrasts versus off-axis
distance, r.
Figure 14
The real and imaginary electric field contrasts versus specimenhorn distance, R.
Figure 15
The real and imaginary parts o f the electric field generated from
ten experiment data sets on the 16 grit specimen.
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Figure 16
The mean real and imaginary parts o f the electric field (unrotated)
for the 16 grit specimen with r = 3 cm.
48
Figure 17
The mean real and imaginary parts o f the electric field (unrotated)
for the 16 grit specimen with r = 6 cm.
49
Figure 18
The mean real and imaginary parts o f the electric field (unrotated)
for the 20 grit specimen with r = 3 cm.
50
Figure 19
The mean real and imaginary parts o f the electric field (unrotated)
for the 20 grit specimen with r = 6 cm.
51
Figure 20
The mean real and imaginary parts o f the electric field (unrotated)
for the 24 grit specimen with r = 3 cm.
52
Figure 21
The mean real and imaginary parts o f the electric field (unrotated)
for the 24 grit specimen with r = 6 cm.
53
Figure 22
The mean real and imaginary parts o f the electric field (unrotated)
for the 36 grit specimen with r = 3 cm.
54
Figure 23
The mean real and imaginary parts o f the electric field (unrotated)
for the 36 grit specimen with r = 6 cm.
55
Figure 24
The mean real and imaginary parts o f the electric field (unrotated)
for the 40 grit specimen with r = 3 cm.
56
Figure 25
The mean real and imaginary parts o f the electric field (unrotated)
for the 40 grit specimen with r = 6 cm.
57
Figure 26
The mean real and imaginary parts o f the electric field (unrotated)
for the 50 grit specimen with r = 3 cm.
58
Figure 27
The mean real and imaginary parts o f the electric field (unrotated)
for the 50 grit specimen with r = 6 cm.
59
Figure 28
The mean real and imaginary parts o f the electric field (unrotated)
for the 60 grit specimen with r = 3 cm.
60
Figure 29
The mean real and imaginary parts o f the electric field (unrotated)
for the 60 grit specimen with r = 6 cm.
61
Figure 30
The mean real and imaginary parts o f the electric field (unrotated)
for the 80 grit specimen with r = 3 cm.
62
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Figure 31
The mean real and imaginary parts o f the electric field (unrotated)
for the 80 grit specimen with r = 6 cm.
63
Figure 32
Specimen surface roughness measured by the laser profilometer
and microwave technique.
65
Figure 33
Specimen surface correlation length measured by the laser
profilometer and microwave technique.
66
Figure A .l
Path length difference is illustrated by a ray (of light or microwaves) 86
intersecting and reflecting from a surface that is displaced by h.
Figure D .l
The wiring o f analog and binary lines between the setup and the
D/A board in the computer.
135
Figure D.2
The V-band parabolic antenna.
139
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LIST OF TABLES
Table 1
Laser profilometer results.
36
Table 2
Predicted contrasts based on the laser profilometer results.
45
Table 3
Surface roughness and correlation length measured by the
microwave system.
64
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1.
INTRODUCTION
The determination o f surface roughness is an important measurement in many
manufacturing processes and corrosion detection schemes. These applications vary
widely from the detection o f surface weathering and unwanted wear o f our national
monuments to the detection o f corrosion under insulation on the interior o f aircraft
skins. Besides the need for nondestructive surface inspection techniques there is also a
need to monitor surface roughness during processing. One example o f this is the
molten alloy spray forming process which will be discussed latter. In this process the
roughness o f the freshly sprayed surface is considered one o f the best indicators of
material end quality.
The science o f surface evaluation is perhaps one o f the oldest disciplines o f
materials testing. As a result there are many methods to determine surface roughness.
Each o f these methods has its strong points and none is ideal for all measurement
scenarios. Some methods require a surface contour map, a map o f surface elevations,
to be constructed first. These data are then processed to calculate surface roughness.
Other methods measure roughness directly. This second group o f techniques tend to be
less time consuming.
In this work microwaves are used to evaluate surface roughnesses in a manner
derived from a similar optical technique studied in the early 1970's. The apparatus
illuminates a spot on a rough surface with V-band microwaves. The resulting scattered
energy contains a complex pattern o f nodes and antinodes, also called a speckle
pattern. The sharpness or contrast o f the pattern's variations are directly related to the
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roughness that caused them. The technique is useful on conductive surfaces where a
significant portion o f the energy is reflected. Microwave speckle contrast
measurements are effective on roughnesses that do not exceed a quarter wavelength.
2.
BACKGROUND
2.1
Surface Roughness Measurements
The methodologies of determining surface roughness are quite varied. The
study o f surfaces includes a diverse group o f techniques to determine surface
variations for a broad range o f materials and roughnesses. The oldest technique is the
visual or tactile comparison of rough surfaces to standards o f known roughnesses. The
short coming o f this method is that while the eye is very sensitive to small changes o f
texture it is hard to quantify such results. It is difficult to implement such a m ethod for
repetitious measurement o f roughness because o f its limited (human based)
reproducability.
A needle tipped dial depth gauge or stylus profilometer can be used to quantify
results. The time honored method o f tracing surface contours using a stilus is useful in
many applications where contact with the surface is permitted. The raster scanning o f
such a mechanical profilometer is the most common method o f contouring a surface.
The method's drawbacks are that it is time consuming and requires contact with the
surface. These qualities are unacceptable in most process control situations and
typically lim it the technique's use to the laboratory. A "modern" adaptation of the
mechanical stylus profilometer is the atomic force microscope (AFM) which floats a
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microscopic stylus over the surface o f a material, using a feedback loop to maintain an
optimal lift-off.
2.2
Non-Contact Methods of Roughness Determination
A t present a variety non-contact methods o f determining surface roughness
exist. Many o f which are based on interesting principles. Blessing et a l x have used a
contouring system akin to sonar to examine submerged surfaces using 10 to 50 M Hz
transducers. This rastering system is pulse-echo in principle, operating at repetition
rates o f a few kilohertz, and can be used on surfaces bathed in non-attenuative fluids.
The system has a resolution o f approximately 1 pm and is limited by the trade off
between footprint size and attenuation, both functions o f frequency. The system has
limited lateral resolution making it more suited for contouring gently varying surfaces
rather than for examining randomly rough surfaces.
Caber 2 and Deck and de Groot3 have used a white light interferometer to by­
pass the problem o f phase unwrapping in monochromatic interferometers. This
implementation is full-field using a CCD camera and high speed digital signal
processing to detect the fringe location as the reference path is swept through some
distance. The processing circuits quickly detect the fringes, locate the peak signal, and
develop an image o f the surface contour with micron resolution. The system is
typically used with a microscope front-end and is limited by focusing issues as well as
the quality o f the surface reflection.
An optical reflectometer may be used on polished surfaces to measure surface
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gloss or, conversely, surface roughness. This device has been used by Lauffenburger et
al.A to measure surface erosion on marble. However, since the reflectivity is dependent
on the surface index o f refraction and color, the values obtained can only be used
when compared with previous measurements on the same material.
2.3
Process Control in the Molten Alloy Spray Forming
An example application o f the microwave speckle contrast technique for
surface roughness determination is the process o f molten alloy spray forming.5 Spray
forming is a relatively new technique o f generating high quality alloys with fine grain
structure in a process that is more economical than conventional alloy and powder
milling. In this process molten alloy (100°C above melting temperature) is atomized
by a jet o f high pressure, inert gas. The resultant stream o f droplets is used to coat a
"form" or substrate yielding a fully dense, near-net shape, homogeneously fine grained
material (Figure 1). An inert atmosphere in the spray chamber eliminates oxidation and
inclusion o f impurities.
A variety o f alloys and alloy systems have been spray formed including nickel,
zinc, aluminum, copper, cobalt, steel and titanium. One superalloy o f particular interest
to the United States Navy is Inconel alloy 625 which is composed o f nickel (58 %),
chromium (20 %), molybdenum (10 %), iron (5 %) and a handful o f other trace
elements.5 This alloy has been used extensively in marine applications, such as ship
machinery, because o f its high corrosion resistance and high temperature strength.
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CRUCIBLE CONTAINING
MOLTEN ALLOY
(PR E SSU R IZ E D )
IN ERT ATOMIZING GAS
INLET (P R E S S U R IZ E D )
ADJUSTABLE ANGLE
SPRAY HEAD
MANIPULATOR ARM
PARTICLE STREAM
SPRAY CHAMBER
CONTAINING AN
IN ERT ATMOSPHERE
EXHAUST GAS OUTLET
Figure 1.
T h e m o lte n allo y sp ra y fo rm in g c h am b er.
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The spray forming process is simple in principle but difficult to implement
because o f the many system variables. When it was first developed the system had
only human feedback. The operator would make adjustments based on experience and
the surface appearance of the alloy. The beneficial qualities o f this material, caused by
an optimal grain size, were associated with a particular external texture. The quality of
the material was therefore a complex function o f variables. The melt composition,
m elt temperature, melt (over) pressure, atomizing gas pressure, spraying height,
spraying head angle and manipulator arm/substrate rotation and translation speeds were
all important adjustments.
M oran et al. 6 showed that the success o f the spray forming process was
dependent on the development o f an intelligent control system primarily based on inprocess surface roughness information. This control system 7 uses artificial neural
networks to process information from a laser stripe/CCD camera roughness gauge.
The spray forming process would be an ideal application o f the microwave
technique. Its non-contact nature, like that o f the laser stripe/CCD camera roughness
gauge, is required to examine the rapidly spinning and still hardening alloy surface.
However, unlike the laser stripe roughness gauge, the microwave system would not be
blinded by debris clouds. The microwave system would only experience signal
attenuation which is divided out when the contrast is calculated.
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3.
SCATTERING OF ELECTROMAGNETIC WAVES
3.1
Background
Many electromagnetic wave surface roughness measurement techniques use the
wave scattering nature o f a rough surface. Scattering theories are typically based on
the K irchhoff approximation and are adapted for special cases throughout the
electromagnetic spectrum.8 O f these theories, perhaps the most successful has been the
form ulation discussed by Beckmann 9.
Back scattering from periodic surface waves has been used for such diverse
applications as satellite based ocean wave detection. Valenzuela 10 reviews (with
extensive references) the development o f orbital observations using synthetic aperture
radar (SAR) to detect the modulation o f short wavelength ocean surface waves by long
wavelength ocean waves. The long wavelength waves, which are gravitational in
origin, extend down several hundred meters. This technique is therefore useful for
bottom mapping in shallow areas as well as the detection o f under water structures.
Similarly Fan et al. have used laser beam scattering from machined,
periodically rough cylinders in both a grazing angle 11 and normal incidence
configuration.12 They have developed a system for on-line quality control o f machined
parts.
The existence o f enhance incoherent backscatter from random rough (optical)
surfaces has drawn much consideration recently. 13 14 15 16 17 These authors have
explained this effect by using a number o f different phenomena including weak
localization o f electrons, multiple scattering and interaction with surface plasmons.
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3.2
Optical Speckle
The development o f the laser as a portable coherent light source has made it
possible to use optical speckle as a tool in nondestructive evaluation (NDE). Speckles
at optical wavelengths are visualized by the eye as a grainy texture which spatially
modulates the laser light. The treatment o f optical speckle patterns is usually handled
statistically since the illuminating beam is typically thousands o f wavelengths across,
illuminating millions o f features.
Speckles are a phenomenon observed throughout the electromagnetic spectrum.
Optical speckles have been used in pattern correlation systems to detect in-plane
surface displacements as well as surface morphology changes.18 Optical speckle
contrast measurements have been demonstrated to yield roughness information on
surfaces with variations o f up to approximately two thousand angstroms.19 Although
optical speckle contrast measurements can be used to measure microscopic roughness,
many production and NDE applications require testing o f much greater roughnesses,
even on the order o f millimeters. For such cases, microwave speckle contrast methods
have been shown to be effective.20 Appendix A contains an early article showing the
use o f X-band (v=10 GHz, h=3 cm) microwave intensity speckle patterns to examine
the roughness o f spray formed specimens.
Speckle arrangements are typically separated into imaging and non-imaging
configurations (Figure 2).19 In the non-imaging case a laser beam is used to illuminate
the area o f interest. The resultant diffusely reflected energy is made up o f speckles. In
the imaging case a lens is used to form an image of the surface. This image is
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^
Image
111 u n i n a t i o n
PI a n e
Lens
I magi ng C a s e
Speckl e
P attern
Rough
Surface
1 11u n i n a t i o n
N o r - 1 magi r g
Ca s e
Figure 2
Defocus
PI a r e
The imaging and non-imaging arrangements for optical speckle.
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-1 0 -
m odulated by a speckle pattern. An important difference between the two cases is that
the non-im aging speckle pattern is characteristic o f the total surface area illuminated.
In the imaging case the speckle modulating a particular part o f the image directly
relates to that area on the object. There is an one to one relationship between the
speckle modulated image and the object.
In general, speckles arise whenever there is any disturbance in a coherent
electromagnetic wavefront. The resulting scatter and phase variations cause areas o f
constructive and destructive interference. While speckle can have many causes, in this
work the speckle in the diffuse reflection o f light from a rough surface is o f interest.
Figure 3 shows a "rough" surface where the variations are on the order o f a
wavelength.
W hen illuminated, the energy will be reflected in two components. The direct
(or specular) reflection will leave the surface at an angle identical to the angle o f
incidence. The different facets and angles o f the surface will result in a diffuse
component, spraying energy in near-random directions. The intensity o f the diffuse
field forms a Gaussian distribution centered about the direction o f the specular
reflection. The width o f this distribution, the full width at half maximum, is inversely
proportional to the surface roughness.21
The roughness o f a surface can be characterized by the amplitude and extent of
the surface variations. The correlation length is used to express the lateral dimension
o f the surface feature. Therefore, comparing a surface with a gravel-like appearance
relative to a surface with a series o f large, smooth bumps can be done by comparing
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Rough S u r f a c e
( Magni f i e d )
mi n a t i ng
Bean
D iffuse R eflection
(Composed o f S p e c k le )
Specul a r
R e f I e c t i on
Figure 3
The specular and diffuse reflections from a rough surface.
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their correlation length.
The statistical nature o f optical speckle makes it possible to make a number o f
generalizations about the size and contrast o f speckles. The average diameter, x, o f a
single speckle is given as
(i)
.
X is the wavelength o f light being used.22 The variables d and / control the size o f the
solid angle o f light that will interfere to form the speckle. For the imaging case, d and
/ are the lens diameter and focus length, respectively. While in the non-im aging case,
d and / are the illumination spot size and surface to viewing plane distance.
Optical speckle contrast is a measure of the definition or sharpness o f the
speckle pattern. If a linear intensity scan is taken across a speckle field then an array,
I(x), can be constructed showing intensity versus position data. For such an array the
contrast is given by 23
( < J 2> - < J >2) 1/ 2
J
<J>
_ o(J)
( 2)
<J>
W here <I> is an ensemble average o f the intensity data. For random patterns, which is
true in this case, this expression for contrast is equivalent to the standard deviation of
the array normalized by its mean. In both the imaging and non-imaging cases the
contrast is small while the surface roughness is much smaller than a wavelength and
begins to saturate at 100% as the RMS surface roughness approaches a quarter
wavelength.
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Experimental results using optical speckle contrast have agreed with these
predicted results.19 A measurement o f speckle contrast would be a useful surface
roughness gauge for roughness up to a quarter wavelength o f the illuminating energy.
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4.
THEORETICAL DEVELOPMENT OF SPECKLE CONTRAST
4.1
Formulation
A mathematical expression relating surface roughness to the speckle contrast
can be derived by examining the experimental situation shown in Figure 4. A solution
will be generated for the case o f transmission through a random phase grating for
simplicity. This initial development follows that of Ohtsubo and Asakura.24 Later, it
will be adjusted for the case o f diffuse reflection from a rough surface.
Figure 4 shows an electromagnetic wave source (i.e. a laser or microwave
source) emitting a beam o f energy that is collected and focused by a lens. The waist of
this focus is positioned at a diffuse, random phase grating which is orthogonal to the
optical axis. The grating is on a stage and can be translated perpendicularly to the
optic axis. The lens/grating separation distance,/, is approximately the focal length of
the lens. The detector plane is located at a distance R behind the grating. In this plane
at some distance r off o f the optical axis the detector is located.
Ohtsubo and Asakura only detect the irradiance (with a photodiode) o f the
speckle field. In the microwave experiment the real and imaginary parts o f the electric
field are detected by replacing the detector with a horn fed mixer. The information
gained by measuring the electric field's real and imaginary parts allows us to
specifically solve for the surface roughness in-plane and out-of-plane dimensions. R '
is the magnitude o f the vector connecting a point on the grating (at the r\ 0) to the
detector, r' is the magnitude o f the position vector in the plane o f the grating.
Using the Huygens-Fresnel principle25 the electric field at the detector can be
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Phase
G r a t i ng
Lens
Source
D etector
^ T r a nn s l a t i on
Figure 4.
An arrangement to produce a speckle pattern in transmission through a
random phase grating.
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expressed as
A ( f , t ) = f f E(f')
T [f,t)
x> d r f 60 .
(3)
“ 7t 0
W here K is expressed as
K { x ' , x ) = ~ o s ^n ' ^ ' \ e 3kR> t
j\R '
(4 )
A, is the illuminating wavelength; k is 2x/A; and j is the square root o f -1. In
Equation 3, E is the illumination function in the plane o f the phase grating. E is
assumed to be Gaussian in form and can be expressed as
(5>
Since the grating is at the waist's center it is assumed that the illuminating phase front
is planar and, therefore, constant, co and M are the illumination spot radius and
amplitude, respectively.
T is the grating transmission function which introduces only a phase variation.
It is expressed as
T { f , t ) = e i * (f/' fc) ,
(6)
where <)) represents the phase variation across the grating. (J) is assumed to be a
stationary Gaussian random variable with a zero mean value. The vector magnitude R '
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can be expressed as
R,=)/R2+ (r'-r)2=y/R2+ r 2+ (rx)2- 2 r r /cos0 .
<7)
In Equation 4 the cosine term (the cosine o f the angle between the grating normal and
the vector pointing toward the detector) is rewritten as
cos { n, R/) = — .
R'
(8)
Combining all o f the pieces an equation for A takes the form
-
M
r
P p jk y /R t+
r**
( r ') 2-Z r r'c o s 0
A { S , f c )= -4 f f
,e I , . _--------;-----s
J -Jt 0 ^ r
(r ) 2 r r COS0
.
e
-[ — ]2
B
,
,
r'd r'5 0
(9 )
The only assumption made to write this equation is that R is much greater than the
source wavelength. Now the Fresnel approximations will be used to rewrite
R'=y/R2+ r 2+ (r') 2-2rr'cose
=RU+riM r0fI 2 r r W e )
2R2
r 2 a. ( r ' ) 2 _ r r ' c os6
2R
2R
R
The square root has been approximated by dividing through by R and using the first
two terms o f the Taylor series expansion. This expression appears in the exponential
(Equation 9) and is very important to the overall accuracy o f the integral. The
denominator in Equation 9 can be more simply approximated as
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R 2+ r 2+ ( r ' ) 2- 2 r r /cos 0 «i?2 .
( 11 )
Using these approximations the equation for A can be rewritten as
#<*♦.£!)
A ( f , t) =
(r / ) 2 (
7:
2R
f e
- j k r i 1c o s 0
R
I
ae d r '
0
( 12 )
The integral over 0 can be rewritten as a Bessel Function o f the zeroth order,
2nM
JkR
j k j r 1)2
r' e
“
e
2R
(13)
The above equation describes the electric field at the detector's location (r). The
grating function (j) is assumed random with a Gaussian distribution. Therefore, to
develop insight into the structure o f the electric field (i.e. the speckle pattern), A must
be treated statistically. The assumption o f Gaussian statistics is often valid even when
the surface statistics are non-Gaussian. Goodman21 invoked the Central Limit Theorem
to show that, for a large number o f scatters, the speckle statistics would approach a
Gaussian distribution.
In the experiment the stage carrying the phase grating is translated across the
illuminating beam and the speckles are recorded as they pass the detector. The total
field at the detector can be written as the sum o f the diffuse and specular components.
A(F, t) = a ( f , t) + c ( f , t)
(14)
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Here a, the diffuse component, is defined to have zero mean value and c, the specular
component, represents the bias (DC value). The real part o f A would therefore be the
sum o f the real parts o f the diffuse and specular components. A similar summation can
be written for the imaginary parts.
The mean value o f the real and imaginary parts o f A can be written as
<Az >= <ar +c r > =<ar> +<cr > =cr
<Ai >=<ai +ci >=<ai >+<ci >=ci .
(15)
The variance (standard deviation squared) o f the real part o f the electric field, A n can
also be derived
(16)
Similarly, the variance o f the field's imaginary part can be written
o\= < A j> -< A i >z =<aj>
(17)
The four values o f interest are <A>, <A>, a 2 (the square o f the standard
deviation o f A r), and a 2 (the square o f the standard deviation o f A,). They can be
experimentally calculated from the data arrays representing the electric field's real and
imaginary parts.
The derivation o f the expressions for <A>, <A>, a 2 and a 2 starting from
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20
-
Equation 13 is involved and is presented in Appendix B. The results o f the derivation
are:
<A> =2%M e
_ il
o
"
f
2 J r / J Q( ^ .rz - ) g
o
<Ar > =Re<A>
- Sl hl
jn(r')2
Xr
e
gr f
(18)
<Ai >=Im<A>
a 2= { J Z M M )2
e -o%
t _ F ( _ 0 2 ) _ _ 4 iT(a | )
yj
,
(19)
a 2= ( _jr^co) ) 2 e -o| [ _ F ( _ a | ) + 4 fr, ( a 2) jpj
^
(20)
o
CO2
2
CO2
where P i s expressed as
”
„
/
-lilU l
P = R e [ f r ' j 0 ( 4^ r ) e
o
j2n ( r Q 2
e **
3r']
.
(21)
The function F i s expressed as
ao
F(x) =.gi ( l , x ) +Lrz(x) +y (0)
.
n=l
^
(22)
^
Ei(ljc) is the exponential integral function; y(0) is Euler's constant.
In the above equations, which may be used to calculate the speckle pattern's
mean and variance, or* and a represent the phase variation's standard deviation and
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correlation length (lateral dimension), respectively. The correlation length, a , is
defined as h alf o f the width o f the surface autocorrelation function at e 1 o f the
maximum (Appendix B). In order to simplify solving for
and a the contrast will be
calculated by taking the ratio o f the speckle pattern's standard deviation and mean,
y=
ft*
r
< A C>
y .= f t
*
,
(23)
.
(24)
<A,1'>
This action not only eliminates one occurrence o f c^, but also eliminates M and any
detector efficiency constants.
Normally the contrast used in speckle papers is the intensity contrast. An
equation similar to Equations 23 and 24 may be written for intensity contrast using the
relationship
(25)
I=Ar+Af .
Inserting this equation into Equation 2 and using the definitions in Equations 15, 16
and 17, the intensity contrast may be written as
Tr -
4.2
( < J 2> - < J > 2) 1/2
=
<^>
"
l/ [2 (Or +g j ) +4 [ C r O r + cj a'i)
]
(2g)
c l+ a \+ c b a \
Calculating the Speckle Field Contrasts
In a later section the behavior o f the electric's field's real and imaginary
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22
-
contrast are plotted to demonstrate their (predicted) behavior. For ease and
computational speed the integrals in Equations 18 and 21 must be expressed as
summations. (Simpson's Rule solutions are approximations and less accurate.) Both o f
these integrals are similar and o f the form
This equation can be found in an (extensive) integral table and can be expressed as the
summation
» ( - 1 ) “ ( f ) 2*
- ( - 1 ) " ( f ) 2*
y* _________2
_ _ l _ +y v
2
2 n ! d 2n+2
2d2 h i
2 n ! d 2n+2
(28)
The right-hand half avoids the factorial o f 0 which some programs do not define to 1.
Equation 18 can be rewritten as
<A> =2%M e
-ii
2
,
(-D ” (1 )“
[-± -+ Y ‘
==^—] ■
2d 2
2 n \ d 2n*2
Equation 21 can be rewritten as
0>= J ? e [ - ^ + f ' — {~1) a a2n ] ,
4d 2 f a 2 n \ (\fZd) 2/1+2
(30)
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where
d=
co
g= H
y
I
XR
(31)
N ow combining Equations 19, 20, 23, 24, and 29 the real and imaginary electric field
contrasts may be rewritten into a consolidated form.
Tr _
-co2 F ( - g | ) - 4 f ( o | ) y
,
» ( - 1 ) " ( | ) 2n
4 R e [ - ± - + Y ------------- ±------]
2d 2
2 n \ d 2n+z
« ^ / -CO2
(32)
F ( - o | ) +4 F ( o | ) T
- ( - l ) a ( | ) 2n
4 Im [ —— + y -------------- =------ ]
2d2 h i
2n \ d 2n+2
(33)
Using these two equations and Equations 22, 30 and 31, the real and imaginary
electric field contrasts may be calculated for the speckle pattern at a given detector
location.
In the configuration for the microwave experiment, shown in Figure 5, an
illuminating beam is incident on a rough surface at an angle P to the surface normal.
An expression can be written to relate the standard deviations o f the surface
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—2 4 —
San d p a p e r
S p e ci m e n
T r a n s l a~ti on
D e-tector
Figure 5
The arrangement to produce a speckle pattern in reflection as used in
the microwave experiments. P is the angle o f incidence.
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roughness, crh, and the resultant phase variation, c^,
0+=-X
cosP
(34)
This equation is proven in Appendix B.
If certain precautions are taken it can be assumed that the formation o f speckles
in this case are similar to those in the transmission case (Figure 4). It is assumed that
P and the maximum slope o f surface features are small enough that variations with
angle in the Fresnel reflection coefficients can be ignored. Also it is assumed that
there is no shadowing or multiple scattering by surface features. Finally, the
illuminating beam is polarized transverse electric (TE) to the plane o f incidence to
lim it coupling to surface modes. Improper polarization and multiple scattering may
launch surface plasmons, a cause o f polarization rotation at the surface. The
microwave system is polarization sensitive so erroneous signals could result from any
rotation.
4.3
Back-Calculating the Roughness Dimensions
The dimensions o f the microwave apparatus (R , r, X and co) as well as the
experimentally measured field contrasts are known. The only unknowns in the two
equations are o h and a (the surface height variation's standard deviation and
correlation length). When Equations 22, 30-34 are used together there are two
equations and two unknowns. Using this information an expression for the correlation
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length may be written,
V' Re<A>
F- Im<A>
<* = -
_ 4 J* F{Ofy)
W2
(_7tW )
TicJ '
2
<35)
This equation can be rewritten as
- i ^ ( - a | ) [ (F, i?e<A>)2- ( F j I m< A> )2] +
F ( o |) 3, [ , ^ ^ ^ >
)2- ( 2 ^
0)
<A > ) 2) - q
_
<3 6 '
0)
In both o f these equations F / and F / represent the experimentally measured real and
imaginary field contrasts. Equation 36 may be rewritten as
F ( - a l ) - Q F ( o | ) =0
(37)
where
n _p
,( 2V[L Re<A> x)2, +
^
to
;
(f ' Re< A>) 2 -
,( 2 V -* Im<A> 4
\ ,2
1
to
;
(vi Jm<A>) 2
(38)
Because o f the complexity o f the function F(x) (Equation 22) the only way to solve
for oy2 is to use a multiple iterations method. Appendix C contains the M aple
programs used to solve for
and, thus, ah .
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5.
EXPERIMENTAL APPARATUS
5.1
Introduction
The microwave apparatus, shown in Figure 6, is designed to measure the real
and imaginary parts o f the electric field. The energy from an Impatt diode, V-band (60
GHz), microwave source is split by a 10 db directional coupler. A tenth o f the power
goes into the local oscillator leg. The remainder proceeds through an isolator and an
adjustable phase shifter eventually reaching a parabolic antenna (/= 1", diameter=3").
The reflector-feed distance o f the parabolic antenna is adjusted to image the feed's end
onto the specimen's surface with TE polarization. A beam o f laser light (not shown in
Figure 6) is used to illuminate the feed's end. The parabolic reflector therefore images
an optical image o f the feed in the same place as the microwave image. The
microwave image is only a dozen or so wavelengths (X=5 mm) across so it is expected
to be slightly blurred by diffraction effects. (Appendix D further discusses the focusing
of the parabolic antenna.) The optical image assists system aiming. Its dimensions are
used as a estimate o f the microwave spot size, co.
The specimen to be examined is a piece o f sandpaper on masonite backing.
The sandpaper is painted with silver contact paint to reflect the microwaves. Eight
different grit sandpapers, ranging from 80 to 16, serve as roughness standards. The
sandpaper is mounted on a translation stage and is moved across in front o f the
microwave apparatus.
Two horns examine the speckle pattern. They are at distance R (= 60 cm) from
the specimen. The larger o f the two, which feeds diode detector #1, is the aiming
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P arabolic
Antenna
D irectional
C oupler
C onducti vel y
C o a te d
S andpaper
OC
A d ju sta b le
Phase
(
S h ifter
'
Phase
R eference
Loop
Is o la to r
Aining
.Horn
A d ju sta b le
A tten u ato r
OC
(OC
Ml crowave
Source
60 GHz
SI gnat
Horn
Transl ati on
Di r e c t i on
Figure 6
OC
E-H T u n e r
Boloneter
J Local
O scilla to r
Leg
Si gnat
^Dut
The microwave apparatus used to measure the real and imaginary parts of
the electric field in the speckle pattern.
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hom (19 x 17 mm). The aiming horn is positioned laterally to maximize its signal.
This action is used to locate the center specular reflection. The second horn, the signal
horn (3 x 1.5 mm), is a cutoff piece o f waveguide. The horn separation is r which is
3 cm or 6 cm, depending on the test configuration. W hile the aperture o f the signal
horn is small and collects less energy, its size is necessary to prevent smearing o f the
speckle pattern. To prevent smearing, the speckle size (given by Equation 1) should be
several times larger than the aperture o f the signal horn.
The energy collected by the small horn antenna is then mixed with the local
oscillator at the bolometer. The bolometer is a true square law detector, measuring
microwave power as it heats a black body absorber. The diode detectors do not behave
well enough to ensure the accuracy that is needed. Appendix D discusses the
equipment choices.
The phase o f the local oscillator can be shifted relative to the illumination
beam by adjusting the phase shifter. The phase reference loop mixes nearly equal,
small amounts o f the illumination and local oscillator energy. The square o f the
coherent sum o f these signals is detected by diode detector #2. As the phase shifter is
tuned the voltage signal from detector #2 follows a sinusoidal pattern. This pattern
repeats with every 360 degrees o f phase delay. The first maximum encountered as the
phase shifter is adjusted is labeled the point o f 0° phase difference. The following
slope midpoint and minimum are labeled the 90° and 180°, respectively.
The experiment is computer controlled. A GPIB link allows the computer to
program the translation stage controller. An A/D board in the computer triggers the
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stage motion over binary lines and digitizes the analog signal from the bolometer and
diodes. A program created with Labview controls these actions and runs all o f the
aspects o f the testing. For a given data set the stage is translated and data is collected
three times, once for each o f the phase angles 0°, 90° and 180°. The details of
program m ing are in Appendix C. The specifics and wiring o f the experimental setup
are located in Appendix D.
The three phase adjustments are executed by hand and are o f limited
reproducability. Therefore, ten data sets are collected for averaging per specimen in
each o f the two test configurations.
5.2
Determining the Real and Imaginary Parts of the Electric Field
As discussed previously, the signals from the horn and the local oscillator are
summed and squared by the square law nature o f the bolometer. The horn signals can
be written as
ES=Ci Q{ t )
(39)
The local oscillator signal is expressed as
(40)
In these equations Q(t) and @(t) are the amplitude and phase variations in the speckle
pattern, respectively, c, represents the combination o f horn and other efficiencies while
t represents time or, equivalently, stage position. Qa and A are the local oscillator
amplitude and relative phase as set by the phase shifter. The irradiance (power)
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detected by the bolometer is proportional to the sum o f the fields times their complex
conjugates. The bolometer produces a voltage proportional to the incident power. An
expression may be written for the bolometer voltage as
VBol { t ) = c t [ £ 2 ( t ) +Qo+2Q{t) Q0cos{d> [ t ) - A ) ]
.
(4 1 )
Here ct is a constant containing all o f the other constants.
W hen an experiment is run the voltage array, VBol(t), is collected for the three
phase angles, 0°, 90° and 180°. In each case Equation 41 appears as
VBoli0( t ) = c t [Q2 { t ) +QZ+2Q{t ) Q0c o s ( < S >( t ) ) ]
: A=0°
VB0li9Q( t ) = c t [Q2 ( t ) + Q Z + 2 Q ( t ) Q 0s i n ( < i > { t ) ) ]
:A=90°
,
VBolilB0( t ) = c t [Q2 ( t ) + Q ^ - 2 Q ( t ) Q0cos{<S> ( t ) ) ]
: A=180°
.
,
(42)
The real part o f the field is then proportional to
(4 c t Qa) Q ( t ) c o s ( & ( t ) ) = V Boli0- V BolilB0 .
(43)
The imaginary part o f the field is proportional to
(4 c t Q0) Q ( t ) s i n { < S > ( t ) ) = 2 V Boli0- V Boli0- V BolilB0 .
(44)
The constant, 4 ct Q0 , will divide out when the contrast is calculated.
Note that the phase labels, 0°, 90° and 180°, are relative and most likely do not
represent the actual phase relationship. The real and imaginary field components from
the experimental data (Equations 43 and 44) are converted by a reference frame
rotation to align the experimental and mathematical reference frames. The equation
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6pred= a r c t a n (
Im<A>
Re<A>
(45)
gives the mathematically predicted dominant phase angle. W hile the equation
(46)
represents the dominant phase angle in the data. The reference plane o f the data arrays
must be rotated by
0A
0p re d
0 ex p
(47)
■
The rotation is accomplished by the transformations
Ar
[(^BoltO ^Bol, 18o) C O S (0A) ]
[ ( 2 V goi^
^Bol, 0~^Bol, 1801 s i n ( 0 A ) l (48)
Aj- [ ( VBoi i 0 - V Boi ' i B0) s i n (0^) ] + [ (.2 V b o i i 0 ~ V b o i , o ~ V b o 1 , i b q ) cos (0^)1
where the arrays A / and A / are the experimentally determined and correctly oriented,
real and imaginary parts o f the electric field. As noted previously these values are o ff
by the factor 4 ct Q0 , which will be divided out when the contrasts are calculated.
The real and imaginary field contrasts o f the experimental data may be
calculated by
l
Tr/ _
r
[ < ( a ^ ) 2> - < a ' > 2] 2
/------------<a 'x>
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( 49 )
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and
^
[ < ( * ] ) *2>S - <a [ > 2]
(50)
<A->
In practice, a Labview program is used to run the experiment and record the
raw data sets. A M aple program is then used to rotate and process the data sets,
solving for the in-plane and out-of-plane roughness dimensions.
5.3
Verification of Surface Roughness by Laser Triangulation Profilometer
W hen the sandpaper specimens are painted, creating a conductive surface, their
roughness is modified. As a result the grit number may no longer be an exact measure
o f the surface roughness. Instead, a laser triangulation profilometer is used to measure
the actual surface variation o f the specimens.
The laser triangulation profilometer is placed (optimally) two inches in front o f
the specimen which is mounted on the translation stage (see Figure 7). It projects a
laser beam orthogonal to the mean surface, which illuminates a oval spot on the
sandpaper. This oval is nominally 200 by 40 microns. A lens in the laser triangulation
profilom eter located off to one side images the spot to a position sensitive detector.
The electronics process the signals that come from each end to the position sensitive
detector and by triangulation produce a voltage proportional to the distance to the
surface.
During the sandpaper calibration the translation stage is moved (horizontally)
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Maxi n u n
Range
□ p-ti n u n
Range
Mi ni n u n
Range
Lens
/
Lasen
Di o d e
El e c t r o n i c s
Lens'
Posi ti on
S e n s i ti v e
D etector
Figure 7
The laser triangulation profilometer is used to verify surfaces roughnesses.
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multiple times at ten different levels. The voltage signal which is recorded by the D/A
board in the computer is scaled to represent true displacement. These contours are then
used to generate RMS roughness values. This calibration is done for each o f the
specimens.
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6.
RESULTS
6.1
Laser Triangulation Profllometer Results
Eight different sandpapers are used as the roughness standards (specimens). The
grits, before painting, are: 80, 60, 50, 40, 36, 24, 20 and 16. The results o f the
calibration are shown below in Table 1. The RMS roughness and correlation length
data are also plotted in Figure 8.
Table 1
Grit
Roughness
Skewness
Kurtosis
RMS {mm}
Correlation
Length {mm}
16
0.4695
1.07
4.07
0.805
20
0.5205
1.10
3.80
0.565
24
0.4496
1.46
5.48
0.421
36
0.4282
1.43
5.55
0.345
40
0.3905
1.10
4.53
0.330
50
0.3369
1.09
4.62
0.240
60
0.3243
1.11
4.93
0.215
80
0.2619
0.91
4.32
0.180
The skewness is the third moment (statistics) divided by the cube o f the standard
deviation. It indicates the degree o f symmetry in the surface elevation distribution, ie
the histogram. A value o f zero indicates perfect symmetry. The Kurtosis is the fourth
mom ent divided by the standard deviation to the fourth power. It is a measure o f the
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1.00
—
Millimeters
0.80
0.60
0.40
0.20
0.00
16 20 24
36
40
50
60
Grit
Figure 8
The RMS roughness (dot) and correlation length (diamond) versus
grit from Table 1 as detected by the laser triangulation profilometer.
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80
-3 8 -
amount o f energy in the distribution tails relative to its center. A value o f three is
expected for a Gaussian distribution
6.2
Predicted Behaviors
The equations presented at the end o f Section 4.2 predict the behavior o f the
real and imaginary electric field contrasts in the speckle pattern. Using the M aple
programm ing language and substituting Equations 22, 30, 31 and 34 into Equations 32
and 33 the speckle contrasts may be plotted. In Figures 9-14 the variables, RMS
roughness ( c h), surface correlation length (a), angle o f incidence (P), microwave spot
size (co), the horn off-axis distance (r), and the specimen-horn distance (R) are in-turn
varied to plot the contrast's behavior. Nominal values (cfh=0.5 mm , a = 0.84 mm, P =
23.7°, <a = 4 cm, r = 3 cm, R = 60 cm, X = 5 mm) which reflect realistic conditions
are used.
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-3 9 -
0.22
0.2
0.18
£
0.14
0.12
«
0.1
0.06
0.06
0.04
0.02
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
RMS Surface Roughness {meter}
0.6
0.5
to
1
8
o
c
o>
0.4
0.3
o
E
0.2
>
O.l
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
RMS Surface Roughness {meter}
Figure 9
The real and imaginary electric field contrasts versus surface roughness, a h.
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-4 0 -
Vr Rea| Contast
0.04
0.02
0.01
0.007 --
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
O.OOOB
0.0009
0.001
0.0009
0.001
Vi imaginary Contrast
Surface Correlation Length {meter}
0.07
0.04
0.02
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
O.OOOB
Surface Correlation Length {meter}
Figure 10
The real and imaginary electric field contrasts versus surface correlation
length, a.
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-4 1 -
0.04B
Vr Rea| Cont(clst
0.046
0.044
0.042
0.04
0.038
0.036
0.034
0.032
0.03
0
10
20
30
40
The Angle of Incidence {Degrees}
0.15
Vi imaginary Contrast
0.14
0.13
0.12
0.11
0.1
-
0
10
20
30
40
The Angle of Incidence {Degrees}
Figure 11
The real and imaginary electric field contrasts versus angle o f incidence, p.
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-4 2 -
0.075
Vr Real Contrast
0.07
0.065
0.06
0.055
0.05
0.045
0.04
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Microwave Spot Size {meter}
0.8
- -
Imaginary Contrast
0.7
0.6
--
0.5 --
0 .4 --
0 .3 --
0.2 --
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Microwave Spot Size {meter}
Figure 12
The real and imaginary electric field contrasts versus illumination spot size,
<D.
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-4 3 -
Vr Real Contrast
5. --
0.5 --
0.1 -0.05 ---
0.01
0.02
0.03
0.04
0.05
0.06
Off-Axis Distance {meter}
Vi Imaginary Contrast
1
o.
1
0.1
Off-Axis Distance {meter}
Figure 13
The real and imaginary electric field contrasts versus off-axis distance, r.
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-_44~
Vr Real Contrast
0.08
0.06
0.05
0.04
0.03
0 .3
0.4
0 .5
0.6
0.7
0.8
0 .9
1
Specimen-Horn Distance {meter}
Vi Imaginary Contrast
10. --
0.1 --
0.3
0 .4
0 .5
0.6
0.7
0.8
0.9
Specimen-Horn Distance {meter}
Figure 14
The real and imaginary electric field contrasts versus specimen-horn
distance, R.
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1
-4 5 -
The sandpaper RMS roughnesses and correlation lengths from the laser
triangulation profilometer data (Table 1) may be used in the above mentioned
equations to predict the real and imaginary field contrasts. In Table 2 these values are
listed for the off-axis distance, r, equal to 3 cm and 6 cm.
Table 2
Grit
a
vr
v,
vr
r = 3 cm
{mm} {mm}
v,
r = 6 cm
16
0.4695
0.805
0.0376
0.1204
-0.7485
-0.1330
20
0.5205
0.565
0.0308
0.0972
-0.6080
-0.1081
24
0.4496
0.421
0.0185
0.0595
-0.3891
-0.0656
36
0.4282
0.345
0.0141
0.0459
-0.2841
-0.0504
40
0.3905
0.330
0.0119
0.0392
-0.2417
-0.0429
50
0.3369
0.240
0.0072
0.0241
-0.1470
-0.0261
60
0.3243
0.215
0.0062
0.0207
-0.1262
-0.0224
80
0.2619
0.180
0.0040
0.0137
-0.0832
-0.0147
6.3
Experimental Results
The microwave apparatus discussed in Section 5.1 is used to examine the eight
sandpaper specimens. Ten data sets are taken per specimen using the two test
configuration. The only variation between test configurations is the off-axis distance, r,
which is 3 cm in the first test and 6 cm in the second. Figure 15 shows the ten data
traces for the 16 grit specimen. In this figure, as with the following sixteen, the three
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0 .8 0
0.40
0.00
-0.40 —
-0.80
1
0.00
Figure 15
|
100.00
1
1
200.00
1
1
300.00
1
1
400.00
1
1
500.00
The real and imaginary parts o f the electric field generated from ten
experimental data sets on the 16 grit specimen. [Arbitrary units]
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- 47-
data sets from the experiment have been used in Equations 43 and 44 to generate the
(unrotated) real and imaginary electric field data sets. In Figure 15 all ten pairs o f
traces are shown to illustrate the variability between data sets. This variation is mostly
caused by the variability associated with the phase adjustment. Note that in
Figures 15-31 the units o f the Y and X axes are arbitrary field amplitude and data
array index. The data points are actually at 0.2 mm increments o f the translation stage
over a 100 mm distance
In Figures 16-31 only the average trace will be shown for each part o f the
electric field. Error bars representing the standard deviation o f the data are shown to
help assess the variability. The first two figures, Figures 16 and 17, show the data
from the 16 grit specimen for r equal to 3 cm and 6 cm, respectively. The following
figures are paired likewise and proceed in order o f increasing grid number.
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0 .8 0
0.40
0.00
-0.40 —
-0.80
0.00
Figure 16
100.00
200.00
300.00
400.00
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The mean real and imaginary parts o f the electric field (unrotated) for the
16 grit specimen with r = 3 cm. [Arbitrary units]
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0 .8 0
0.40
0.00
-0.40
-0.80
0.00
Figure 17
100.00
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300.00
400.00
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The mean real and imaginary parts o f the electric field (unrotated) for the
16 grit specimen with r = 6 cm. [Arbitrary units]
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-5 0 -
0 .8 0 — |
0.40
0.00
-0.40 —
-0.80
0.00
Figure 18
100.00
200.00
300.00
400.00
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The mean real and imaginary parts o f the electric field (unrotated) for the
20 grit specimen with r = 3 cm. [Arbitrary units]
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-5 1 -
0 .8 0 — i
0.40 —
0.00
—
-0.40 —
-0.80
0.00
Figure 19
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
20 grit specimen with r = 6 cm. [Arbitrary units]
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0 .8 0
0.40
o.oo
-0.40
-0.80
0.00
Figure 20
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
24 grit specimen with r = 3 cm. [Arbitrary units]
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0 .8 0 — ,
0.40
0.00
-0.40 —
-0.80
0.00
Figure 21
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
24 grit specimen with r = 6 cm. [Arbitrary units]
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0 .8 0 — 1
0.40
0.00
-0.40 —
-0.80
0.00
Figure 22
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
36 grit specimen with r = 3 cm. [Arbitrary units]
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0 .8 0 — |
0.40
0.00
-0.40 —
-0.80
0.00
Figure 23
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
36 grit specimen with r = 6 cm. [Arbitrary units]
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0 .8 0 — |
0.40 —
0.00
-0.40 —
-0.80
0.00
Figure 24
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
40 grit specimen with r = 3 cm. [Arbitrary units]
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0 .8 0 — |
0.40
0.00
-0.40 —
-0.80
0.00
Figure 25
100.00
200.00
300.00
400.00
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The mean real and imaginary parts o f the electric field (unrotated) for the
40 grit specimen with r = 6 cm. [Arbitrary units]
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0 .8 0 — |
0.40
0.00
-0.40
-0.80
0.00
Figure 26
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The mean real and imaginary parts o f the electric field (unrotated) for the
50 grit specimen with r = 3 cm. [Arbitrary units]
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0 .8 0 — .
0.40
0.00
-0.40
-0.80
0.00
Figure 27
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
50 grit specimen with r = 6 cm. [Arbitrary units]
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-6 0 -
0.00
-0.80
0.00
Figure 28
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
60 grit specimen with r = 3 cm. [Arbitrary units]
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-6 1 -
0 .8 0 — ,
0.40
0,00 —
-0.40 —
-0.80
0.00
Figure 29
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
60 grit specimen with r = 6 cm. [Arbitrary units]
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-6 2 -
0 .8 0 — |
0.40 —
0.00
-0.40 —
-0.80
0.00
Figure 30
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
80 grit specimen with r = 3 cm. [Arbitrary units]
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-6 3 -
0 .8 0 — ,
0.40 —
0.00
—
-0.40 —
-0.80
0.00
Figure 31
100.00
200.00
300.00
400.00
500.00
The mean real and imaginary parts o f the electric field (unrotated) for the
80 grit specimen with r = 6 cm, [Arbitrary units]
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-6 4 -
6.4
Surface Roughness and Correlation Length Back-Calculation
The data sets o f the real and imaginary (experimentally determined) parts o f the
electric field (Figures 16 through 31) may be used to calculate the surface roughness
and correlation length. These data sets are rotated using Equation 48. A backcalculation can then be done using the relationships in Section 4.3 which are
programm ed in Maple. Thereby the speckle traces may be interrogated to reveal a h
and a using only some o f the physical dimensions o f the microwave apparatus.
Table 3 and Figures 32 and 33 show measured values o f a h and a determined
by the laser triangulation profilometer and the back-calculation o f microwave speckle
data for both r = 3 cm and r = 6 cm.
Table 3
Laser Profiler
Microwave Contrast Experiment
r = 6 cm
r = 3 cm
Grit
a
{mm} {mm}
a
oh
a
{mm}
{mm}
{mm}
{mm}
16
0.4695
0.805
1.5330
0.999
0.9333
0.943
20
0.5205
0.565
0.7342
0.593
0.6512
0.589
24
0.4496
0.421
0.4518
0.533
0.4501
0.516
36
0.4282
0.345
0.4344
0.441
0.4100
0.403
40
0.3905
0.330
0.4013
0.401
0.3917
0.393
50
0.3369
0.240
0.3599
0.311
0.3399
0.291
60
0.3243
0.215
0.3986
0.255
0.3329
0.264
80
0.2619
0.180
0.4430
0.238
0.3832
0.347
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-6 5 -
1.60
1.20
E
E
tn
</>
a)
c
O)
0.80
+
o
Cd
(/)
s
a:
o
+ O
•
»
0.40
0.00
16 20 24
36
40
50
60
Grit
Figure 32
Specimen surface roughness measured by the laser profilometer (dot)
and microwave technique (cross r = 3 cm, diamond r = 6 cm).
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80
-6 6 -
1.00
Correlation Length mm
0.80
0.60
0.40
0,20
—
0.00
16 2 0 24
36
40
50
60
80
Grit
Figure 33
Specimen surface correlation length measured by the laser profilometer
(dot) and microwave technique (cross r = 3 cm, diamond r = 6 cm).
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-6 7 -
7.
DISCUSSION
7.1
Laser Triangulation Profilometer
The laser triangulation profilometer results shown in Table 1 and in Figure 8
confirm the inverse relationship between grit number and surface roughness. The
exception is the roughness data for the 16 grit specimen which has a smaller roughness
than the 20 grit specimen. This result is likely due to the increased correlation length
or "bump" spacing. On the 16 grit sandpaper the abrasive granules were visibly farther
apart than the granules on the 20 grit sandpaper while their size was not proportionally
bigger. These large gaps cause the RMS roughness to drop.
The correlation length information is also inversely proportional to the grit
number. This is expected because rougher sandpapers are coated with larger granules.
A granule's width and height are approximately equal. (Equal in the case o f a sphere).
However, the conductive coating which was applied to the sandpaper m ight tend to
reduce the RMS roughness. This statement is especially true on the higher grit papers
where the surface tension o f the coating smooths edges and rounds-out pits.
The laser triangulation profilometer has an oval spot with a major axis o f
approximately 200 microns. On higher grit specimens, the spot size might tend to
smear out features and cause the under estimation o f surface roughness.
7.2
Predicted Behaviors
Figures 9 through 14 predict the expected speckle contrasts for a given
experimental arrangement. Figures 9 and 10 indicate the basic trend that contrast
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-6 8 should increase (non-linearly) with RMS surface roughness while it decreases with
surface correlation length. Note that for large surface roughness the intensity contrast
(Equation 26) saturates at unity.
Figure 11 shows that an increased angle o f incidence reduces the apparent
surface roughness and decreases the speckle contrast.
Speckle contrast increases with off-axis distance (Figure 13) indicating that the
speckles become sharper the further into the diffuse reflection you go. Moving off-axis
would increase resolution but decrease range.
The most interesting prediction, in Figure 12, is the relationship between
speckle contrast and microwave spot size. However, the minimum seen in the real part
is caused by a non-physical situation. The wavelength is 5 mm; so spot sizes
approaching this dimension are prohibited by diffraction.
7.3
Experimental Contrast Measurement and Back-Calculation of Dimensions
In the electric field data plots acquired during the experiment, shown in Figure
16 through 31, changes in surface roughness are evident by the degree o f trace
waviness. From these graphs it is possible to distinguished between different grits.
Also, as predicted in Figure 13, the further off-axis position exhibits greater waviness
for a given grit. This effect can be seen by comparing the (two) traces for a given grit
number.
The back-calculation results, listed in ta b le 3 and shown in Figures 32 and 33,
have good agreement with the laser triangulation profilometer data. In general, the
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-6 9 -
microwave system seems to over estimate both surface roughness and correlation
length. Larger discrepancies occur on the lower grit specimens.
Normally the paint coating on the specimens serves to round sharp edges and
fill cracks. This effect helps to make the surface features less stark and is beneficial to
the basic theoretical assumptions about maximum slopes. Therefore on the lower grit
sandpapers the predicted behavior is less valid.
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-7 0 -
8.
CONCLUSIONS
In conclusion, microwave speckle contrast measurements are sensitive to
macroscopic surface roughness. The technique should be useful in many process
control and nondestructive evaluation applications where surface roughness must be
determined in a non-contact fashion. Microwave speckle contrast measurements have
the potential o f being used to locate corrosion under dielectric insulation such as on
the inside o f aircraft or the exterior o f petroleum storage tanks and pipes. The
technique has already been used in the laboratory to test molten alloy spray formed
specimens.
The behavior o f microwave speckle/roughness measurements has been
developed from basic principles. The technique is a direct offspring o f a similar optical
technique developed soon after the invention o f the laser. Equations predicting the real
and imaginary speckle contrast relative to roughness properties have been generated.
A microwave apparatus was built to measure the real and imaginary electric
field speckle contrast using a bolometer as a detector. Conductively coated sandpapers
were used as roughness standards. Eight grits in roughness from 18 grit to 80 grit were
tested both with a laser triangulation profilometer and with the microwave system. In
both cases the sandpaper specimen, which was mounted up-right to a translation stage,
was scanned. Results o f the microwave system were mathematical manipulated. The
resulting back-calculation of surface roughness had good agreement with the laser
triangulation profilometer data.
In the future, the method might be implemented using cellular phone
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-7 1 -
technology to make a more precise and compact apparatus. Eventually, development
could lead to a hand held unit for field inspection o f roughnesses. The technique may
even be applied to air coupled ultrasound which would allow roughness determination
on rough dielectric surfaces such as masonry.
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-7 2 -
APPENDIX A: PREVIOUS WORK
A .l
'Microwave Speckle Contrast for Surface Roughness Measurement"
This appendix contains a copy o f an article entitled "Microwave Speckle
properties for Surface Roughness Measurement." 20 It details our early work using Xband (10 GHz, 3 cm) microwave intensity to examine five molten alloy spray formed
specimens. The article is found in Nondestructive Characterization o f Materials V I.
This book is a collection o f papers presented at the Sixth International Symposium on
Nondestructive Characterization o f Materials held June 7-11, 1993, at the Turtle Bay
H ilton Hotel on the north shore o f Oahu, Hawaii. The editors are R.E. Green, K.J.
Kozaczek and C.O. Ruud.
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MICROWAVE SPECKLE CONTRAST FOR
SURFACE ROUGHNESS MEASUREMENTS
Douglas A. Oursler and James W. Wagner
The Johns Hopkins University
Center for Nondestructive Evaluation
102 Maryland Hall
Baltimore, MD 21218
ABSTRACT
Microwave speckle contrast measurements can be used to perform remote
determination o f macroscopic surface roughness. This procedure is non-contact and can
be performed through windows of certain dielectric materials. Therefore it has many
potential applications in process control and corrosion detection. Measurements of root
mean squared (rms) roughness up to 7.5 millimeters have been made using the
microwave system.
INTRODUCTION
Speckle is a phenomenon observed throughout the electromagnetic spectrum.
Optical speckle have been used in pattern correlation systems to detect in-plane
surface displacements as well as surface morphology changes.1 Optical speckle contrast
measurements have been demonstrated to yield roughness information on surfaces with
variations o f up to approximately two thousand angstroms.2 Although speckle contrast
measurements can be used to measure microscopic roughness, many production and
nondestructive evaluation (N D E ) applications require testing o f much greater
roughnesses, even on the order of several millimeters. For such cases, microwave
speckle contrast methods have been shown to be effective.
Causes o f Speckle
In general, speckle arise whenever there is any disturbance in a coherent
electromagnetic wavefront. The resulting scatter and phase variations cause areas of
constructive and destructive interference. Speckle can have many causes but for this
work the speckle in the diffuse reflection o f light off of a rough surface is of interest.
Figure 1 shows a "rough" surface where the variations are on the order of a
wavelength. When illuminated, the energy will be reflected in two components. The
direct (or specular) reflection will leave the surface at an angle identical to the angle
Nondestructive Characterization ofMaterials VI
Edited by R.E. Green, Jr. et al.. Plenum Ptess, New York, 1994
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-7 4 -
ROUGH SURFACE
(MAGNIFIED)
OBJECT
m
Figure 1. A magnified view of an optically rough surface. A. is the wavelength of light.
IMAGING CASE
s
(
\
;
\
i
NON-IMAGING CASE
Figure 2. The imaging and non-imaging arrangements for optical speckle.
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-7 5 1 of incidence. The different facets and angles o f the surface will result in a diffuse
; component, spraying energy in near-random directions. The intensity o f the diffuse
, geld forms a Gaussian distribution centered about the direction o f the specular
reflection. The width o f this distribution, the full width at half maximum, is inversely
I. proportional to the surface roughness.3 The roughness o f a surface can be
characterized by the amplitude and curvature o f the surface variations. The curvature
is used to express the lateral dimension o f the surface feature. Therefore, comparing
a surface with a gravel-like appearance relative to a surface with a series of large,
smooth bumps can be done by comparing their curvatures.
Optical Speckle
The development o f the laser as a portable coherent light source has made it
possible to use optical speckle as tool in N DE. Speckle at optical wavelengths are
visualized by the eye as a grainy texture which spatially modulates the laser light. The
treatment o f optical speckle patterns is usually handled statistically since the
illuminating beam is typically thousands o f wavelengths across, illuminating millions o f
features.
Optical speckle arrangements are typically separated into imaging and non­
imaging configurations (Figure 2).2 In the non-imaging case a laser beam is used to
illuminate the area o f interest. The resultant diffusely reflected energy is made up o f
speckles. In the imaging case a lens is used to form an image o f the surface. This
image is modulated by a speckle pattern. A n important difference between the two
cases is that the non-imaging speckle pattern is characteristic of the total surface area
illuminated. In the imaging case the speckle modulating a particular part of the image
directly relate to that area on the object. There is a one to one relationship between
the speckle modulated image and the object.
The statistical nature o f optical speckle makes it possible to make a number of
generalizations about the size and contrast o f speckles. The average diameter, r, o f a
single speckle is given as
fl* 2 ^
d
.
(1)
A. is the wavelength o f light being used.4 The variables d and f control the size o f the
solid angle o f light that will interfere to form the speckle. For the imaging case d and
f are the lens diameter and focus length, respectively. While in the non-imaging case
d and f are the illumination spot size and surface to viewing plane distance.
Speckle contrast is a measure o f the definition or sharpness o f the speckle
pattern. If a linear intensity scan is taken across a speckle Feld then an array, I(x), can
be constructed showing intensity versus position data. For such an array the contrast
is given by 5
r, . (</2>-</>2)1'2
(2)
</>
Where < I > is an ensemble average of the intensity data. For random patterns, which
is true in this case, this expression for contrast is equivalent to the standard deviation
o f the array normalized by its mean. Figure 3 shows the predicted optical speckle
contrast versus surface roughness for both the imaging and non-imaging cases. In both
cases the contrast begins to saturate at 100% as the root mean squared surface
roughness approaches a quarter wavelength. Experimental results using optical speckle
contrast have shown good agreement to these predicted results.2 A measure of speckle
contrast would therefore be a useful surface roughness gauge for roughness up to a
quarter wavelength o f the illuminating energy.
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-7 6 -
100.0
eo.o
Non-Im aging
Imaging
CONTRAST
6 0 .0
4 0 .0
20.0
= 0*63 fun
= 3 .0
0 .0 0
0 .0 3
0 .1 0
0 .1 S
0 .2 0
0 .2 S
0 .3 0
WAVELENGTHS
0 .3 5
0 .4 0
cm
0 .4 5
Figure 3. Optical speckle contrast versus rms surface roughness normalized to wavelength.
Figure 4. The metal spray form specimens labeled from left to right, A through D.
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TURN TABLE
COMPUTER
A/O
LENS
1.2 WATT
IMPATT
X-BAND
HORN ANTENNA
Figure 5. A schematic o f the test apparatus used to make microwave speckle contrast measurements to
determine surface roughness.
W31:
SPeCIMgN
w s2 :
A
3.0
s p e c iu e N
0
11
3 . 0*
2.0
>
0.0
wm
S P B C IM C N
1 2 .0
1 0 .0
2 4 .0
S E C O N D S _____________
1 . 0 ’
TT
0. 0
!
1! ! i
/H A
0 . 0
1 2 .0
J| '
j {
A k
IT
1 9 .0
s e o □N O S
24
0
W54! SPeCIMgN P
c
3 .0
2.0
1 9.0
2 4 .0
1 2 .0
1 9 .0
SECONDS
2 4 .0 '
•
W3 S : SPECIMEN E
0.0
III
1 2 .0
18.0
SECCMOS
Figure 6. Thirty seconds of raw signal from the microwave receiving horn for each specimen. (Scales are
identical except for Specimen E.)
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MICROWAVE SPECKLE CONTRAST MEASUREMENTS
The demonstration of surface roughness measurements using microwave speckle
contrast determination was performed using five test specimens, four of which were
tubular specimens from a metal spray forming process. Shown in Figure 4, these
specimens represent varying degrees of roughness and have been ordered from A to
E based on their apparent roughnesses. Specimens C and D are end sections. The steel
tube forms are visible at the top of these specimens. Specimen B is relatively smooth
except for a few large bumps. Specimen A is a finished piece; the inner steel tube and
outer rough surfaces have been milled away leaving a smooth surface. This specimen
is five inches tall with a five inch outer diameter. Specimen E is a square steel beam
added to demonstrate a roughness that will cause speckle contrast of nearly 100%.
The laboratory apparatus used to test these specimens is shown in Figure S. It
was a non-imaging system consisting of a microwave source and lens to illuminate the
specimens which are placed on a motor driven turn table. The rotation of the
specimens mimics the process by which they were created. The rotation speed was
approximately 17 RPM or roughly 03 Hz. A microwave hom was carefully placed in
the diffusely reflected field at an angle 40 degrees away from the specular reflection
and at a distance of 13 meters to insure that the receiving hom aperture was smaller
than the average speckle size (Equation 1). The microwave source operated in the Xband (X=3cm) and illuminated roughly a ten centimeter square area of the specimen
and was in the same plane as the hom. The signal from the hom was fed to a
preamplified analog to digital converter board in a personal computer. The a/d board
sampling rate was SO Hz.
A second method of determining the surface roughness was needed to calibrate
the system because the specimens have irregular surfaces. A profilometer was
constructed using a potentiometer and lever arm with a roller on the end. A spring was
used to maintain constant pressure between the roller and the specimen surface. The
roller was 4 millimeters in diameter and S millimeters wide. The specimens were
rotated on the turntable while the profilometer was in contact. After several rotations,
the profilometer was elevated, and data was taken again at S millimeter intervals.
RESULTS
Figure 6 shows thirty seconds of raw data taken from the microwave receiving
hom for each specimen. Note that all of the scales are the same except for the vertical
axis for Specimen E. Three interesting observations can be made from this figure. First,
the d.c. offset for each of the specimens is not identical. This effect seems to be caused
by a combination of surface angle and overall surface roughness. In the case of
Specimen C, the angled surface is deflecting the specular reflection vertically, out of
the plane of the microwave source and hom. The result is that the hom is effectively
sitting at an angle greater than 40 degrees so the average intensity in the diffuse
reflection is lower.
A second effect that should be noted is a wobble variation in the signal which
occurs at the frequency of rotation. This low frequency variation is caused by the
imperfect centering of the specimen on the turntable and in some cases by specimen
end (bottom) cuts that are not perpendicular to the axis of the specimen. Finally, and
most importantly, note that the amplitude of the higher frequency variations do seem
to increase with surface roughness.
To determine the speckle contrast independent of signal offset and "wobble,"
the specimen signals were processed. Each signal was normalized by its mean and highpass filtered at three times the rotation frequency. Figure 7 shows the processed signals
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w a it FILTERED NORMALI ZED SPECIMEN A
Wflg- FILTERED NORMAL 1260 SPBCIIigN 8
MB
1 2 .0
1 8 .0
SECONOS
2 4 .0
W 6 3 E IL T E R ED NORMAL I ZED SPECI mEN C
1 2 .0
1 8 .0
SECONOS
2 4 .0
W64: FILTERED.NORMAL 1ZED SPECIMEN_D
2 4 .0
1 2 .0
If. Q
SECONDS
2 4 .0
W6S: FILTER6Q NORMALIZED SPECIMEN B
4 .0
2.0
0.0
8 .0
0 .0
1 6 .0
2 4 .0
secoN oa
Figure 7. The filtered normalized signals for each of the specimens.
100.0
80 .0
hn
<
K
I§
eo.o
4 0 .0
20.0
Q.O
0 .0 0
0 .0 S
0 .1 0
O .I S
0 .2 0
0 .2 S
0 .3 0
WAVELENGTHS
0 .3 5
0 .4 0
0 .4 S
Figure 8. Speckle contrast versus rms surface roughness showing predicted (lines) and experimental data
[squares). The data points are in order for specimen A through E from left to right.
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for each of the five samples. Again, note the scale change on the vertical axis of
Specimen E. The variation of these traces clearly increasing with apparent surface
roughness.
To correlate these data with surface roughness, the standard deviation of each
of these normalized filtered traces (speckle contrast) was computed. To calibrate these
findings, the results of the profilometer tests were used as a standard. In the same
manner as with the speckle data, profilometer data was high-pass filtered at three
times the rotation frequency and assembled into a matrix. The root mean squared
surface roughness was then calculated for the region illuminated by the microwave
beam. In Figure 3 the predicted (visible) optical speckle contrast was plotted versus
rms surface roughness in wavelengths. Figure 8 shows the results of both the predicted
and actual microwave contrast measurements as a function of surface roughness. The
squares represent the data points which are for Specimens A through E in order, left
to right There is good agreement between the predicted optical results and the
experimental microwave results.
CONCLUSION
Speckle resulting from X-band microwaves, with a wavelength of three
centimeters, have been demonstrated to give a accurate indication of surface
roughnesses for variations of up to a quarter wavelength. The relationship between
speckle contrast and the surface roughness has been demonstrated using specimens
from a metal spray forming process. Surface roughness data were collected using a
potentiometer based profilometer to calibrate the speckle contrast results.
The results indicate agreement between the predicted and the experimentally
determined behavior of microwave speckle. This agreement is somewhat better than
expected considering that the microwave source illuminates a spot only four
wavelengths across. For this reason the microwave speckle would be expected to
violate the basic hypothesis that allow statistical assumptions used for predictions in
the optical case, Tlie small illuminated spot size relative to wavelength may make it
possible to characterize in greater detail the nature of the surface roughness.
Preliminary results have shown that features in the frequency spectra of the speckle
contrast signals can be related to the characteristic curvature of die surface roughness
The use of microwave speckle contrast methods for remote surface roughness
determination may make possible a range of control sensor and NDE applications.
REFERENCES
1. F. P. Chiang and D. W. Li Decorrelation functions in laser speckle photography, J. Ont. Soc. Am. A.
5, 1023, (1986).
Z J. Ohtsubo and T. Asakura, Statistical properties of speckle patterns produced by coherent light at the
image and defocus planes, Qptik 45, 65 (1976).
3. 1. W. Goodman, Statistical properties of laser speckle patterns, in 'Laser Speckle and Related
Phenomena’ (J.C. Dainty, ed.). Springer-Verlag, Berlin and New York, 1975
4. F. P. Chiang and D. W. Li Laws of laser speckle movement in space, Optical Engineering. 25(5), 667670, (1986).
5. R. K. Erf (ed.). Speckle Metrology. Academic Press, NY, 1978.
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-8 1 -
APPENDIX B: DERIVATIONS
B .l
Derivation o f Equations 18, 19, 20 and 21
In this section the derivation o f the expressions for <A>, <A>, a 2 and or/ is
performed following the derivation given by Ohtsubo and Asakura24 and Goodman21.
To derive <A> start with Equation 13,
M r , t) =
*££-') dr' .
r'
0
(1 3 )
W hen the ensemble average is taken o f the above equation the variable being averaged
over is the stage motion, t. Therefore we can write
„
< A { r , t ) > = —? ^ e
Ja R
u
ikiR+ll'i
2R
n
J
0
t]> i * e
- r r/i2 jk W )2
“
e
2R J 0 (
.
R
)d r '.
(Al)
Using the relationship
t) >
_ «|>2 (
<e i<t>(^ - 1) > =e
2
_
=e
fA21
2
we can rewrite Equation A l as
^
<A(r, t ) > = 4 ^ e
2R e
-^1
- r r / i2 jk lr1)2
.
2 J r f e ° e 2R J 0 ( ^
o
/
)dr/.
(A3)
(J) has been assumed to be a zero mean random Gaussian variable. The first equality in
Equation A2 is a result o f the central limit theorem while the second one uses
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-8 2 -
definition o f variance.
The derivation o f <A2> is much more difficult. Starting with Equation 9 the
approximations, Equations 10 and 11, are used and any term independent o f r' is
moved out o f the integral. The real and imaginary parts o f A can be written as
Ar =A f E { z ' ) c o s (<|) { z ' , t ) +H{ z ' , z ) ) d 2z '
(A4)
oo
A -= A J E { z r) s i n (<J> ( r ', t ) +H{ z ' , z ) ) d 2z f .
Here A contains all o f the f independent parts and E is given in Equation 5. The
function H is
H{z't z)=^
/ ll-(j^)S '.f
,
(A5)
In the last two equations the vectors, originally used in Equation 3 and defined in
Figure 4, have been re-installed to make the next step easer. The mean, squared parts
o f A can be written as
CO
< a |> = - |
CO
e"°*Jf E { z [ ) E ( z i )
[C+{ z i ~ z i ) c o s [ H{ z i , z ) - H [ z { , z ) )
~ 00—00
+ C_ { z [ - z i ) c o s ( H ( z £,
z
) - H { z [,
z
) ) ] d 2z i d 2z ^ ,
(A6)
00 00
< A l> = - |e ~ ° * J J e [ z I ) E { z £ ) [C+ ( z [ - z £)
c o s {H{z £ , z ) - H { z [ , z ) )
- o o -e o
- C. ( z i - z i ) c o s ( H ( z £,
z
) - H { z [,
z
) ) ] d 2z '
d Zz x .
The functions C- and C+ are
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-8 3 -
(A7)
P(, i'"12') is
correlation function o f the phase variation ({>. However since cj) is
assumed to be a Gaussian random function we can write
p (/ r 'a) =e _(i “r )2
<A8)
a is the correlation length o f the roughness. C+ and C- may be constructed using the
last two equations. However, because o f the complexity o f the integral in Equation A6
an approximate value is normally chosen26. C+ and C- (approximated as being
independent o f
r')
are expressed as
C+« l - 2 i t a 2e " ° * F (- a |) ,
C_«l-2rra2e '° * F ( o |)
(A9)
.
Here the function F(x) is given back in Equation 22. Using Equations A6 and A9 we
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-8 4 -
can write
<A!>=<A1>2 + ^ e ~ a* [ - F { - o j) J e 2 ( z /) d 2z '
—eo
CO
- F ( o | ) J e 2 {?') c o s ( 2 H ( r z ) d 2z ' ]
,
— oo
(A10)
to
<A?>=<Ai >2 + ^ | ! e ' ° M - F ( - a | ) J e 2 ( ?' ) d 2z l
—os
oa
+ F ( a |) J f 2 ( r ') c o s { 2 H { z ' , z ) d 2z '] .
—eo
Using the above equations and Equations 17 and 18 we may write Equations 19
and 20.
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-8 5 -
B.2
Derivation o f Equation 34.
In the following figure, an optical ray intersecting two vertical surfaces is
shown to illustrate the path length difference resulting from the surface displacement
h. P is the ray's angle o f incidence. The path length difference is
A =p + q
(62)
and, from the geometry,
a
By further examining the figure, p
= 90° - 2 p
(63)
.
and q may be defined as
_ _
P
q
h
q
cosp
=p s i n a
/
(64)
.
The path difference can be rewritten as
A =—
COS
r
P
( 1 + s i n a ) =—
COS
P
( l + s i n ( 9 0 ° - 2 P ) ) =2.ftcosP
(65)
where trigonometric identities and the previous three expressions have been used. This
equation relates the path length difference to what will now be called surface height
and the angle o f incidence. P is considered a constant for a given setup so an
expression relating path length and surface height variances may be written as
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-8 6 -
h
i :
oc
q
Figure A .l
Path length difference is illustrated by a ray (o f light or microwaves)
intersecting and reflecting from a surface that is displaced by /*.
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-8 7 -
a \ =< [ 2 h c o s P ) 2> - < 2 i i c o s P > 2
=2 c o s p [< h 2>-<h>2]
=2 a 2h c o s p .
(66)
The phase variance may be expressed by multiplying the above equation by 2 ti/X. The
square root is taken o f both sides to produce Equation 34
a <l>=- ^
ah c o s p
.
( 34)
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-8 8 -
APPENDIX C: LISTINGS OF IMPORTANT PROGRAMS
C.1
Labview Programs
In this section contains two Labview programs. The first program, called
"Raster LAS Scan.vi", is used to raster scan the laser triangulation profilometer over
the surface o f a specimen. The program creates displacement and intensity data
matrices. If the intensity drops below a given value the displacement information is set
to some default value. This program can be found on Pages 89 through 97.
The second program, called "Microwave Speckle.vi", runs the microwave
speckle contrast experiment. This program translates the specimen three times in front
o f the microwave system. Each time it prompts the user to adjust the phase settings.
The three data sets are then used to calculate the real and imaginary parts o f the
electric field. This program is listed on Pages 98 through 130.
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— 89—
Page 1
Raster LAS Scan.vi
01/26/96 03:51 AM
Connector Pane
Raster LAS Scan.vi
Front Panel
Vert. Distance mm
BpOCO
I
Return Speed mm/s
B115.00
* Row*
I
Stage Speed rnm/i
E 3
Hog. Distance mm
Row Length
j gooS -n
™
“
Point Spacing mm/pt
Oversampling
--------- -
!* □
# of Points
in a ROW
Start Scan
Input UmHs
El5”
Point Rate
Ptf»
pw
FoSwl
I
pUt
Intensity
cutoff
BP-5000 II
SCAN
TIME
)Fle Name(wto .art) |
STOP
1EE3
(mini
,
M
[To Many Points |
FS
BEE] □ □ Q E Q lE IB
pi •*i f i m
flZEIEl
Elevation
50.0-
45.0-
45.0-
40.0-
40.0-
35.0-
35.0-
30.0-
30.0-
25.0-
25.0-
20 .0 -
20.0 -
15.0-
15.0-
10 .0 -
10.0 -
5.0-
5.0-
1 -2 5 0 0 .0 B 1-4.500
pune* i
c—
| |C:¥abview^epocKrt«W6a
Poet Trigger m«
50.0-
-3 0 0 0 .0 1 -4.000
-3.500
1-3.000
I -4 0 0 0 .0 1 -2.500
1 -3 5 0 0 .0 1
i I -4 5 0 0 .0 1
- 2.000
I -5 0 0 0 .0 1 -1.500
1- 1.000
1 -5 5 0 0 .0 1 -0.500
J-6000.0( -0.000
(tensity
0.0 -,
0 .0 -,
0.0
Sample Rate
3.0
6.0
9.0
12.0 15.0 18.0 21.0 24.0 27.0 30.0
0.0
3.0
6.0
9.0
12.0 15.0 18.0 21.0 24.0 27.0
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30.0
-9 0 -
Page 2
Raster LAS Scan.vi
01/26/96 03:51 AM
B93I
7^
Block D iagram
a □ a □ a □ g.g.g n o o a n Q n a n i i n n n Q i i i i n n n i i n ^ o ^ n n n D D D D O D a n D a D D D a o n n D a D D h n n n n i
History Data
popllrfril
IBiitltnzlI
History Data
EtowMon |
|M t ||
| [s o tl |
Hi!
post samp
jnb 52
trig
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Raster LAS Scan.vi
01/26/96 03:51 AM
DODDODDDDO
-9 1 -
Page 3
7*
0 0 0 0 0 0 0 0 0 0 HJU LQ H
OHbbbdpdaD D D anaDD D b
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Page 4
- 9u 2-; -.
Raster LAS Scan.vi
01/26/96 03:51 AM
n a P D t i n a D n n n D D D D n n D D n a n c a D D D a i ] DU 2 M 0 P Q O P □ □ Q O BO D D n o o □ □ □ tJ □ □ n n □ □ n ri~ff
in a ROW
iofz. Otstanco mm
Row Length
jOversampej
t# pis of Post trig I
Point Spacing mm/pt lo g tj[
(Oversampling (i n e 1}
(Stage Speed mm/s |ru o tjj
(Post Trigger ms
umUpwnptoR**«
ISpdL"{|
IJMMJboint Rata
atum Speed mm/s ^"ppQ
£
Input Limits
{Return Spaad u m /s|
fro Many Points
I of Rows
j » w w » i |r n t i l
64000
K!
|RowSpadnflum | 5CW
[mini
|V«rt. Dbanc* mm | [TWO
fSlMl Scan | [CEBU A > f j > ( C i |
X Minimum X Minimum
X Majdmum X Maximum
X Increment *X Increment
delta X
Y Minimum
Y Maximum
Y Increment
detta Y
[Elevation |
[Row Length um (
mrmrfrn n n n n cm
Y Minimum
Y Maximum
Ylncramant
(Renslty|
□ □ □ □ □ cm
nn Dinrn
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Page 5
Raster LAS Scan.vi
01/26/96 03:51 AM
7 ^
0 , 0 , 0 □ □ 0 . 0 . 0 Q D D O D D D D Q D D O O P D D P P P n n K 3 W □ a a a Q a n ^| a B o D D D a n n n n n □ a □ □ a n a n n ?
o17 p ~Q a
□□
d □
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Post
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n n n p a t r nm n n n n Trrm T rrn r n
mrira a n a
(?1 ffl
W
[♦ W
Irf r f r W
iTruo
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Page 6
Raster LAS Scan.vi
01/26/96 03:51 AM
flW □ □ □ □ □
-$>
a
n a
a
Q a g g
i n u P B s m m u M 3 tt
O g j l ^
o
^
o □
□ D oaD D D D anoooPD nnn
rnm nnrpm
3 1 1 □ □ □ □ a □ b. Q □ □ □ □ □ □ □ □ □ n n r]_[^ 1 ^ p j
i-fp n
LD.nnnanan
□ □ □ D d a D D D D O D p n o" n n n h
|o.oo| I
ED— -
SSL
[VftVt
a a ta g a m
m
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Page 7
Raster LAS Scan.vi
01/26/96 03:51 AM
j a i . f l .n .n ,B a p .o a a o n .a .n .a a a a n a
d
□ □ a □ □ □ o □ □ □ o □ b □ □ □ n c ro c r
"HTnwW
n g Dnm^ i ^ D n a a g
[STOP]
□ a n a a r r e n x n n cr
Utin'p n nH'fT|
n.aPDQ[Ho^i6flgD~a
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r
in
_ 0 -'
i n a n n nTr r r r r cm Trrr
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 8
Raster LAS Scan.vi
01/26/96 03:51 AM
g. D
■3 I
a a O Q Q Q O a n o a o a a a a n a a a n a a a g g^ ^ u m □ D n n n n p i n o n D n D n n ' o n n n n n n n n n m j
la ri
n n n n n rr rTrm n r r
mi
mi
nn n n n n nnnnnn nnnn
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 9
T*>
Raster LAS Scan.vi
01/26/96 03:51 AM
ODQo o a a o o a a p g o n a n n a n n aDQDacLnJml^s^DDaaQanDD aWa□□nnnooandaanoDd
Naro»(Wo .axt) |
Fm Haadar. 5-character strings, column: rows, for
total of 10 character*
2-0 array date folowa fmmadiataly.
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 1
Microwave Speckle.vi
01/26/96 04:11 AM
Tba Channal maans ara
TTraval DbUnca mm >,________ 214.046389E-3
465.526514E-3
“|
for Pid
CONTINUE
^ o s s n — 'tana*
3
SS5L
ICROWAVES
STOP
[Trawl Sp—d mm/s
SO
BveSampSg]
npu» Limits
♦ /-
T E E IT
{Post Trigger ms
3 0 .0 0
PoW Spacing
mm/pt
E”03250 1
D
(CM MAX|
(Samping Rat* |
paEsn
|CMMkltov|
|Ch4 Maan |
FMaNama
(no axt)
[p4Ctn10 j
-0.6-
OEEl 0 0
fT F IF I
□
0.000
0.200
0 .4 0 0
0 .6 0 0
0 .6 0 0
1.400
1.600
1 .6 0 0
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
2.000
Page 2
Microwave Speckle.vi
01/26/96 03:58 AM
Block D iagram
DDOflDnnPOnQnQBDBOD^ Q ^ C D o a a D D n a n n D D D D a n n l
|Graph|
Y Minimum
1 Y Maximum
Legend Visible
I0114Meanl RUdI
(Offset ch 4 1
ICONTlNUEl
|01fsetch6|
MICROWAVES
ON
|Aimlng|
(o.oo| ptol
B
|Offsetch2|
|Botometer|
E}-<w>
IditelPol
Input Limits
|CLEAR GPIB AND STAGE CONTROL
+ /-
(Ch2A|
I Messages |
| SETTING UP DEVICES |
scan rate
| MICROWAVES
ON |
S ri
|Ch 2 B|
IRESET abo s e U t t ^ ^ outs to ZEROl
CM Mid lev
Cat
# of Pts|
I
(ch 2 C|
CM Mean
|Ch4 Mid lev |
pop]
m
m r no n n n m i"n d n n Sk b
*
n*9 t
|oversp|
post
trig
pts
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 0 0 -
P age 3
Microwave S peckle.vi
01/26/96 03:58 AM
! □ □ □ □ □ a . g . g □ □ a a a a a n EU3JH 1 m n a c m o n n a » o n a~a □ b a r m
I p t t d n n c ru u u a n n p - S r a c B o f f i p r B m n r S n P c
a trn T rc r
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 4
Microwave Speckle.vi
01/26/96 03:58 AM
in n □ □ □□□□dp □a □ □ □ n □□ i|^ 2 ^ o n n n a n a n m o o n D D n n n
- The JOYSTICK is now turned on When done entering
Values press CONTINUE
GPIB TURN JOY STICK ON
|lOT1111ti\nS\r\n
B
1
m—
Eh
H
H
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout p erm ission .
Page 5
Microwave Speckle.vi
01/26/96 03:58 AM
p
.p
p p p
p p p p
p
p
fravel Distance mm |
.p
p p p p p p
(Point Spacing
mm/pt
^ wa
d p
□o □ n p □
a □ p p ip p a
d
CONTINUE
|Overeamptng1
ersampfngl
[LS^cJI |SampCng~Rati]
[Travel Speed mm/s
[Post Trigger ms
Total # PTs
r55Tl|
stage
return
speed
Fie Name
[no ext)
lEriNTXOYO-LBiriTIXXXXTaaiXIXX^DW Oa-OTOXXX’X F l-
| ‘BN*DWQ1*BF*OT1XXX*CT33IX1XX*GT11•LB33,PS”/M n ,
nm rn-aD n a na-oall l i a c ^ - n ^ ni^in -D-i^ ^
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 0 3 -
Page 6
Microwave S peckle, vi
01/26/96 03:58 AM
n n o n n Q n n a n o n a a n o Q Q i^ 4 ^ □ □ □ □ □ a n n ^ n o D D D D D n n
While the Microwave Source is off
THE OFFSETS WILL BE TESTED
Messages
•D-g-mrm ra □ d n o a □
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 0 4 -
Page 7
Microwave Speckle.vi
01/26/96 03:58 AM
f t n . a - a . g . n n c a n n a a a n n n n n i^
SSL
5
Ml
tita n
|# sm ||1 5 0 0 0
[Calculate Offsets |
1
I
B
M
mmci.n □ □n n n a n c ii lrm r ^ -g ^in ^ r a a r ^ nWc
alf a a g
I
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 8
Microwave Speckle.vi
01/26/96 03:58 AM
| n n n D n n a n a n g . iiD[iaQDn ^ e ^ ° P ° ° ° P n P M ° ° ° ° ° ° n n n
MICROWAVES
ON
1
MICROWAVES ON....JOY STICK ACTIVE
Adjust Phase thru >180 then to 0
Press CONTINUE to START test
fMessages']
1
m
p e
[TURNING ON MICROWAVES]
m
iH r u L i y M u u L i J i c
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 9 p P T
Microwave Speckle.vi
01/26/96 03:58 AM
□ □ □ □ □ □ □ □ D O D n a n D n n o i j ^
j
^ a a a n p a n n a o n a a b D n n n
m
'□aanaotrtin'D'D'HtT
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 10
Microwave Speckle.vi
01/26/96 03:58 AM
H aD O .nP O Q O O nQ angg.m U M s ^ n n n n n n p p i n n n a n n n n n
| Input Limits
♦/■
CM Mean
Ef Lf £
|Cal scan rate
Cat # of Pts
S * * -fGraphl
■u *JI
status
□ n o d u n lj o n □
| CONTINUE |
W SSSSM SSi
|6 ,4 ,2 ,0 H s H H }1
C M Mid lev
0] jO.OO
h/iew Traces as the Referance a adjusted
f mr a tTU-QITP□ □ □ □ ci.fln iifi] dW d i^rri
5a
dB
□ O P'D T T I
o o a a H 2 H ° aat:
(STOP)
Innnnmraim
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 1
Microwave Speckle.vi
01/26/96 03:58 AM
□ □ □ □ □ □ Em a a n D n n n n n n i H 9 ►| o n n n n n n D e n a a a n n n r T ? n
|TURN j o y STICK OFF|
[Start stage program #9|
|A3V\n |
mu uuuuuuuna nPk mEtl o^ dtffii n n51
d^
St
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-109-
Page 12
Microwave Speckle.vi
01/26/96 03:58 AM
3
E
CONTINUE
d
B
1
1
s
u u d u u u a a a u b u u I l L 'D J U r i ^ U t ^ l P Cl
p ffc
m rean i
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-110-
P a g e 13
o*>
Microwave S peckle.vl
01/26/96 03:58 AM
I Q □ g g g D .D .Q □ g Q g Q g g g a . D . ^
n ^ D D n D D C D D » D a b n n n n
rT n
I Messages I
— Ready to start speckle test —
! IS the PHASE set to ZER07I
El
1
B
1
&
R
|CONTINUEM 5>Hi
n n n n n rrrr
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-111-
Page 14
Microwave Speckle.vi
01/26/96 03:58 AM
ID a n n a p anaDDI i n [1 0 n n n ^ lz^ j n n n n n n a Mn n n n n D n n n
| Messages]
I
NOV\ TESTING
NOW
of 3
1
Si
[Trigger stage controler
port 0, ine 1, to TRUE
m
f u u u u o o U U U n D D U p L u r d n^ u Jrp! n m jrlrnffri
I
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 1 2 -
Page 15
Microwave Speckle.vi
01/26/96 03:58 AM
□ □ □ □ □ □ □ □ D P g j 3 .g g □ □ PLO-H 13
SSSL
n o a o n n D i o n p n o a n ntt
|Get Data set 1 of 3 |
Tr r r n n im n n n n e r t n r ■(ffiip
era r a n li i a o i ^ nl c
i
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 16
Microwave Speckle.vi
01/26/96 03:58 AM
a a o - D Q .a .a .a a □ o x i □ □ □ □ □ □ □
□ □ □ □ □ □ □ □ ■ □ □ p a a n n nTT
Trigger stage controler
port 0, ine 1, to FULSE
n n n n o a u ri L i a t i b J
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-114-
Page 17
=3>
Microwave Speckie.vi
01/26/96 03:58 AM
p q □ q . p q n □ a □ d .q - q a □ a a r m
1 5 ►)u i a a , Q . a o x i . a i t n D g p n a a n n i
m
m
m
tan erm r emer m xrra u ilk n ell nffin
m PS aP i a M f t f f i'a f f i l i'cn
R ep ro d u ced with p erm ission of the copyright ow ner. Further reproduction prohibited w ithout p erm ission .
-1 1 5 -
Page 18
Microwave Speckle.vi
01/26/96 03:58 AM
a g a a a n a a n a a a a □ □ g x ix m i 6 Mn D n n n n a a " D n n C D n o D n
u „ „ „ l I No w adjust the PHASE 80 Degrees
Messages
CONTINUp
| Input Limits
♦ /-1
Ch4 Mean
| Cat scan rate|
■^status |
L ----
| Cat # of Pts |
CONTINUE
□□□□
S.4,2,0
True
OWLOXLQX
ol 10.00
tLflXLOH 1M 0 a ° f
onnnnnnrm
tLa£LDj^2^QQae
nnnnnnrrpprr
g x m x t H 3 ►Ix l o x i
u i_m □ □ g g
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 1 6 -
Microwave SpecKle.vi
01/26/96 03:58 AM
EESLaflH 4
TTD-p n n n n u p T
[False]
□ □ □ n o o n o n n n n n n n n n
n o g □ a □ n o ■□□ □ n n □ n n n
T n rtT D D U U J U H n r r r r
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 1 7 -
Page 20
Mlcrowave Speckle, vl
01/26/96 03:58 AM
| q n n a . [ j a a o n . Q a a a o a a Q E m i 8 H or l onanaa, t : i aonci r i r i r i n
1
m
CONTINUE
.
□ a n a a n □a n a a n p ^ i n r ^ nffin
m
m
B
af P& n r
R ep ro d u ced with p erm ission of th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Hall
Page 21
Microwave Speckle.vi
01/26/96 03:58 AM
Jia.n n a a D D O a a n a u n a m
m
19 ►y.0 o o n n n a a B n n n D a n n nTT
Messages
NOW TESTING
2 of 3
Trigger stage controler
port 0. inel.toT R U E
i T D ' D n n n a a a B B n i r ;M nrrfil D^crt^ r a □t^ u Wi
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
-1 1 9 -
P a g e 22
Mlcrowave Speckle.vi
01/26/96 03:58 AM
a o a a n . a a a . D o o n o n o n n j u x ^ ; o ^ a n n a D n n a a o n a & a n n nTT
|5QQ.o|
la ri
p a a a o"d Dxnrcm'a a
n iranW n i^ i a □ J S-a*iri
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 23
Microwave Speckle.vi
01/26/96 03:58 AM
n n n o o o r m o n n n a c mn n£L^21
o a a DP c mMa o o o a n o o '
Trigger stage controter
port 0, ine 1, to PULSE
n n t i u u n tr m r t m crcr
R ep ro d u ced with p erm ission o f the copyright ow ner. Further reproduction prohibited w ithout perm ission.
Page 24
Microwave Speckla.vi
01/26/96 03:58 AM
rm nD D Pononaaooantum a^aoocm ocm T m nnnnnrM T
m
□ □ d an aJxa.CLa tu p
n J f i n ^ p - i ^ m -n t^ m W i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 25
Microwave Speckle.vi
01/26/96 03:58 AM
n n P a a D n p n n .a n a o a g p o ^ 23
I
lJ N
[ Messages
| Input Limits
ow
n n n n ^ b n n n n n aci a
adjust the PHASE 180 Degrees
PRESS CONTINUE
JRC-I
♦ /-1-----
/C M Mean
Cat scan rata
C alsofP ts
CONTINUE
□an a[^o^ a o □
1
HBB.BiBiHi? 1H
o 10.00
u u n u u n n n n n n u u vm a rro mr o traaiTPTmTi
tltLO-DH 1
rnnnnnntmn
itLaooH 2H b ftb r
rauannnnjnr
0 0 0 0 ^ 3 Ia a a
[iL ResetI
iru □ n na'p pin i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 26
Microwave Speckle.vi
01/26/96 03:58 AM
(STOP]
mn c mn n r T T n
□ □□□ Q a o a oQ a a a □ □ n n a ^ 24Wanooi=li:iaa" a a a o n n nnrf
□ 'IXITLTD □ U'U a n □ n c r M r u J rl n ^ n i l n - n i j ^ r n ^ r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 27
Microwave Speckle.vi
01/26/96 03:58 AM
m a a a n a n Q Q a Q n a a n a a cm
25
a □ □ □ □ □ □ » n n □ □ □ □ n n~n
1
I CONTINUE F
1
m
1
1
□ Li Li u u T T n ITTTTT d 0 p ( ^ L U
n^U
J5!l D P
iffil
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 28
Microwave Speckle.vi
01/26/96 03:58 AM
fla n □□□□n a a a a a o o n n n n ^
2 6
MPa n a ° a o a " i:in[:id'Briri
[Messages I
NOW TESTING
3 of 3
E ra
E P t
Trigger stage controler
portO, Ine1, to TRUE
1
E
i
Binru n n n u n n n n n n i ii n i^ nffin t ^ u n r^ -crWn
nS
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-1 2 6 -
P a g e 29
Microwave Speckle.vi
01/26/96 03:58 AM
□ □ □ □ □ □□ □ □ □ □ □ □ □ a n 0 ^ 2 7 ^ a n o D o o o o « o a c m o c m n n '
Input Limits
♦/-
pOO.O
n
|Get Data set 3 of 3 |
n n n n n n n n n n n n n
S n J M
m
n U
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
—1 2 7 —
Page 30 | p |
3^
-------
Microwave Speckle.vi
01/26/96 03:58 AM
a a a n o n n a D D D D O o a n n o
Trigger stage controler
portO, ine 1, to FULSE
MICROWAVES
ON
ELS"
TnnTDTnnro-o'p-ffB'n
;
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 31
Microwave Speckle.vi
01/26/96 03:58 AM
O O 0 O O □ .0-0.0 □ O □ □ □ □ □ g g ^ a ^ n n n p g a n p a n n n n n n n riTT
[TEST OVER. R e s are saved as
[dat
Press CONTINUE to See the Stored Fies
CONTINUE
mem n n g i r o n n n n n -
n rfl gffin tPPro n t^nW i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-129-
Page 32
Microwave Speckle.vi
01/26/96 03:58 AM
□ □ □ □ □ □ □ □ P O n P L m a n PJPJ^ 30 ►f.a a n n o c m n M n a o a n n n aTT
Graphj
Y Minimum
iTho Channel means are
Messages
n ^ E l*
—
n n
http
TT5T
^Graphj
□ c re m a r m cr• ^ r n e ffl-p f f i a t ^ i o n i l r r i f f i i
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 33
Microwave Speckle.vi
01/26/96 03:58 AM
Q g .g g .g □ □ Q g □
g Q g □ cm
3T ►fX l.g O g g n n n w n o n o a p q p n
|RESET also »et» tha digital outs to ZERO
n n n o w m j o n n n n
S n n & U r a M
,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
—131 —
C.2
M aple Program
The following program is used to perform the back-calculation o f the RMS
surface roughness, a,„ and the surface correlation length, a . It starts by importing a
two column (abc) data file such as would be written by "Microwave Speckle.vi".
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-132-
>surfacer:=proc(fllenanie,extll3mbda,w,R/r)
> # SURFACE ROUGHNESS DETERMINATION BY Re AND Im FIELD SPECKLE CONTRAST
>ti Enter FILENAME o f the data sets to import
>lprint( ' Running SURFACER to calculate the Roughness and Correlation Length');
>!print( *This will take about 6 .4 m inutes');
>readllb(readdata): wlth(stats): with(linalg):
> n m e := ' O.WIabvlewWspeckdatW' .filename.' . ' .ext:
>lprlnt( 'The base filename Is *,nme);
>lprint( 'The Wavelength in Meters is ',lambda);
>lprint{ ' The Spot radius in Meters is ' rw);
>lprint( 'The Detector dist as projected on the specular radius In Meters Is ',R);
>lprint( 'T he Disc from the specular reflecton in Meters is ',r);
>lprlnt{ '# # # # # IMPORTING DATA ARRAYS # # # # # ') ;
>da:=3rray(readdata(nme,2)):
>len:=rowdim(da):
>ear:=col(da, 1): eai:=col(da,2):
>pts 1: —[seq([i,ear[I]],i — 1J e n )]: pts2: = [seq([l,eai[l]],i- 1..len)]:
>plot1:=plot(ptsl,style=point,color=red):
piot2:=plot(pts2,style=point,color= blue):
>piots[display]({plot1,plot2},title= 'The Re and Im RAW speckle traces');
>lprlnt(' The mean o f the RE Raw data ls',mean{ear));
>lpr!nt('The mean of the IM Raw data is',mean(eai));
>lprint( ' M f t M CALCULATING EQUATIONS # # # # # ') ;
> c:= 2*P i*{ln t (rho*{BesselJ{0,a*rho)rexp(-(rho/w)A2)*exp(r{b*rho)A2 ), rho=0..infinicy)):
>s: = {inc (rho*(Bessel]{0J2*a*rho))*exp(-2*{rho/w)A2)*cos((sqrt(2)*b*rho)A2 ), rho=0..inflnlty)):
> F : = x - > E i(l,x)+ln{x)+gam m 3(0):
>d:=sqrt( wA(-2) • l*b*b):
> c:=evalf(c):
cr: = Re(c):
b:=sqrt{Pi/(iambda*R)):
ci: = lm{c):
a:= 2*f,i*r/(iambda,',R):
s: = (evalf(s)):
>lprint( '# # # # # MANIPULATING DATA ARRAYS #####')-,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
—1 3 3 —
>lprlnt{ 'The Angie raw data in Radians is
arctan(me3n(eai)/mean(ear)));
>lprint( 'T he Angie by calc should be in Radians is ' , arctan{ci/cr));
> b eta:= arctan (ci/cr) • 3rctan(m ean(eai)/m ean(ear)):
>lprint( ’ The Angie data rotation angie in Radians is ’ , beta);
>ppr:=slgnum(cr)*slgnum((cos(beta))*mean(ear)-(sln(beia))*mean{eal)):
>ppi:=signum{ci)*signum((sin(beia))*mean(ear) + (cos(beta))*mean(eai)):
> a ea r:= ( add(ear,eai,(ppr*cos(beta)),(-ppr*sin(beta)))):
> aeai:= ( add(ear,eai,(ppi*sln(beta)),(ppi*cos(beta)))):
>lprlnt{ 'T he NEW data angie in Radians is ' , arccan(mean{aeai)/mean(aear)));
>Vaear:=sdev(aear)/mean(aear):lprint( ‘ Data real contrast is’ ,Vaear);
>Vaeai:=sdev(3eai)/mean(ae3i):iprint{' Data imaginary contrast is' ,Vaeai);
> gg:=abs(evaif((P I*vv*(7/10000)/2)A2 *(-F{-( 1.2 5 6 6 3 7 )A2)-4*s*(F(( i .2 5 6 6 3 7 )A2))/(w*vv)))):
> ff:« abs(evalf((P i*w *{7/10000)/2)A2 *{-F (-(1 .2 5 6 6 3 7 )A2 )+ 4 * s* {F ({1 .2 5 6 6 3 7 )A2))/{w *w )))):
>lprint(' Predicted alp=.7m m rm s=.5m m real contrast is’ , (sqrt{gg))/cr);
>lprint(' Predicted alp= . 7mm rm s=.5m m imag contrast is ', (sqrt(ff))/ci);
>K: = (4 * s/(w * w )) * ( ( (Vaear*cr)A2) + ({Vaeai*cl)*2))/(( (Vaear*cr)A2)-{{Vaeai*ci)‘2)):
>iprint{ '# # # # # SOLVING FOR ROUGHNESS M M # ' ) ;
>si: = fsolve(F(-sigmaA2) - K*F(sigmaA2),sigma,0..2*Pi):
>alpha: = 3bs{evalf(Vaear*cr/({Pi*w/2)*sqrt{-F(-siA2)-4*F(siA2)*s/(W'A2))))):
>srms:= evalf(si/(4*Pi));
roughness:= evalf(srms*lambda):
>!print( 'T h e Correlation length in MM is ' , (alpha* 1000));
>lprint{ 'The ROUGHNESS in MM is
(roughness* 1000));
>end:
>save ' surfacer.m';
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-134-
APPENDIX D: EQUIPMENT
D .l
Equipment and Wiring
The microwave speckle contrast measuring system (Figure 6) operates in V-
band at 60 GHz (X = 5 mm). The source is an Epsilom Lambda Electronics
Corporation mechanically tuned Gunn oscillator (ELMI64). It produces 150 mW
(22dBm) o f power. The accompanying power supply/modulation may be FM or AM
modulated. In this experiment the AM ability is used to give the computer on/off
control over the microwave source.
M icrowave circuits are constructed o f WR-15 metal waveguide and an
assortment o f surplus components.The bolometer (made by Anritsu/W iltron) is used
because it is a true square-law detector. The two parts o f the bolometer are the
thermocouple mount (MP 716A4) and the power meter box (ML 83 A). The power
meter outputs an analog signal which is connected to a DAC input channel.
The specimens are mounted on a vertically oriented pair o f translation stages.
These big stages (RB 200 with 17 inch travel) are attached orthogonal to each other. A
Unidex 11 controller powers and commands the stage motions. This controller has
both GPIB communications and binary input and output lines.
The center o f the experiment is the computer (486DX66) which contains the
National Instruments GPIB and DAC (Lab PC+) boards. The GPIB is used to program
the stage controller. Shown in Figure D .l binary input and output lines on both the
stage controller and the DAC trigger the stage motion during an experiment. This
method o f handshaking to trigger the stages is used because o f its reliability.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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100
Mi c r o w a v e
Crystal
Detector
47k
PC +
Pi n C o n e c t i o n s
Lab
-A A /M t AAA
. Connector
pi n #
Pi ns 6 , 5
| Pi ns 8 , 7
-Pin
DAC
Channel
= ch4
= ch 6
11 = An a l o g G r ou n d
Gain = 471
Uni d e x S t a g e
Controler
□u t l - - p i n 3 I n ------1 - - p i n 5 ■
I n ------2 — pi n l 2Gr o u n d
DAC Pi n C o n n e c t i o n s
14 DIO A0" o u t p u t
15 DIO Al" o u t p u t
16 DIO A2" o u t p u t
22 DIO 'B0" i n p u t
- c 38 Ext , Tri g g e r
50 Di g. Gr ound
49 +5v
To The
Mi c r o w a v e
Source
Modul a t i on
820
1.5k-
Inverter
7404
Figure D .l
2N25
□ptoCoupl e r
In
The wiring o f analog and binary lines between the setup and the D/A board
in the computer.
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-136-
Figure D .l also shows how the DAC binary line AO turns the microwave
source on and off. In this circuit an opto-coupler is used to avoid ground loops
between the computer and the microwave apparatus.
Finally, Figure D .l shows the termination and amplification o f a microwave
crystal detector. Two crystal detectors are used in the experiment. One is used with the
aiming horn and the other is in the phase reference loop.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-1 3 7 -
D.2
Focusing the Parabolic Antenna
The parabolic antenna (f = 1 inch) used in the apparatus focuses the
microwaves to a spot on the specimen. Shown in Figure D.2 the device consists o f a
parabolic reflector supplied by a curved piece o f waveguide. The mouth o f the
waveguide facing the reflector is called the "feed". The waveguide is single mode so
diffraction at this opening serves to spread the microwave energy and "fill" the
reflector.
The curvature o f the reflector focuses the microwaves just like a lens.
1= 1+ 1
f
o
i
(D l)
K J
Equation D l is the lens equation relating the focal (f), image (i) and object(o)
distances. However, for the parabolic reflector it is more convenient to use the
dimensions a and b (Figure D.2). A new equation can be written as
!= !+ -!f b a+jb
(D2)
v ’
where
o= b,
(D3)
i= a + b
Equation D2 can be rewritten as
b = f - l a + 1 ^ 4 t f 2+ a2 .
a
u
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(D4)
—1 3 8 —
The reflector which is adjustable can be slid along the waveguide. Equation D4
facilitates the adjustment o f the reflector position when imaging the microwave feed
onto the specimen.
A second method can also be used to focus the parabolic antenna. As discussed
in Section 5.1, a laser beam can be used to illuminate the feed. The parabolic reflector
then images the light to the surface the identical way the microwaves are imaged. The
reflector position is adjusted for the sharped optical image.
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Parabol ic
R e f Ie c t o r
a
Mi c r o w a v e
Fe e d
Wa v e g u i d e
I npui;
Figure D.2
The V-band parabolic antenna.
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—1 4 0 —
D.3
Diode D etector versus Bolom eter
M icrowave diode detectors, also called crystals, ideally produce a current that
is related to the applied voltage by
i = I s ( e nVt - 1)
<D5>
where I,, n and V t are the reverse saturation current, material param eter and thermal
voltage, respectively. The voltage, v, associated with the electric field can be written
as
v = A c o s ( w t)
.
(D6)
Here w and A are the radian frequency and the field amplitude, respectively. Using the
first two terms o f a series expansion o f Equation D5 and substituting in Equation D6
we can write
r
A c o s w t+A 2 c o s 2t / t i
nVt
2 (n V t ) 2
1
}
Using a trigonometric identity on Equation D7 and keeping only the DC terms we can
write
i
T
A 2
a —- 8 —
.
dc (2jnV t ) 2
(D8)
K }
This equation shows that ideally the current is proportional to the square o f the field
amplitude and, therefore, power. Equation D8 is approximate and is more accurate at
lower energy levels. In reality, diodes must be terminated very carefully and can only
be used as square-law detectors over small ranges o f power levels.
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—1 4 1 —
A bolometer, on the other hand, senses power as the heat created when the
microwaves irradiate a blackbody. The temperature increase is measured with a
thermistor. The bolometer is limited by thermal transit speeds and heat capacity and
therefore, is slower than a diode detector. Also, bolometers need to be zeroed
periodically because their readings will drift slowly.
In the microwave speckle contrast device speed is unimportant while square
law accuracy is mandatory. The bolometer is therefore used because o f its accuracy
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APPENDIX E: LASER TRIANGULATION PROFILQMETER
E.1
Specifications
The laser triangulation profilometer (Figure 7) is made by Aromat Corporation
under the product name, laser analog sensor. In this work a model ANL2534RAC head
is used with a LM200 base unit. The laser diode source (A, = 670 nm) emits 1.9 mW.
The electronics can be switched between bandwidths o f 30, 300 and 3000 Hz. At these
bandwidths the displacement resolution are 4.5, 15 and 45 microns, respectively.
The unit produces both displacement and intensity voltage signals. In automatic
gain mode the intensity signal is used internally as feedback to boost gain on dark
surfaces. In manual gain mode the intensity signal can be use as an indicator o f
shadowing at the surface.
The device projects an oval spot which at the nominal standoff distance (50
mm) is 200 by 40 microns. When scanning roughnesses with small correlation length
the size o f the roughness may be underestimated because o f blurring.
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-143-
REFERENCES
1.
G. V. Blessing, J.A.Slotwinski, D.G. Eitzen, and H.M. Ryan, "Ultrasonic measurements
o f surface roughness," Applied Optics, v 32 n 19 July 1993. p 3433.
2.
P. J. Caber "Interferometric profiler for rough surfaces," Applied Optics, v 32 n 19 July
p 3438, 1993.
3.
L. Deck and P. de Groot, "High-speed Noncontact Profiler based on Scanning WhiteLight Interferometry," Applied Optics v 33 n 31 p 7334, 1994.
4.
J.A. Lauffenburger, C.A. Grissom, and A.E. Charola, "Changes in Gloss o f Marble
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Y.Y. Fan and V.M. Huynh, "Investigation o f light scattering from rough periodic surfaces
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E. Jakeman "The Physical Optics o f Enhanced Backscattering," in Scattering in Volumes
and Surfaces, ed. M. Nieto-Vesperinas and J.C. Dainty, Elsevier Science Publishers B.V.,
North-Holland, 1990.
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—1 4 4 —
14.
E.R. M andez and K.A. O'Donnell, "Scattering Experiments W ith Smoothly Varying
Random Rough Surfaces and Their Interpretation," in Scattering in Volumes and Surfaces.
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Holland, 1990.
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J.C. Dainty, M -J Kim and A.J. Sant, "Measurements of Angular Scattering by Randomly
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Nieto-Vesperinas and J.C. Dainty, Elsevier Science Publishers B.V., North-Holland, 1990.
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E. Bahar and M. Fitzwater, "Depolarization and backscatter enhancement in light
scattering from random rough surfaces: comparison o f full-wave theory with
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M. Saillard and D. Maystre, "Scattering from metallic and dielectric rough surfaces," J.
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-145-
VITA
Douglas Andrew Oursler was bom in Baltimore, M aryland in 1964. He
received a Bachelor o f Science in Electrical Engineering from The Johns Hopkins
University in 1987. He then received a Master o f Science in Electrical Engineering
from the University o f Virginia. His Master's thesis was entitled A M ultim ode Pressure
Sensor f o r Commercial Applications. He returned to Johns Hopkins where he earned a
M aster o f Science in Engineering from the Department o f Materials Science and
Engineering. His essay was entitled Full-Field Vibrometry using a Fabry-Perot Etalon
Interferometer. Since that time he has conducted research in the field o f
Nondestructive Evaluation. He has used optical, fiber optic, microwave, and EMAT
techniques to sonically and ultrasonically test materials.
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