NASA Contractor Report 172316

r

(NASl-CR-1723T6) NEW COHEBEHT-" OPTICAL"

TECHNIQUES FOE HftTIONfiL TEANSCNIC WIND

TOiJJIEL FACILITY Final Report, 1 May 1982, -

1 Hay 1983 (Carnegie-Mellon Univ.) 76 p

LISIT GOVT. tCONTB. ,

X84—10259

Unclas

E3/74 18954

NEW COHERENT OPTICAL TECHNIQUES FOR NATIONAL

TRANSONIC WIND TUNNEL FACILITY

David Casasent

CARNEGIE-MELLON UNIVERSITY

Pittsburgh, Pennsylvania 15213

Grant NAG1-265

March 1984

IWNSA

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23665
ABSTRACT

" The goal of this one year study was to survey the use of optical data processing techniques for distortion-parameter estimation in the National Transonic

Facility and to assess, quantify and compare various methods to determine wh'ich

are best for this specific application. The conventional nondestructive testing

techniques studied included interferrometry, moire and speckle methods. From

these, we find projection moire using fringe multiplication to provide sufficient

accuracy and to be a most attractive approach for this application. Several

advanced moire techniques for future research are also described. We also investigated several correlation techniques: space-variant processing, stereo

correlation and autocorrelation shape analysis. Stereo correlation is found to

have sufficient accuracy and new modified stereo correlation techniques for this

application which are most appropriate are described. Autocorrelation shape

analysis is a quite unique approach to distortion-parameter estimation. Finally,

several optical feature extraction techniques were considered. These included

Fourier transform coefficients, wedge ring detector-sampled Fourier transform

data and moment features. In all cases, each feature is optically-generated;and

a 'digital post-processor is used to determine the target's distortion parameters.

We find: projection moire (with fringe multiplication), wedge ring detector^

Fourier transform plane analysis and moment-based optically-generated features

to be the most attractive techniques that merit further attention for this application.
11

TABLE OF CONTENTS

PAGE

ABSTRACT i

1. INTRODUCTION . 1

1.1 PROBLEM DEFINITION : 1

1.2 WIND TUNNEL MODEL SAMPLE TESTS : 4

1.3 SCOPE OF REPORT 7

2. INTERFERROMETRIC , MOIRE AND SPECKLE TECHNIQUES •. 9

2.1 INTRODUCTION 9

2 .2 OVERVIEW :— 9

.2.3 PROJECTION MOIRE AND FRINGE MULTIPLICATION : 15

2.4 ADVANCED APPROACHES AND SUMMARY 22

3. CORRELATION AND OTHER TECHNIQUES 24

3.1 INTRODUCTION . . 24

3.2 TURBULENCE AND VIBRATIONS 24

3.3 SPACE-VARIANT IMAGE PROCESSING : 25

3.4 STEREO CORRELATION TECHNIQUES . 27

3.5 AUTOCORRELATION SHAPE ANALYSIS : 35

3.6 SUMMARY AND CONCLUSION 40

4. OPTICALLY-GENERATED PATTERN FEATURES FOR DISTORTION-PARAMETER

ESTIMATIONS 41

.'4.1 INTRODUCTION • : 41

4.2 PATTERNS USED : • 43

4.3 FOURIER COEFFICIENT FEATURE SPACE '• 45

4.4 WRD-SAMPLED FOURIER COEFFICIENT FEATURE SPACE CONCEPT 51

4.5 INITIAL ISSUES IN THE ANALYSIS OF A WRD/FOURIER-COEFFICIENT

FEATURE SPACE : 54

4.6 OPTICAL MOMENT FEATURE SPACE SYNTHESIS— '• -. 55

4.7 MOMENT PROCESSOR FOR DISTORTION-PARAMETER ESTIMATION

'(COMPONENT REQUIREMENT) : • 57

4.8 SUMMARY AND CONCLUSIONS 62

5. SUMMARY, HIGHLIGHTS AND FUTURE WORK • 64.

5.1 SUMMARY 64

5. 2 HIGHLIGHTS 66

5.3 FUTURE WORK . 68

REFERENCES • : 70

LIST OF TABLES •.— iii

LIST OF FIGURES . iii
Ill

LIST OF TABLES

t

PAGE

1.1 Initial New Coherent Optical Techniques Considered M

1.2 Additional Coherent Optical Techniques Considered '4

2.1 Interferrometric and Other Techniques Considered . ^— 10

4.1 Experimental Data Obtained Using Fourier Coefficient Measurements 48

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r

LIST OF FIGURES

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PAGE

1.1 Photographs of Sample Using White Light Source and Using Laser

Source 6

2.1 Optical Setup for Projection Moire Surface Metrology Tests 16

2.2 Image of Original Grating Pattern on Object 18

2.3 Moire Image (Object Contour More Apparent) 18

2.4 Examples of Fringe Multiplication for Improved Accuracy Projection

Moire Contouring 21

3.1 Schematic Diagram of a System that can Produce Stereo-Pairs

of Photographs 29

3.2 Schematic Diagram of an Optical Frequency Plane Correlator 32

3.3 Cross-Sectional Scans of the Autocorrelations of an Undistorted ;

and Distorted Input Pattern 37

4.1 Simplified Grating Pattern Inputs Used in Analysis 43

4.2 Simplified Schematic of the Scaling Fourier Transform Processing

System 46

4.3 Partial Fourier Transform Plane Pattern Obtained on the System of

Figure 4.2 for Two Distorted Grating Patterns 49

4.4 Selected Cross-Sectional Scans of the Fourier Transform Pattern

Obtained on the System of Figure 4.2 With and Without Scale

Distortions in the Input Object Grating Pattern 49
IV

LIST OF FIGURES (CONTINUED):

PAGE

4 .'5 Pictorial Diagram of the Wedge Ring Detector-Sampling Unit

Proposed for Dimensionality Reduction and Distortion-Parameter

Estimation • • 52

4.6 Schematic Diagram of a Parallel Coherent Optical Processor to

Compute the Moments of an Input Image 57
Final Technical Report

"New Coherent Optical Techniques for National

Transonic Wind Tunnel Facility"

David Casasent

Carnegie-Mellon University

Department of Electrical Engineering

Pittsburgh, Pennsylvania 15213

1. INTRODUCTION

1.1 PROBLEM DEFINITION

The new National Transonic Wind Tunnel Facility (NTF) at NASA Langley

produces much larger model deformations due to increased aerodynamic loading

and temperature thus requiring advanced deformation measurement techniques.

A spatially continuous real-time description of the model deformations is

desired, although deformations at about 50-100 discrete points or regions on

the model surface at discrete times are sufficient. It is preferable that no

patterns be placed on the model as this can disturb its performance under NTF

2

testing. The model (0.9x0.9m ) can exhibit deflections of 7.62cm which must

be measured to an accuracy of +_64ym.

Other features that arise in the NTF are the large dynamic density variations present in the test chamber (due to the strong turbulence involved) and

to the very smooth model surface. The density variations cause differences in

the optical path length for different parts of the medium. The smooth specular

surface of the model may allow light to be reflected only in narrow angular

directions rather than in all directions (as would occur with a diffuse surface)

Due to the physical constraints of the NTF, cameras or other viewing devices
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used in the measurement system can be mounted only in the floor or ceiling of

the wind tunnel. This excludes the possibility of using side-on viewing angles.

It is assumed that the measurement system will be subjected to signficant vibration levels and that isolation or some form of compensation will be required.

This is discussed briefly later.

The purpose of this project was to investigate new coherent optical processing techniques for this application. The ten techniques originally proposed

and considered are noted in Table 1.1.

Since the Fourier transform operation is directly realized in a coherent optical system, the presence and value of the Fourier coefficients is an obvious'

initial choice. Sampling of the Fourier transform plane with a wedge ring

 :

detector (WRD) is a potential useful technique. The wedge information should

provide .angular orientation.information and the ring data should yield scale

information on the input object. A new optical system that can compute the

moments of an input image is also considered, since such features are well- -

known to be attractive geometrical image features. Stereo correlations (used

in topographic map synthesis) also appear appropriate for this application. ;

The shape of the autocorrelation peak of the deformed object can contain sig,-

nificant information that may be of use if the effects of distortions on the

peak intensity of the correlation pattern are too severe. Image preprocessing

(edge enhancement, etc.) will be considered to help maintain correlation in s

different applications and to enhance the performance of pattern recognition

correlators. Image encoding refers to the use of specific patterns rather

than simple circular or rectangular shapes. Image segmentation refers to the

location and calculation of the deformations for several (e.g. 50) regions of

the model, rather than a continuous deformation description. This is the

approach we will use and emphasize. The estimator noted in Table 1.1 is used
-3-

to determine the deformations of the object from a given set of measured

features.

Most of our approaches will involve the measurement of the deformations

of separate regions of the object. If 100 such regions must be investigated,

then we must extract features from each of these regions or perform 100 autocorrelations. The amplitude of the vibrations in the wind tunnel will affect

the measurement accuracy and the rate at which the various measurements must

be obtained. If the vibration amplitude is small and the model deformation

is in steady state, then it may be possible to sequentially perform the 100

measurements. Otherwise (and this appears preferable), all 100 measurements

must be obtained in parallel and real-time to ensure that the relative positions of each of the separate regions of the object are measured at the same

instance of time (and hence are independent of vibrations). The high computational rates required to achieve this make the use of advanced high-speed

and parallel-processing techniques, such as optical data processing, appear

most attractive.

Following initial tests on samples of the model (Section 1.2), we determined that the model surface was sufficiently diffuse to allow patterns to be

imaged onto it. This therefore allowed the use of many more techniques. We

modified many of the techniques in Table 1.1 to include the projection of

various patterns onto the object. We also expanded our initial list of candidate techniques to include the items noted in Table 1.2. These represent

classic deformation measurement techniques, with the addition of fringe multiplication and phase conjugation. Fringe multiplication was included to improve

the sensitivity of the conventional projection moire methods. Phase conjugation
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techniques were included as one approach to overcome the turbulence and index

i

of refraction changes in the imaging medium. These topics and several initial

tests performed using these methods were included to quantify the performance

possible and to uncover unforeseen difficulties in such methods.

TABLE 1.1 Initial New Coherent Optical Techniques Considered

Fourier Transform Coefficients

WRD Fourier Transform Features

Space-Variant Transformations

Moments

Stereo-Correlations

Correlation-Shape Analysis

Preprocessing

Image Encoding

Image Segmentation

•Estimator

TABLE 1.2 Additional Coherent Optical Techniques Considered

Holographic Interferometry

Contour Holography

Shadow Moire

Projection Moire

Speckle

Phase Conjugation

1.2 WIND TUNNEL MOEiEL SAMPLE TESTS

A sample of the typical material used in tests in the wind tunnel was

obtained from NASA Lahgley. It contained three regions of material (characterized by different finishes) and hence each region of the material exhibited

different optical properties. The long (right-hand end) of this test sample
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is the most specular region (it has a very small reflection acceptance angle

•tolerance). The mid-region of this sample is the most diffuse (Lambertian)

region and the short (left) end of this sample is the least diffuse region.

The right end of this sample could not be easily photographed, since the camera

was constantly "blinded" by the strong reflectance from this material when it

was oriented near its reflectance angle. At other angles of observation and

incidence, no light was reflected. Our initial concern in testing and analyzing

(

this sample was to determine if a pattern could be projected onto the target

object and photographed. All of the photos that follow in this section were

obtained on high-contrast film (since a binary pattern was projected onto this

target sample). We considered the use of white light imaging of a grating onto

(

the object (using a 300W projector bulb, imaged through an aperture onto the

grating and then with an imaging lens onto the sample, with the optical axis

normal to the surface of the material) and with the use of a 633nm laser (collimated, illuminating a pinhole, and through it the grating pattern imaged

normally onto the sample). ,

>

Figure 1.1 shows the results obtained. The left column shows the images

obtained with white light illumination, and the right-hand column shows the

i

images obtained with coherent laser light. The bottom figure shows the entire

sample. As seen, good quality images were obtained for the left (short) end

of the sample at most angles of illumination. This is a good diffuse Lambertian

surface. The long end of the sample was found to be too specular and gave poor

images in all cases. The photographs shown are insensitive to exposure because

of the high-contrast film used to obtain these images. From these initial

sample tests, we conclude that a non-contact optical approach in which a pattern
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OF

is imaged onto the surface is applicable (thus, associated holographic interferrometry and Moire techniques are also suddenly appropriate) since a model

surface such as the middle or left end can be expected.

WHITE LIGHT . ' IASBR, ', ' ' = > .>

SHORT

END

MIDDLE

LONG

END'

FIGURE 1.1

Photographs of Sample Using White Light Source and

Using Laser Source
-7-

1.3 SCOPE OF REPORT

The major emphasis of this one year research study was to provide an initial

survey of the ten techniques noted in Table 1.1 (and six other techniques, such

as those noted in Table 1.2, which arose in the course of this research) with

primary attention to their application to the NTF problem. Applications to other

distortion measurement problems at NASA was a secondary goal. The objective of

this study was to determine if conventional Fourier transform, correlation and other

similar coherent optical data processing techniques and systems were appropriate

i ;

for the NTF (or other) NASA data processing applications. In all cases, attention was first given to the accuracy obtainable with the different methods and

to the system components required to achieve the needed accuracy.•: Pursuing sixteen different approaches in one year with two people obviously means that only

preliminary results can be expected and that emphasis should be given to determining which techniques (if any) are appropriate and merit detailed further

study.

Our general remarks and conclusions on several of the items noted in Table

1.1 are now addressed, since they affect the decisions we made in the course of

our studies of the other techniques. We determined that image preprocessing was

not a vital operation. Thus, it was not pursued in detail. Image segementation

was felt to be vital and necessary (i.e. recording deformation data on 50-100

separate target regions). It was thus used throughout, except for our new modir ' ; 3

fied moire technique we discuss in Chapter 2. it appears to be possible to exr

tract the necessary target deformation information on the full object by extrapolation and interpolation from the deformations in 50 specific regions of the

target. We assume that the target deformations are uniform within -each of these
-8-

50-100 local target regions. Image encoding was likewise felt to be essential

to allow the necessary accuracy to be obtained. Our results in Section 1.2

t

showed that images projected onto the model could be subsequently reimaged. 1 -i

Thus, in all cases, we will consider projection (or only where necessary, printing) of a pattern (such as a grating, PPN code, etc.) onto 50-100 separate regions of the target model. This is preferable to the use of simpler circular

or square objects, because the higher space bandwidth product of the pattern

provides much more change with deformation and much more processing gain in

the system.

In Chapter 2, we discuss the holographic technique (Table 1.2), the methods

we selected to pursue (particular emphasis was given to projection moire and

fringe multiplication techniques), our laboratory experiments performed on these

approaches, our new results and our conclusions and recommendations, in Chapter

3, we briefly note the results of our space-variant transformation, stereo correlation, phase conjugation, and correlation' shape studies. Major attention in

our research was given to feature extraction techniques, especially the Fourier

transforms and moments. Our work in this area is summarized in Chapter 4. Our

summary and conclusions then follow in Chapter 5.
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1 2. INTERFERROMETRIC, MOIRE AND SPECKLE TECHNIQUES

2.1 INTRODUCTION

Following our tests on the wind tunnel model (Section 1.2) , we included the

techniques noted in Table 1.2 and other variations of them in our research. Much

of our work on-these approaches concerned the study of the many possible techniques of this type and assessing their applicability to the NTF problem. [1] is

quite useful in this regard. We thus do not include reference to other individual

papers that describe each technique. Our initial assessment and a brief discussion of the various methods we considered is included in Section 2.2. Our primary

concern was to isolate the major problems and issues to be addressed for each

approach and by brief initial laboratory tests, determine and verify the most

promising techniques and uncover any unforeseen problems. Our initial experimental data and results are presented in Section 2.3. They include the use of projection moire, our demonstration of the increased accuracy possible with fringe

multiplication, and other new methods to use such techniques for the NTF wind

tunnel measurement problem. In Section 2.4, we summarize our results and suggest

several new techniques to employ this method and to enhance its use even further.

2.2 OVERVIEW

In Table 2.1, we summarize the techniques we considered and our<>remarks Ion

each. Holographic interferometry is sufficiently accurate. However, it is too

precise. Specifically, too many fringes are produced and the analysis of the

output fringe pattern (as well as its detection and .the sampling of it) is very complicated. Hence, this approach is rejected. Contour holography involves making

two exposures of the object pattern with two wavelengths of light, superimposing
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TABLE 2.1 Interferometric and Other Techniques Considered

TECHNIQUES REMARKS

Holographic Interferometry:

Contour Holography (2 Wavelengths) :

Scanning Heterodyne Interferometry:

Speckle:

Shadow Moire:

Reflection Moire:

Contact Moire:

Differential Moire:

Holographic Moire:

Projection Moire:

Too many fringes. Hard to analyze

output results.

Appears attractive. Requires pulsed

laser with 2 wavelengths.

Scan. 2 beams at 2 wavelengths and

interfere. Maintaining superposition

of beams is a problem.

Ensuring overlap of speckles limits

measureable deformation displacement.

Requires grating close to the object,

poor sensitivity, insufficient accuracy.

Not practical for vibrating deformed

objects.

Requires pattern on target.

Superposition of deformed and undeformed

patterns.

Requires 2 exposure hologram and high

stability requirement.

Preferred technique, needs increased

accuracy by fringe multiplication.
-lithe patterns and analyzing the results. This is a good, sound and appropriate

approach. It is useful of course only for calculations of out-of-plane- displacements. It provides better sensitivity for a given pattern than does conventional moire. However, since we do not have the required multiple wavelength

lasers nor pulsed lasers, we did not pursue it further with laboratory tests.

Scanning heterodyne interferrometry employs the scanning of two beams at .two

different wavelengths across a pattern, interfering both and detecting the

phase of the beat frequency provides the resultant information. The major

problem with this technique is the requirement to keep the two beams superimposed during scanning. Fabrication of the necessary system to achieve this

is a quite extensive effort and it cannot be done casually or the performance

obtained will suffer. A new idea and technique that one could pursue is to

use two coded signals, correlate them and obtain the phase and hence the range

shifts from the phase of the correlation output. Speckle techniques were also

considered. Initially, they appeared to be quite attractive. However, when

quantified, we found that the maximum target displacement possible for which

overlap of the speckles could be insured was only 1.5mm. This is significantly

worse than the displacements required in the NTF problem and application. Thus,

we did not consider this technique further.

Various other techniques [2-4] werealso considered that appear more promising for the specific wind tunnel testing program. These included shadow

moire methods [4]. In these techniques, a grating is placed close to the test

surface and illuminated with a point source. The shadow of the grating is

then placed onto the object. When an image of the shadow is viewed through the

grating, a moire contour results. The grating must be placed close to the object

to keep the shadow in focus over the depth of field. As a result, the sensitivity
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achievable with this technique is quite poor. Only Irtun deformation resolution

is possible. Thus, for this specific NASA application, this technique is not

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viewed as practical since its accuracy is insufficient.

Reflection moire was also considered. It is similar to the shadow moire technique,

except it is appropriate for specular rather than diffuse surfaces. In this '

scheme, a reflection grating is imaged off from the object and passed through

a "reference grating. In this system, it is necessary to view the object at the

specular angle. This is not practical for NTF objects with the deformations and vibrations expected. Deformations and vibrations will determine where the image projects to. For these reasons we do not consider this technique further.

'' Contact moire techniques were also considered. In this scheme, a grating is

placed on the object and an image of it, after deformation, is compared to a

reference grating. This technique is easier than the previous one since one

only needs one access angle to implement it. fhe major objection to this technique

is. that again one must contact the grating to the model and this may disturb

the model. In contact moire, the fringes depend upon the displacement between

the input plane and the output plane. Thus, such methods can provide strain

measurements; this is not always desireable and the analysis of the resultant pattern

that is produced with such techniques is more complex than with other moire methods.

•. Differential moire is yet another concept we considered. In

this technique, a photograph of the grating on the undeformed object itself is

used as the reference. In this case, the object's topography is not present

in the resultant moire pattern, rather only its distortion are, hence the name

differential moire. It is also possible to project a second grating onto the

object and to produce the moire on the object itself. If the projected grating

is a photograph of the grating on the deformed object, then the topography of
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the object can again be removed. In the indicated NASA application, the topography of the object is probably desireable, thus this technique does not appear

to merit further attention.

In the holographic moire technique that we considered, one makes a realtime double

exposure hologram of the test object and the reference object and one compares

the holographic fringes between the two. This technique is very sensitive,

however vibration problems and high stability are required in the processor and

the fringe pattern that is produced is quite difficult to easily interpret. For

these reasons, it does not appear to be attractive and practical. The final

The final technique considered is referred to as project ion moire [3]. This is a

superior technique to the aforementioned ones. In this method, a grating is projected

onto the test object. It is then photographed at an angle not equal to the

projection angle and the image that results is compared to the image of the

reference grating to produce the desired moire. If the reference grating is an

image of the grating on the object and if this is projected through an image

of the distorted object, then the contour of the object can again be removed

and the moire fringes will show only displacements of the object from the

reference positions. This will occur for all object regions. This appears

very appropriate for the wind tunnel application.

The sensitivity of moire techniques is

Az =

tana + tan3 '

where p is the period of the grating, and a and g are the angles of projection

and viewing with respect to the normal to the object. As the surface shape

changes, so do the angles and hence so does the fringe pattern. From an analysis

of the fringe pattern, the shape (i.e. the deformation) of the object can be

obtained.
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As the technique we decided to experimentally test and evaluate, we chose

j

projection moire for the reasons noted above. It is the most attractive and

appropriate one. It can potentially provide1analysis of deformations for the

entire object using only one image and without the need to print a pattern onto

the model. This technique provides only out-of-plane deformation information,

of course. To increase the deformation measurement accuracy obtainable from

this technique, we suggest the use of fringe multiplication by optical processing.

The idea in this technique is to increase the frequency of the reference and

deformed gratings, then to superimpose the two. This increases the number of

fringes and hence the deformation measurement accuracy possible. This technique

is very attractive since it allows us to use a lower frequency grating and thus

more moderate quality optics. With fringe multiplication, we can then achieve

the same accuracy as one could obtain using a higher frequency grating and more

expensive optics.

A second new approach that we suggest is the formation of a projection moire

pattern of the entire object (at low resolution) and then to form an analysis

(by fringe multiplication using optical processing techniques) of different portions of it. This will allow us to measure displacements in certain areas to

high accuracy and yet obtain the full-field image with less accuracy and with

less complex fringe pattern required. This can easily be achieved by aperturing

off regions of the moire pattern of the entire object and applying fringe multiplication only to these regions. We can also use optical data processing to

enhance low-fringe contrast (due to blur, lens aberrations, etc.). This can be

achieved by spatial filtering the output dc order in the Fourier transform plane

and thus removing the background. We can also remove high frequency noise (dust
-15-

etc.) by use of a donut-shaped spatial filter in the Fourier transform plane.

This will greatly enhance the contrast and quality of the moire image produced.

2.3 PROJECTION MOIRE AND FRINGE MULTIPLICATION

To become acquainted with the various techniques for surface measurements

and to uncover unforeseen problems, various projection moire patterns were obtained. Several examples of these data follow. The object chosen was a gas

canister cylinder with an indentation on one side. Data was obtained with-both

white light and coherent laser illumination. The white light source data was

the easiest to observe and thus data obtained with this system is included.

The optical system used is shown in Figure 2.1. The projection arm of the system

consists of imaging optics that project an image of a grating pattern (grating 1 =

G ) onto the object. The observation arm of the system consists of imaging

optics that project the image of the grating pattern as it appears on the object

onto a camera through a second grating pattern (grating 2 = G_). The superposition of the G pattern and the image of G on the target is then observed by eye

or through a camera and monitor. For our experiments, identical optics were

used in both arms of the system. Thus, the optical axes in both arms are equivalently in the same plane and the lines in both gratings are perpendicular3to

the above plane. We chose to use d = d ' = 251mm, d = d ' = 1255mm and imaging

lenses with f = 209mm. This yielded a magnification M = 5 for the projection

L

arm. The gratings G- and G~ were identical with a spatial frequency u = 100

lines/inch = 4 lines/mm. . ,

We could visually observe the grating output on the object with our eyes

d mm behind G„. However, due to our light budget, photographs of the contour
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fringes produced were not of good quality. Thus, we chose to simply focus the

camera in the observation arm of the system directly onto the object and to photo-

•:

graph the projection grating pattern obtained (this is the image of the grating

as projected onto the object). We then place this photograph in contact with G

in plane P of the projection system, we remove the object, place an observation

screen in place of the object, and photographed the resultant moire contour

pattern obtained on this screen at plane P_ of Figure 2.1. In Figure 2.2, we

show an image of G projected onto the object. In Figure 2.3, we show the projected moire contour fringe pattern observed. The contour lines or the equalorder surfaces in the moire pattern are perpendicular to the bisector of the

angle a = 29 between the projection and observation arms in Figure 2.1. Thus,

the distance between the two equal-order surfaces (i.e., adjacent contour lines

in Figure 2.3) is

do =

where p1 is the pitch of the projected grating and 29 = a is the angle between

the projection and observation arms.

For our experiments, the pitch of the original grating G, is p = 1/u =

1 G

0.25mm, the magnification M = 5 and thus

p' = pM - M/u = 5/4 = 1.25mm. (2.2)

t

For our system, Sin9 = 0.125 and thus

dQ = p'/2Sin9 = 1.25/2(0.125) = 6mm. (2.3)

Thus, in our laboratory system, the spacing between the contour fringe lines.
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FIGURE 2.2

Image of Original Grating Pattern on Object

FIGURE 2.3

Moire Image (Object Contour More Apparent)
-19-

in the moire pattern in Figure 2.3 corresponds to displacements of the object's

surface of d = 6mm. If a grating with u = 20 lines/nun were used, the distor0 G •

tion between consecutive equal-order surfaces would correspond to 1.25mm depth

differences in the object. Thus, from our experiments, we found that moire

contour patterns are easily produced and obtained with white light illumination.

It should be noted that telecentric or collimated imaging light is very

helpful in moire pattern analysis, since it greatly simplifies the mathematical

description of the results obtained and the associated analysis of the resultant

fringe pattern obtained. Specifically, the corresponding object displacements

associated with different contour fringes will be a constant in this case. We

also note that projection moire allows out-of-plane deformation measurements to

be obtained. In projection moire, obtaining an adequate depth of field is an

issue of concern. Thus, large pitch gratings are attractive for use, since less

depth of field problems then result. When the grating pattern is imaged onto

the full object, the depth of field requirements become even more demanding.

Thus, an accuracy of 1mm in the displacements of points on the object is realistically possible with projection moire techniques. This will prove to be adequate for our NTF application as we will see below.

To improve the object measurement accuracy beyond 1mm to the 64ym resolution

required in the NTF problem, we suggest the use of fringe multiplication [10].

In this technique, the deformed grating pattern observed on the object (or the

associated contour fringe pattern) is multiplied by a different grating (G_) with

a different pitch from that of the original grating (G.. = G ) . The Fourier

>

transform of this product of two grating patterns is formed. The N-th order in

I

the Fourier transform; of this composite multiplicative grating pattern will
-20-

have N fringes for each original image fringe. Thus, this technique allows

the fringe accuracy, and hence the accuracy associated with adjacent contour

fringes, to be increased by a factor of N.

If we assume that we have an original fringe accuracy of F = 1mm and that

we can read fringe patterns to an accuracy of A = 0.25 of a fringe, then fringe

multiplication by a factor M = 10 provides an accuracy in the target deformations of

F

1 = F*A/MF = 1(0.25)/10 = 25um, (2.4)

which is better than the accuracy required in the NTF problem. Thus, this technique of projection moire, augmented with fringe multiplication, appears most

promising and attractive and capable of providing sufficient accuracy needed in

the NTF application.

To verify the accuracy improvement possible in projection moire using

fringe multiplication, a simple experiment was conducted. The original moire

contour pattern was placed in contact with a grating of slightly different

frequency and the Fourier transform of the product inputs f,f9 was formed. This

t

yielded the output pattern

^

[flf

2

] = Fl * F

2' ' (2'

5)

where F and F denote the Fourier transforms of F. and F . It is possible to

obtain moire fringe multiplication by using two gratings of different pitches)

or with two gratings of the same pitch (if one grating is rotated with respect

to the other). In Figure 2.4, we show two of the fringes in the original moire

pattern and their multiplication by factors of 2 and 4 using the aforementioned

i

fringe multiplication technique.
-21- ORIGINAL PAGE ES

OF POOR QUALITY

, Original .Pattern

Multiplication by 2

Multiplication by 4

FIGURE 2.4

Examples of Fringe Multiplication for

improved Accuracy Projection Moire Contouring.
-22-

2.4 ADVANCED APPROACHES AND SUMMARY

As described in Section 2.2 and as quantified by our initial experiments

in Section 2.3, projection moire (when augmented with fringe multiplication)

can provide the necessary accuracy and performance for the NTF problem. The

depth of field requirements for the projection of the original grating pattern

were noted. Application of projection moire requires that different points

on the object be treated separately (as we have done), since this significantly

reduces the depth of field requirements for the projection optics.

We now note several advanced techniques to further enhance the performance

and implementation of such an NTF processor.

(1) We note that the resultant moire pattern is a combination of

image shape and image deformation information. We suggest (for

future work) that one can separate these two effects by use of

differential moire techniques (i.e. by forming two moire patterns,

one with distortions present and one' without distortions present).

This would provide an output display with only the required and

desired target deformation information present on it, rather than

the shape of the object also included.

(2) We note that it is also possible to contact-print the grating

pattern directly onto the object. If this is done, then in-plane

target deformations can also be obtained by this technique (in

addition to out-of-plane distortion information).

(3) The evaluation of the optically-generated moire contour patterns

can still require extensive post-processing. The use of optical

Fourier transform and convolution techniques that can aid in
-23-

such an analysis of the fringe pattern contour and deformation

information present.

! (4) Optical matrix-vector techniques [11] appear most appropriate to

relate deformations at different spatial locations to global

deformations (in-plane and out-of-plane distortions) appear

i

, . . -possible. -'""

As noted earlier, all of these moire techniques require a non-specular surface.

The actual model surface is between the extremes of specular and diffuse. Thus,

a range of angles exist over which images with high contrast can be obtained

from images projected onto the model. Vibrations are of concern in all systems.

The moire technique in which the entire model is imaged at once is thus most

attractive, since any sequential analysis technique will be plagued with practical problems associated with having deformations of different points of the

object at different points in time (i.e. at different points in a vibration

cycle). If the vibrations of the target are periodic, we can probably sequentially image and avoid such difficulties.

Our proposed techniques are new, in the sense that they have seen only

limited application and in no instance has the accuracy required in the NTF

problem been considered using this method. Hence, fringe multiplication

appears most attractive for the NTF applications. The output detector system

to analyze the moire pattern produced still remains to be addressed.
-24-

3. .CORRELATION AND OTHER TECHNIQUES

3 .

:1 INTRODUCTION

In this chapter, we consider various alternate approaches to the wind tunnel

test and measurement problem that received only initial consideration and ,

analysis during our study. These include the effects of turbulence and vibra^-

tiqns, the use of phase conjugate optics to remove these effects, the use of

time-average moire and real-time moire and how they affect this problem, plus-,

the use of pulsed and video moire. Finally, we consider stereo-correlation

methods to some extent and finally a novel autocorrelation shape analysis concept.

We then briefly address space-variant transform methods and techniques for deformation analysis. Our summary and conclusions are then advanced.

3.2 TURBULENCE AND VIBRATIONS

Initial studies indicate that various turbulence, shock waves, and other

such effects which result in changes in the index of refraction of the imaging

i

medium will be present in the wind tunnel data. We have considered several

approaches to overcome this problem. Only brief remarks are advanced on each.

The use of phase conjugate optics was considered. This technique is useful in

imaging through a turbulent media. However, we have been unable to devise a way

to apply it to the NTF problem, since the turbulent medium lies between us and

the object. Any architectures we devised and studied removed the effects of

the turbulence as well as any deformation effects on the model itself.

The use of time-average moire [5] was also considered. In this approach,we simply

time-averaged the moire for a vibrating object over a time long with respect to the frequency

of the vibration. The vibration frequencies in the NTF system are noted to be
-25-

up to 200Hz. The result of such a time-average is that the only points in, the

grating image that will be seen are those at the two extremes of the vibration

cycle. All intermediate ones average out, since they are random. In this, manner, the moire that results is due to grating images at the two extremes of the

deflection and thus maximum object deflection is measured. The use of different

integration times can allow different vibrations to be addressed. However, the

vibrations must be well-behaved. Further analysis is necessary and details are

3

necessary to determine if this is the case in the NTP system.

Real-time moire is another possible candidate approach we considered. This

technique can provide the time-history of the dynamic vibrations for the entire object.

However, vibrations can also occur due to the tunnel, air turbulence, acoustic

noise and even the mechanical support for the processor. In real-time moire,

considerable vibration isolation is necessary and multiple vibration effects

will be present in the data. Thus, any such approach is expected to require

quite significant analysis to extract out the separate vibration effects inj

eluded. Other techniques considered include pulsed moire. In this concept, two

short pulsed images of gratings at two different times are produced.- The moire

from the overlap of these patterns then maps changes in the topography of the

model, rather than displacements between two time pulses. Thus, this technique

does not appear appropriate.

Video moire [6] is another technique that may be worth pursuing. We did

not evaluate its possible potential

3.3 SPACE-VARIANT IMAGE PROCESSING , %

An alternate technique that we briefly considered was the use of various

space-variant optical processing concepts. This class of processor is much more

flexible and powerful than the conventional shift-invariant systems. These sysA&

.•ft'*-*"' y-tems comprise a coordinate transformation preprocessing step followed by a;
-26-

Fourier transform, correlation or similar shift-invariant operation. The resultant system architecture (and its impulse response) 'are space-invariant.

The attractiveness of such techniques to the present wind tunnel deformation

measurement problem are that by proper choice of the coordinate transformation,

one can obtain an output correlation peak (whose intensity is invariant to.

various geometrical distortions in the input pattern) whose location is" proportional to specific deformation parameters in the input pattern. From the correlation peak location, object deformations can be extracted and thus data obtained on the distortion parameters of the object pattern.

One specific example of this concept is the optical Mellin transform [7]. In this

solution, a logarithmic transformation is applied to the input data and this is

<

followed by a Fourier transform. The result is a Mellin transform of the input

image. Mellin transforms are most attractive for scale-invariant processing,

since the amplitude of the Mellin transform coefficients are invariant to scale

changes in the input object. Scale changes in the object appear as phase terms

in the Mellin transform pattern. Thus, to extract scale (or associated out-ofplane rotations which can be modeled as different 1-D scale changes), we must

extract the phase of the Mellin transform coefficients. One can extract such information

by heterodyne detection, however the resultant system will become quite complex.

A simpler, and often times preferable, solution is to perform a

correlation using Mellin transforms rather than Fourier transforms, in this

instance, the classic frequency-plane optical correlator [8] can be used. The

correlation is simply performed between coordinate-transformed patterns rather

than the conventional Euclidean space versions of these patterns. In this case,

the amplitude of the output correlation peak will be invariant to scale changes

in the input object and the position of the correlation peak will now be
-27-

proportional to the scale changes between the reference and input object. Such

methods of extracting phase information are preferable.

If we can insure that each object pattern is positioned approximately; in

the center of the input plane, then such techniques are appropriate (they are

space-variant, thus they are not shift-invariant, and hence we require the:

input object to be centered in the input plane). By performing a gross correlation of the entire object, it appears that such centering can be achieved.

The accuracy associated with this technique should be quite high, since now

we position-encode the associated scale change data. The shortcomings of this

system are the requirement to perform many correlations, with the additional

requirement of a coordinate-transformation preprocessing step. Such systems

and architectures are of course possible, however we again choose not to consider them for future detailed study at this time. Instead, we defer to simpler

systems (see Chapter 4).

3.4 STEREO CORRELATION TECHNIQUES

Stereo correlation [9] involves comparing the correlation pattern obtained

from a stereo pair of photographs of an object taken prior to deformation with

the correlation pattern obtained from a stereo pair of photographs taken after

deformation (only out-of-plane deformations are appropriate). The relative

locations of the correlation peaks in one correlation pattern, with respect to

the locations of the same peaks in the other pattern provide information about

the out-of-plane deformation of the object. By comparing N points in the undistorted object to the corresponding N points in the distorted object image,

we can produce an n-th order polynomial approximation for the object's distortion . i
-28-

From photographs of an object obtained from two different viewpoints (this

ris easily possible with the viewing port arrangement present in the wind tunnel),

it is possible to obtain a full description of the object in terms of contours

and profiles by using this stereo correlation technique. This procedure is used

extensively in topographic map plotting, in the course of our work, we have

expanded this technique and applied it to the measurement of out-of-plane deformations in wind tunnel imagery. Since in-plane translational deformations can

be accommodated without the need for stereo photographs (by using only one .pair

of photographs), in-plane deformations will be discussed only briefly. In

Figure 3.1, we show a simple system for forming a stereo pair of photographs.

In the ideal case of vertical photographs, the camera axes are parallel to each

other and normal to the reference plane and both image planes are perpendicularly

centered on the plane y = y .

In Figure 3.1, f is the distance between the camera lens and the image plane.

The height of the object is h. It is defined with respect to the reference plane.

The separation between the camera axes is defined as the stereo base B. The differential x-parallax is

P = x -x = fB/(H-h). (3.1)

X J. ^

t

By simple geometry, one can derive (3.1). From (3.1), we see that as the height

Ojf the object h varies from point-to-point in the image, the distance x -x_ between the image of the point in the two image planes also changes. For the case

in which the image planes are centered at y=yQf the differential y^parallax will

be zero.
-29-

Image Plane

One

ORIGINAL PAGE IS

OF POOR QUALITY

Image Plane

Two

Reference Plane

FIGURE 3.1 Schematic diagram of a system that can produce

stereo-pairs of photographs.

We now discuss how to relate object deformations to the locations of points

in the two image planes. We consider a pattern to be placed at coordinates (x,y)

on the object. The image of this pattern will then be located at some coordinates (x ,y') in image plane 1 and at coordinates (x ,y') on image plane 2. If

the difference x -x is determined, then the height of the object at the point

(x,y) can also be determined from (3.1). For the wind tunnel problem, this would

be done for selected points on the model. These data can then be used to provide a contour map of the height or deformations of the target. This is not the
-30-

goal in the wind tunnel problem however. In our case, we desire the object's

2

deformation. A suggested procedure to achieve this is discussed in the next

paragraph. The cross-correlation operations required in this processing lend

T

themselves quite nicely to optical processors which can thus determine the

relative position of each pattern in the two image planes. If different patj

terns with minimum cross-correlations (e.g., Walsh-Hadamard matrices) are used,

)

cross^correlations between separate patterns will be minimized and thus the required correlations can be performed from one view of the target (if sufficient

resolution is possible for each object pattern).

5

We now advance a new method to extend these concepts to measuring out-6fplane deformations of an object. The object is assumed to have N patterns on it

at N different locations. The number of patterns used, the type of pattern,

and their relative positions will determine the accuracy with which the object

deformations can be measured. To obtain more detailed and accurate deformation

estimations, we can divide the object into more patterns within each segment.

Once the object's surface has been prepared as described above, a stereo photor ?

graph pair is taken of the N patterns on the object segment. This is done for

1

the undistorted object (before wind tunnel testing). This stereo pair is then

used in a correlator to calculate the x-parallax difference for each of the N

patterns. This provides us with information on the height of each pattern (in

the undeformed object). Next, the object is deformed (i.e., it is placed under

wind tunnel testing). A new stereo pair of photographs is then taken of the

s

Jame N points. This new stereo pair is then used to determine the height of

each pattern in the deformed object. The amount of out-of-plane deformation

for each point can then be computed by subtracting the height of each pattern

object before deformation from the height after deformation.
-31-

We note that this technique is useful only for measurement of out-of-plane

deformations. If in-plane deformations occur (such as translations), these

distortions will not be detectable using the above technique. This can be seen

by assuming that the pattern on the object is translated in the object plane

by an amount (Ax,Ay). A corresponding change (Ax.,Ay.) will then result in

both image planes. In this case, the parallax difference between the locations

in the two image planes

(x^Ax^ - (x2+Axi> = x1 -x2- (3.2)

will be unchanged. We can extend this method to provide in-plane translational

measurements by correlating one of the stereo pair photographs taken prior'to

the deformation with the corresponding photograph taken after the deformation.

Thus, with these modifications, both in-plane and out-of-plane distortions can

be measured with this technique.

This stereo photometric approach requires the measurement of the difference

x -x of the locations of a given image point (or object.pattern) in the two

different stereo views. This can easily be achieved by correlation techniques

[especially when the points are actually patterns (which is the case in our wind

tunnel application)]. An optical frequency plane correlator (such as the one in

Figure 3.2) is thus very attractive for providing such data. We first briefly

review the operation of this well-known system [8]. We then detail how this

system would be used for our specific cross-correlation stereo-photometric .technique for object distortion analysis.

Refer to Figure 3.2. Two images (transparencies 1 and 2), which we wish to

correlate are used. To achieve correlation, we will place transparency 2 in the input plane
-32-

and a matched spatial filter of transparency 1 in the second plane. The correlation pattern of the two transparencies will then appear in the output plane.

The matched spatial filter is formed by placing the pattern in the input plane

and interfering its transform and a planewave reference beam. For 'the case when

transparency '1 contains a particular pattern and transparency 2 contains several

occurrences of the reference pattern, 'then the output correlation plane will

consist of several peaks of light, with the location of the different pe'aks of

light corresponding to the locations of the reference pattern within input transparency 2.

TRANSPARENCY 2

'MATCHED 'FILTER OF

TRANSPARENCY 1

SAMPLING

APERTURE

(xo'V

FIGURE 3.2 Schematic diagram oif an 'optical frequency

plane correlator.

We now consider the application of this technique to the specific wind

tunnel problem. We form two stereo images of the entire target', containing

many object patterns. A matched spatial filter of orte of these stereo images

is placed at the second plahfe of the system of Figure 3.2. The other stereb

image is placed in the input plane of the system; An aperture is moved
-33-

Sequentially about the input transparency 1. As it moves, separate regions,

and hence separate ones of the pattern recorded on the target are illuminated.

(Thus, in sequence, the output correlation plane pattern will contain peaks of

light at locations which indicated the difference x -x in the locations of

each of the patterns recorded on the target. From these different values,, the

height of each pattern on the target (undeformed target) can be determined.

This procedure is then repeated for the second stereo pair of images (with the

- t

target now deformed). By properly combining the outputs from both correlation

plane analyses, the deformations of each individual pattern region on the target

c •

can be obtained. The moving input plane aperture required can easily be realized

with various binary spatial light modulators (without the need for any moving

parts) or with available telecentric scanning systems.

r The accuracy of our deformation estimations will depend upon the accuracy

with which the difference x -x (i.e. in our case, the location-of the correlation peak) can be determined. Thus, it is quite important to utilizeeobject patterns,

rather than points, since the increased space bandwidth product of such patterns

will provide much higher correlation peak values and .much narrower correlation

peaks (thus providing us with a better measure of the desired x -x value ):.

We now consider a specific case and detail the performance of this system.

We consider a pattern to be located in the reference plane at coordinates (x,y,z ).

From the correlation of a stereo pair of photographs of this pattern, the location x1 -x of the correlation peak can be obtained and from it the x-parallax

1

difference. We consider the case when the focal lengths of the two Fourier transi .-.•.-. • ' -

form lenses in Figure 3.2 are equal. For this case, the height of the pattern

on the undistorted object is given by

Zf — , — n H _ — L\iD^/vx_—x_/j r t fv*\ / f v — v ^ i / . \3m-j *> *}f ^
-34-

Next, the object is deformed. A ,new stereo pair of images/of it is produced

and these are also correlated. For this case, we assume that the deformed 1 t

object is how located at coordinates (x,y,z ). From the correlation .output of

this second (deformed) stereo pair we obtain a correlation peak at x,1 -x'.

The height of the pattern on this deformed object is -then :found :td be

z2 = H- [(FB)/(x| -x2)] . . (3.<4)

The out-of -plane deformation of the particular object is then found i>y .combining (3.3) and (3.4) to be

si

z 2-Z l = fB{[l/(xj-x2 )] - [l/(x1-x2;)]} = Az: r(3v5)

If this procedure is repeated for N patterns (located at different jpbsitions x , x (or in 2-D at y , y , etc.) , then an N-th order polynomial can

be produced (using the method of least squares, for example) and froi this

« the distortions of the object over its entire viewed area can b'e

obtained to N-th order. The results obtained for smaller regions pf each ob^

ject pattern can also be used and combined to provide information about the

deformations across a given object region. In practice, the original set of

correlation peak coordinates need only be calculated and stored once. Thereafter, as the input aperture is moved about transparency 2, we obtain on-line

r .

the point-by-point height of all patterns recorded on the target:

This technique appears to be quite attractive and apprdpriatte for the

wind-tunnel application. The various modifications that we noted in it should

be incorporated to provide the best results . In other analyses , we quantified

the accuracy obtainable from such a system and found that it appears to bis
-35-

csuitable for the wind tunnel application. Our only motivation for not pursuing

ithis architecture further is its comparative complexity (multiple correlations

tare required, and a real-time holographic matched spatial filter is needed,, to-

.gether with a real-time input transparency device). Several versions of this

n

isystem (using photographic film) exist and have been used by Harris Corporation

and the Engineering Topographic Laboratory. Thus, although this technique

appears to be attractive and useful, we do not consider it further and defer more

(detailed studies to the simpler architectures and processing systems in Chapter 4.

c -.

3.5 AUTOCORRELATION SHAPE ANALYSIS

Another most novel technique which we have suggested, and for which we

performed initial experimental tests, is the analysis of the shape of the

i

autocorrelation function for the different object patterns recorded on the ,

target. From this shape analysis, we propose to extract various parameter;,

deformations of the target in each object pattern region. This technique again

requires the use of patterns rather than points at various locations on the.

target. The main motivation for this concept is the fact that the peak value

of the correlation will change rather significantly and in addition different

distorted patterns can provide the same peak intensity value for the correlation. Thus, separate distortions can give rise to the same peak correlation

value I . However, the shape of the correlation function has significant P

P . j

information contained in it, besides just its peak value. Specifically, as:

the pattern becomes distorted, the shape of the correlation function also changes.

We thus suggest that such an analysis of a correlation output pattern

can provide the required information on the distortion parameters present in

the particular object pattern (or target region) under investigation. Initially,
-36-

we considered using cross-correlations between the undistorted object pattern

i • ;

and the distorted patterns present on the target. We found very .severe degradations

in the peak correlation intensity to occur and feel that these will result in

seyere detection problems in a practical system. Thus, we then modified our

. • c

technique to include and require only the computation of the autocorrelation of

i '.'•"« "

the distorted'object pattern. This is most attractive for many reasons. First,

- ^ "

the location of the autocorrelation function in the output plane is known

and is fixed (it always occurs in the center of the output plane). Second, the

intensity present in this output pattern will remain approximately constant with

C ' ' ' i ~

deformations. This will greatly simplify and enhance detection of this output

plane data.

An initial experiment was performed to verify the dependence of the shape

of the autocorrelation output on distortions in the input pattern. This was;

achieved using a scaling optical correlator. An optical matched spatial filter

of the original undistorted object was formed and correlated with the original

i

object. A cross-section scan of the output correlation function obtained is

>

shown in Figure 3.3a. text, the input was subjected to various distortions, (i.e.

<

input plane rotations were introduced by simply rotating the input object; scale

*

changes were produced by translating the object along the optical axis. In the

i ' j ••

scaling correlator used, this introduces scale changes). A new matched spatial

i

filter for the distorted input pattern was obtained, its autocorrelation was

1

formed and cross-.sectional scans of it were produced. A cross-sectional scan

of a typical autocorrelation for the same object in Figure 3.3a (for a distorted

?

input image) is shown in Figure 3.3b. Comparison of Figures 3.3a and 3.3b shows

j '

differences.in the widths and distribution of the two autocorrelation functions.
-37-

ORIGISMAL PAQE §S

OF POOR QUALITY

FIGURE 3.3

Cross-Sectional Scans of the Auto-Correlations of an Undistorted

(a) and a Distorted (b) Input Pattern.

Attempts to relate the correlation shape to the input distortions became

much more complex than we originally anticipated. Thus, quantitative data was

not possible on the accuracy with which input distortion parameters can be

measured by this technique. Rather, we elaborate on the various issues involved

in such an analysis and note initial results for translations which indicate

that sub-pixel distortion parameter measurement accuracy is possible. First,

we reiterate that since we perform an autocorrelation, the location of the output pattern is known and fixed. Thus, a small fixed set of detectors can be

placed in the output plane. This greatly simplifies the output measurement

data. Because an autocorrelation is performed, an optical joint transform correlator appears to be an attractive architecture. However, since the autocorrelation need be evaluated only for several relative shifts of the pattern, it

is quite possible to perform the autocorrelation digitally (since evaluation of
-38-

th e correlation at different shifts involves only a simple projection operation).

Use of an optical correlator introduces several effects which we found to

greatly complicate the quantitative interpretation and relation of a sampled

1

autocorrelation function to input object distortions. First, the frequency plane

i

material used in an optical correlator will saturate at dc and low spatial frequencies, thus producing the autocorrelation of an edge-enhanced or high-pass

filtered object image. Secondly, the output detectors used to sample the autocorrelation function are area detectors, not point detectors as in a digital

i

correlator. Thus, each sampled correlation value is actually the integrated

value over a finite area of the correlation plane. Modeling of these two effects

to the degree necessary to quantify the performance obtainable is beyond the

scope of our present effort.

Another vital issue of concern in this approach is that input plane translation of the object does not affect the autocorrelation. Thus, in-plane shifts

of each pattern on the target must be obtained by other methods. It appears

possible to obtain such information from the output correlation plane samples.

t

This follows, since input plane translations never occur alone. They are ali

ways associated with an input plane rotation (i.e. the entire wing does not

= " J

shift, rather it rotates about the fuselage and shifts), and in addition, the

j £

input object is rigid and hence abrupt changes between adjacent pattern regions

i

on the object are not possible (rather, smoothly varying distortions will result) .

a To initially address these issues, we used the cross-correlation of twoj

patterns that were shifted by a very small amount. We formed their crosscorrelation and sampled it at 5 points (the peak and 2 points on each side of
-39-

it). The sampled cross-correlation pattern obtained was sampled with area

.detectors to model the optical system's detectors. The amount of shift between

the two patterns was sub-pixel (i.e. less than the size of one output detector

element). For the input pattern, we used a Gaussian-distributed random variable analytical model with known correlation length. We then used a parabolic

curve fit of the sampled correlation function and from this obtained a sub-pixel

estimate of the shift between the input and reference functions.

r

In the NTF problem, the pattern used affects the correlation shape function assumed and hence our sub-pixel interpolator model. A parabolic model is

often used, but the input pattern should be chosen to properly have such an

assumed distribution. The highpass filtering nature of the optical correlator

complicates this, since it will change the correlation length of the data and

hence the shape of the correlation function. Analysis of all of these issues

and quantization of the distortion parameter measurement accuracy obtainable is

possible, but does not appear merited since other distortion parameter estimators using simpler feature extractors, simpler post-processing analyses and

providing in-plane shift information appear more attractive. An alternative

use of this technique that may be preferable is to perform a coarse correlation

to determine approximately where the different object patterns are in the input

and to then perform a fine zoom correlation (or to use feature extraction techniques) to obtain more precisely the locations and shapes of each object pattern.

This coarse preprocessing may be quite attractive for our stereo correlation

approach.
-40-

3.6 SUMMARY AND CONCLUSION

In this chapter, we have considered the effect of vibrations and turbulence

(

on the resultant processor for the wind tunnel problem. Various candidate schemes

have been advanced. None appear to be extremely attractive, except perhaps>for

time-averaged moire. Recent results obtained by NASA [10] have indicated that

the problems associated with turbulence and changes in index of refraction are

not too severe and thus can be overcome. We thus do not consider such issues

further. Space-variant pattern recognition techniques were considered. They

appear to be able to provide the necessary accuracy, however these systems are

more complex than others and are thus not considered further.

* A new version of stereo correlation processing was advanced. With the

modifications which we noted, this technique can be applied to the analysis

of object distortions for wind tunnel model testing and to achieving both inplane and out-of-plane distortion measurements. This technique is likewise

capable of achieving the required accuracy. However, again, because of the

complexity of the resultant system, it is not considered further.

; 3

i Finally, a novel and most attractive new approach (analyses of the shape

of the autocorrelation of the distorted object pattern) was advanced. This i

technique also appears to offer significant promise. Its accuracy and the optimum pattern to use remain to be quantified. As before, in-depth analyses and

laboratory demonstrations of every possible approach are not possible. Our -initial laboratory demonstrations of this technique are quite attractive.

 !

\ • •

This concept and our stereo scheme merit further attention. Time did not

permit this, thus we chose to next investigate various simpler feature extraction algorithms as discussed in the next chapter.
-41-

4. OPTICALLY-GENERATED PATTERN FEATURES FOR DISTORTION PARAMETER ESTIMATIONS

4.1 INTRODUCTION

In this chapter, we discuss several coherent optical deformation-measurement

techniques that can broadly be classified as feature extraction methods. In all

instances, we consider projecting a pattern onto selected regions of the model

surface, imaging the deformed pattern (as it appears when projected onto the

model) into an optical processor, where it is operated upon to optically extract

various image features. By image features, we refer to various scalar quantities that describe the deformed object pattern for different regions of the

model. The use of optical processors for feature extraction is very new. The

analysis of such features for distortion parameter analysis (rather than for

object identification) is thus a very virgin area of research.

For reasons mentioned before, patterns for each object region, rather than

.simple points on the target are used. The types of patterns considered are

discussed in Section 4.2. We consider ten patterns in ten spatially distinct

regions along the wing for simplicity and with no loss of generality. If we

know (from our feature extraction and processing) the 3-D displacements of

these ten local regions of the target, then the continuous distortion function

•)

for the entire wing can easily be obtained as a tenth-order polynomial (by

solving the resultant set of ten.simultaneous equations). If greater than ten

points are used, the complexity of the associated extraction of the surface

deformations will require solving a much larger set of equations. In this'case,

various optical matrix-vector processing techniques [11] should be considered.

Determining the 3-D displacements of discrete regions of the target at discrete
-42-

times appears to be adequate, since we expect the model to deform slowly and

<''•••" • ... . • (

continuously (rather than abruptly). The increased space bandwidth product

that results by using patterns rather than simpler circular or rectangular

shapes was noted earlier.

..-,"•.'' • . »

J As the two optically-generated image feature extraction techniques to be

considered, we address the use of Fourier coefficients and moments. In Section

4.3, we consider the use of a Fourier coefficient feature space. We also include our initial laboratory experiments and quantitative analyses using such

a 'feature space. In this initial study, emphasis is given £o the accuracy of

this (and all) techniques and to their practical realization. In Section 4.4,

we consider a wedge ring detector (WRD)-sampled Fourier transform feature

space. This type of feature space is easily produced optically. It has the

advantage of a greatly reduced dimensionality, thus significantly reducing the

complexity of the post-processing required. In all of our feature extraction

techniques, some form of post-processing is required to extract the deformation

parameters of the object. This can take the form of a specific post-detection

processor, or an estimator. In Section 4.4, we describe our estimator that we

propose to utilize. In Section 4.5, the digital simulation requirements to model

this algorithm are discussed. A quite significant resolution, fine sampling and

extensive computing time is required to obtain a full quantitative analysis of

this approach for the NTF problem. In Section 4.6, we consider a new optical

processor that computes the geometrical moments for each pattern in each object

region of the target. We also detail how a nonlinear estimator can be used to ^ . - . i ••->..- ; -j: . * •. - ' ' •" . ' • . • "'•'. • . - -

: ' • ' ;

determine the necessary distortion parameters of each object pattern from the

optically-produced image features. In Section 4.7 , we provide an

initial analysis of the component requirements for such a system,
-43-

with attention to mask resolution and mask and detector dynamic range and gray

level and noise effects. Initial quantitative results obtained are noted and

i

included. Our summary and conclusions and recommendations for future work in

c

this area are then advanced in Section 4.8.

4.2 PATTERNS USED

The simplest pattern considered was a square-wave grating. This grating

is shown in Figure 4.1. The grating is of size a, with the bars of the grating

being of width c and with a center-to-center spacing b. It is described mathematically by

f(x) = Rect(x/c) * Z6(x-ib) • Rect(x/a).

i

The Fourier transform of this pattern is given by

F[f(x) = F[Rect(x/c)] • F[E6(x-ib)] * F [Rect(x/a) ] .

i

(4.1)

(4.2)

) t

The components of the Fourier transform of this pattern are well-known and

j

easily determined.

h- • H -fch

H

FIGURE 4.1

Simplified Grating Pattern Inputs Used in Analysis
-44-

For simplicity, all analyses and experiments were performed with such a

grating pattern. Our results can easily be extended to other patterns and

cases. Thus, our use of only a 1-D grating represents no loss of generality.

The associated post-processing system to extract 3-D deformation information

may require more elaborate processing than is required in the presently considered .simpler example. A 2-D pseudorandom pattern could also be used, as

could 2-D patterns such as Walsh-Hadamard matrices. Such patterns are attractive since they increase the space bandwidth product of each object pattern,

help to avoid the presence of cross-correlations between the patterns in different object regions, and should increase the accuracy obtainable in the

measured data. If several object patterns are present in the same field of

view, or if the location of a given object pattern is not known to sufficient

accuracy, the use of 2-D patterns coded such that there is negligible crosscorrelation between any two of them can allow us to locate a specific pattern

in the input image. Different pseudorandom codes and the Walsh-Hadamard

matrices exhibit these desireable very low cross-correlation properties. If

the patterns can be placed on the target, different LEDs can be placed behind

each (within the target model). These can be pulsed on and used to locate

each pattern directly. This latter approach is a distinct possibility. It

may prove to be one that can easily be incorporated into a version of the wind

tunnel test system that NASA is presently considering fabricating.

As before, we assume that the deformations in each object region are piecewise constant. In Section 4.3, we discuss how the resultant Fourier transform

pattern changes with selected simple distortions of the input pattern.
-45-

4.3 FOURIER COEFFICIENT FEATURE SPACE

I

The pattern in the back focal plane P of a lens L is the 2-D Fourier

transform of the amplitude transmittance function f(x,y) placed in the front

focal plane P . Plane P is located a distance f (the focal length of lens

1 2. L

L ) from LI . The input plane P.. can be to the left or right of L . In the

system we used in our laboratory tests (see Figure 4.2) , plane P.. is to the

right of L and is located a distance d from P_ as shown in Figure 4.2. This

system has less severe lens aberration requirement than does a system with

the input pattern placed in front of the transform lens. This system is 'a

scaling Fourier transform processor, in which the scale of the input image

(and the resultant Fourier transform that is produced) can be adjusted by

simply varying the location of the input object (i.e., varying the distance d

in Figure 4.2) . The relationship between the location x in P of input spatial

frequencies u and the spacing d in Figure 4 .2 (and optical system parameters such

as the light source used X and the focal length f of the transform lens) is

L

given by t

x2 = Xdu. "(4.3)

As seen from (4.3), the scale of the Fourier transform plane (or equivalently

the scale of the input image) can easily be adjusted by varying the distance

d in Figure 4.2. Similarly, the rotational orientation of the input object,

and hence the angular location of the spatial frequencies in plane P can also

£t

easily be varied by simply rotating the input image in plane P . This experimental system is thus most attractive for producing various input image distortions. It must be modified to accommodate 3-D distortions (unless we simply
-46-

view such distortions as scale changes in the input image). This assumption

appears to be most valid since 1-D scale changes in the x or y direction are

appropriate models of various out-of-plane rotational distortions of the object

test pattern. If the image in the input P plane is tilted out-of-plane, then

linear phase terms are introduced into the input data. This will cause a shift

I

in the P pattern data recorded as well as a form of 1-D scale change in the

input object pattern..

A

V

4

P2(FT)

FIGURE 4.2 Simplified Schematic of the Scaling Fourier Transform Processing

System.

The P_ pattern contains diffraction orders separated by

x = Ad/b (4.4)

that are oriented at small angles 9 with respect to the axes of P (for an input

r . •

pattern inclined at an angle 9). The input distortion Aw is proportional to

the change Ab in the pitch of the grating. The expected resolution of the

system is given by the Fourier transform of the aperture function, specifically

by
-47-

AR = Xf /a. (4.5)

L

This is the minimum Ab distortion that is measurable with this system.

'• In our experiments to verify this theory, we used a 100 line pair per inch

grating and a Fourier transform lens with focal length f = 760mm, He-Ne laser

L

with X = 633nm and a spacing d = 650mm. -We measured the displacement of the

various diffracted-order spots in the transform plane for different changes Ad

in the distance d in Figure 4.2. By this, we thus simulated different scale

)

changes in the input image. The shift in the location of the n-th diffractedorder thus describes the change Ad (or equivalently an input distortion change

Ab) in (4.4). Thus, as a technique to achieve distortion parameter estimation

?

with improved accuracy and performance, we suggest that the location of the

higher-order diffracted spots be measured and from their shifts the distortion

parameters (e.g., scale change, etc.) be measured. By this new technique (using

the n-th diffracted order), we effectively increase the input spatial frequency

and hence the shift expected for a given scale change (e.g. a given change in

the grating spacing Ab) of the input data pattern. Use of a grating pattern

rather than an aperture significantly improves the sensitivity of our measurements.

Our results are summarized in Table 4.1. From these data, we see that a

scale change of approximately 0.1% can easily be measured with this system.

The measured shifts were compared to those predicted by theory. In all cases,

better than 0.5% accuracy was obtained (i.e., we found that we could measure

c

the magnitude of an 0.1% scale change to an accuracy of 0.005%). The accuracy

in our present system was limited by the Fourier transform lens used. With a

specially-designed Fourier transform lens, better shift linearity is possible.

For the present application, the accuracy achieved is sufficient.
-48-

For our case of an aperture with a = 10cm, the resolution accuracy of the system

is 4um (this is the resolution accuracy in position in the Fourier transform

plane). Since a 50ym shift in P_ corresponds to an 0.15% scale change, the

present system is capable of measuring scale changes of (4/50)(0.15) = 4(0.003) =

0.012%. This corresponds to a scale change Ab in the grating by 4ym. This is

much better than the requirements dictated for the NTF problem.

TABLE 4.1

Experimental Data Obtained Using

Fourier Coefficient Measurements

Ad (mm)

65

6.5

1

% Scale Change

10%

1%

0.15%

Observed Shift

(20-th order in ym)

3207

330

51

In Figure 4.3, we show the optically-produced Fourier transforms of the

)

grating in Figure 4.1 using the optical system of Figure 4.2. Figure 4.3a

I

corresponds to one location d = d;L of plane PI with respect to plane P . Figure

4.3b corresponds to a d = A^ location of PI/ corresponding to a scaled or outof-plane rotated and distorted input image. We clearly see from these patterns

that the Fourier transform coefficients occur at spatially different locations

in the two cases. From these locations, input scale changes or out-of-plane rotational distortions can be calculated.
-49-

ORIGINAL PAGE l§

OF POOR QUAUTY

(a) (b)

FIGURE 4.3

Partial Fourier Transform Plane Pattern Obtained on the System of Figure 4.2

for Two Distorted Grating Patterns

A cross-sectional scan (obtained with a scanning photometric microscope)

of several of the Fourier transform coefficients for the grating Fourier transform pattern in Figure 4.3 are shown in Figures 4.4a and 4.4b for one scale

change distortion in the input image. As seen from this data, the higher Fourier

| transform orders in Figure 4.4b are shifted more to the right than are the cori| responding orders in Figure 4.4a. The amount of shift and hence the location

of the Fourier transform peaks is proportional the input scale change (iie. the

I input distortion) and thus their location provides the desired input pattern

i

$ distortion data. I

(a) No Scale Distortions (b) Scale Distortions

Figure 4.4

Selected Cross-Sectional Scans of the Fourier Transform Pattern Obtained on

the System of Figure 4.2 With (a) and Without (b) Scale Distortions in

the Input Object Grating Pattern
-50-

« The sensitivity of this technique is superior to what is obtainable using

moire techniques for a given grating spatial frequency. The moire accuracy is

simply set by the pitch of the grating (0.25mm for our case). We can achieve

significantly better accuracy (by a factor of about 50) by use of our higherorder Fourier transform plane measurement technique. (Fringe multiplication,of

a,projection moire pattern can likewise achieve improved accuracy, however.)

Many techniques exist by which the sensitivity of the Fourier transform system

can be increased further. These include use of a higher spatial frequency grating

and the use of higher grating orders. It is possible to fabricate gratings with

strong diffraction orders past the 25th order. Thus, the use of such techniques

iq quite potentially attractive. Presently, 0.01% scale changes correspond to a

tilt of the input object (modeling out-of-plane rotation by 9 as a scale change}

by, A6 = 5.7x10 degrees. This is the accuracy of our present system.

However, there are several limitations in this technique that must be

 [

noted. This technique is most attractive for measuring input plane distortions

such as stress and strain. Such distortions cause the input image f(x,y) toLbe

changed into a new function f(ax,by), where a = 1 +e and b = 1 +te where e is

the strain and t is the Poisson coefficient (t = 0.3 for many materials). Image

plane rotations can also be measured from the angle at which the Fourier transform plane spots occur with respect to the axes of plane P . However, if we use

a 'higher-order Fourier coefficient, then a very large number of Fourier transform plane detectors are required. This is a significant disadvantage of this

system. If in-plane rotations can be avoided, and if out-of-plane rotations >

can be effectively modeled as 1-D scale changes horizontally and vertically,

then it should be possible to position a sufficiently sparse detector array at

the proper higher-order Fourier coefficient spatial location in the transform

plane. This would make this technique quite attractive. In Section 4.4, we

describe an alternate technique (with significantly reduced Fourier transform

plane dimensionality) that is preferable (if its accuracy is sufficient). ]
-51-

In conjunction with the aforementioned experiments, we also used a fan'to

produce air turbulence between the input and Fourier transform plane. This'was

an attempt to model the turbulence present in wind tunnel images. No measured

differences were observed in the shape or location of the Fourier transform

plane diffracted orders however. Although this experiment is not conclusive,

it is promising, since it indicates that such a technique may be less susceptible to air turbulence than are other methods. Other disadvantages associated

with a Fourier transform technique (for out-of-plane deformations, which we ;

model above simply as scale changes) is that a large depth of field for the

imaging lens which projects the object pattern onto the target will be required.

This is necessary to insure that the pattern remains focused on the target over

the entire range of deformations to be expected. From discussions with NASA,

it appears that cameras with sufficiently large depth of field are available.

The use of a pattern behind each laser diode, in a system that NASA is presently

considering, appears possible. We also note that the scale changes (or

rather the accuracy with which the scale change must be measured) is expected

to be quite small. Such small changes can be quite difficult to measure if

techniques -such as the ones we have proposed are not considered.

4.4 WRD-SAMPLED FOURIER COEFFICIENT FEATURE SPACE CONCEPT

: The dimensionality associated with the Fourier transform plane pattern i

analysis scheme noted in Section 4.3 can become quite excessive. Specifically,

the space bandwidth product of an image and its Fourier transform are equal.

This, coupled with the various distortion parameters to be investigated can .

require a significantly large number of detectors for sampling of the Fourier

transform space of the object pattern. The digital post-detection analysis .
-52-

_system required for such analysis can also be quite complex, especially when many

tinput samples must be interrogated and linearly combined. As one attractive technique, whereby the dimensionality of such a feature space can be significantly

^reduced, we consider the use of a wedge ring detector (WRD) to sample the Fourier

transform plane.

This device (depicted in Figure 4.5) consists of 32 annular-shaped detector

elements in one-half of a one inch silicon detector, with 32 wedge-shaped detector

elements in the other half of this detector. Such detector elements exist commercially. They are quite useful and efficient for data-reduction purposes. In

the instance that we consider here, we employ them to reduce the dimensionality

of the Fourier coefficient feature vector (and to produce Fourier coefficient

data with more opportunity for invariance to scale, rotation, and in and out-ofplane displacements). The wedge-shaped detector elements should be most useful

for providing angular information on the orientation of the input pattern. They

are also invariant to object scale changes. The ring (or annular)-shaped detector

t

elements should be most useful in providing scale change information on the' object

pattern. They are also invariant to plane rotations of the input object.

 rThus,

as a new approach to distortion-parameter estimation, we suggest the use off a

wedge-ring-detector-sampled Fourier coefficient feature space to analyze 2-D object patterns placed at different locations on a target in a wind tunnel. .

FIGURE 4.5

Pictorial Diagram of the Wedge Ring Detector-Sampling Unit '

Proposed for Dimensionality Reduction and Distortion Parameter Estimation.
-53-

In conjunction with this reduced dimensionality space concept, we propose

.the use of a new and unique digital iterative estimator. To understand this

concept, we view the 64 WRD-sampled Fourier coefficients produced at the output as the 64 elements of a feature vector v. The purpose of the post-processor

is to compare the elements of this observed vector v with the associated elements v_(b_) of distorted versions of the reference vector. We denote the distortion parameter vector by b_. It contains elements such as R (the range or

scale of the object pattern), a and b (the horizontal and vertical scale factors),

x and y (the horizontal and vertical shifts of the object pattern), and. 6 and

<j) (the in and out-of-plane rotational angles of the object pattern) . Our postprocessor begins with an initial estimate of b_. The elements of y_(b) are then

computed for this set of distortion parameters. The difference v-v(b) for

.this particular choice of b is then computed. A new estimate of the parameters

of b is then obtained, the aforementioned calculations are then repeated, and

the procedure repeats until a sufficiently small difference in v-v(b) is. obtained. The iterative algorithm to achieve this is [12]

kj

 = ^j -i + [iV1

!> "V^"1 fv - y^ (bj _1) 1 , (4.6)

where J^ is the Jacobian and E^ is the covariance matrix.

l

Our initial investigations [12] showed that this algorithm can be realized

in fewer than 7 iterations and that each iteration can be computed using less

than 6500operations. By an operation, we refer to a multiplication or an addition. Included in these 6500 operations are 1500 bookkeeping and data management operations. Thus, it appears that this algorithm can be implemented with

fewer than 35,000 post-processing operations. It should thus not significantly

tax a dedicated digital post-processor. This technique and concept appears most
-54-

attractive and we recommend it for future research considerations. A major issue

in future research on this concept is an extension of it to 3-D distortions and

a quantification of the accuracy and component performance requirements needed.

Our initial remarks on these topics are included in Section 4.5. (

4.5 INITIAL ISSUES IN THE ANALYSIS OF A WRD/FOURIER-COEFFICIENT FEATURE SPACE

Digital simulation is essential to provide answers to the various issues

associated with a WRD-sampled Fourier coefficient feature space and the necessary

parameters of our post-detection iterative digital estimator. The object pat-

•% i

tern's space bandwidth product required to achieve this prohibits a full analysis of such a subject in our present program effort, even using digital modeling

and simulation. To quantify the work required, we first consider the

realization of a model of a WRD detector in a digital system. This requires

considerable attention to interpolation and area integration. A most important

issue associated with such a program is the extension of the aforementionedconcept to 3-D image distortions. In such a case, we require a description' of

the various versions of the object pattern as functions of all parameters '

'associated with a 3-D distortion. This is far more complex than the case noted

in Section 4.4. Specifically, consider the case in which out-of-plane rotations occur for object patterns located at different positions on the wing..

Even for the case of a fixed out-of-plane rotational angles 6 and <f> (about the

fuselage). These correspond to quite different results for each of the different object patterns located at different distances from the fuselage. Thus,

3-D affine transformation matrices are needed to describe the resultant pattern

as a function of 3-D distortions. It appears that 3-D distortion data per pattern can be obtained from two images of each pattern taken from different view
-55-

iangles. This is a vital subject for future research.

r4. 6 OPTICAL MOMENT FEATURE SPACE SYNTHESIS

As yet another possible optically-generated image feature space, we consider the calculation and use of the moments of an input pattern as the elements

of a. feature vector. The moments of an input image f(x,y) can be defined as

mpq = //f(x,y)xpy

q

dxdy. (4.7)

1

Insight into the physical understanding of the various moments is possible (for

the lower-order moments). Specifically, the moment m is the average value of

the input image. The moments m and m correspond to the centroids of the

object in the x and y direction. They thus convey information on the horizontal

and vertical displacements of the object in the input plane. The moments m

and m correspond to the radius of gyration of the object. This has significance and various structural mechanics problems and applications. As a measure

of the out-of-plane rotational angle, we can form the ratio of the m _ and m?

moments. The sine of this angle can be obtained from the sine of any odd-order

moment.

Next, we consider an optical processor that is capable of realizing the

computation of the moments of an input object pattern in parallel. The simplified version of this system is shown in Figure 4.6. in this figure, the input

image f (x,y.) is imaged onto a fixed mask, whose amplitude transmittance is

described by g(x,y). The light distribution leaving the mask plane is thus the

product fg. This pattern is integrated in space to produce

i

u = //f(x,y)g(x,y)dxdy (4,8)
-56-

on an on-axis output plane detector. Comparing this output pattern expression

to the expression for the moments, it becomes quite apparent that by the use of

various monomial functions for the mask transmittance, the moments of the:input

image can be produced on the output detector. Specifically, if the mask function is nothing (unity transmittance, i.e. g(x,y) = 1), then u = m . If the

mask is linearly varying in transmittance in the x direction, i.e. g(x,y) =x,

or in the y direction, i.e. g(x,y) =y, then the observed output plane pattern

corresponds to u = m1 or u = m . respectively. Extension of this scheme to

higher-order moments, using higher-order monomials for the mask, follows directly.

In the recommended version of the system of Figure 4.5, we would spatially-=-mul-

' tiplex the various monomial functions onto different spatial frequency carriers and

record the composite sum of these on the mask in this system. The output lens

is then viewed as a Fourier transform lens. In this case, the output light

distribution on a 1-D or 2-D set of output plane detector elements comprises

the moments of the input image f(x,y). This architecture is most attractive,

since it is capable of generating the moments of an input image in parallel.

It is also attractive since the same optical system is capable of computing the

moments of any input object pattern. In other words, the optical system (or

t

the mask function) need not be changed if different input images or object

patterns are used, in [12] , we discussed how the observed output feature

vector, m (whose elements are the moments of the input object) can be corrected

for various possible error sources present in the components of the system.

This is a most attractive and practical aspect of this feature extraction system. Specifically, we have found that the output feature vector in need only

be multiplied by a fixed matrix to allow it to be corrected for all possible

errors in the optical system. In Section 4.7, we discuss the use of such a
-57- ORIGINAL PAGE 19

OF POOR QUALITY

^optically-generated moment-element feature space for the present NTF distortion

parameter estimation problem.

Input

f(x.y)

Imaging

Optics

Mask

Q<x,y)

FIGURE 4.6

Schematic Diagram of a Parallel Coherent Optical Processor

to Compute the Moments of an Input Image

4.7 MOMENT PROCESSOR FOR DISTORTION PARAMETER ESTIMATION (COMPONENT REQUIREMENT)

The basic idea in our moment feature space distortion-parameter estimation

concept is to compute the moments m of each deformed input pattern, compare them

to the moments m(b_) of the reference object and to then perturb the distortion

parameter b_ as in (4.5) until the weighted distance measure | |m-m(b) | | is minimized. The Jb that minimizes this then describes the distortion parameters for

each object pattern region. In this approach, we note that these features can

be- obtained at different times in the testing of the model within the wind tunnel

and that the results can be stored for off-line analysis later. Thus, the required post-processing of the m features can be performed off-line. This is

quite attractive here, since only 20-25 moments will probably need to be calculated and thus the A/D conversion and storage of 25 scalars per measurement is
-58-

ORIGIIMAl

OF POOR QUALITY

rquite easy to achieve. Hence, the high-speed portion of the processing is the

Computation of the moments and this is what is optically achieved and hence1 it

:is quite fast. In the technique that we considered briefly in bur present effort,

we advance other methods by which the distortion parameters can be computed, directly from the moments, rather than by use of (4.5).

i

* We consider the moments in (4.7) but for the case of a sampled function' f. .

j .

with' a sample size Aw in x and y. Thus, the discrete moments that'will be calculated are

m = £ Z(iAw)P(jAw)q(Aw)2f..

pq i j ID

- wP+q+2E ZiPj

q

f... (4.9)

i j X3

We consider patterns f. . that are binary and thus set f. . in (4.9) to 1 or 0 for

each (i,jj pixel. The summations in (4.9) are from 0 to N-l where N is the

number of pixels in the image in x and y. in this case of a binary image, the

optical -system required is simpler (but also fast digital techniques may bes

possible).

Let us consider scale and translation distortions (with scale factors A and

X

A and with translations X- and y.). in the first case, the new moments m1 of

y 0 -'O pq

a scaled function are related to the moments m of the original undistorted

pq

function by

.»• = AP+q+1A

 P+q+1m . (4.10)

pq x y pq

In the second case> the hew moments m1 are related to the original moments by

pq

m' = ? ?IT1I n *n7yn

jm_ , _ ,, (4.11)
-59-

where i varies from 1 to p and j varies from 1 to q. Similar transformations

can be derived in plane rotations, but are not considered here. Out-of-plane

rotations by 6 are equivalent to a 1-D scale change given by A = Cos9. If m1

and m are known for several (p,q) moments, then the distortion parameters

(A , A , x , y , etc.) can be obtained using (4.10) and (4.11).

The choice of the test pattern f. . merits future attention. For now, we

simply select a square aperture with uniform transmittance of one inside it.

This simplifies evaluation and analysis of the equations and reduces recording

and lighting effects and requirements. If the images were perfect, if there were

no errors in the moment-generating system, and if resolution were infinite, we

could evaluate and quantify the differences in the moments for different distorted versions of our input pattern. For now, we note four sources of error and

briefly quantify the effects of each.

(a) The input image has finite resolution, e.g., N x N pixels (N = 500 is

i I

typical).

(b) The recorded monomial will be recorded with finite gray-level resolu-

: i

., tion Ag, e.g., 500 gray levels.

i_

(c) The recorded monomial and the carrier each monomial modulates, will be

recorded with finite spatial resolution, e.g., Ax = lym resolution over

1. 5cm. •'

(d) The optical detector has E levels of detectable values and hence a

finite dynamic range, e.g., the moment value will be measured to an

' accuracy of 1 part in E (1 part in 10 is realistic).
-60-

Effeet (d) limits the minimum moment change and hence the minimum distortion can be measured. For the case when the moments are measured to an accuracy

of one part in E, the accuracy to which different distortions can be measured

can be determined. For example, for scale distortions, the change in the moments

is

Am = m' -m = m (1 - AP+q+1 AP+q+1) (4.12)

r pq pq pq pq x y

and hence the minimum scale distortions must satisfy i

(4.13)

4

For E=10,p=3,q= 0 and A = 1 (no scale change in y) , the minimum detector

scale change in x that can be measured is

A < 0.999975, (4.14)

X "~~*

or one part in 40,000. Thus, excellent accuracy appears possible and this error

source does not appear to be significant.

' Next, we consider effect (c) of a finite Ax sample size in the monomial

mask or the input (effect (a)). Here, we must define an m1 as a function of

pq

Ax and determine if m1 /m as a function of Ax and the order of the moments.

pq pq

Then, we can determine the effect of a given Ax on the measurement accuracy of

a given moment. Deriving a general form for this relationship is quite complex.

However, for m , we find, for an N x N input square pattern

m^ = (1/4) t(N+l)/N]2, (4.15)

rwhere m = 1/4. From (4.15), we see that m1 approaches m as N approaches
-61-

.jinfinity. For N = 500, the error is 0.4%. Thus, sufficient resolution appears

to be possible to produce sufficiently accurate moments to enable measuring the

.pattern deformations to a quite good accuracy. .

Lastly, we consider error source (b). A finite gray-scale resolution Ag =

-1

 ?

(number of gray levels) produces a new moment

] )

m' = m + (Ax)(Ag)M, (4.16)

pq pg

where M is the number of pixels in the pattern (the pattern is again assumed to

be of uniform transmittance unity). For 1000 points in each direction and 100

1 :

gray levels, 1% error results in the moments m if the scale changes from 1.0

> ' \J\J

to 0.75. The effect on other moments can be quantified similarly.

The effect of each of these error sources on the accuracy with which distortions can be measured can be quantified from our initial analysis. This determines the resolution and the dynamic range required in the system. Alternatively,

it defines the degree to which different system error sources and noise musi be

corrected (recall from [12] that the optically-computed moment values can be

corrected for various system and noise errors). These are the major issues to

be addressed in future work. Our initial analysis summarized above indicates

that this feature extraction technique is quite capable of determining distortion

parameters and that (4.6) need not necessarily be used to achieve this. This

represents a most attractive new approach to object distortion measurements.

Clearly, higher-order moments will show higher sensitivity in distortion parameter measurements. A realistic detector dynamic range of 40dB appears to be

appropriate. The number of points in the monomial (i.e. its physical size) and

the moment order and output SNR are all interrelated. Clearly, physically
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larger masks will require more dynamic range. The scale change that results ,

2

from a 64ym change over 7cm (as in the NTF data) will be quite small (7 x 10 /

—6 7 64 -x 10 s 10 ) and thus improved dynamic range will be required (since discrete detectors are used, this appears possible). Since only the edge pixels

in .the pattern contribute, we can alter the pattern used. Alternately, if a

full scale change (from 0.0 to 1.0) is not expected, then the amount of the

monomial recorded can be significantly reduced (with an associated reduction

in the system's resolution etc. requirements). Similarly, not all moments need

to be used (this can significantly reduce the monomial recording requirements).

In our future work we plan to quantify these issues, effects, and the accuracy

possible with this most attractive technique.

4.8 SUMMARY AND CONCLUSIONS

We find the use of a feature space description of the object pattern at

separate locations on the target to be a quite attractive method for distortion

parameter estimation. From an analysis of the elements of these feature vectors, and by use of our new iterative estimation algorithm, the distortion

parameters associated with the object pattern can be determined. The system

architectures we have proposed utilizes the real-time and parallel processing

features of coherent optical systems to compute the desired set of image features in parallel. A dedicated post-detection digital processor can then determine the distortion parameters of the object pattern under analysis, with t '• • i

a quite minimal computational load. We recommend that these concepts be

pursued and quantified in future research. Both the Fourier coefficient feature space (using a wedge-ring-detector to reduce the dimensionality of the

resultant vector) and a moment-based set 'of image features should be considered.
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Both of these features can be optically-generated in the architectures and systems we have described in this chapter. Such an architecture and system represent a simple and most attractive technique for novel applications such as distortion parameter estimation for isolated regions of a deformed target.
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5. SUMMARY, HIGHLIGHTS AND FUTURE WORK

Our recent one year of research in summarized in Section 5.1, our major

accomplishments are noted in Section 5.2, and future work directions are summarized in Section 5.3.

5.1 SUMMARY

 £

e

Our brief one year research effort addressing the application of optical

data processing techniques to the NTF problem has been quite fruitful. Ten

coherent optical data processing techniques were assessed and (following tests

on a sample of the target material used in the NTF facility) six additional

holographic, moire and speckle pattern techniques were added to our original

list. Addressing all sixteen techniques for a new problem and application was

a most formidable task. The direction of our research was to survey all methods

noted, select the best ones, and for those selected perform laboratory experiments, quantify the accuracy obtainable and define future work directions (to

the levels that time permitted.

In Chapter 1, we noted and briefly described all techniques considered, and

noted our rationale for omitting many approaches. We also outlined our research

and performed initial tests on the diffuseness and specularity of the material

used in the NTF facility models. In Chapter 2, we detailed our summary remarks

on interferrometry, moire and speckle techniques and we performed initial experiments in the most promising areas of research. This included the description

of a new moire projection technique coupled with fringe multiplication which has

the ability to obtain the desired deformation measurement accuracy. We also

j

suggested several new advanced moire techniques for future research that are
-65-

most attractive and appropriate for the NTF application.

, . =

' In Chapter 3, we addressed several new correlation techniques for optical

metrology. We surveyed space-variant techniques and found them to be less

attractive than others. We also considered stereo-photogrammetry correlation

< ........----- - - — — > -

approaches and found them to be capable of providing sufficiently accurate data

and results. We suggested several new applications of this type of approach

specifically for the NTF application. The stereo photogrammetry methods are

•( ,

attractive for optical realization, since optical systems easily perform the

.1

correlation operation (and since many correlations are required in this approach).

(

We also considered a novel approach to distortion-parameter estimation in which

c .

the autocorrelation of a distorted pattern was sampled at only several locations,

and from the shape of the resultant correlation pattern, the deformations in the

input pattern are extracted. Initial experimental demonstration of this approach

was provided and the various areas requiring further attention were noted. This

approach requires considerable additional analysis and quantification to determine its appropriateness for the NTF application.

In Chapter 4, new optical feature extraction techniques for the new application of optical metrology were advanced. The use of Fourier transform coefficients and moments (each optically-generated) were given major attention.

Initial experimental demonstration of the use of optical Fourier coefficients

for distortion-parameter estimation were provided and the various steps needed

for future research in this area were noted. A most attractive feature extraction technique, with a considerable dimensionality reduction, involves sampling

of the Fourier transform plane pattern using a wedge-ring detector. This approach merits detailed analysis and quantification of the distortion accuracy
-66-

possible. The use of optically-generated moments of the input pattern appears

to be perhaps the most attractive feature extraction method considered. Our

initial quantitative analysis indicates that such a technique can provide ader

quate distortion-parameter estimates for the NTF application.

Of all of the techniques considered, the projection moire method (with

fringe multiplication), the wedge ring detector-sampled Fourier transform technique, and the moment method for determination of pattern distortions appear

to be the most attractive ones that merit future detailed attention, quantifi"

t ' •

cation, and laboratory demonstration.

i

5.2 HIGHLIGHTS

The highlights of our one year research effort were:

(1) Isolation of the major attractive new optical data processing techniques for NTF target surface metrology (Chapter 1).

(2) Projection moire with fringe multiplication appears capable of the,

required accuracy and performance (Chapter 2). ~

T (3) Experimental verification of item (2) was provided (Chapter 2).

(4) A new moire projection technique was described in which the entire

object is illuminated and in which the full distortion parameters of the entire

j

object are obtained at once (Chapter 2).

(5) A new moire projection technique was described in which deformations

rather than object contour is available (Chapter 2).

(6) Phase conjugate optical techniques were suggested together with video

moire methods (Chapter 3).

(7) Space-variant techniques do not appear appropriate (Chapter 3).
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(8) Space-variant pattern recognition techniques appear adequate fdr some

distortions but require a much more complex system than do other approaches

(Chapter!3).

(9) Conventional stereo correlation techniques appear to provide sufficient

accuracy (Chapter 3).

(10) The use of different object patterns on the target to determine5 the

full object deformation by cross-correlations was suggested (Chapter 3).

(11) A new modified stereo-photogrammetry technique was advanced to achieve

object deformation information rather than just object depth data (Chapter 3).

l

(12) A new modified stereo correlation technique was devised to achieve ini

plane and out-of-plane target deformation information (Chapter 3).

(13) An autocorrelation shape analysis method for object distortion measurement was advanced and initial experimental data obtained (Chapter 4).

(14) A new feature extraction technique for distortion-parameter estimation

using Fourier transform coefficients was described and initial experimental data

obtained (Chapter 4).

(15) A new feature extraction technique for distortion-parameter estimation

using wedge ring detector-sampled Fourier transform plane data was described

(Chapter 4).

(16) A new feature extraction technique for distortion-parameter estimation

using moments was described and initial quantification provided (Chapter 4).

c

The application of feature extraction techniques to distortion-parameter esti-

)

mation is a virgin new application area that is significantly different from

the conventional pattern recognition and object identification uses previously

pursued for feature extraction methods.
-68-

5.3 FUTURE WORK

; Much future research has been defined as a result of our initial study.

These future research topics include:

'

l (1) Further projection moire and fringe multiplication studies, demonstrations and quantification are needed. '

: (2) Fully detailing, quantifying and demonstrating the full object moire

technique we described should be pursued.

(3) Fully detailing, quantifying and demonstrating our contact print moire

i

technique to provide in-plane distortions should be addressed.

(4) Fully detailing, quantifying and demonstrating of our differential

moire technique to extract only object distortion information rather than object

shape information should be pursued.

(5) Processing of the information on the location of different LED images

on different cameras by optical matrix-vector processors merits attention.

> • • -

(6) Optical correlation, convolution and Fourier transform techniques can

aid in the interpretation of the moire contour output patterns produced.

(7) Optical matrix-vector techniques can aid in providing global object

distortion information from several spatially-measured distortion values. ^

(8) Extension of, detailing and quantification of the use of our present

stereo-correlation techniques to provide in-plane and out-of-plane 3-D object

distortion information merits attention.

(9) Video moire techniques appear to merit initial study. .(

(10) Phase conjugate optical techniques merit attention if they can be

used to correct the medium turbulence present in the NTF application.

( (11) The new modified stereo-photogrammetry techniques we advanced to ,
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determine object deformations rather than object depth information and in-plane

as well as out-of-plane distortions merit further research.

(12) Wedge ring detector-sampled Fourier transform data is attractive but

requires additional analysis by digital simulation.

(13) The moment-based feature extraction technique merits future research,

quantification and experimental verification.

From the many techniques addressed, studied, suggested and analyzed, the simplest

techniques are of course the most attractive ones. For future research, we recommend pursuit of the following three items:

(A) Projection moire with fringe multiplication.

(B) Wedge ring detector-sampled Fourier transform feature extraction.

(C) Moment-based feature extraction.
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REFERENCES

1. B. Hildebrand and J. Doty, "A Study of Model Deflection Measurement Techniques Applicable within the National Transonic Facility", NASA CR-165853,

February 1982. .

2. J. Harris and K. Harding, "Evaluation of Moire Techniques for Wind Tunnel

Metrology", NASA CR-164477, June 1981.

3. W. T. Welford, "Some Applications of Projected Interference Fringes",

Optica Acta, 16, 371 (1969).

4. D. Meadows et al, "Generation of Surface Contours by Moire Patterns",

Applied Optics. _9, 942 (1970).

5. R. Ritter and H. Mayer, "Vibration Analysis of Plates by a Time-Averaged

Projection-Moire Method", Applied Optics, 19, No. 5 (1979).

6. B. Hildebrand and J. Doty, "A Study of Model Deflection Measurement Techniques Applicable within the National Transonic Facility", NASA CR-165853,

February 1982, pp. 43-50.

7. D. Casasent and D. Psaltis, "New Optical Transforms for Pattern Recognition",

Proc. IEEE, 65 (1977). See also D. Casasent and D. Psaltis, "Space Bandwidth

Product and Accuracy of the Optical Mellin Transform", Applied Optics, 16,

1472 (June 1977).

8. A. VanderLugt, IEEE, Information Theory, 128 (1964).

9. N. Balasubramanian, Chapter in "Optical Data Processing; Applications",

; Editor-D. Casasent, Springer-Verlag (1978).

10. D. Post, "Analysis of Moire Fringe Multiplication Phenomenon", Applied Optics,

6_, 1938 (1967).

i

11. C.P. Neuman and D. Casasent, "Optical Systolic Solutions of Linear Algebraic

Equations", NASA Langley Research Center, Optical Information Processing

Conference II, Hampton, Virginia (August 1983).

12. D. Casasent, L. Cheatham and D. Fetterly, "Optical System to Compute Intensity

Moments: Design". Applied Optics, 21, 3292-8 (September 1982).

1. Report No.

NASA CR-172316

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

Coherent Optical Techniques for National Transonic

Win'd Tunnel Facility

5. Report Date

March 1984

6. Performing Organization Code

7. Authors)

David Casasent

8. Performing Organization Report No.

10. Work Unit No.

9. Performing Organization Name and Address

Carnegie-Mellon University

Department of Electrical Engineering

Schenley Park ;

Pittsburgh, PA 15213 ^

11. Contract or Grant No.

NAG1-265

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546

13. Type of Report and Period Covered

Contractor Report "

14. Sponsoring Agency Code

15. Supplementary Notes

e

Langley Technical Monitor:

Fina,! Report - 1 May 1982 •

H. D. Hendricks

1 May 1983 ^->

16. Abstract

£

The goal of this 1-year study was to survey the use of optical data processing

techniques for distortion-parameter estimation in the National Transonic Facility and

to assess, quantify and compare various methods to detemine which are best for this

specific application. The conventional nondestructive testing techniques studies

included interferometry, moire and speckle methods. From these, we find projection

moire;using fringe multiplication to provide sufficient accuracy and to be a most

attractive approach for this application. Several advanced moire techniques for.

future research are also described. We also investigated several correlation '

techniques: space-variant processing, stereo correlation and autocorrelation shape

analysis. Stero correlation is found to have sufficient accuracy and new modified

stero.correlation techniques for this application which are most appropriate are

described. Autocorrelation shape analysis is a quite unique approach to distortionparameter estimation. Finally, several optical feature extraction techniques were

considered. These included Fourier transform coefficients, wedge ring detectorsampled Fourier transform data and moment features. In all cases, each feature is

optically-generated and a digital post-processor is used to determine the target's

distortion parameters. We find: projection moire (with fringe multiplication), wedge

ring detector Fourier transform plane analysis and moment-based optically-generated

features to be the most attractive techniques that merit further attention for this

application.

17. Key Words (Suggested by Author (s))

Optical Data Processing Techniques

Stere'o Correlation

Auto Correlation

Fourier.Transform

18. Distribution Statement

FOR U.S. GOVERNMENT AGENCIES AND

THEIR CONTRACTORS ONLY

19. Security Gassif. (of this report)

Unclassified

20. Security Classif, (of this page)

Unclassified

21. No. of Pages

75

22. Price