This Dissertation Has Been Microfiimed Exactly As Received Target Imaging from Multiple-Frequency Radar Returns

71-27,587 f

YOUNG, Jonathan David, 19^1- • TARGET IMAGING FROM MULTIPLE-FREQUENCY ! RADAR RETURNS. ! I I The Ohio State University, Ph.D., 1971 j Engineering, electrical !

University Microfilms, A XEROX Company, Ann Arbor, Michigan j i ...... _ , 4

THIS DISSERTATION HAS BEEN MICROFIIMED EXACTLY AS RECEIVED TARGET IMAGING FROM MULTIPLE-FREQUENCY RADAR RETURNS

DISSERTATION

Presented in P artial Fulfillm ent of the Requirements fo r the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jonathan David Young, B.E.E., M.Sc.

*********

The Ohio State University 1971

Approved by

Adviser Department of E lectrical Engineering PLEASE MOTE:

Some pages have indistinct print. Filmed as received,

UNIVERSITY MICROFILMS. ACKNOWLEDGMENTS

The author would lik e to acknowledge the advice and encouragement of his graduate adviser, Professor E.M. Kennaugh, which were important to the success of this effort. Don A. Irons assisted in the micro wave system development, and the computer could not have been used and maintained without the assistance of Dr. Dean E. Svoboda. The scattering measurements were made by S.A. Redick. The constructive criticism during preparation of the manuscript by Professor Kennaugh and the other reading committee members, Professor Leon Peters, Jr. and Professor A.A. Ksienski, is greatly appreciated. VITA

June 29, 1941 Born - Dayton, Ohio

1964 . . . . B.E.E. {Summa Cum Laude) The Ohio State U niversity, Columbus, Ohio

1964-1965 . . Research assistant, Antenna Laboratory, The Ohio State U niversity, Columbus, Ohio

1965 . . . . M.Sc. The Ohio State University, Columbus, Ohio

1965-1971 . . Graduate Research Associate, Electro- Science Laboratory, The Ohio State U niversity, Columbus, Ohio

FIELDS OF STUDY

Studies in Electromagnetic Field Theory Professor E.M. Kennaugh

Studies in Antenna Systems Professor C.H. Walter

Studies in Communications and Network Synthesis Professor W.C. Davis

Studies in Applied Mathematics Professor H.D. Colson

Studies in Classical Physics Professor W.H. Shaffer

i i i PUBLICATIONS

"Integrated Circuitry for Electronic Beam Steering of Wide Band Slot Antennafier Arrays," M.Sc. Thesis, The Ohio State University, 1965.

ORAL PAPERS

"Antennafiers for Beam-Steering Arrays," Fourteenth Annual Symposium on USAF Antenna Research and Development, University of Illin o is , 6-8 October 1964.

"An Electronically Controlled Slot Antennafier," co-author, A.6 . Jen netti), Fifteenth Annual Symposium on USAF Antenna Research and Development, University of Illin o is , 12-14 October 1965.

"Determination of the Constitutive Parameters by Scattered Fields of Spherical Bodies," (co-author, J.S. Yu), 1966 IEEE International Antennas and Propagation Symposium, Palo A lto, C alifornia, 5-7 December 1966.

"Loop Antenna Systems For HF and VHF," (co-author, Dr. C.H. W alter), Antenna Workshop, U.S. Army Electronics Command, Fort Monmouth, New Jersey, 13-15 February 1968.

"A New Approach to High-Frequency A irc ra ft Antennas," (co authors, T.L. Flaig and G.A. Richards), U.S. Army Advanced Planning Briefing and Symposium on Aviation Electronics, Fort Monmouth, New Jersey, 5-7 March 1968.

"The Multi-Turn Loop Antenna," (co-authors, T.L. Flaig, G.A. Richards, G.A. T h ie le ), 18th Annual Symposium on USAF Antenna Research and Development, University of Illin o is , October 1968. CONTENTS

Page

ACKNOWLEDGMENTS...... i i

VITA...... i i i

TABLES...... vi i

ILLUSTRATIONS...... ix

Chapter

I INTRODUCTION...... 1

I I RAMP RESPONSE MEASUREMENTS...... 8

A. A Radar Signature Measurement F a c ility 8 B. Approximate Ramp Response Waveforms 25 C. Correlation Between the Ramp Response and Geometrical Target Features 37

I I I THE APPROXIMATE LIMITING SURFACE TECHNIQUE FOR IMAGE GENERATION...... 44

A. An Imaging Technique 44 B. Image Input Waveforms from Measured Data 59 C. A Q uantitative Image Accuracy Indicator 61 D. Choice of a Scaling Constant fo r the Imaging Process 67

IV TARGET IMAGES USING THE LIMITING SURFACE TECHNIQUE 72

A. Images Using Calculated Ideal Profile Functions 72 B. Images Derived from Measured Radar Data 82 C. General Characteristics of the Basic Imaging Technique 85 D. Image Resolution of Target Features 87

V IMAGING STUDIES - EXPERIMENTAL DATA INPUT SIMPLE MODIFICATIONS FOR IMPROVED IMAGES ...... 90

A. Modification of the Hyperbolic Contour Shape 91

v CONTENTS (continued)

Chapter Page

B. Initial Target Orientation Estimation 93 C. An Ite ra tiv e Procedure fo r Modifying the Basic Technique 101

VI SUMMARY AND CONCLUSIONS...... 108

APPENDIX A...... I l l

APPENDIX B...... 125

APPENDIX C...... 143

APPENDIX D...... 156

APPENDIX E...... 179

BIBLIOGRAPHY...... 187

vi TABLES

Page

Estimated System Accuracy vs Frequency ...... 21

In itia l System Accuracy Estimates ...... 112

Improved System Accuracy Estimates ...... 113

2:1 Cylinder,

2:1 Cylinder, e Polarization, Complex Return vs 6.. 114

Sphere-capped Cylinder, Polarization, Complex Return vs e...... 115

Sphere-capped Cylinder, e Polarization, Complex Return vs e...... 115

Cone Cylinder, Polarization, Complex Return vs 0. 116

Cone Cylinder, e Polarization, Complex Return vs 0. 116

Step Cylinder, Polarization, Complex Return vs 0. 117

Step Cylinder, e Polarization, Complex Return vs 0. 117

Cube, <}> = 0, <|> Polarization, Complex Return vs 0... 118

Cube,

Cube, $ = 150°,

119

Cube, 4 = 15°, e Polarization, Complex Return vs e. 119

Cube, = 30°, Polarization, Complex Return vs 0. 120

Cube, - 30°, 0 Polarization, Complex Return vs 0. 120

Cube, 4 = 45°, Polarization, Complex Return vs 0, 121

Cube, 4 = 45°, 0 Polarization, Complex Return vs e. 121

vi i TABLES (continued)

Table Page

20 60° Cone, Polarization, Complex Return vs 0...... 122

21 60° Cone, 0 Polarization, Complex Return vs 0...... 122

22 Half Spheroid, <{> Polarization, Complex Return vs 0...... 123

23 Half Spheroid, 0 Polarization, Complex Return vs 0...... 123

24 Large Sphere-capped Cylinder with Stub = 0, <|> Polarization, Complex Return vs e...... 124

25 Large Sphere-capped Cylinder with Stub, = 90°, «j> Polarization, Complex Return vs 0...... 124

26 CPU Registers...... 157

27 Sense Functions ...... 159

28 Action Taken on Overflow ...... 161

29 CPU Instructions ...... 163

30 CPU Instruction Timing ...... 169

31 Control Character Codes...... 172

32 1/0 Instructions ...... 174

33 Teletype 1/0 Code...... 176

34 P lotter Code...... 178

vi i i ILLUSTRATIONS

Figure Page

1 Transmitter-receiver using target motion...... 10

2 L-band source frequency spectrum ...... 11

3 Unmodulated harmonic generator frequency spectrum ...... n

4 Transmitted frequency spectrum ...... 11

5 Target motion control system ...... 15

6 "Minimal Informer" computer block diagram...... 17

7 Computer measurement program block diagram...... 18

8 Computer-controlled measurement flow chart...... 19

9 Computer-plotted raw measured data...... 20

10 2:1 circular cylinder model...... 23

11 Sphere-capped cylinder model ...... 23

12 Cone-cylinder model ...... 23

13 Step-cylinder model ...... 23

14 Cube model...... 24

15 Cone model...... 24

16 Half-spheroid model...... 24

17 Large sphere-capped cylinder model ...... 24

18 2:1 cylinder ramp response waveforms ...... 30

19 Sphere-capped cylinder ramp response waveforms ...... 31

20 Cone-cylinder ramp response waveforms...... 32

21 Step-cylinder ramp response waveforms...... 33

ix ILLUSTRATIONS (continued)

Figure Pa9e

22 Cube ramp response waveforms...... 34

23 Cone ramp response waveforms...... 35

24 Half-spheroid ramp response waveforms...... 35

25 Large sphere-capped cylinder ramp response waveforms...... 36

26 Cross-sectional area times (-1/ tt) vs ramp response for 2:1 cylinder, endfire orientation ...... 41

27 Cross-sectional area times (-1/ tt) vs ramp response for step-cylinder, backfire orientation (2:1 cylinder ramp includes for reference ...... 42

28 Cross-sectional area times (-1/ir) vs ramp response for 2:1 cylinder, broadside orientation ...... 43

29 Profile function, R(x), for 4 cm cube ...... 47

30 Target cube and reference frame, isometric view...... 48

31 Hyperbolic limiting contour, C = 2 v ...... 50

32 Hyperbolic limiting contour, C = 4 ...... 52

33 Limiting contour vs cube outline in the plane X = 2 ...... 53

34 X look angle limiting surface for the cube...... 54

35 Limiting surface image construction for a cube ...... 55

36 Profile function for 4 cm diameter sphere ...... 57

37 Limiting surface image construction for a sphere ...... 58

38 Original ramp waveform...... 60

39 Modified ramp waveform, D.C. level s h ift...... 60

40 Modified ramp waveform, time s h ift...... 62

41 Modified ramp waveform, eliminate leading ripples...... 62

42 V irtual p ro file function obtained from ramp response 63

x ILLUSTRATIONS (continued)

Figure

43 Input and output profile functions for the cube image of Fig. 35...... 64

44 Input and output profile functions for the sphere image of Fig. 37...... 64

45 Sphere and cube images, C = '2i t, 5.5, 5 .0 ...... 69

46 Sphere and cube images, C = 4.5, 4.0, 5.72...... 70

47 E vs C for sphere and cube...... 71

48 Cube images compared to lin e drawings, p ro file function input...... 73

49 2:1 prolate spheroid images compared to lin e drawings, profile function input ...... 74

50 2:1 prolate spheroid images compared to lin e drawings, profile function input ...... 75

51 2:1 parallelopiped images compared to line drawings, profile function input ...... 77

52 2:1 parallelopiped images compared to line drawings, profile function input ...... 78

53 Cylindrical object images compared to line drawings, profile function input ...... 79

54 Simulated rocket images compared to lin e drawings, profile function input ...... 80

55 60° cone image compared to lin e drawing, profile function input ...... 80

56 Wedge image compared to lin e drawing, profile function input ...... 81

57 Square doughnut image compared to lin e drawing, profile function input ...... 81

58 Sphere image compared to lin e drawing, virtual profile function input ...... 82

xi ILLUSTRATIONS (continued)

Page

Cube images compared to lin e drawings, virtual profile function input ...... 83

Cylindrical object images, virtual profile function input (compare to Fig. 53) ...... 83

60° cone image compared to lin e drawing, virtual profile function input ...... 84

Half 2:1 spheroid image compared to line drawing, virtual profile function input ...... 84

Body outline vs limiting surface outline in center region of square doughnut...... 89

Limiting circles vs L...... 92

Modified limiting contour, L = 2 ...... 93

Sphere image vs L, profile function input...... 94

Cube image vs L, profile function input...... 95

Target images with cusps removed (compare to Figs. 59, 60, 61, 62) ...... 95

Rotating spheroid geometry...... 97

Improved spheroid images compared to lin e drawings (same shapes as Fig. 59)...... 102

Improved spheroid images compared to lin e drawings (same shapes as Fig. 50)...... 103

Improved parallelopiped images compared to lin e drawings (same shapes as Fig. 51)...... 104

Improved parallelopiped images compared to lin e drawings (same shapes as Fig. 52)...... 105

Images depicting ite ra tiv e improvement for parallelopiped, $ = 45°...... 107

Block diagram showing the relation between the 1/0 converter, the central processor and the the 1/0 devices...... 170 CHAPTER I

INTRODUCTION

There is presently a need for the capability of target identification, or at least separation of different classes of objects, by electromagnetic scattering properties. Much research has been conducted in this area for satellite identi fication, and many other applications are foreseen.DU One de sirable way to achieve identification is by the creation of a synthetic image which can be visually interpreted to indicate object size, shape, and possibly functional characteristics as wel I .

A new approach to electromagnetic imaging is described and demonstrated in this study, utilizing different electromagnetic parameters, target observation angle requirements, geometrical interpretation of the measured electromagnetic parameters, and a different synthetic image presentation than have been tried before.

A b rie f discussion of some other imaging approaches serves to i l luminate these differences.

The image of an object may be defined as a "plot" of the scattered light intensity vs direction over a small solid angle containing lines-of-sight to the object, under external illumination by either a localized or diffuse source of light. A two-dimensional mapping of intensity, i.e ., a "picture", is obviously indicative of object size and shape. Besides providing an o utlin e, a good picture presents many additional visual cues, such as shading effe cts , which yield subjective three-dimensional information on the object dis played. Existence of similar visual cues is equally important for comprehensive, accurate interpretation of synthetic images. A radar imaging technique d ire c tly related to optical processing might sweep a small interrogating radar pencil beam over the visible region of a target, and record the backscattered energy as a function of transverse coordinates. The size of the pencil beam at the target location must be a fraction of the target dimensions in order to achieve satisfactory resolution fo r such an approach. For re a lis tic resolution, range distances, and radar frequencies, the required radar antenna aperture size, which is inversely proportional to beamwidth, becomes very large

(on the order of tens of square m iles). The synthetic aperture tech nique of side-looking radars does achieve this type of performance using a smaller, moving antenna; thus the approach described has been successfully applied to surveillance of geographical scenes . £23 How ever, a stationary scene is required while the antenna is moved to simulate the very large antenna. The image produced by this technique, moreover, simulates a view of a shiny object for coherent illumination from the observer's position. The washed-out q uality of flash-bulb pictures illustrate that many three-dimensional cues are lost under such illumination. As the interrogating frequency is raised in order to obtain improved resolution with smaller aperture requirements

this effect worsens producing an image of several bright "flare-

spots" which contains little target shape information.

Another possible approach to radar imaging uses a "short

pulse" radar. A short pulse, consisting of just a few cycles of a microwave carrier frequency, is capable of achieving high range

resolution over the longitudinal extent of a target. At least one powerful^ radar system of this type has been implemented, and studies of target characteristics are continuing.C3,4J Image information can be obtained by tracking the range variation of the scattering centers resolved by the short pulse for a spinning target. Problems inherent in this approach include the spinning target requirment, and insuf ficient shape definition in the blurred "flare-spot" pictures which are produced.

A spatial transform approach for generation of a 3-dimensional image from either short pulse or swept-frequency radar data has been suggested by Lewis.[5 ] However the required number and spatial d is tr i bution of the radar look angles for rigorous implementation is not feasible, and no application of the technique has been attempted to this author's knowledge.

A radar parameter which duplicates the range resolution of the short pulse but is more directly related to target shape is the time-domain transient signature, f i r s t proposed by Kennaugh and

Cosgriff.C63 The impulse response F j( t ) , defined as the time-domain backscattered signal for a target illuminated by an impulsive traveling electromagnetic discontinuity, is the fundamental transient response parameter. This response waveform and the complex fre - quency-domain backscattered target cross section are a Fourier transform pair. Thus, the impulse signature summarizes in a single waveform the to tal time- or frequency-domain response properties of a target. Also, the impulse response is unique with respect to target

size, shape composition, and orien tation . Techniques fo r calcu

lating and laboratory systems fo r measuring the impulse response of targets are receiving increased attention.C7,8,9H

The main problem in implementing a radar impulse response measurement system is the wide bandwidths required. Bandwidths of at least 100:1 are necessary to obtain a satisfactory impulse response approximation. Microwave components with appropriate performance fo r fu ll-s c a le operation over such a bandwidth are not available at present.

The radar parameter on which this imaging technique is based is the time-domain ramp response signature, proposed and investigated by Kennaugh and M o ffa tt.[1 0 ] The ramp response FR( t ) , defined as the backscattered time-domain waveform in response to a traveling electromagnetic ramp discontinuity, is the second integral of the impulse response. Therefore, the ramp response retains the uniqueness and range resolution properties o f the impulse response.

However, i t has been shown that the ramp response can be success fu lly approximated by using a 10:1 frequency bandwidth in the target's low resonance range.D13 Radar implementation of this parameter is thus more feasible than an impulse response system. 5

The characteristics of the ramp response from which geometrical information can be inferred are of primary importance for this study.

The ramp response signal can be interpreted as either the time- dependent electromagnetic fie ld strength seen by a stationary ob server as the target return travels past, or an instantaneous

"snapshot" of the spatial d is trib u tio n of the travelin g response transient. For normalization corresponding to the spatial distri bution concept, where the response is amplitude vs distance, it has been found that the ramp response is related to the cross sectional area vs distance along the line of sight, or "profile function" of the target, at least for simple shapes. [123

Thus, the ramp-response possesses target resolution capa b ility, appears feasible for full scale application, and finally has characteristics from which geometrical information for the con struction of an image can be inferred. Yet it it is seen that the ramp response is a low frequency approach, using frequencies at which the target is from 1/10 to 5 wavelengths in extent, in con tra s t to the previous imaging approaches where the targ et dimen sions are typically hundreds of wavelengths at the measurement frequency.

The technique to be described obtains a mathematical specification for a three-dimensional approximate limiting surface, using input pro file functions for three orthogonal target look angles. A contour plot simulating an isometric view of the limiting surface is then used for visual image presentation. Since three dimensional cues are preserved in the contour plot, a definitive image results when

the lim iting surface produced closely approximates the target shape.

This technique differs from the short pulse approaches in that neither a spinning target nor a continuum of look angles are required. Also, the images produced are more representative of gross shape character

istics than of corners and edges which produce the flare-spots for the high-frequency approaches. F in ally, a p icto rial image simulating an arbitrary viewing angle can be derived from the three-dimensional limiting surface specified by this process.

Possible radar applications of this imaging technique include: satellite identification, site security, air-borne surveillance, and national missile defense. Possible electromagnetic sensing appli cations include concealed object detection and underground object identification. Finally, the low frequency feature of this approach might be important in considering many other electromagnetic, optical, or acoustic uses.

Chapter I I describes a laboratory system for ramp response measurements and presents experimental data for several simple target shapes. The system performs complex cross-section meas urements at ten harmonically-related frequencies, and provides as output an approximate ramp response waveform. Correlation between the p ro file function and the measured ramp response is discussed.

The technique for obtaining an image from profile function data is described in Chapter I I I . Adjustment of the measured ramp response for imaging use is described, and a quantitative indicator of image consistency is defined. Images produced using the basic technique, with both ideal

and ramp-response derived p ro file function input, are presented

in Chapter IV. Surprisingly good images are obtained for simple

conducting shapes whose principal planes of symmetry are aligned with the radar look angles. Aspects of the basic technique which could be modified for improved image quality in more general

situations are discussed.

Chapter V presents some in itial modifications on the basic technique which could be simply implemented, and demonstrates the resulting image effects. Results indicate that satisfactory per formance fo r more general situations should be ultim ately attain ab le, and that quantitative evaluation of image consistency can be made without a p rio ri knowledge of the target shape.

Summary and conclusions are presented in Chapter VI. The overall approach presented is seen to have several unique features, and promising performance considering its stage of development. Some specific areas in the approach which deserve further concentrated study are recommended. I

CHAPTER I I

RAMP RESPONSE MEASUREMENTS

This chapter describes a multipi e-frequency automated re

fle c tio n measuring system (MFARMS), constructed as a laboratory

tool to obtain necessary radar data on a number of simple objects.

The ultimate form of the data generated is the periodic ramp

response waveform (band-limited approximation) a t a number of aspects

of the scattering body. These data will be required to test radar

imaging techniques using ramp response waveforms.

MFARMS is unique in many respects, although it is a logical

development of single-frequency re fle ctio n measuring systems which

have been in use for many years. The essential characteristics of

the system are presented in Section A, below. The reduction of

multi pi e-frequency data to obtain the ramp response waveform of a

target is described in Section B. Finally, comparisons of the ramp

response waveform and the p ro file function fo r several targets are

made in Section C, including the effect of polarization.

A. A Radar Signature Measurement F a c ility

The RF measuring system employs suppressed c a rrie r AM signals

at ten harmonically related carrier frequencies. Generation of the

10 transmitted signals is illustrated by the block diagram and

transmitted spectra of Figs. 1 through 4. The fundamental frequency

8 ( 9 of 1.08 Ghz is generated by a solid state source which uses harmonic multiplication of a VHF oscillator, producing a 2-volt output signal.

A small portion of this signal is coupled to the receiver to provide a reference, the rest is used to generate the transmitted signal.

The spectrum of Fig. 3 is generated by each of three step recovery diodes functioning as harmonic generators. At this point, the har monic spectrum is s p lit into four bands designated L, S, C, and X-

Band as indicated in Fig. 1. Each band will basically handle only the harmonics indicated although there is some overlap.

The signal is modulated at 20.278 MHz to achieve the fin a l transmitted signal of Fig. 4. Standard double balanced diode mixers covering octave bands are used. These are fed by balanced center- tapped transformers a t the modulating frequency to obtain the phase reversal needed fo r suppressing the c a rrie r. Although these mixers are not ideal for the purpose, careful adjustment of carrier and modulation levels yields carrier suppression of 2-5 dB with respect to the sidebands, which is satisfactory, but not optimum.

The modulated spectral components are amplified by three traveling wave tube (TWT) amplifiers covering S-band (2.16, 3.24 GHz),

C-band (4.32, 5.40, 6.48 GHz) and X-band (7.56, 8.64, 9.72, 10.80 GHz).

A narrow band solid state am plifier is used fo r the fundamental

(1.08 GHz). There are no strict requirements on the output harmonic power levels of the amplified spectrum, since computer calibration from reference target measurements is used to obtain effective 10 system sensitivity at each frequency. This technique eliminates the need for several microwave filters and attenuators in the transmitter section of this system. Only a pinched X-band waveguide is used to obtain equalization of the excessively strong 7th harmonic.

L.S.C.X BAND MULTIPLEXER

REF. Rp e«IOA/84tlA osc. O utput X-BAND C -8A N D S-BANO L - BANO NETWORK TWT TWT TWT SOLID ANALYZER re r. AMP. AMP. AMP. STATE WlPUT AMP. REF. TEST OUTPUT OUTPUT

I.F. BAL BAL. BAL. BAL. AMP MOD MOD. MOD. MOD.

PHASE-GAIN INDICATOR PLUG-IN HARMONIC HARMONIC HARMONIC AMPLITUDE PHASE GENERATOR GENERATOR GENERATOR OUTPUT OUTPUT

5 OB HYBRID MINIMAL INFORMER N£ 2 3 dB HV0RID

L.S.B. MOD. 20 dB COUPLER

20 dB COUPLER

L-BANO SOURCE 1.1 GHf

Fig. 1--Transm itter/receiver using target motion. 1.059722 GHz Fig. Fig. Me' e O O CM - e 0 0 CO o 3 CM o r n e CM CM Umdltd amnc eeao feuny spectrum. frequency generator harmonic —Unmodulated . CM 00 o CM r- GO CJ Fig. Fig. V i. -Tasitd rqec spectrum. frequency 4--Transmitted Fig. 2 --ad ore rqec spectrum. frequency source --L-band 0 u> cn CM O N 0 0 CM^NCM >

e- e- en e' M COCM CM 00 CM o CM r- 00 12

The transmit and receive antennas in Fig. 1 are 10-1 bandwidth log-periodic fed 3 ft diameter parabolic dishes operating at an 8 f t range with a bistatic angle of 20 degrees. They are oriented so as to reduce specular re fle ctio n from the walls of the microwave darkroom, and moveable absorbing screens are used to further reduce background reflections. The output signals are connected to the transmitting antenna on a single band basis, fo r reasons which w ill be discussed la te r.

The receiving portion of the system uses a Hewlett Packard

841OA/8411A Network Analyzer which receives all 10 frequencies simul taneously. The test channel portion of the receiver operates as a dual conversion superheterodyne receiver with 1st I.F. of 20,278 MHz and 2nd I.F. of 278 KHz. The first local oscillator frequency is determined by the signal fed to the reference input. The local oscillator phase-locks to the reference at a frequency 20.278 MHz above it. Since this 1st L.O. is harmonically generated, feeding in a signal 20.278 MHz below the system fundamental {1.08 GHz), w ill recreate the spectrum of Fig. 3 plus some sub-harmonics which have no effect on the operation. If the modulation of the transmitted signal is at the same frequency as the firs t I.F ., then the received signal at all harmonics will mix down to the firs t I.F ..

To obtain this modulating frequency, a port at the output of the crystal oscillator which determines the receiver's first I.F. was installed. This signal is amplified by a bank of R.F. amplifier modules and applied to the balanced modulators. It is also applied 13 to the lower sideband modulator, fed by the reference signal coupled o ff the transmitter source. This modulator yields the proper offset needed to generate a signal of 1.08 GHz + harmonics in the receiver.

This modulator is of the phase shift type with a 3 stub tuner on its output and achieves 35 dB of suppression of c a rrie r and unwanted sidebands.

The received signal is mixed down to the 2nd I.F. of 278 KHz and both the test and reference signals at this frequency are applied to the Hewlett Packard 8413A Phase-Gain Indicator. The re lative phase of the test and reference signals is measured and the test signal applied to two envelope detectors which produce voltages linearly and logarithmically proportional to the amplitude of the received signal. Voltage outputs proportional to phase and amplitude are provided, and the phase in degrees and amplitude in dB are dis played on a meter.

Since a ll harmonics are mixed down to the same I .F . , the informa tion in each individual harmonic is not available as long as the target remains stationary. However, i f the target is moved, an interference pattern is produced between the signal from the target and the resid ual background or leak-through signal between transmit and receive antennas. This w ill appear as a complex variation in the output of the amplitude and phase detectors. If this variation in amplitude and phase is plotted vs target travel, a periodic waveform is obtained whose Fourier series components are proportional in amplitude and phase to the scattered return at the microwave harmonic spectrum. 14

To determine these Fourier components the complex received waveform vs target range distance is converted to digital form and Fast-Fourier-

Transformed in the computer.

I t is noted that i f a ll ten harmonics were properly weighted and transmitted simultaneously, an interference pattern which was a replica of the periodic ramp response waveform could be obtained.

This approach was not used for two basic reasons. First, the inter ference pattern is not sinusoidal for single lower frequency harmonics as desired because of spurious wall reflections, etc. which could not be eliminated. Fourier analysis of these interference patterns yields apparent content at harmonics which are not being transmitted.

Operating on a per-band basis permits this non-physical harmonic in formation to be disregarded. Furthermore, optimization of the meas urement range absorber panels, receiver sensitivity, etc. on a per- band basis yields improved measurement accuracy.

The target motion control system is illustrated in Fig. 5. It uses digitally controlled stepping motors for linear motion along the line of sight (bisector of the bistatic angle) and for rotation.

These motors in the gear drive system employed here move a t 800 steps/inch in linear motion and 160 steps/degree in rotation.

The instrumentation computer used in the system serves as a process controller and data recorder, as well as performing all of the algebraic manipulation required to calculate normalized fre quency domain data and the ramp response target signature waveforms.

The computer being used is a surplus IBM "Minimal Informer", 15

T rrrrrm

MOTOR STEPPING CONTROLLER MOTORS

POSITION COMMANDS

MINIMAL INFORMER COMPUTER

A/D CONVERTER

AMPLITUDE

PHASE RECEIVER | TRANSMITTER

Fig. 5—Target motion control system 16

o rig in a lly developed fo r Army fie ld use. A block diagram which

illu s tra te s the computer organization and the peripheral equipment

presently interfaced is shown in Fig. 6 . The operation and program

ming of this computer are more fu lly described in Appendices D

and E.

A block diagram which portrays the basic organization of the

primary computer program fo r the multi-frequency system is shown

in Fig. 7. Teletype instructions are decoded and executed by the

executive to control the program flow and choose the storage files

to be used by each subprogram. The subprograms, whose t it le s in

dicate their function, each perform a predetermined sequence of

operations which may include target positioning using the stepping motor controller, data recording using the A/D converter, data

storage or retrieval from the core storage files, etc. The final

output of this program is a lis t (or plots) of the normalized

complex harmonic scattering response co e fficien ts. A separate, much simpler program is loaded into the computer at the conclusion of a measurement run which plots the impulse, step, or ramp

response waveform fo r given harmonic frequency data. The computer core storage capacity is such that it will not hold both the meas urement program and the time-domain waveform p lo tte r program simul taneously.

Printouts of these two programs are included in Appendix B.

A flow chart illustrating the significant steps in a typical measurement run is shown in Fig. 8 . The initial portion of the sequence is a rapid series of data runs, one for each band, on CORE MEMORY CENTRAL* DISK MEMORY 4 0 9 6 DISK 20.5 MILLION G-BIT DATA ADDRESS 3 7 - BIT WORDS PROCESSOR CHARACTERS

DATA 3 7 - BIT WOROS DATA B-DIT CHARACTERS

CONVERTER

DATA O - B IT CHARACTERS

16-CHANNEL DEVICE ADDRESSABLE SELECTOR TELETYPEWRITER A/D (DIGITAL ANALOG CONVERTER INPUTS MULTIPLEXER)

TARGET DIGITAL ■*4------PEDESTAL TO TARGET STEPPING MOTOR PLOTTER PEDESTAL CONTROLLER

DIGITAL PAPER COMPUTER LINK TAPE READER TO ANOTHER MINIMAL INFORMER

Fig. 6— "Minimal Informer" computer block diagram. JMEASUREMENT_PROGRAM

EXECUTIVE IINSTRUCTIONS SUBROUTINES AMP 1 RECORD RAW DATA SYSTEM PHASE 2 MEASURED DATA PLOT 3 FOURIER TRANSFORM 4 STORE PLOTTER 5 WRITE ON TELETYPE POSITION 6 ASSEMBLE ON COMPOSITE PEDESTAL 7 FREQUENCY DATA PLOT B CALIBRATE 9 ENTER FROM TELETYPE

DATA

CORE STORAGE

1 RAW DATA FILE 2 SPECTRUM FILE (14)

Fig. 7--Computer measurement program block diagram. NO TARGET REFERENCE TARGET TEST TARGET - O DATA NO A S-B BAND DATA D N A -B C NE CLBAIN DATA CALIBRATION ENTER BAND OATA D N A -B L DATA X— BAND BN DATA -BAND C BAND DATA D N A -B S BN DATA BAND - L BAND DATA D N A -B C BAND DATA D N A -B S OATA D N A -B X BAND DATA D N A -B X i. -Cmue-otold esrmn fo chart. measurement flow 8--Computer-controlled Fig. r r- ORE, TRANSFORML-BANOFOURIER, OATA STORE COMPOSITE COMPOSITE COMPOSITE ASSEMBLE e l b m e s s a ASSEMBLE O TARGET NO O TARGET NO CALIBRATE SUBTRACT SUBTRACT

WRITE the target itself and on reference targets whose results are

used to calibrate the system. For each run, the target is moved

X /2 at 1.08 GHz along the line-of-sight at a speed of approximately

6"/minute and returned to its starting location, while 128 evenly

spaced data points (magnitude and phase) are recorded and stored

in ‘the computer memory. A computer plot of the raw data fo r a

typical run (a IV ' sphere at C-band) is shown in Fig. 9.

ui RELATIVE Q MAGNITUDE A

.Ui

PHASE / - 9 0

-1 0 180 0 0.25 0.5 TARGET TRAVEL (WAVELENGTHS)

Fig. 9—Computer-plotted raw measured data.

The experimental procedure presently used with this system

provides calibration and accuracy checks on each target measurement

run. Measurements of the styrofoam column alone, and of a t least

two reference spheres accompany each target measurement run. Then the computer calibration sub-program subtracts the background data, normalizes the background-free data to produce exact complex cross- section values for the "reference sphere", and checks system ac curacy and lin e a rity by comparing calculated and measured cross- sectional data for the different-sized "check" spheres. A data run is accepted only i f its check sphere results are accurate .to within specifications presented in Appendix A.

The estimated accuracy of this measurement, based on long term reference sphere comparison measurements, is presented in

Table I .

TABLE I

Estimated System Accuracy vs-Frequency

Frequency (GHZ) Amplitude Accuracy (%) Phase Accuracy (deg)

1.08 ±10 ±10

2.16 ±10 ±10

3.24 ±10 ±10

4.32 ±20 ±20

5.40 ±10 ±10

6.48 ±10 ±10

7.56 ±10 ±10

8.64 ±20 ±20

9.72 ±20 ' ±20

10.80 ±20 ±20 22

Our experience has indicated at least two sources of variation in the measured data. The disturbance of the field configuration by the styrofoam support seems to affect the X-band measurements. Positioning of the target on the top surface of the column can affect the return by as much as 10% at the higher frequencies. "Long-term" d rift, caused by repositioning of absorber panels, pedestals, etc. for other measure ments being performed in our anechoic room, is the second facto r. On a given day, re p e a tib ility of the measurements range ty p ic a lly from

3% in amplitude and 3° in phase at the higher frequencies to 1%, 1° at the 'lower frequencies, which is considerably better than the long term re p e a tib ility obtained fo r a complete data set.

A series of ten-frequency complex spectral response measure ments on representative targets were made for this study. The specific metallic targets, which are detailed in accompanying fig ures, are:

1. a 2:1 circular cylinder, Fig. 10.

2. a 2:1 circular cylinder with a spherical cap, Fig. 11.

3. A 2:1 circular cylinder with a conical cap, Fig. 12.

4. A 2:1 circu lar cylinder with a smaller 1:1 cylinder

on one end, Fig. 13.

5. A cube, Fig. 14.

6 . A 60° cone, Fig. 15.

7. A half-spheroid, Fig. 16.

8 . A 3:1 sphere-capped cylinder with a side-mounted stub,

Fig. 17. L/., 4

•Fig. 10—2:1 circular cylinder model. Fig. 11—Sphere-capped cylinder model

Fig. 12—Cone-cylinder model Fig. 13—Step-cylinder model. 60 '< k

Fig. 15—Cone model.

7.5 cm

5 cm

15.2 cm 17.7 cm

Fig. 16—Half-spheroid model. Fig. 17—Large sphere-capped cylinder model. 25

A set of metallic spheres with diameters of 1/2", 3/4", 1",

1 -1 /4 ", 1-1 /2", 1-3/4" and 2" were also measured and used as c a li bration references during this program.

Complex spectral return data for the measured targets are pre sented in Appendix A, where the signal magnitude is the square-root of echo area, in centimeters, and the phase reference is the geo metric center of the object. Scaling can be used to apply these data to other targets of identical shape but different size from those measured. For a target object N times as large as our measured object, the magnitudes are multiplied by N to yield data on the larger object for frequencies which are reduced by a factor of N.

The phase values remain unchanged. Thus, i f the dimensions of the targets in Figs. 10-17 were in feet rather than centimeters, the square root of echo area would be given in fe e t rather than centi meters, at frequencies from 35.43 MHz to 354.3 MHz.

B. Approximate Ramp Response Waveforms

The ramp response signature of a target FR{t) is defined as its time-domain backscattered signal at a distant observation point in response to a traveling electromagnetic ramp discontinuity.

The ramp response signature is the second integral of the time- domain impulse response, F j{ t ) , which is related to the fa r -fie ld frequency-dependent phasor response G(jco) by the transform p air:

0 ) = -j" Fjft1) dt1 0

1 26

(2) Fj(t') i

■•00 where t 1 - t - r/c, c is the speed of light. G{jw) is normalized so that the radar cross-section of the scatterer is given by '* P a = tt |G(jto) | • Thus, the ramp response function is related to the phasor response by

»CQL

The ramp response signature of any object is essentially zero after some time interval TR, so that a periodic train of ramp ex citations w ill obtain a valid periodic ramp response signature i f its period T is greater than TR. The periodic ramp response sig nature can be expressed as

(4) R(t) =[ I 6 (t-nT) L n=-°° where * symbolizes convolution, and fi(t) is the unit Dirac delta function. Thus the related spectrum is

(5) Gp( ju) = f ■ S j j i . 27 which is a periodic sample of the original spectral response at the repetition frequency F s y of the periodic excitation. The measure ment facility obtains values A^/(tn for complex ,/a* These yield

known values of G(jw) = — An for the first 10 (n s 1,2,***,10) 'Tv periodic samples of the sampled spectra of Eq. (5). Therefore, the periodic ramp response R(t) can be expressed in a Fourier series using the measured data as

10 A (6 ) R(t) = N J • — g cos + ^ k=l ,/jTn where u0 = (2 ir)(l.0 8 ), i f t is measured in nanoseconds, fo r our system. •

Thus, the measured data are used to construct a 10-frequency Fourier series approximation to the ramp response signature of an object in response to a periodic ramp excitation occurring at a frequency of r 1.08 GHz.

The time domain ramp response FR(t ) can be normalized to obtain a waveform which has units of area vs distance, and which w ill be correlated with times the target cross-sectional area.

With this normalization the approximate waveform is related to the measured data by

10 A / (7) R(x) = N I ~ cos (n + n=l n V o where

a f o *o = 2tt = 2ttcT" = 27,7 cm» x = distance in cm

i 28

fo r a 1.08 GHz fundamental frequency. The value of N is fr- j 'qq

for the normalization described and the fundamental frequency used.

The corresponding periodic electromagnetic excitation signal for

the signature waveforms is

(8 ) E j(x) a \ cos ( n ^ 1 n=l n \ 0 /

Some representative ramp response waveforms fo r various

target objects are shown in Figs. 18 through 25. The waveforms

show one period of the periodic ramp response fo r excitation a t a

1.08 GHz fundamental frequency. S p e c ific a lly , the waveforms correspond to:

Fig. 18; a: 2:1 cylinder (Fig. 10) at endfire.

b: 2:1 cylinder at broadside.

Fig. 19; a: sphere-capped cylinder (Fig. 11) a t nose-on.

b: sphere-capped cylinder at broadside.

c: sphere-capped cylinder at ta il-o n . CM O • Fig. A a: cone-cylinder (Fig. 12) at nose-on.

b: cone-cylinder at broadside.

c: cone-cylinder at tail-on.

Fig. 21; a: step-cylinder (Fig. 13) at nose-on.

b: step-cylinder at broadside.

c: step-cylinder at tail-oh. i * Fig. 22; a: cube (Fig. 14) at broadside.

b: cube a t 45°. 29

Fig. 23; cone (Fig. 15) at nose-on.

Fig. 24; half-spheroid (Fig. 16) at nose-on.

Fig. 25; large sphere-capped cylinder (Fig. 17) with stub

n and j l to E -fie ld , nose-on incidence.

Of course the ramp waveforms may also be scaled sim ilarly to the spectral data. Multiplication of the distance scale by N and the . 2 amplitude by N yields the ramp waveform for a target N times larger than the measured sample.

The waveforms of Figs. 18 through 24 represent objects which are small enough that th e ir ramp response duration is less than the fundamental period. Hence, the waveforms are considered to be v a lid , band-limited representations o f the ramp response wave form. The response fo r the large sphere-capped cylinder target model has a duration which is longer than the period of the incident waveform. Thus, the responses fo r successive illum inating pulses overlap and the resulting periodic waveform does not resemble the ramp response signature Fr ( t ) . The waveforms of th is object, shown in Fig. 25, definitely are characteristic of the object, and the orientation of the stub is indicated by the measured waveforms. How ever, the geometrical features of the valid ramp response do not hold in th is instance. DISTANCE (cm) | (b) ! * t !

(cm2} Fft (cm2} 4 0 4: 2 2 i. 821 yidr ap epne waveforms. response ramp cylinder 18—2:1 Fig. 10 — HORIZONTAL VERTICAL 5 0 5 ( 0 ) ENOFIRE BROADSIOE 10 30 I f 31

NOSE-ON HORIZONTAL I VERTICAL j

I I

(a)

BROAOSIOE

/ / f / \\ t / t - \ / /,

- . , 1 ______I ... .. 1 1 . (b)

TAIL-ON

u£

5 0 5 10 DISTANCE (cm )

(C ) ' i ' ‘ ..... Fig. 19—Sphere-capped cylinder ramp response waveforms. 32

NOSE-ON ------HORIZONTAL — — VERTICAL

1 1 1 • 1 (a)

BROADSIDE

«# £ Km*o uf

TAIL-ON

5 o • p *

10 5 0 5 10 OISTANCE (cm) (C)

Fig. 20—Cone-cylinder ramp response waveforms. 33

NOSE-ON ------HORIZONTAL __ ------VERTICAL

1 1 1 1 (a)

BROADSIDE

U oB lLK

- 8 (b)

TAIL-ON

- 5 OISTANCE (cm)

(C)

Fig, 21—Step-cylinder ramp response waveforms. ( cm*) Fo ( cm*) I 1 I _ - 1 S 0 5 0 -S -10 i. 2Cb rm rsos waveforms. response ramp 22—Cube Fig. VERTICAL HORIZONTAL ITNE (cm) DISTANCE (b) > a J JI

1 1 F BROADSIDEOFF A IG 45* FACING BROADSIDE 10

S ( cm2 ) F# ( cm*) — — i. 4Hl-peod ap epne waveforms. ramp response 24—Half-spheroid Fig. 1 -SO 5 10 5 O S - -10 ------1 1 10 i. 3Cn rm rsos waveforms. response ramp 23—Cone Fig. VERTICAL HORIZONTAL VERTICAL HORIZONTAL —5 DISTANCE { cm) { DISTANCE DISTANCE 0 (cm)

... % INCIDENCE NOSE-ON NOSE—ON INCIDENCE 5

i I \ 10 35 36

NOSE-ON INCIDENCE STUD HORIZONTAL STUB VERTICAL

6 —

10 5- 0 5 10 DISTANCE (cm)

Fig. 25—Large sphere-capped cylinder ramp response waveforms. 37

C. Correlation Between the Ramp Response and Geometrical Target Features

The possible correlation between the ramp response signature and the target cross-sectional area vs distance along the line of sight, A{x), was f i r s t suggested by Kennaugh and M o ffa tt.D 3 ] An

electromagnetic analysis using a physical optics approximation predicts that the normalized ramp response is equal to -1/ t t A(x) ahead of the shadow boundary, in the "visible" region corresponding to the forward portion of the ramp response waveform. Calculation of the complete waveform fo r simple shapes has shown th at this re latio n ship holds approximately in the shadowed portion of the waveform also. The function equal to -1/ t t times the actual transverse cross-sectional area vs distance along thfe line of sight is de fined as the "p ro file function" fo r this study. The imaging tech nique to be described uses profile functions as its input data.

This section discusses the approximate profile function derived from measured radar data, resulting in some general conclusions on the characteristics of images derived from the measured data.

Some other comments on the general characteristics of the ramp responses of the target models are included. These character istics are not used in the imaging and are hence not analyzed, but th e ir existence may aid more advanced imaging techniques or serve as keys for further electromagnetic analysis of the ramp response signature. 38

An illu s tra tiv e comparison of the ramp response waveform and

actual profile function for an endfire vidw of the 2:1 circu lar cylinder is shown in Fig. 26. It is seen that the use of ten fre quency samples rather than an in fin ite set results in a band- limited approximation of the profile function, with finite rise time and some ripples related to the highest frequency sample used.

This implies that the images derived from measured data w ill have no sharp corners, and structural detail is expected to be somewhat smeared.

Figure 26 also demonstrates that the la tte r portion of the ramp response, corresponding to the shadow region for that particular view, is a less accurate approximation of the profile function.

Figure 27 shows the ramp response of the step cylinder a t endfire where the small cylinder lies completely in the shadow region.

It is seen that the small cylinder causes an appropriate change in the ramp response compared to the 2:1 cylinder, but that the agreement between the p ro file function and measured ramp waveform is worse than fo r the leading edge of the waveform. Therefore, i t is expected that image regions corresponding to shadow regions of the experimental profile functions used w ill be characteristic but less accurate representations of the target shape.

The ramp response waveforms fo r a broadside view o f the 2:1 circular cylinder shown in Fig. 28 illustrate a variation with respect to polarization which is not predicted by a physical optics analysis. A ll measured waveforms fo r oblong objects made during 39

this study agree best with the profile function when the E-field is

perpendicular to the major axis of the target silhouette. Such be

havior seems reasonable if one were to use a multipole analysis of

target scattering for resonant range frequencies. If sets of multi -

poles were aligned with the principle axes of a quasi-ellipsoidal

shape, the observed polarization behavior would imply th at the multi -

pole moment magnitudes are proportional to the body dimensions along

the principal axes. An analysis of this type is not included here,

but seems a worthwhile research topic. For this study, ramp wave

forms with E perpendicular to the silhouette major axis will be

used to obtain approximate profile functions.

Analysis of the ramp response signature shows that the value

of its integral over all time is proportidnal to the Rayleigh

coefficient, and hence to target volume. The integral over one i period of the measured ramp response waveforms in th is study is

polarization sensitive, similar to the waveform amplitude previously

discussed. Furthermore, the ratio of Rayleigh coefficient values

for E parallel and perpendicular to the silhouette major axis is ap

proximately proportional to the aspect ratio of the silhouette for

the targets of this study. This Rayleigh coefficient information may be useful in the future for normalizing the sensitivity of

radars at different look angles to obtain consistent ramp response data for a single target. Also, use of polarization information to

estimate silhouette orientation at each look angle is a technique

for estimating the dimensions and orientation of the target which deserves further study. 1 40

Another feature of the measured waveforms is that the magni tude of the ringing following the main response region seems in dicative of the correlation between the ramp response and the profile function. It is seen that the ringing is more pronounced in the waveforms of Fig. 28 than for Figs. 26 or 27, and the agree ment between the measured waveforms and p ro file function in Fig. 28 is correspondingly degraded. Further study of this feature might lead to techniques for modifying the main region of the ramp response to better approximate the p ro file function on the basis of its general shadow region characteristics. i

RAMP RESPONSE CROSS-SECTIONAL AREA x ( - 1 )

E o

c u.

- 5 DISTANCE ( cm ) Fig. 26—Cross-sectional area times (-1/ t t ) vs ramp response for 2:1 cylinder, endfire orientation. STEP CYLINDER RAMP RESPONSE 2 M CYLINDER RAMP RESPONSE AREA x ( - • £ ) FOR STEP-CYLINDER

tl.

1 -I J \ t I

- 1 0 - 5 0 5 10 DISTANCE (cm)

Fig. 27—Cross-sectional area times (-1/ t t ) vs ramp response for step-cylinder, backfire orientation PO (2:1 cylinder ramp included for reference). i I i ! i i i ( cm2) —2 0 1 - Fig. 28—Cross-sectional area times times area 28—Cross-sectional Fig. or : clne, rasd orientation broadside cylinder, 2:1 r fo 5 - DISTANCE (- 1 (cm) / t t ) POL. (0) HORIZONTAL ETCL <> POL. () VERTICAL vs ap responseramp R A ( ) AREAx (— AP RESPONSE RAMP AP RESPONSE RAMP CHAPTER I I I

THE APPROXIMATE LIMITING SURFACE TECHNIQUE FOR IMAGE GENERATION

We now describe a "limiting surface" technique for obtaining

a three-dimensional image of a target,using the profile function

or the ramp-response signature a t three orthogonal look angles as

input data. Several assumptions on target shape parameters are

used along with the input data to obtain the approximate image.

A figure of merit is proposed for objective evaluation of image

consistency. The determination of virtual profile functions from

the measured ramp response data of Chapter I I is discussed, and a

series of isometric views are presented to illustrate the effect of an arbitrary scaling factor upon the images obtained.

A. An Imaging Technique

A "target characteristic function" P(x,y,z) suggested by Bojarski[143

is defined for a specific point in space {x-],y-|,z^) as:

(9) P(x.j ,y.| ,z.j) = 1 if (x

« 0 i f (x-j ,y-j , 2-j) is located outside of the target.

The reference frame for the coordinate system (x,y,z) may be arbitrary. However, a reference frame whose origin is at the geometric center of the target and which is aligned with its 45 principal axes can considerably simplify the form of this function.

An ideal imaging technique w ill determine.a three-dimensional target characteristic function P(x,y,z) whose reference frame origin will be at the center of mass (assuming constant density) of the target and specify the alignment of the principal axes of the target with respect to the radar line of sight.

P(x,y,z) contains sufficient information for defining the pictorial image of the body at one or more arbitrary viewing angles.

An optimum visual format for presenting the image information w ill not be attempted here. An isometric view has been chosen for visual presentation of images in this study. The reason for this choice is that an isometric view, although it really presents only two- dimensional information, s t i l l gives a three-dimensional effect in a single view. Three orthogonal views might convey more three- dimensional information, for instance, but would also be more cumbersome for human interpretation.

The input data for this technique provide geometrical param eters which can be inferred accurately from the target profile function or approximately from the virtual profile function

(ramp response) at three orthogonal look angles. S pecifically these include:

A. Cross-sectional area vs distance along the line of

sight.

B. Total object volume.

C. Object length along the lin e -o f-$ ig h t. 46

The general approach is to calculate one "approximate limiting target characteristic function" Pn(x,y,z) and an associated limiting surface for each look angle, using the above parameters. Specifically, the three characteristic functions and limiting surfaces are denoted by Pv{x,y,z), P„(x,y,z) and P,(x,y,z) where the reference frame is a y z aligned with the three orthogonal look angles. Each one of the lim itin g surfaces supposedly encloses the target with the tightness of fit varying with target shape and look angle. The choice of an appropriate surface which encloses a wide variety of shapes with a satisfactory f it is an important step in the technique which will be discussed.

It is known that the profile function for a particular target and a p articu lar look angle is unique, but the converse is not tru e.

Many shapes have the same profile function along a given axis; fewer may have the same profile functions along several axes. Also, a generally applicable surface assumption cannot be a perfect f i t fo r a ll p articu lar shapes. Thus, the lim itin g surface and its as sociated Pn(x,y,z) constructed from a single target look do not in general yield a good approximation of the target shape, but by calculating an improved target characteristic function which is the union of the Pn(x,y,z)'s for the three look angles, more satisfactory images are obtained. Specifically, the final target characteristic i , function

(10) P(x,y,z) = Px(x,y,z) U Py(x,y,z) U P 2 (x ,y ,z ) or 47

(11) P(x,y,z) = 1 if: Px(x,y,z) = 1, Py(x,y,z) * 1, Pz(x,y,z) * 1, •••

= 0 otherwise.

The corresponding fin a l lim itin g surface defines the volume which is common to all the limiting surfaces for the look angles used.

The basic technique for obtaining Pn(x,y,z) will be described with the help of the idealized p ro file function R(X) of Fig.. 29.

t 1 I 1 t 1 1 1 0 -i - 3 - 4 X - DISTANCE (cm)

—

Fig. 29—Profile function, R(x), for 4 cm cube 48

This waveform has amplitude equal to -1/ t t times the cross-sectional area of the target vs distance along the line of sight, which is defined as A(x). The specific target for the profile function of

Fig. 29 is a 4 cm cube, with a look angle perpendicular to a face.

A drawing of the cube correctly oriented in the reference frame is shown in Fig. 30. Note that the cube is centered at the origin of the reference frame. The form of the profile function implies:

Fig. 30—Target cube and reference frame, isometric view i.e ., the cross-sectional area of each target "slice" (x=xQ) is specified by the input waveform, although the outlines of that slice are unknown. Some lim itin g contour which gives an approximate outline of the slice must now be chosen.

The lim itin g contour assumed for this technique is a hyper bola, which bounds a set of simple shapes a ll having area A(xQ) but with varying aspect ratio (length/width), and which are all centered on the x axis (y=z= 0) with their major axes oriented either vertically or horizontally. If the contour is defined by the relation

(15) Px(x 0.y ,z ) = 1 when C|yz| < -tr R(xq)

= 0 elsewhere and C = 2tt, then the hyperbola bounds a ll horizontally and v e rti cally oriented ellipses of area A(xQ) = - tt R(x0) , as in shown in Fig. 31. If the contour is defined by the relation

(16) Px(xQ,y,z) = 1 when C|yz| < - R(xQ)

- 0 elsewhere V.

Fig. 31—Hyperbolic limiting contour, C = 2it. 51 and C - 4, then the hyperbola bounds all horizontally and vertically oriented rectangles of area A(xQ) = -ir R(xQ), as shown in Fig. 32. It is seen that choice of the scaling constant C varies the size of the hyperbolic contour, without changing its shape.

This constant w ill be chosen la te r on the basis of the imaging per formance of this method.

The total limiting surface is made up of several of the above contours, one for each value x=xQ. An isometric view of the contour in the plane x - 2, and with C = 2tt, is shown superimposed on the actual outline of the cube at x a 2 in Fig. 33. Because of the form of R(x) in Fig. 29, all limiting contours in the planes x = xQ, 2 >_ xQ -2 are the same as the one shown in Fig. 33.

This process produces the to ta l lim itin g surface shown in Fig. 34 that represents the cube for one angle of incidence with contours at x a -2, -1, 0, 1, and 2 specifically drawn. It is noted that parts of the surface and hence the limiting contours are shadowed in this view. Shading is used in the figure to heighten the perspective.

A computer-generated plot of this cross sectional shape, with more contours and the "tails" terminated at y - ±11 and z = ±11 is shown in Fig. 35a. Note that the use of closely spaced contours automatically provides shading to give a three dimensional effect. The corresponding single look-angle target characteristic function, for the x look angle, is

(17) Pv(x,y,z) a 1 when |2nyz| <.16, 2 >. x >_ -2 52

1—

Fig. 32—Hyperbolic limiting contour, C = 4. z

DIMENSION UNITS 1

Cl Fig. 33—Limiting contour vs cube outline in the plane x « 2. co c o n t o u r n u mb er ing © x = 2

Siting surface for 55

X-AXIS LOOK ANGLE Y-AXIS LOOK ANGLE

(Q) ______Lb.L_......

FINAL IMAGE Z-AXIS LOOK ANGLE (COMBINING g,b,c) (c ) (d)

Fig. 35—Limiting surface image construction for a cube. 56 where C = 2Tr,is the scaling constant value used.

If the waveform of Fig. 29 was also obtained for a y-axis look angle, the y-axis limiting surface of Fig. 35 would result.

The corresponding target characteristic function,

(18) Pv(x,y,z) = 1 when | 2 t t x z | < 16, 2 >_y ^ - 2

= 0 elsewhere

F in a lly , a z-axis look angle, using the same input waveform, would result in the 2-axis limiting surface of Fig. 35, with

(19) P2(x,y»z) = 1 when |2ttxy | < 16; 2 >_z >_-2

= 0 elsewhere

It is noted that while none of these single look-angle surfaces fits the actual target satisfactorily, there are regions of each that are relatively accurate. The faces perpendicular to the look angle are well-defined in each case; i.e ., the front face can be discerned from the x look-angle surface, the side face from the y look angle, and the top face from the z look-angle surface.

Combination of the surfaces is thus expected to y ie ld an improved image. The union o f a ll three surfaces results in the fin a l image of Fig. 35. The final characteristic function

2Tryz <16 2 >_ x >_ -2 2irxz <16 2 >_ y ;> -2 2 vxy Jl 6 2 >. z >. -2 = 0 elsewhere.

The cube^like nature of this image is obvious. i A 4 cm diameter sphere serves as another example fo r the imaging process. The profile function for this target is shown in Fig. 36. 57

I I 0 - I - 3 - 4 i DISTANCE (cm)

—4 }

I . Fig. 36—Profile function for 4 cm diameter sphere.

Computed plots of the limiting surfaces for the x-axis, y-axis, and

z-axis look angles are shown in Fig. 37, parts a, b, and c. The

final image for this target is shown in Fig. 37, where

12iryz | <_t t ( 4 - x 2 ) 2 >_ x >_ -2 (21) P(x,y,z) = 1 12-irxz | <_ Tr(4-y2) 2 ^ y >_ -2 k 12irxy 1 <. tt(4-Z2) 2 ^ z ^ ~2

s 0 elsewhere.

A relatively accurate image is seen to result in this case also.

A lis tin g o f the computer program which produces images on the

digital plotter using the above technique is presented in Appendix

C. The program basically plots contours in the planes x-x 0+n,

n*l,2,3,4**« in isometric orthographic projection using two shadowing 58

1 X-AXIS LOOK ANGLE Y-AXIS LOOK ANGLE ( a ) (b )

S < f

FINAL IMAGE Z-AXIS LOOK ANGLE (COMBINING a,b,c) ...... (C ) .... (d )

Fig. 37--Limiting surface image construction for a sphere.

4 59

algorithms for the top and bottom image portions. As can be seen, the

subjective effect of this process is an isometric target view with

simulated optical illum ination coming from a source located on the

x axis.

B. Image Input Waveforms from Measured Data

The procedure for obtaining appropriate cross-sectional area

functions (virtual profile functions) from the measured data of

Chapter II will now be described. The starting point is the normalized ramp response waveform described in Chapter I I . Assuming

a valid ramp response, its shape was shown to be approximately equal to - 1 / tt times the area function with the following exceptions:

1. D.C. level is shifted

2 . regions outside of the "main response" have no

significance

3. main response region may not be centered correctly

with respect to the reference frame.

The waveform modification process corrects fo r the above features in order to obtain a valid approximate profile function.

■Starting with the waveform of Fig. 38, the D.C. level is shifted by the operator using the in teractive computer program IMSTRS, lis te d in

Appendix C. The operator takes into account the average waveform shape ju s t before the main response region and precursive ripples in arriving at an estimated D.C. shift value, with the result shown in Fig. 39. 60

ORIGINAL RAMP WAVEFORM I —

N e o u

-I

,.J J . ______1 I_____ -10 - 5 0 5 10 DISTANCE (cm )

Fig. 38—Original ramp waveform.

CHANGE D.C. LEVEL SO LEADING EDGE STARTS FROM ZERO

CM 0

-1 0 -5 DISTANCE (cm)

Fig. 39—Modified ramp waveform. D.C. level s h ift. Next the main response region of the waveform is centered.

The imaging process assumes a coordinate value of zero in the center of the period of the waveforms, and also assumes that the center of mass of the target is located at the origin of the reference frame. In order to satisfy these assumptions, the wave form of Fig. 39 is shifted left or right so that the centroid of the main response region is centered, resulting in the wave form of Fig. 40.

I f the waveform of Fig. 40 was used fo r input to the imaging process, ripples before and a fte r the main response region would cause extraneous blobs to appear surrounding the target image.

The operator assumes that these ripples are non-physical, and chooses a forward blanking lim it to eliminate the precursive ripples resulting in the waveform of Fig. 41. Then the imaging computer program blanks out all waveform regions Outside of the firs t two zero crossings of Fig. 41, resulting in the final waveform of Fig.

42. The modified ramp response shown in Fig. 42 is used as the virtual profile function R(x) in all experimentally derived images presented in Chapters IV and V. Since the la s t step of modification is done by the imaging program, however, the input to the program resembles Fig. 41.

C. A Q uantitative Image Accuracy Indicatbr

In the discussion of the imaging technique only visual sub jective evaluation was indicated in order'to evaluate the accuracy of the images derived. This section presents a quantitative indicator 62

CENTER THE MAIN RESPONSE REGION

-1 0 - 5 0 5 10 DISTANCE (cm)

Fig. 40—Modified ramp waveform, time s h ift.

ELIMINATE LEADING RIPPLES

-I

-1 0 DISTANCE (cm)

Fig. 41—Modified ramp waveform, elim inate leading ripples 63

ELIMINATE WAVEFORM PORTIONS OUTSIDE I — FIRST TWO ZERO CROSSINGS

. V - J

1 1 1 - 1 -- -10 -5 0 5 10 DISTANCE (cm) Fig. 42—Virtual profile function obtained from ramp response.

of image consistency which does not require a p rio ri knowledge of the target shape.

Quantitative evaluation of an image is based on the comparison of image profile functions along the three look angles to the input profile functions. For the cube of Figs. 29 to 35, the R(x) of the image is shown in Fig. 43, with the input R(x) from Fig. 29 dashed for comparison. Input and output R(x) for the sphere image of

Fig. 37 are shown in Fig. 44. In both of'these cases, because of symmetry, the output waveforms are the same for all three look angles.

Henceforth, the output waveforms w ill be denoted by R0 (x ), R0(y)»

RQ(z) and corresponding input waveforms by Rj(x), Rj(y) and Rj(z). RU) OF IMAGE

INPUT R U I

Fig. 43— Input and output p p ro ro file file functions functionsoutput fo r the cube image o f Fig. 35

R U) OF IMAGE i I N P U T Rl*J 1I I

— 3 -4 OISTANCE I cm) i i

— 4 I

Fig. 44—Input and output profile functions fo r the sphere image of Fig. 37. 65

For a pair Rj(x), RQ(x), a normalized error area value 1s defined as: oo

|Rj(x) - R0 {x) |dx 00

|Rj(x) |dx

00 This error value represents the difference area between the two waveforms divided by the total area under the input waveform. A single error indication representing all three look angles is defined as:

(23) E 4 K x + Ey + Ez: >

For some shapes, the error indication E has rigorous physical significance. Suppose that the image generated for a particular target lies completely inside or outside of a target, with char acteristic functions Pj(x,y,z) as compared to the actual character istic functions Pj(x,y,z). Then the total target volume

(24) V - JJjjpT(x,y,z)dx dy dz

" * J|Rj(x)|dx = ttJ |Rj(y)|dy = tt J|RX( z ) |dz, assuming correct input profile functions are used. The error volume between the image and the actual target shape is «

I jjj[P T(x,y,z) - Pj(x,y,z)I|dx dy dz|. For the image completely inside or outside of the target, 66

(25) n |Rj(x) - Rq( x ) | « |J D>T(xty,z)-PI (xfy,z)3dy dz|

Thus

(26) VER = 7T J|Rj(x) - RQ(x)|dx

||RI(x) - R0(x)|dx v

||R r (x)|dx

For the image completely inside or outside of the target, E =E B V * * FR Ez = using proof sim ilar to the above, so

In these cases, E represents the ratio of error volume between the image and actual target to total volume of the actual target. In cases where the image and target surfaces intersect, it is possible in drastic cases for the negative and positive errors to cancel in some planes x - x0 , and in general

(29) tt |Rj(x) - RQ(x)| ^ JjcPT(x,y,z,) - Pjtx.y.zJJdy dz .

For these cases, E may be regarded as indicative of but not equal to the relative volume error of the image.

For the cube and sphere images of Figs. 35 and 37, E values of 0.183 and 0.065, respectively were calculated using the above method. I t is obvious, a fte r observation of the images, that E is I

i an approximate indicator of the accuracy of the image which the eye perceives.

This quantitative error indicator will serve as a basis for objective evaluation of image accuracy in Chapter IV and for evaluation of image improvements in Chapter V.

D. Choice of a Scaling Constant fo r the Imaging Process'

In the description of the imaging technique, the scaling constant

C was used in the calculation of the limiting contours. The value of this constant was le ft unspecified in the description, and was chosen to be 2 ir in the images presented. Using the normalized error area value E, an appropriate value for this constant, to be used throughout the remainder of these studies, w ill now be chosen.

The choice of C w ill be based on the image accuracy fo r two shapes - the sphere and the cube. These two were chosen because the sphere is a smooth shape whereas the cube has prominent edges and tips, and both are simple shapes representative of the targets to be used in this study.

The cube and sphere images already presented show that this technique tends to chop off object corners, and introduce some bumps on smooth objects, and both of these characteristics are affected by C. Figures 45 and 46 show the images of the sphere and cube as C is varied from 4 to 2v. It is seen that nearly perfect performance fo r eith er shape is obtained a t the expense of accuracy for the other. Figure 47 is a plot of the error indicator E for the sphere and cube images as a function of the scaling constant C. It is seen that the errors are equal when C =5.72. This value of the scaling constant will be used henceforth for imaging in this study. The sphere and cube images fo r C = 5.72 are shown in 69

(a) C »2 tr

(b) C t

F ig . 45—Sphere and cube images, C = 2 tt, 5 .5 , 5.0. 70

(a) C - 4 .5

. V .V .^ v V ^ ft' i W^-ViX-

0 . 4 . 0

Fig. 46—Sphere and cube images, C - 4 .5 , 4 .0 , 5.72, 3

4 5 6 2 t SCALING CONSTANT -C

Fig. 47—E vs C for sphere and cube. I

CHAPTER IV

TARGET IMAGES USING THE LIMITING SURFACE TECHNIQUE

Radar images of several targets at various orientations are presented in this chapter to demonstrate capabilities of the tech nique presented in Chapter III. Input data are either calculated

(ideal) or measured ramp response-derived (virtual) profile functions.

Qualitative conclusions are given on the shape and orientation classes for which this technique yields satisfactory images.

A. Images Using Calculated Ideal Profile Functions

The images of Figs. 48 through 57 use calculated input data, and demonstrate the basic technique of deriving a three-dimensional image from the target profile function at three aspects. Several of these images w ill also serve as benchmarks fo r comparison with images derived from measured data or those produced after modifications on the basic technique. Each image is accompanied by a lin e drawing of the target object and a normalized error area value. The images in

Fig. 48 depict a cube as it is rotated in the yz plane. Rotation angles of e - 0°, 15°, 30°, and 45° from alignment in the reference frame are shown.

Figures 49 and 50 show a 2:1 prolate spheroid whose major axis is rotated in the xy plane with 0° <_ <|> <_ 90° in 15° steps.

72 73

(a) 9-0* E-0.I2B

(b) «m|9* E-O.IO

(d) 0 ■ 43* E« 0.161

Fig, 48—Cube images compared to lin e drawings, profile function input. 74

(a) * -0 *. E-0.125

(b) + -15*. E -0.114

(e) f -5 0 *, E >0.159

(d) f -4 5 *,’ E - 0.147

Fig. 49—2:1 prolate spheroid images compared to line drawings, profile function input. 75 i

(o) 4 ■60, I E - 0.139

(b) 4 ■ 75* ,E -0,114

Fig. 50— 2:1 prolate spheroid images compared to lin e drawings, profile function input.

> 76

Figures 51 and 52 show a 2:1 parallelopiped whose major axis is rotated in the xy plane in the same manner as the spheroid.

Figures 48 through 52 illustrate that the basic technique always results in symmetrical image approximations to non-aligned shapes, as will be discussed later. All images seem at least characteristic of the target object.

The images of Fig. 53 correspond to the cylin d rical objects of Figs. 10 through 13. The 2:1 cylinder, sphere-capped cylinder, cone-cylinder, and "step-cylinder" are depicted. Images in Fig.

54 show two views of a simulated rocket object whose main body is the cylinder of Fig. 53. The cylindrical nature of all these targets is well characterized, and the image variations are in dicative of the particular modification to the basic cylinder.

Figure 55 shows a 60° cone with its axis in the x-direction.

Figure 56 is the image for a wedge with its diagonal face forward.

F in a lly , the image of a "square doughnut" is shown in Fig. 57. , «$&•*

(a) *-o *(a) *, f 0.133

(b) ♦■13* £'0.16*

Fig. 51—2:1 parallelopiped images compared to line drawings, profile function input. 78

(a) +.«o*. E«o.2ie

(10 ♦■73", E -0.164

■(c) C-0.135

Fig. 52—2:1 parallelopiped images compared to line drawings, profile function input. 79

(a) E « 0.141

(b) E« 0.132

m x m

Fig. 53—Cylindrical object images compared to line drawings, profile function input. 80

(b)

Fig. 54—Simulated rocket images compared to line drawings, profile function input.

£ -0.155

Fig. 55—60° cone image compared to lin e drawing, profile function input. 81

E * 0.164

Fig. 56—Wedge image compared to lin e drawing, profile function input.

E - 0.469

Fig. 57—Square doughnut image compared to lin e drawing, profile function input. 82

B. Images Derived from Measured Radar Data

The images of Figs. 58 to 62 have been generated using experimental ramp response data measured as described in Chapter II and modified for this process to obtain a virtual profile function as described in Chapter III. The measured data for these shapes are the vertical polarization ramp responses shown in Figs. 18 through 24.

Shapes and orientations which yie ld good images from the p ro file func tion values were chosen for the most part, since the principal aim is to demonstrate the effects on the images caused by using information obtained from radar measurements.

E* 0.291

Fig. 58~Sphere image compared to line drawing, virtual profile function input.

Figure 58 shows the image for a sphere, using a calculated

10-frequency ramp-response waveform (as opposed to a calculated p ro file function). The reason fo r using a calculated input in this case is that spheres were used as reference standards in the measurement system, and thus the sphere measured results were found to conform to the calculated values.

Fig. 59—Cube images compared to lin e drawings, virtual profile function input.

{ a ) 2 'l CYLINDER . (b) SPHERE-CAPPED CYLINDER E-0.437 E« 0.402

Fig. 60—-Cylindrical object images, .virtual profile function input (compare to Fig. 53). 84

E - 0.377

Fig. 61—60 cone image compared to lin e drawing, virtual profile function input.

E - 0.366

Fig. 62—Half 2:1 spheroid image compared to line drawing, virtual profile function input. 85

The images in Fig. 59 depict a cube s ittin g on a face and sitting on an edge, with its front face perpendicular to the x axis.

Figure 60 shows experimentally derived images of the 2:1 cylinder, sphere-capped cylinder, cone-cylinder and step- cylinder comparable to Fig. 53. Figure 61 depicts a 60° cone and is comparable to Fig. 55. F in a lly , Fig. 62 is the image fo r a half 2:1 prolate spheroid, with its axis in the x direction.

C. General Characteristics of the Basic Imaging Technique

The figures in this chapter demonstrate that the technique yields images which are indicative of the gross shape characteristics o f a target. The images visually resemble the target shape in many in stances, and possess features which may be interpreted to indicate target character in less optimum cases. With a trained operator, this simple process may be a useful tool for some target identification applications.

Improvements in the images can be made, i f one uses a more sophisticated imaging procedure. Several types of image errors are attributed to the simple assumptions in itially made. The cor relation between these assumptions and image features is discussed here, and modifications to obtain improved images are discussed in Chapter V.

The assumed hyperbolic lim iting contour is the primary cause of error in Fig. 57. In the case of any doughnut shape, or any shape where the cross-sectional area may consist of more than one 86 part for some transverse cuts, the hyperbolic contour is grossly inaccurate. The contour chosen forces the image to resemble a shape with a solid interior. Figure 63 shows the contrast be tween the assumed contour and the actual contour for a transverse cut in the center region of Fig. 57. The hyperbolic contour method is applicable to "convex" objects, where the dot product between the local surface normal and the vector from the target center of mass is positive over the total surface of the body.

The theoretically infinite "legs" of the hyperbolic limiting contour are a principal cause of the extraneous edges and cusps which appear in many of the images shown. The input waveform and single look-angle limiting surfaces for the sphere, shown in

Figs. 36 and 37 illustrate the origins of these image features.

At distances where the input R(x) is comparitively small, as at the s ta rt of the sphere lim itin g surfaces, the lim itin g contour resembles an in fin ite "x" shape. The in fin ite legs of these

"x" contours are not completely eliminated in the combined surface, resulting in the cusps of Fig. 37 and elsewhere. An operator- defined lim it on the length of the legs of the limiting contours to alleviate this feature will be discussed in Chapter V.

Two assumptions in the basic technique cause the image errors for shapes which are not aligned with the look-angle reference frame, as shown in Figs. 49, 50, 51, and 52. First, the legs of the limiting contour were arbitrarily assumed to be aligned with the principle axes of the look-angle reference frame. It is 87 necessary to permit rotation of the hyperbolic limiting contours about their axis for objects of arbitrary orientation. In addition, the assumed axes for the limiting surfaces are inappropriate for objects which are not aligned with the look angle reference frame.

The center lines of the single look-angle limiting surfaces as defined are forced to be parallel to the look angle and to intersect the body center of mass. Thus, a ll the images demonstrate symmetrical characteristics, even for targets not symmetrical with respect to the look angle reference frame. The actual centroids of transverse slices of a non-aligned target trace out a center-line which may be a 3- dimensional curve, and is not parallel to the look angle in general.

Some modification of the center-line for the single look angle limiting surfaces is thus necessary to improve the image q u ality fo r non- aligned targets.

The use of a simple technique to better specify the rotational orientation of the hyperbolic contours and the centroid paths of the single look-angle limiting surfaces, and the effect this has on imaging performance, w ill be discussed in Chapter V.

D. Image Resolution of Target Features

The images in Fig. 53 are indicative of the detail resolution lim itatio n s which are caused by the assumptions used. The cylindrical nature of all the objects is evident and some differences between the images can be observed. However, the shape of the modification on the front of the cylinder is difficult to discern. Perhaps the cones used in Figs. 53 and 54 are identifiable. It is seen that 88

the images are sensitive to target shape differences even when the

target itself is not accurately represented. There are always dif

ferences in "angularity" and other shape characteristics between

the spheroid and square cylinder images of Figs. 49 through 52 which a trained observer could possibly interpret.

Effects which resu lt from the use of measured ramp response data are evident in all of the experimentally-derived images. The difference between the ramp-response and the actual cross-sectional

area waveform is greatest in the rear, or shadow regions of the input waveforms. Thus, a less accurate shape is seen in the rear regions

of the experimental images in almost all cases. Correspondingly

higher values of the error indicator E are also obtained for the ex

perimentally derived images. The region which should be most accurate

in these images is the front, top, right quadrant, since it is in the forward or visible portion of the ramp waveforms for all three orthog onal look angles. The isometric view chosen is thus optimum in the sense that the most accurate quadrant is also the most prominent, being the only quadrant fully in view.

Comparison of the images in Fig. 60 to those in Fig. 53 shows that the s lig h t differences between the shapes have v irtu a lly disappeared in the experimentally derived images.On the other hand, an experienced eye can detect the difference between the cone and the half-spheroid shape from their experimentally derived images in Figs. 61 and 62.

If the observer concentrates on the gross characteristics of the image, then there seems to be satisfactory correspondence between the normalized error area values and a subjective image accuracy

evaluation. As stated in Chapter I I I , however, subjective visual evaluation appears to be more sensitive to detail errors in the

images than the quantitative error indicator.

ACTUAL BODY OUTLINE IN CENTER REGION ASSUMED BODY OUTLINE BOUND IN CENTER REGION

/ \ / \ / \ / \ s ' ______— ■ *-* ------— — — — V. S \ / • \ /

Fig. 63—Body outline vs limiting surface outline in center region of square doughnut* CHAPTER V

IMAGING STUDIES - EXPERIMENTAL DATA INPUT SIMPLE MODIFICATIONS FOR IMPROVED IMAGES

The images presented in Chapter IV show that assumptions of the limiting surface technique cause errors for certain targets and target orientations. Simple modifications of the original assumptions w ill now be described, and applied to improve image quality. In each case, the technique modifications are operator controlled: input parameters which reflect initial estimates of gross object dimensions and orientations are used to obtain the improved images. The fin a l section of this Chapter illu s tra te s an iterative technique for improving image quality be reducing the normalized error estimate.

We now modify the single look-angle limiting surface defined in Chapter I I I . Combination of three single-look angle surfaces is done as before. Modifications include a limitation on the length of the legs of the hyperbolic limiting contour and a rotation and change of axis of the single look-angle limiting surface to obtain a better fit for arbitrary target orientations.

90 91

A. Modification of the Hyperbolic Contour Shape

The hyperbolic contour defined in Chapter III is an upper bound for constant area ellipses of aspect ratio from 1 to °°. How ever, the expectation of ellipses of very large aspect ratio is usually small, and requiring the contour to bound these shapes results in cusps, as discussed in Chapter IV. A modification of the contour so that it bounds only ellipses of less than a chosen aspect ratio w ill now be considered.

The basic technique is to circumscribe on the original limiting contour a circle whose radius is a function of cross-sectional area and the aspect ratio lim it, and define a new limiting contour as the union of these two shapes. I f the cross-sectional area is A fo r the contour shown in Fig. 64 and aspect ratio lim it is L, the radius of the circle is given by

(30) r = J ^ ^ * where 5.72 is the contour scaling constant value C. Using this definition, an aspect lim it value of 1 results in a limiting circle which just fits into the original limiting contour. Some limiting circles for various values of L are shown in comparison with the hyperbolic contour in Fig. 64. The shapeof the modified limiting contour, for L = 2, is shown in Fig. 65. The single look-angle target characteristic function for this modified surface is (as suming x-axis look angle)

r 92

L -16

L* 9 L«4 L=2 L-l

Fig. 64—Limiting circles vs L. 93

Fig, 65—Modified limiting contour, L = 2,

5.72 yz| <_ - ttR( x ) (31) Px(x,y,z) = 1 ' 5.72 (y 2 + z2 ) < -2 ttL R(x)

Pv(x,y,z) = 0 elsewhere. 7\ The effect of aspect ratio limiting on a sphere image is shown in Fig. 66. A perfect image is obtained when L = 1.

Figure 67 shows the modified cube image with L = 1 and 2. I t is found that the small cusp error is removed fo r v irtu a lly any choice of L for this shape. Figure 68 shows the effects of cusp * elimination on several measured target images. An improved image results in virtually all cases, and the improvement is reflected in smaller values of the error indicator E.

B, Initial Target Orientation Estimation

Suppose that an estimate is made by the operator of a spheroid which encloses a given target. Once orientation and aspect ra tio of the spheroid are specified, the orientation and center-line l l l f

» f p • / f t * V - *— * X

(o) L»l, E -0.029 (b) L*2, E* 0.078 (C) L * 3 , E« 0.0 9 8

(d) L-4.E-0.I08 (t) L* 10, E* 0.125

Fig. 66—Sphere image vs L, profile function input. (a ) L- I , E * 0.1537 1 (b ) L - 2 , E - 0.141 Fig. 67--Cube image vs L, profile function input.

(a ) 2 !l CYLINDER (b ) HALF SPHEROID L -2 .5 , E - 0.324 L-2 , E-0.200

Fig. 68—Target images with cusps removed (compare to Figs. 59, 60, 61, 62). 96 alignment of the limiting surfaces can be modified to fit the spheroidal shape. In order to sim plify the computer program the orientation of the major axis will be limited to the xy plane.

A solution for the shape and position of the cross-sectional slices for such a prolate spheroid is presented firs t.

A top view of a prolate spheroid which defines the pertinent reference frames is shown in Fig. 69. The x 'y 'z ' frame is aligned with the spheroid axes, while the x y z frame is the look angle reference frame. An x-axis look angle will be assumed. The problem is to solve for the shape and position of a yz-plane cut for an arbitrary distance xQ along the line of sight. The center of such a slice will specify a modified center-line for the x axis limiting surface.

The two reference frames are related by

(32) and

(33)

The prolate spheroidal surface is specified by

(34) 97

PROLATE 4 SPHEROID t

X I X

Pig. 69—Rotating spheroid geometry. In the x, y, z frame, this becomes

(35) (x cose + y sin e)2 + (-x sin 8 + y cos e)2 t z^ a]

( 3 6 ) x 2 f s s p . + + / + SjAj +

+ 2xy sin e cos 0 f ^ ) + ^ = 1 \ a b / b

Now let x = xQ in order to define a particular transverse

s lic e . Then

z2 (37) / f i ^ S . ♦ c p !a j + 2yX() s i n e cos 7

..2 ( cos2e , s i n ^ = 1 " x° \ i r i r ) Now le t

xQ sin e cos e ( ■ ? • ' • ? ) (38) 7 = y + T ~ r ? ( sin e + cos b2 ' Then \

an£* / \ 2 xQ sin 0 c o s e Q j- ^ x2 sin 2e cos2e ^ -

(40) y2 = y2 - 2y / s™ 2e + co^ e~^ ( s i^2e \ c° s2e f V a2 b2 / V a2 b2 y

Substituting Eqs. (39) and (40) into Eq. (37) yields

.2 . 2, (41) y2 (5™-° + £2|_2A-2yx0 sin 0 cos 0 -4 ) \ a b' «\a b /

*o s1nZe cos2e( ^ - - ^ 2 ) + ------X------X i sin 0 , cos 0 \ V 7 ~ I 2 / .2 -„2 2. ( x 2*£ s i"t0 ^ ( 7 - br ) +2yx0 sin e cos ef-^-77 ) “ / \ r— 2, + Va^ b^V /sin 0 | cos a \ I" ? b2 1

z2 _ , i f cos2o , sinZ< 7 - 1 - xo l T 2 - + T T - ) Simplifying,

xz (42) y2 ^cos20 + ^ sin 20 ^ + z2 - b2 - g- a (sin20 + ^ cos2©)

I t is seen that Equation (42) is the equation of a symmetrical

ellipse which, for the prolate spheroid case (a > b) has its major 1 ■ axis in the x y plane, an aspect ratio of ■ : 1. 2 / 2 :'bu _j_2 \C O S 0 + sin 0 ~ 2 100 and a major axis dimension of

1 2 b

Also, y - y defines the offset of the axis of the limiting surface vs xQ for correct bounding of the spheroid.

The imaging program IMAG4 u litiz e s the above information to modify the axis of both the x-axis and y-axis look angle limiting surfaces. The angle (+e) of the spheroid with respect to the x axis look angle, and the inverse spheroid aspect ratio (b/a) are typed in and used to calculate y for the x-look angle limiting surface and the related angle (e- 90°) is used to calculate x for the y look angle limiting surface. i The program IMAG4 modifies the z-axis limiting surface by rotating it by the angle e about the z axis. Also, for a given aspect ratio lim it L, a properly aligned elliptical lim it is used for the z-axis surface, so that Pz(x,y,z) satisfies

= 0 elsewhere where x',y' In the above equation are aligned with the spheroid axes as before. 101

The images for the rotated prolate spheroid and 2:1 parallelopiped using this modification are shown in Figs. 70, 71, 72, and 73. Direct comparison of these images to those of Figs. 49, 50, 51 and 52 i l lustrates the improvement which has been made. Not only are the modi fied images indicative of target orientation, but the two shapes are more easily distinguishable using the improved technique. Error area values for the z look angle could not be calculated in the modified program due to computer space lim itatio n s. Therefore, the E values presented are the average fo r x and y look angles only. Corresponding error indicator values for the images of Chapter IV are shown in parentheses to illu s tra te the quantitative improvement which has been made.

C. An Interative Procedure fo r Modifying the Basic Technique

The images in parts A and B of this chapter demonstrate the improvement which can be obtained i f the imaging procedure is supplied with some in itia l information on expected target aspect ratio and orientation. Such information is not available initially fo r unknown targets, however. This section suggests one possible technique fo r supplying those constants.

The idea is to begin with the image produced by the basic technique, and then try d iffe ren t combinations of L, e, and b/a for the aspect limiting and orientation modifications, while observing the effect on the image obtained. An improved image is obtained after several iterations of this trial and error procedure. 102

(a) >-o*t*o.OBi» ((•0.1 IB I

f t

(b) f *IBVe«0,03M ((•0.(14)

(d )^ .4 S *. C-O.OBBI (E* 0,147)

Fig. 70— Improved spheroid images compared to lin e drawings (same shapes as Fig. 49). 103

<1 >0 .111)

(blfT S *, C-0.09M (1*0,114)

(c)f>»0*, (■ 0.081* (C >0.1(4)

Fig. 71— Improved spheroid images compared to lin e drawings (same shapes as Fig. 50).

i I I !

i i

i 104

(a) f-O*. E-O.iII ( E - 0.1331

(b) +-19*. E-O.OTI IE-0.164)

CO I E - 0.216)

Id) ♦■43*. E-0.0840 (E -0.2 22 )

Fig. 72— Improved parallelopiped images compared to lin e drawings (same shapes as Fig. 51). 105

♦-•0*, £-0,0*73 ( E - 0 .II9 )

Fig. 73— Improved parallelopiped images compared to lin e drawings (same shapes as Fig. 52). \ The normalized error area E serves as a quantitative index

for evaluating image accuracy in such an iterative procedure.

Furthermore, comparison of plotted input and output cross-sectional

area waveforms, as was done in Fig. 43, is indicative of the region o f the image where error occurs. For example, the output p ro file

function of Fig. 43 differs significantly from the input function in

its front and rear regions. Therefore it can be deduced that the

error occuring in the image of Fig. 35 is located in the vicinity of

the edges of the body.

Further study is necessary to arrive at some rules for auto matic iteration of the modification constants on the basis of the

image accuracy results. Also, other parameters, such as the scaling

constant C, may be optimized using the same technique.

Figure 74 depicts an iterative modification procedure applied

to the 2:1 parallelopiped at 45° shown originally in Fig. 51, where

the operator provided values for the modification constants. It is

seen that the error indicator is a valid index for evaluating the

convergence to the correct image.

The slow speed of the p lo tte r used presently must be changed

before this ite ra tiv e process w ill re a lly be p ra c tic a l. The

implementation of a cathode-ray tube display is necessary. Study of ite ra tiv e procedures is seen as a promising approach to fu rther modifications of the imaging technique, resulting in improved image accuracy. 107

(a) LINE ORAWINO (b) UNIMPROVED IMAGE E * 0.222

Fig. 74— Images depicting Ite ra tiv e Improvement for parallelopiped, *» 450. CHAPTER VI

SUMMARY AND CONCLUSIONS

A new method for generating synthetic target images from multiple-

frequency radar data has been presented. The input data for this process

are the backscattered signal amplitude and phase over a 10:1 frequency

band at three orthogonal look angles. A laboratory system, designed for

scattering measurements at ten harmonically-related frequencies,

provides necessary data.

Geometrical information for image generation is inferred from

the multi-frequency scattering data at each look angle. Specifically,

a periodic ramp response signature is constructed, from which a

target virtual profile function, representing the approximate-cross

sectional area vs distance along the line-of-sight, is derived.

A mathematical specification of a three-dimensional "approximate

limiting surface" is obtained using profile functions from the three orthogonal look angles. Visual images simulating an isometric view of the limiting surface are then plotted. Visual images for a variety

of simple shapes and orientations, using ideal and measurement-

derived profile function input data have been presented.

This study yields conclusions on three hypotheses inherent in

the imaging approach presented.

F irs t, is i t feasible to measure the complex broadband spectral

data necessary for image generation using this technique? The meas-

108 109 urement system described and the scattering data presented demonstrate that laboratory measurement is practical. Also, the spectral sampling method used deserves consideration in future studies of fu ll-s c a le implementation of the technique.

Second, can a geometrical profile function be reliably inferred from spectral measurements at an arbitrary target look angle? Results for the objects measured indicate that the profile function is ap proximately proportional to the measured ramp response waveforms, with slightly less accurate correlation observed in the rear, shadow region of the waveform, and some smoothing evident due to the fin ite bandwidth of the interrogating signal. The waveforms also indicate a possible relationship between the target silhouette and the polari zation dependence of the ramp response signature.

Third, can a meaningful synthetic image be constructed from profile function data at three orthogonal look angles? The images presented using the basic technique are good for convex objects whose planes of symmetry are aligned with the radar look angles.

The simple modifications of the basic technique which were tried indicate that comparable image quality seems obtainable for general convex shapes at arbitrary orientations. Considering its demon strated capabilities and its potential fo r further improvement, this approach is regarded as a promising imaging technique.

Further study in four basic areas is recommended:

A. Ramp-response signatures.

B. Image generation using ramp-response derived information

C. Radar systems for implementation of the technique

D. Extensions of the technique for other applications. n o

Laboratory measurements of more complex m etallic and non-metal lie shapes are needed for more extensive evaluation of th is approach.

Correlation with the object profile function and general waveform characteristics fo r non-convex or multiply-connected shapes, should be investigated. Correlations between object shape and higher order waveform characteristics such as polarization dependence and ringing also deserve study.

Further studies of image construction from profile function data would be fa c ilita te d by use of a larger and faster computer than used for this study. Implementation of improved computer capability in conjunction with a cathode ray tube display would speed and sim plify the development of adjustment strategies which converge to a con sistent image for arbitrary target situations. Also, application of this approach using nonorthogonal look-angle information, and possibly more than three look angles, should be studied.

A system study which considers the s ta te -o f-th e -a rt in VHF hardware along with propagation and noise effects is needed to determine the feasibility of radar applications of this technique.

The spectral sampling approach used in the measurements of th is study might be adapted as one approach. A combination of spectral sampling and short pulse radar measurements also appears promising.[153

Finally, this technique seems suitable for several nonradar appli cations. Concealed weapons detection, postal package search, geological subsurface investigation, acoustical (sonar) imaging, and fine-detail optical microscopy are among those applications which might be studied. APPENDIX A

This section presents the tabulated complex scattering data measured for the targets of Fig. 10-17. Values of normalized complex square-root of cross-section, in cm, are presented for two orthogonal linearly polarized interrogating signals, at frequencies of 1.082, 2.164, ... 10.82 GHz.

The phase reference for these data is approximately, but not exactly at the centroid of the target. Specifically, the styrofoam holders for the targets were designed to accomodate a set of spheres as well. For the 2:1 cylinder and its modified versions (Figs. 10-13) the center of the sphere was located as exactly as possible at the centroid of the 2:1 cylinder portion of the target. For the other targets, the sphere centers were located as near as possible to the centroid of the total shape. The actual zero-phase point, then, is the center of the reference spheres.

The accuracy of these data was estimated by measuring at least two reference spheres along with each target measurement t r i a l . Then after the data was normalized using one reference sphere, the experi mental values obtained for the "check" sphere(s) were compared with calculated data to provide an accuracy estimate.

I l l 112

Two sets of accuracy estimates apply to these data. Prior to

January, 1971 the system microwave hardware and range configuration were adjusted to a compromise situation to yield satisfactory ac curacy and minimum measurement time. Maximum deviation estimates fo r the above arrangement are given in Table 2.

TABLE 2 INITIAL SYSTEM ACCURACY ESTIMATES

Frequency Amplitude Accuracy Phase Accuracy

1.08 GHz ±10% +10° 2.16 ±10% ±10° 3.24 ±10% ±10° 4.32 ±20% ±20° 5.40 ±10% ±10° 6.48 ±10% ±10° 7.56 ±10% ±10° 8.64 ±20% ±20° 9.72 ±20% ±20° 10.80 ±20% ±20°

As the waveforms in the text indicate, these accuracy levels are su fficien t to assure adequate ramp response waveforms.

More recently, repeated measurement runs with the system o p ti mized for different frequencies have resulted in the accuracies given in Table 3. 113

TABLE 3 IMPROVED SYSTEM ACCURACY ESTIMATES

Frequency Amplitude Accuracy Phase Accuracy

1.08 ±10% ±10 2.16 ±10% ±10' 3.24 ±10% ±1 o' 4.32 ±10% ±10' 5.40 ±10% ±10' 6.48 ±10% ±10* 7.56 ±10% ±1 o' 8.64 ±10% ±1 o' 9.72 ±10% ±10' 10.80 ±10% ±10'

The tables of these data are denoted by an asterisk. Such data is considered suitable for step and impulse as well as ramp response waveforms. TABLE 4 2:1 CYLINDER, $ POLARIZATION, COMPLEX RETURN VS e

Frequency {GHz) e=0° 0=15° 6= 30° 0= 45° 0=60° 0=75° =90° 6 A( cm) i> A (cm) i A(cm) * A(cni) «* A(cm) 6 A(cm) 6

1 .0 8 1 .4 87 341 .7 7 8 336 .631 329 .687 357 .696 4 .775 31 .7 4 0 12 2 .1 6 2 1 .5 8 329 1 .6 3 329 1 .7 4 328 1 .9 5 331 2.22 336 2 .4 9 341 5 .8 9 343 3 .2 4 3 .9 4 4 309 1 .0 4 295 1 .6 3 292 2 .6 3 300 3 .7 2 312 4 .7 5 323 5 .8 2 326 4 .3 2 4 2 . 0 8 109 2.02 111 1 .0 3 123 .6 4 3 271 2 .5 4 304 4 .3 5 323 4.91 350 5 .4 0 5 4 .5 3 72 4 .5 3 70 4 .1 8 76 2 .5 5 81 .8 5 9 349 3 .5 9 321 4 ;6 9 341 6 .4 8 6 2 .3 2 51 2.68 45 3 .7 4 52 3 .8 3 72 1.68 51 3 .5 0 348 4 .3 9 18 7 .5 6 7 2 .8 0 199 2.12 189 • .5 9 2 120 1 .8 9 61 1 .8 5 54 1 .9 4 18 2 .7 2 18 8 .6 4 5 .5 0 8 173 5 .0 4 168 3 .4 5 158 1 .5 5 132 .85 63 3 .0 5 33 4 .3 2 51 9 .7 2 9 3 .1 9 191 4.01 179 3 .0 5 158 1.87 150 .759 159 2.00 36 5 .3 5 75 1 0 .8 0 • 10 4 .5 0 251 1 .1 5 42 .3 9 4 -2 .8 77 355 1 .3 0 81 5 .4 8 225 5 .2 6 99

TABLE 5 2:1 CYLINDER, e POLARIZATION, COMPLEX RETURN VS G

Frequency (GHz) 6=0° 0= 1 5 ° . 0==30° 0=45° 0=60° 0==75° 0=90° A(cm) 6 A(cm) 6 A (cm) 6 A (cm) A (cm) 6 A(cm) 4 A (cm) 6

1 .0 8 1 .6 2 6 345 .629 350 .833 348 .9 3 3 336 1 .2 3 351 1 .3 5 350 1 .4 2 353 2 .1 6 2 1 .4 0 0 1 .6 9 337 2 .7 2 303 4 .1 5 327 5 .8 2 327 6.91 329 7.51 333 3 .2 4 3 0 .7 8 7 355 1.00 320 1 .7 3 271 3 .7 0 288 5 ,7 5 285 7 .1 0 289 8.01 293 4 .3 2 4 2 .0 5 159 1.86 142 1 .4 3 136 2 .1 7 253 3 .7 6 101 4.66 116 5.24 304 5 .4 0 5 3 .7 4 114 3.81 118 3.36 128 1 .4 7 133 1.68 326 3.91 339 4 .7 8 348 6 .4 8 6 0 .9 1 6 153 1 .1 7 135 2 .9 4 106 2 .8 2 m 1 .0 6 352 2 .5 0 352 3 .3 8 16 7 .5 6 7 2 .4 5 227 1.41 219 2.71 108 3 .4 8 121 5 .7 7 1 3 .7 4 9 4 .7 8 313 8 .6 4 8 4 .7 4 210 4.09 232 1.59 208 2.15 132 0.634 177 2 .7 5 291 4 .7 0 294 9 .7 2 9 4 .0 6 203 6.86 246 2 .4 9 285 1 .5 7 138 1 . 8 o 167 3.89 349 5.27 315 1 0 .8 0 10 5 .4 4 4 3 .7 4 37 1 .0 7 68 1 .4 5 113 2 .8 3 98 1 .3 2 71 3 .7 0 105 TABLE 6 SPHERE-CAPPED CYLINDER, 4 POLARIZATION COMPLEX RETURN VS e

e=o 0=30 0 = 4 5 “ =60 e=90u 6= 120° 6=135° 0 = 1 50 “ 6=180° A{cr.) A (cm) A(cn) A(cm) 4 A(cn) 4 A(cn) 4 A(cm) 4 A(cm) 4 A(cm) 4

1 O.SG5 351 0.543 12 0 .715 358 0 .802 29 0.706 27 0 .738 12 0.614 30 0 .76 19 0 .6 7 15 2 1 .4 0 340 1.56 348 2.02 334 2.31 339 2 .76 348 2.40 355 2.03 1 1.68 - 7 1.34 13 3 0 .183 162 0.702 312 1.74 312 3.13 327 4.83 343 3.29 354 1.97 359 0.851 356 0 .0 3 158 4 3 .05 134 2.41 139 0 .903 158 1.67 312 5 .49 340 2.49 3 0.206 121 1 .90 181 2.92 190 5 3.01 105 3 .57 109 3.21 113 1.01 83 5 .86 342 1.52 55 2 .7 4 151 3 .75 176 3.32 194 6 0 .7 37 323 1.13 94 2 .2 7 114 1 .98 98 5 .29 1 1.75 112 3.01 166 2 .2 3 204 0.972 264 7 4 .4 3 263 3.01 261 0 .9 2 9 198 1.81 104 3 .40 24 1.79 141 1 .2 8 202 2.12 308 4.12 348 8 2 .4 4 231 3 .05 239 2.21 221 1.35 145 4 .3 3 57 1.24 147 2 .16 282 3 .3 8 330 3 .97 19 9 3 .0 5 56 0 .385 200 0 .9 8 0 253 2.20 202 6 .72 63 0.585 235 1.92 330 2 .82 0 3.81 115 10 0 .626 153 1.75 20 1 .70 170 3.89 3 6 .5 0 1 2 .37 55 1.42 186 11.81 92 3 .60 2

TABLE 7 SPHERE-CAPPED CYLINDER, 0 POLARIZATION COMPLEX RETURN VS 0 iO- T 6=0° 0=30° 6=45° 6=60° 6=90° 0=120“ 6=135° 6=150 6=180 A(cn) 0 A(cm) 4 A(cm) 0 A{cm) 4 A(cn) A(cm) 4 A(cm) A(cn) 4 A{cm)

. i 0 .55 358 1.00 352 1 .25 351 1.75 355 1 .24 4 1 .60 349 1 .2 8 353 0.994 355 0.61 5 2 1.19 357 2.79 331 5 .0 4 321 6 .84 319 10.5 298 7.45 319 4 .89 326 2 .9 3 328 1.22 10 3 0 .4 8 147 1.31 267 3 .4 0 283 4 .9 8 271 8 .79 256 5 .0 7 287 3 .12 290 1 .1 8 294 0.221 97 4 2.69 141 2.73 175 1 .7 5 194 2.24 268 0 .6 4 45 2 .42 292 1.36 194 2 .25 166 2.67 165 5 2.32 144 3.99 149 3 .2 0 151 0.335 125 2.31 335 1.50 7 3.01 149 3.65 145 2.66 191 6 1.01 326 1 .57 138 2 .7 4 149 0 .398 155 6 .9 8 39 1 .28 36 2.49 156 2 .0 5 167 1.19 290 7 3.35 315 1 .74 359 1.51 175 2.03 203 5 .47 30 0.691 70 1 .57 204 1.E5 241 3 .53 339 8 2.01 313 3 .20 351 0 .5 6 217 2 .6 0 217 5 .25 50 0.477 154 1.71 233 2.32 286 3 .8 2 9 1.59 312 2 .84 352 1 .42 64 2 .4 8 206 6 .5 4 97 0.1S5 318 1 .08 275 1.86 350 3.04 70 10 2 .75 330 0 .3 3 281 .006 298 6 .62 313 6 .09 197 3.04 132 0 .013 5 291 4 .4 4 328 3 .17 316 TABLE 8 CONE CYLINDER, 4 POLARIZATION COMPLEX RETURN VS 0 t> o o ii o Frequency (GHz) e 6= CO e==60° e==90° 6=120° 0=150° 0=180° A (cm) A(cm) A (cm) A(cm) A(cm) A(cm) -o- o A(cm) # 4 4 4 4

1 .0 8 1 0 .5 4 7 349 0 .5 8 7 359 0 .9 4 4 17 0 .9 0 5 29 0.761 34 0 .6 7 5 19 0 .6 2 2 357 2 .1 6 2 1 .3 5 339 1 .5 9 341 2.27 340 2.59 355 2 .2 7 6 1.66 18 1 .3 6 21 3 .2 4 3 0 .2 6 6 216 0 .8 2 8 308 3.26 330 5.05 356 3 .2 6 14 0 .9 0 32 3 .2 1 2 82 4 .3 2 4 2 .7 3 122 1 .9 6 136 2.02 309 5 .7 3 342 2 .4 0 14 1.5 9 185 2 .4 4 195 5 .4 0 5 2 .7 7 92 3 .1 8 105 0 .6 1 5 13 5 .4 1 358 1 .2 7 80 3 .2 9 205 3 .0 8 218 6 .4 8 6 1 .2 5 298 0 .8 8 4 46 1 .6 7 89 3 .8 9 3 1 .7 8 137 2 .1 4 229 1 .8 3 285 7 .5 6 7 3 .1 7 259 1 .9 5 271 1 .5 2 114 3.31 41 1 .8 4 173 1 .7 4 334 3 ,2 7 10 8 .6 4 8 3 .1 2 219 2 .7 2 238 1.20 183 5 .6 8 91 1 .3 2 196 3 .6 6 13 4 .5 9 58 9 .7 2 9 1 .2 4 129 0 .8 7 0 219 0 .2 1 9 215 5 .8 7 105 0 .6 3 6 267 2.20 66 3 .3 4 115 1 0 .8 0 10 1 .3 4 169 0 .9 7 6 60 1 .5 5 273 4 .9 4 244 1 5 .5 207 6 .1 6 159 6 .3 4 192

TABLE 9 CONE-CYLINDER, 0 POLARIZATION . COMPLEX RETURN VS 0

Frequency (GHz) 6=0° 0=30° 6==60° 6=90° 0=120° 0=150° 6=180° A(cm) 4 A(cin) 4 A (cm) 4 A(cm) 4 A(cm) 4 A (cm) 4 A(cm) 4

1 .0 8 1 0.591 347 0 .8 9 2 3 1.66 349 2 .0 9 355 1 .7 0 1 1.01 17 0 .8 0 8 34 2 .1 6 2 1 .2 4 345 3 .1 4 310 7 .8 0 309 1 0 .3 314 7 .3 7 321 2.71 342 1.31 21 3 .2 4 3 0 .2 3 3 264 1.61 249 5 .2 8 270 7 .7 9 285 4 .8 5 290 0 .6 9 9 302 0 .4 1 6 62 4 .3 2 4 2 .4 3 129 2 .2 4 151 2 .3 9 250 6.02 303 1 .3 7 283 2.66 173 2 .3 9 203 5 .4 0 5 2 .5 7 92 3 .8 0 112 0 .7 4 7 39 6.02 332 1 .9 3 69 2.41 170 3 .5 5 221 6 .4 8 6 0 .3 5 2 181 1.81 123 0 .4 5 2 94 4 .9 3 4 1 .4 5 88 2 .3 0 253 1 .7 2 293 7 .5 6 7 3.11 246 1 .5 6 325 2 .4 4 164 6.66 20 2.20 80 4 .4 3 282 4 .0 3 2G 8 .6 4 8 2 .2 9 205 2 .4 5 285 3 .1 4 178 6 .4 7 39 0 .7 2 8 30 1.21 302 4.22 50 9 .7 2 9 1 .5 3 271 2 .4 9 347 4 .6 4 200 6 .6 5 59 0 .4 5 8 351 1.01 55 1 .4 7 201 1 0.80 10 2 .4 9 134 3 .6 8 219 4 .8 3 137 1 0 .7 6 126 1 .7 6 177 5 .9 9 352 6 .5 0 69 TABLE 10 STEP CYLINDER, $ POLARIZATION COMPLEX RETURN VS 6

Frequency (GHz) e=0° e=30° 6s 60° 0 =-90° 6=120° 0=150° 6=180° A(cm) # - A (cm) <> A (cm) $ A (cm) $ A (cm) i> A (cm) $ A (cm) $

1 .0 8 1 .616 352 .662 1 1.00 18 0 .9 2 8 49 0 .9 0 4 32 0 .6 9 9 15 0.611 359 2.16 2 1 .2 8 341 1 .5 4 342 2 .2 5 343 2 .3 7 352 2 .2 6 4 1 .5 8 16 1 .29 22 3.24 3 .5 2 4 212 0 .7 8 3 292 3 .2 3 333 6 .2 7 358 3 .1 9 14 0 .7 9 4 42 0 .4 4 117 4.32 4 2 .4 5 129 2.01 151 1 .7 5 308 5 .8 0 359 2 .4 7 13 1.70 168 2.18 183 5.40 5 2 .4 4 75 2 .5 7 106 0.646 130 5 .6 6 7 1 .3 3 74 2.66 200 2 .2 3 233 5 .4 8 6 2 .3 9 329 1 .4 4 1 1.42 109 4 .4 3 14 1 .9 3 133 2.10 249 3 .2 2 289 7.56 7 1 .4 2 267 1 .9 2 318 1.12 218 3 .7 8 41 2 .0 8 165 2 .6 4 307 2.12 323 8.64 8 5.21 167 0 .7 9 2 157 1.68 227 5 .9 4 88 1 .2 9 182 2 .1 3 0 5 .0 3 100 9 .7 2 9 4 .5 8 147 2 .1 5 126 0 .3 0 243 6 .0 5 104 0.212 336 1 .7 0 105 5 .5 5 110 10.80 10 2 .0 3 256 1.88 212 0 .5 5 332 4.94 238 11.92 156 2 .9 2 178 6 .8 0 180

TABLE 11 STEP CYLINDER, e POLARIZATION COMPLEX RETURN VS e O o Frequency (GHz) 0=0° 0=30° 0= 0=90° 0= 120° 9=150° 6=180° A (cm) A (cm) $ A (cm) A (cm) $ A( cm) * A(cm) * A (cm) 4

1 .0 8 1 0 .6 1 6 352 0 .9 5 5 2 1.77 351 2 ,2 8 352 1 .7 8 357 1 .0 8 18 0 .8 0 8 36 2 .1 6 2 1 .2 6 344 3 .2 2 309 8 .2 5 306 1 0 .9 6 305 7 .7 2 311 2 .5 9 329 1 .2 8 24 3 .2 4 3 0 .3 7 9 225 1 .7 5 245 5 .3 5 274 7.89 282 4.39 276 0 .4 2 3 235 0.531 81 4 .3 2 4 2 .0 9 141 2 .4 8 150 1 .7 4 251 6 .2 8 302 0 .7 3 8 159 3 .7 0 146 2 .0 8 196 5 .4 0 5 2 .0 9 75 3 .3 6 112 1.31 29 6.00 327 2 .7 3 67 1 .9 3 129 2 .9 5 230 5 .4 8 6 0 .6 3 4 17 1 .0 8 124 0 .9 0 4 80 4 .5 2 356 1.68 97 1.81 265 2 .3 9 294 7 .5 6 7 1.01 268 2 .1 9 344 2.21 147 6 .1 9 24 2 .1 5 101 5 .6 7 297 2 .3 4 350 8 .6 4 8 4 .2 4 143 1.67 308 2.79 169 6 .4 0 46 1.41 114 3.52 300 4 .2 5 86 9 .7 2 9 2 .3 7 127 1 .0 9 3 5.21 184 6.31 44 0 .9 1 6 219 1 .6 4 326 3 .1 6 124 10.80 10 6.61 158 6 .8 0 252 4 .2 3 120 5 .6 6 131 1 .7 6 341 7.16 0 4 .1 8 27 1 1 8

TABLE 12 CUBE, = 0, POLARIZATION COMPLEX RETURN VS 0

Frequency e =0° 0 =15° e =30° 0 =45° (GHz) A(cm) $ A(cm) “I1 A(cm) * A(cm) <}>

1.08 1 2.02 2 2.02 356 2.05 4 2.02 358 2.16 2 6.30 339 6.24 337. 6.38 339 6.18 337 3.24 3 4.04 320 3.92 317 4.36 316 4.44 314 4.32 4 5.67 90 5.60 97 3.80 92 3.48 70 5.40 5 9.16 83 8.16 94 6.54 95 4.13 51 6.48 6 5.27 49 2.08 74 2.69 223 3.19 220 7.56 7 7.16 141 5.85 144 • 3.68 174 3.63 210 8.64 8 7.05 211 5.55 219 2.66 223 1.78 111 9.72 9 7.59 219 8.67 138 2.21 350 0.663 245 10.80 10 4.27 138 1.87 84 3.81 189 5.17 359

TABLE 13 CUBE, 4> = O°,0 POLARIZATION COMPLEX RETURN VS 0 ° CO Frequency 0 =0° 0 =15° 0 = o 0 =45° (GHz) A(cm) 4> A(cm) A(cm) £ A(cm)

1.08 1 2.41 0 2.26 357 2.07 359 2.09 349 2.16 2 6.08 341 6.17 340 6.47 341 6.52 338 3.24 3 4.02 334 4.79 330 6.19 332 6.87 329 4.32 4 5.24 84 3.82 72 3.17 348 4.88 329 5.40 5 8.47 98 6.80 97 3.44 59 3.36 11 6.48 6 9.73 123 8.47 124 3.31 88: 3.18 20 7.56 7 7.95 151 7.10 148 2.32 133 3.45 346 8.64 8 7.75 205 7.23 182 2.89 177 4.68 319 9.72 9 12.2 268 8.05 239 3.15 193 7.00 337 10.80 10 24.2 302 8.25 294 3.42 347 3.40 175 TABLE 14 CUBE, $ = 150, $ POLARIZATION* COMPLEX RETURN VS $

Frequency (GHz) e==0° 6= 15° e==30° 6==45° 6=60° 0= 75° 0 =90° A(cm) ♦ A (cm) 4 A (cm) 4 A (cm) 4 A(cm) 4 A(cm) 4 A(cm) 4

1.08 1 ■ 1.86 347 1.90 355 1.85 357 2.03 347 1.85 357 1.87 352 2.24 355 2.16 2 6.41 331 6.58 329 6.49 329 6.39 330 6.32 332 6.43 336 6.30 339 3.24 3 4.89 309 4.92 308 4.92 305 4.80 306 4.41 309 4.21 317 3.99 320 4.32 4 3.29 56 3.06 59 2.65 56 2.90 56 3.96 76 5.26 89 6.14 98 5.40 . 5 6.98 69 6.17 64 4.42 52 3.92 42 5.44 64 8.00 83 9.61 96 6.48 6 7.50 80 5.47 80 1.51 98 3.14 159 2.83 96 6.77 101 9.19 110 7.56 7 5.74 103 4.19 103 2.44 136 2.76 171 3.51 142 5.66 133 6.79 140 8.64 8 6.91 146 4.97 145 2.48 162 1.92 214 2.56 189 5.77 190 8.15 206 9.72 9 6.52 159 4.21 152 1.73 224 2.82 275 0.745 192 6.48 213 10.69 240 10.80 10 3.55 193 2.95 194 2.66 274 2.60 304 1.72 298 6.52 264 11.23 275

TABLE 15 CUBE, $ = 15°, 6 POLARIZATION COMPLEX RETURN VS 6 il Frequency (GHz) 0: =0° e=15° e=30° e:=45° 0=60° 0=75° 0

A(cm) 4 A(cm) 4 A (cm) 4 A(cm) 4 A(cm) 4 A(cm) 4 A (cm) •O’ o

1.08 1 2.15 344 2.02 353 1.77 342 1.96 354 2.05 352 1.91 359 1.84 359 2.16 2 6.10 321 6.24 320 6.31 319 6.71 326 6.69 347 6.40 335 6.18 340 3.24 3 4.23 295 4 .74 295 6.44 297 6.59 307 5.77 326 5.07 318 4.20 326 4.32 4 3.71 44 2.67 20 3.42 320 4.64 314 3.55 339 3.57 49 4.83 95 5.40 5 7.29 42 5.80 38 3.25 2 3.57 333 3.71 10 6.84 66 9.24 103 5.48 6 5 .08 57 4.57 53 2.59 25 2.03 342 1.94 316 5.64 91 7.37 125 7.56 7 6 .74 86 6.02 76 1.86 50 2.90 289 1.21 86 6.83 123 6.96 128 8.64 8 5.38 119 4.96 106 1.27 97 3.30 267 2.32 124 7.01 154 6.82 182 9.72 9 5.45 154 4.53 123 1.23 105 3.09 250 1.41 135 6.04 176 7.04 222 10.80 10 3.72 8 3.17 146 2.46 133 7.48 62 0.849 152 3.83 239 7.11 271 TABLE 16 CUBE, 4 = 3 0 ° , 4 POLARIZATION* COMPLEX RETURN VS 9 ii Frequency (GHz) e o e =15° 0==30° 6= 45° 9=60° e==75° 9= 90° A(cm) -o -o o A(cm) 4 A (cm) A(cm) A (cm) 4 4 4 A (cm) 4 A (cm) 4

1 .0 8 1 2 .0 5 359 1 .8 0 359 1 .8 7 353 1 .7 3 354 2 .0 4 356 1 .7 9 355 1.90 354 2 .1 6 2 6 .8 5 331 6 .3 6 326 6 .6 0 329 6 .4 8 329 6 .3 8 330 6 .3 3 335 6 .2 7 334 3 .2 4 3 6 .1 3 311 6.31 304 5 .7 3 306 5 .1 4 304 4.71 306 4 .1 6 312 4 .0 8 314 4 .3 2 4 2 .7 2 3b2 2 .0 5 350 1.41 355 1.00 43 1 .9 5 91 3 .1 0 10? 3 .5 2 105 5 ,4 0 5 3 .7 7 46 3 .4 8 38 3 .1 6 29 3 .6 8 41 5 .4 5 60 7 .7 8 75 8.86 87 6 .4 8 6 3 .7 3 51 2 .5 4 45 1.41 23 1.71 37 4 .2 3 73 7 .5 2 9? 9.01 102 7.56 i 1 .4 7 96 1 .1 3 84 0 .7 7 5 122 1 .4 0 134 3 .4 4 116 6 .0 9 1?5 7 .1 8 133 8 .6 4 8 2 .9 0 161 2 .3 7 140 1 .5 2 140 1 .1 8 168 2.66 145 6 .0 4 167 8 .1 5 185 9 .7 2 y 2 .3 6 144 1 .4 3 154 0 .4 4 2 248 1 .0 5 309 1 .3 4 153 6 .9 8 199 10.63 ??6 10.80 IU 2 .1 9 109 0 .0 6 83 1 .3 9 266 1 .2 6 274 1.71 237 7 .6 2 245 11.51 249

TABLE 17 CUBE, 4 = 3 0 ° , e POLARIZATION COMPLEX RETURN VS e

Frequency (GHz) e =0° 6= 15° 0=*30° 0=45° 0=60° 6=75° 6=:90° A(cm) 4 A (cm) 4 A (cm) 4 A(cm) 4 A(cm) 4 A(cm) 4 A(cm) 4

1 .0 8 1 2.10 354 2.02 354 2 .0 5 355 2 .0 4 357 2.10 358 2 .0 4 35S '1 .9 0 1 2 .1 6 2 6 .4 7 330 6 .4 3 334 6 .5 8 337 6 .7 2 336 6.68 339 6 .2 7 339 6.31 343 3 .2 4 3 4 .4 0 306 4 .6 8 313 5 .8 2 324 6 .2 7 320 5 .7 0 324 4 .7 4 327 4 .1 4 330 4 .3 2 4 2 .7 6 62 2 .2 7 35 2 .9 6 348 3 .8 9 334 3 .2 7 0 3 .4 3 63 4 .3 3 81 5 .4 0 5 4 .8 7 60 4 .1 2 57 2 .8 4 39 2 .9 6 0 3 .4 5 31 6 .2 9 81 8 .8 2 87 6 .4 8 6 2 .2 9 106 2.66 94 2 .3 5 65 1 .7 9 24 1.66 78 4 .8 9 112 7 .2 3 110 7 .5 6 7 3.11 161 2 .8 4 138 1 .2 8 98 1.31 328 1 .7 0 159 6.71 155 8.41 155 8 .6 4 8 3 .0 8 195 2.31 182 0 .7 9 4 135 0 .8 5 5 325 3 .0 6 176 7 .1 5 189 7 .7 6 208 9 .7 2 9 1 .5 9 252 1 .3 4 249 0 .2 6 6 78 1 .0 9 306 1.97 193 5.94 216 8.01 267 1 0.80 10 4 .9 8 231 0 .5 5 285 1 .0 7 3 9 .0 6 106 2 .2 7 235 6 .1 5 231 1 7.26 205 TABLE 18 CUBE, $ = 45°, 4 POLARIZATION* . COMPLEX RETURN VS e 0 II u> Frequency (GHz) 0= 0==15° 0= 0 0= 45° 0=60° 6=75° 0=90° - -

A (cm) A (cm) A (cm) 0 A(cm) A{ cm) 4> A(cm) 1 4 - A(cm) 4 4 4

1.08 1 1.97 358 1.84 355 2.15 356 1.78 355 2.10 357 1.89 356 1.99 356 2.16 2 6.80 341 6.89 339 6.63 338 6.51 338 6 .54 338 6.33 339 6 .2 8 341 3.24 3 7.04 326 6.72 325 6.16 321 5.50 320 4.74 319 4.26 320 4 .08 323 4.32 4 5.14 341 4.67 338 3.49 347 2.32 25 2 .98 95 4.29 93 5.47 104 5.40 5 3.63 28 3.33 21 2.95 36 3.63 67 5.95 100 8.08 98 9.14 99 6 .48 6 3.80 13 3.20 16 2.25 27 2.72 71 5.12 93 7.75 109 8.88 114 7.56 7 4.02 333 2.47 335 2.43 67 1.63 125 3.60 135 6 .08 146 7.33 153 8.64 8 5.14 319 2.99 321 1.30 124 2.00 132 2.73 170 5.94 197 7.85 210 9.72 9 5.32 322 2.39 336 2.07 94 1.41 87 1.91 209 7.04 241 10.2 244 10.80 10 5.89 334 2.77 2 1.78 76 0.744 12 1.98 282 7.99 268 12.0 291

TABLE 19 CUBE,

Frequency (GHz) 0:=0° 0=0 5 ° 0 ==30° 0= 45° 0=60° 0=75° =90° A(cm) 4 A (cm) 4 A (cm) 4 A(cm) 4 A(cm) 4 ' A(cm) 4 A(cm) 4

1.08 1 2.03 357 2.06 357 1.92 357 2.04 357 2.09 357 2.00 2 2.04 355 2.16 2 6.17 343 6.31 331 6.30 352 6 .58 340 6.55 340 6.22 340 6.21 339 3.24 3 4.46 327 4.87 317 5.53 338 6.34 329 5.76 329 4 .68 329 4.15 326 4.32 4 2.46 61 2.08 48 2.54 1 4.17 237 3.21 16 3.54 69 4.51 91 5.40 5 3.65 56 3.52 61 2.86 53 4.74 226 3.27 49 6.40 89 9.25 101 5.48 6 1.20 170 1.13 123 2.00 74 3.70 290 1.46 112 4.95 119 7.62 121 7.56 7 3.20 218 1.78 210 1.07 94 0.36 32 2.53 174 6 .88 161 8.09 159 8.64 8 3.63 241 2.19 243 1.31 122 0.371 151 3 .5 8 189 8.27 192 7.89 213 9.72 9 4.14 256 2.42 313 4.52 106 3.55 71 13.1 236 17.66 102 7.10 209 10.80 10 3.81 352 2.73 348 0.849 266 2.03 235 4.60 324 11.93 307 16.95 311 TABLE 2 0 60° CONE, * POLARIZATION* C O ^ L E X RETURN VS 8 O

Frequency {GHz} e=o° e=30° 0=45° 8=60° 6=90° 0= ro O 6=135° 6=150° e=180° 4 A A(cra) 4 A(cn) 4 A (era) 4 A(cra) r A(cra) 4 A(cra) 4 A(cm) 4 A(cra) T A(cra) 4

1.03 1 1.35 3 1.30 2 1.47 357 1.55 359 1.57 356 1.70 350 1.59 353 1.65 359 1.54 348 2 .16 2 5 .93 345 5.67 345 5.79 348 5.76 345 5 .2 3 342 5.49 337 5.76 342 5,57 335 6 .1 3 337 3.24 3 7.35 315 6.64 338 6 .25 325 5 .4 5 326 4 .82 319 5 .39 309 6.05 317 7.16 315 8.42 316 4 .32 4 5 .6 8 265 4 .35 290 1 .87 319 1.52 21 1.41 54 1 .6 8 276 4.02 298 6.41 303 11.53 320 5.40 5 4.65 267 0 .5 3 306 3 .0 3 77 4 .85 88 4 .0 5 87 2.45 113 1.25 97 3.08 355 10.32 351 5 .4 8 6 4.55 310 0.684 109 3.77 135 5.45 123 3.12 85 2 .8 0 82 2 .65 53 2.8 6 329 12.5 283 7.56 7 3.82 223 0.514 327 1.54 90 3.78 148 0.852 191 0.831 144 1.55 115 1.96 27 11.66 356 8.64 8 3.83 255 0.353 22 3.1 5 165 5.77 200 2.32 228 1.71 226 1.77 183 1.02 89 13.13 29 3.72 9 4.65 230 0.794 76 3.65 212 5.97 213 0.96 265 1.56 269 2.05 207 1.85 182 16.98 33 10.80 10 4.37 1E3 1.06 34 1.88 251 5 .7 8 261 2 .2 0 355 1 .0 5 344 1.47 232 1.83 185 14.95 54

TABLE 21 6 0 ° CONE, e POLARIZATION COMPLEX RETURN VS n

Frequency (GHz) e=0° 6=30° 6=45° 6=60° 6=90° 9=120° e= 135° e=150° 6!=180° A A(cm) A (era) 4 A(cn) 4 A (era) T A(cra) 4 A(cra) 4 A(cra) 4 A (era) 4 A(cra) 4 4

1 .0 8 1 1.79 13 1.84 14 1.63 20 1.3 8 20 1.45 8 1 .4 8 351 1 .50 352 1.47 348 1,60 344 2.16 2 5 .7 5 10 5.62 IB 5.04 18 5.01 23 4.93 345 5.3 6 304 5 .0 2 304 5 .9 6 303 5.49 334 3.24 3 7.06 351 6 .0 8 14 6 .4 3 23 7.42 24 5.53 323 5 .8 3 239 6 .0 3 257 7.36 258 8.30 282 4 .32 4 5.86 322 3.69 33 4.49 44 5.15 45 1.80 51 3.47 189 3 .16 171 4.37 252 9.30 245 5.40 5 2 .33 318 2.63 94 5.19 10B 5.85 97 2 .3 4 198 3.32 119 0.837 62 4.40 273 9.32 272 6 .4 8 6 1.34 330 3.07 126 *5 .2 0 143 4.94 143 1.93 356 2.26 75 1.06 335 4.15 252 10.69 290 7.56 7 3.22 331 2.61 122 3.30 189 5.20 184 0.332 298 1.41 30 1.31 189 1.92 215 10.26 2SS 8.64 8 3.54 339 2.55 123 4.10 235 6.81 223 1.1 3 267 0.642 328 2.65 134 1.02 159 13.85 284 9.72 9 4 .0 9 351 3.81 169 3 .4 3 277 5.69 295 1.47 304 1 .60 329 3 .2 6 114 2.21 169 17,41 293 10.80 10 9.07 240 0.739 239 0 .6 6 324 5 .0 3 235 3.72 326 3 .0 0 44 1.62 153 0.246 252 22.56 12

ro ro TABLE 22 HALF SPHEROID, 4 POLARIZATION* ______COi-PLEX RETURN VS fl

Frequency (GHz) 0=0° 0=30° 8=45° 0=60° 6=90° 3=120° 0=135° e 6= 180° A(cn) 4 A(cm) 4 A(ctts) A(cm) A(cra) A(cki) A(cm) $ A(cm) A(cn) 4 4 4 4 «> VI 4

l.O B 1 0 .5 6 329 0.624 13 0.525 347 0.526 359 0.569 358 0.532 2 0.592 3 0.627 6 0.503 357 2.1 5 2 1.96 348 2.05 341 2.07 343 2 .0 5 344 1.92 350 2.04 357 1.90 359 1.82 356 2.09 5 3.2 4 3 3.78 327 3.79 324 3 .8 3 326 3 .8 2 328 3.93 337 3.83 341 3.74 347 3.79 353 3.76 359 4.3 2 4 3 .6 8 272 5.09 291 4.73 287 5 ,1 7 300 5.82 311 5.70 327 5.83 338 5.30 337 5.90 343 5.4 0 5 2,21 266 2.05 279 2.26 292 2 .4 0 306 2.86 322 2.86 331 2 .7 8 342 2.9 5 357 3.19 23 6.4B 6 2 .1 8 194 1.37 172 0.105 303 1.07 4 1.40 6 0.823 319 1.23 4 2.09 33 3 .3 8 67 7.5 6 } 3.01 130 2.12 112 2.20 60 2 .62 60 2.25 56 1.03 88 1.29 76 2.64 66 4.30 104 8.6 4 8 3.14 125 2.14 88 2.64 62 3.5 4 59 2.94 80 1 .8 0 125 1.86 104 3.07 68 6.22 105 9.72 9 . 2.26 115 1 .09 109 1.46 68 2.91 57 2.62 82 1.62 130 1 .08 116 2 ,66 87 6.52 119 1 0 .BO 10 0 .6 29 94 0.741 173 0.634 131 1.57 92 l.BO 106 0.951 144 0 .753 150 1.55 124 5 .70 146

TABLE 23 HALF SPHEROID, e POLARIZATION COMPLEX RETURN VS 6

Frequency (GHz) 0=0° 6'•30° 0=45° 0=60° 0=90° 0=120° 6=135° 0= 150° 6=180° A(cm) 4 A(ati) 4 A(on) 4 A{cm) . $ A(an) # A(era) $ A(crn) $ A(cra) 4 A(cm) $

1.08 1 0.638 40 0.884 30 0.485 19 0.573 355 0.774 44 0.912 2 0.481 359 3.496 357 0.500 354 2.16 2 1.87 344 2.02 348 2.05 354 2 .08 352 2.15 351 2.07 352 2.07 355 1.98 359 1.92 4 3 .24 3 3.41 325 3.90 328 3 .9 9 336 4 .33 334 4.47 332 4.01 330 4.24 337 3 .7 8 348 3.50 0 4 .32 4 2.59 290 3 .0 5 304 3 .2 8 310 3.47 313 3.20 304 2.47 301 2.4 5 309 2 .4 0 325 2.44 342 5.40 5 2.11 267 2.93 309 3.74 328 3 .92 336 2.79 321 2.9 8 324 3 .0 0 334 3 .24 0 3.75 28 6.48 6 1.40 178 1.14 352 2.86 355 3.16 356 1.41 10 2.52 340 1.97 21 2.90 39 4.19 58 7 .56 7 2 .2 0 132 0.302 58 1.72 13 2.93 26 2.02 54 2 .23 200 0.669 286 2.46 38 5.24 72 8.64 8 2 .7 0 108 0.150 83 2.19 34 3.48 44 2.81 66 1.02 119 1.22 68 2.9 5 67 5.50 93 9 .72 9 5 .23 212 1.43 192 2.32 63 5.52 93 4.46 100 1.51 133 1.46 86 3.52 102 5.93 137 10.80 10 0 .469 99 3 .7 9 42 0.762 331 5.02 151 6.45 135 1.62 200 1.31 195 1.59 155 2.42 156

ro co 124 TABLE 24 LARGE SPHERE-CAPPED CYLINDER WITH STUB d, = 0, 4, POLARIZATION COMPLEX RETURN VSe o

Frequency o 0=10° e=20° 0=90° (GHz) A(cm) $ A(cm) $ A{cm) 4> A(cm) 0

1.08 1 3.14 248 2.64 256 1.75 259 10.77 10° 2.16 2 10.67 147 10.63 146 10.48 137 19.58 1° 3.24 3 6.43 25 7.21 21 8.39 5 16.17 91° 4.32 4 4.60 82 3.80 59 3.62 340 24.29 142° 5.40 5 8.52 0 7.34 342 5.49 294 19.87 209° 6.48 6 4.38 312 3.22 310 1.82 240 32.53 289° 7.56 7 5.44 251 6.26 266 5.09 197 26.78 347° B.64 8 1.93 269 2.77 230 4.35 142 29.42 51° 9.72 9 6.48 223 4.50 220 4.78 82 42.24 118° 10.80 10 1.86 94 3.40 125 1.64 72 15.54 144°

TABLE 25 LARGE SPHERE-CAPPED CYLINDER WITH STUB, $ = 90°, POLARIZATION COMPLEX RETURN VS 0

Frequency 0=0° 0=0 0° 0==20° 0==90° (GHz) A(cm) 4> A(cm) 4> A(cm) A(cm)

1.08 1 2.27 285 2.40 295 2.30 317 12.38 12° 2.16 2 4.76 59 4.35 64 4.26 59 16.78 354° 3.24 3 10.50 44 11.15 38 11.44 20 14.93 102° 4.32 4 8.05 82 6.97 79 4.65 28 26.06 150° 5.40 5 4.70 4 3.63 350 4.19 264 22.45 210° 6.48 6 6.54 292 5.46 295 4.83 246 32.19 281° 7.56 7 8.08 302 8.89 277 5.64 244 25.22 342n 8.64 8 2.74 358 0.813 286 2.40 108 27.77 55° 9.72 9 6.13 204 5.24 155 9.56 94 35.20 114° 10.80 10 2.48 150 1.90 71 8.59 124 9.51 150° APPENDIX B

COMPUTER PROGRAMS FOR AUTOMATED SPECTRAL RESPONSE MEASUREMENT

Assembler language lis tin g s fo r the measurement programs are included in this section. The assembler language is explained in

Appendices D and E. The programs lis te d include:

1. REC4 - the main measurement program.

2. FURPL - the periodic ramp response synthesis program.

1. REC4

The block diagram outlining the operation of th is program is shown in Fig. 7 in the text.

125 126

1 HLT SFIRST 2 FIRST TRU INST 3 RUN w a t OBJQU, 3 4 TRL READ 5 TRL SFLINT 6 TRL ADCNVT 7 RPA STRAD 8 WAT BANDGU, 4 9 TRL READ 10 TRL SFLINT 11 STR BAND 12 WAT ChRTQU, 3 13 TRL SREADYN IA TRL GRID 15 SNS *+1,,C SL1) 16 LDX 20,1,0 17 INI CLA CZ) 18 STR TEMP,1 19 TRX INI,1,1 20 RN1 LDX 128,1,0 21 LP1 NOV CIX1>,1X1 22 TRL SMEAS2,3,* 23 HLT DATREC 2 A SEN LP12,,C SL1) 25 TRL PLOT 26 LP12 CLA DATREC 27 SUB C *4000 *3 28 TRL SINTFL 29 TRL SFDVD,1,C *400000000414 30 STR DATREC 31 CLA DATREC+1 32 SUB C * 4000 * 3 33 TRL SINTFL 3 A TRL SFKLY,1,C *622077174402 35 TRL SFDVD,1,C *400000000414 36 TRL SSINCOS 37 TRL SCSTR,1,ANG1 38 MOV CZ>,CO) 39 CLA DATREC AO TRL SCMLY,1,AN61 A\ TRL SCSTR,1,DATREC A 2 CLS DATREC A3 STR DATREC AA LDX 10,3,2 45 LP2 CLA 1X1 A6 SUB C 643 47 MLY CIX3) 48 CLA CQ) 49 TRL SINTFL 50 TRL SFMLY,1,C *622077174373 127

51 TRL SSI NCOS 52 TRL SCMLY*1,DATREC 53 STR MREAL 54 CLA CQ) 55 STR FIMAG 56 CLA TEMP-SV3 57 TRL SFSUB*1*MREAL 58 STR TEMP-2* 3 59 CLA TEMP-1*3 60 TRL SFSUB#1*FIMAG 61 STR TEMP-1*3 62 TRX LP2* 3*2 63 CLA C 2563 64 STR VEL1 65 STR VEL2 66 STR VEL3 67 STR VEL4A 68 STR VEL5 69 MOV CID*DIR I 70 MOV C6D*INC1 71 TRL SM0VE1* 3* * 72 DIR1 BS 1 73 VEL1 BS 1 74 I NCI BS 1 75 MOV C *000100010001*D*DIR2 76 MOV C2D*INC2 77 TRL SM0VE1* 3* * 78 DIR2 BS 1 79 VEL2 BS 1 80 INC2 BS 1 81 MOV E*000101010101'D*DIR3 82 MOV C 2D *INC3 83 TRL SM0VE1* 3* * 64 DIR3 BS 1 65 VEL3 BS 1 86 INC3 BS 1 87 MOV C '000100010001*D*DIR4A 88 MOV C2D *INC4A 89 TRL SM0VE1*3#* 9.0 DIR4A BS 1 91 VEL4A BS 1 92 INC4A BS 1 93 MOV C1D*DIR5 94 MOV E 7D *INC5 95 TRL SMOVEl* 3* * 96 DIRS BS 1 97 VEL5 BS 1 98 INC5 BS 1 99 MOV 1X1* C1X1) 100 TRX L P 1 * 1*1 101 MOV C2563#VEL4 102 MOV C *000202020202*3#DIR4 •103 MOV C8963#INC4 104 TRL SMOVF.l # 3#* 105 DIR4 BS 1 106 VEL4 BS 1 107 INC4 BS 1 108 CLA BAND 109 SUB C13 110 .MLY BAND 111 MOV (Q)#CIX1) 11 2 CLA BAND 113 MLY C 23 114 MOV CQ)#CIX2) 115 LP3 CLA TEMP*1 116 STRAD STR **>1 117 TRX LP3#1 # 1 118 TRU INST 119 GRID MOV CPCS)#PCSGR 120 MOV CIX1)#IX1 121 MOV C1X2)# 1X2 122 MOV C1X3)#1X3 123 MOV C1X4)#1X4 124 TRL SGRID1 125 SNR *+1##CSL1) 126 MOV IX1#CIX1) 127 MOV 1X2#(1X2) 128 MOV 1X3# C1X3) 129 MOV 1X4#C1X4) 130 TRU RN1 131 FIMAG BS 1 132 PCSGR BS 1 133 MREAL BS 1 134 BAND BS 1 135 BANDQU TAB '1500120012' 136 ALPHA 3 FREQUENCY BAND # 137 OBJECT BS 1 138 OBJQU TAB *1500120012' 139 ALPHA 2 OBJECT # 140 CHRTQU TAB '1500120012' 141 ALPHA 2 PLOT DATA ? 142 DATREC BS 2 143 1X1 BS 1 144 1X2 BS 1 145 1X3 BS 1 146 1X4 BS 1 147 ANG1 BS 2 148 TEMP BS 24 149 FILZAD HLT STORAG 150 STORAG BS 168 129

151 PLOT MOV CPCS)*PCSPL 1 52 MOV C IX3>*PLIX3 153 CLA CIX1 3 154 MLY C 123 1 55 CLA CQ) 156 TRL SINTFL 157 TRL SFDVD*1 * C '620000000407 158 STR XI 159 CLA DATREC 160 SUB C *4000* 3 161 SHR 1 162 TRL SINTFL 163 TRL SFDVD*1 * C '620000000407 164 STR Y 1 165 TRL SSGUARE* 3* * 166 HLT XI 167 HLT Y 1 168 TRL SUP 169 CLA DATREC+1 170 SHR 2 171 TRL SINTFL 172 TRL SFDVD*1*C'620000000407 173 STR Y 1 174 TRL STRINGL* 3** 175 HLT XI 176 HLT Y 1 177 TRL SUP 178 MOV PL 1X3* C1X3) 179 MOV PCSPL* CPC) 180 PCSPL BS 1 181 PLIX3 BS 1 182 XI BS 1 183 Y1 BS 1 184 DTR1 BS 1 185 DEG WAT ROTGU* 5 186 TRL SREAD*1*ROTBUF 187 TRL SEXEC 188 TRL SCNVTF*1*R0TBUF 189 TRU DEG 190 TRL SFMLY*1 * C *500000000410 191 TRL SFLINT 192 MOV CZ>* CG) 193 SRL 2 194 STR ANGLE 195 CLA CQ> 196 SHR 34 197 STR REM 198 CAM ANGLE 199 STR R INC 1 200 CAM REM 201 STR RINC2 202 MOV C 2563 ^ RVEL1 203 MOV E 2 563;RVEL2 204 CLA ANGLE 205 TRC CZ> 206 TRU ROTNEG 207 TRU ROTPOS 208 TRU ROTEND 209 ROTPOS CLA C '040400000404'3 210 STR RDIR1 21 1 CLA E '04'3 212 STR RDIR2 213 TRU MVCAL 214 ROTNEG CLA E '101000001010'3 215 STR RDIR1 216 CLA E ' 10' 3 217 STR RDIR2 218 KVCAL TRL SM0VE1* 3 * * 219 RDIR1 BS 1 220 R.VEL 1 BS 1 221 RINC1 BS 1 222 TRL $M0VE1>3j * 223 RDIR2 BS 1 224 RVEL2 BS 1 225 RINC2 BS 1 226 ROTEND TRU INST 227 ROTBUF BS :5 228 ANGLE BS 1 229 REN BS 1 230 ROTQU TAB '1500120012' 231 ALPHA 4 DEGREES OF RROTATION? 232 CAL VAT BFILQUj 4 233 TRLREAD 234 TRL SFLINT 235 TRL ADCNVT 236 STR BDADD 237 VAT DFILQU.* 4 238 TRL READ 239 TRL SFLINT 240 TRL ADCNVT 241 STR DADD 242 VAT DFILQUj 4 243 TRL READ 244 TRL SFLINT 245 TRL ADCNVT 246 STR DADD2 247 VAT RFILQU* 4 248 TRL READ 249 TRL SFLINT 250 TRL ADCNVT 131

951 STR RDADD 252 WAT C ¥ILQUj 4 253 TRL READ 254 TRL SFLINT 2 55 TRL ADCNVT 256 STR CDADD 257 LDX 10^3^0 258 CLO MOV C '000777700000 ’ 3 >(Q) 259 CLA BDADD 260 ADD C 1X3) 261 SHL 1 5 262 MSK CL 2 263 MSK CL 5 264 MSK CL 8 265 MSK CL9B 2 66 CLA DADD 267 ADD C 1X3) 268 SHL 15 269 MSK CL 1 270 MSK CL 3 271 MSK CLIO 272 MSK CL10A 273 MSK CL 13 274 CLA DADD2 275 ADD C 1X3) 276 SHL 1 5 277 MSK CL9A 278 MSK CL9C 279 MSK CL 18 280 MSK CL18A 281 MSK CL21 282 CLA RDADD 283 ADD C 1X3 ) 284 SHL 15 285 MSK CL 4 286 MSK CL 6 287 MSK CL 1 1 288 MSK CL 1 5 289 MSK CL 19 290 CLA CDADD 291 ADD ( 1X3) 292 SHL 1 5 293 MSK CL 7 294 MSK CL9 295 MSK CL 14 296 MSK CL14A 297 MSK CL 17 298 CLA NDADD 299 ADD (1X3) 300 SHL 15 101 MSK CL 12 102 MSK CL 16 ■303 MSK- CL 2.0 304 CL 1 TRL SCLOD* 1 * ** 305 CL2 TRL SCSUB* 1 * ** 306 CL3 TRL SCSTR* 1 * ** 307 CL4 TRL SCLOD* 1 * ** 308 CL 5 TRL SCSUB* 1 * ** 309 CL 6 TRL SCSTR* 1 * ** 310 CL7 TRL SCLOD*1 * 31 1 CL8 TRL SCSUB* 1*** 312 CL9 TRL SCSTR* 1 * ** 313 CL9A TRL SCLOD*1*** 314 CL9B TRL SCSUB* 1 * ** 315 CL9C TRL SCSTR* 1 * ** 316 CLIO TRL SCLOD* 1 * ** 31 7 TRL 5 CM AG 318 TRZ CL 14 319 CL10A TRL SCLOD* 1 * 5f£3it 320 CL1 1 TRL SCDVD* 1 * ** 321 CL 12 TRL SCMLY* 1 * ** 322 CL1 3 TRL 'SCSTR* 1 * ** 323 CL14 TRL SCLOD* 1*** 324 TRL 5 CM AG 32 5 TRZ CL 18 326 CL14A TRL SCLOD*1*** 327 CL1 5 TRL SCDVD* 1» ** 328 CL1 6 TRL SCMLY* 1*** 329 CL1 7 TRL SCSTR* 1 * ** 330 CL18 TRL SCLOD* 1 * ** 331 TRL SCMAG 332 TRZ CL22 333 CL18A TRL SCLOD* 1 * ** 334 • CL1 9 TRL SCDVD* 1*** 335 CL20 TRL SCMLY* 1 * ** 336 CL21 TRL SCSTR*1*** 337 CL 2 2 TRX CLO* 3* 2 338 TRU INST 339 BFILOU TAB •150012001: 340 ALPHA 3 BACKGROUND FILE = * 341 BDADD BS 1 342 DFILQU TAB ’1500120012’ 343 ALPHA 3 DATA FILE = # 344 DADD BS 1 345 DADD2 BS 1 346 RFILQU TAB ’1500120012’ 347 ALPHA 3 REFERENCE FILE = if 348 RDADD BS 1 349 CFILQU TAB ’1500120012’ 3 50 ALPHA 3 CHECK FILE = if - 351 NDADD HLTNORDAT 352 DUMMY BS 5 353 NORDAT bs :20 354 CDADD BS 1 355 NRDAT TRL SGET*3j * 356 WAT FLNOQU*4 357 TRL READ 358 TRL SFLINT 359 STR RND1 360 TRL SREDATA* 3* * 361 HLT NORDAT 362 HLT RND1 363 TRU INST 364 RND1 BS 1 365 FLNOQU TAB ' 15001200121 366 ALPHA 3 STORAGE FILE # 367 STR TRL SGET*3* * 368 WAT FROMQU* 5 369 TRL READ 370 TRL SFLINT 371 TRL ADCNVT 372 RPA STRPT 373 WAT T0QU*4 374 TRL READ 375 TRL SFLINT 376 STR STR2 ; 377 TRL SREDATA* 3/ * 378 HLT STRMM 379 HLT STR2 380 LDX 20* 3* 0 : 381 STRPT CLA *** 3 382 TRZ STRPT1 383 STR STRMM*3 384 STRPT1 TRX STRPT* 3*1 385 TRL SENTER* 3* * 386 HLT STRMM 387 HLT STR2 388 TRL SRESTOR* 3* * 389 TRU INST 390 STR2 BS ]I 391 STRMM BS 20 392 FROMQU TAB ' 1500120012* 393 ALPHA 4 FROM INTERNAL FILE 394 TOGO TAB • 1500120012* 39 5 ALPHA 3 TO LIBRARY FILE # . 396 ADCNVT TRC C 63 397 TRU *+3 398 TRU MSTK 399 TRU MSTK 400 MLY C *24*3 401 CLA CO) 402 ADDFILZAD 403 THS 404 MSTK CLA CPCS) 405 SUB C43 406 STR CPC) 407 PR I WAT FROMQU* 5 408 TRL READ 409 TRL SFLINT 410 TRL ADCNVT 411 RPA PR 12 412 RPA PRI 3 413 ADD I 13 414 RPA PRI 1 41 5 LDX 10*3*0 416 WAT HDG* 6 417 PR I 1 CLA *** 3 418 STR CO) 419 WAT C * 1500120012 *3 * 1 420 PRI 2 CLA *** 3 421 TRL SCMAG 422 TRL SPRFL 423 WAT C '404040404040'3*1 424 PRI3 CLA +**3 425 TRL SATAN2 426 TRL SFMLY*1 * C ' 550000000410'3 427 TRL SFDVD*l*t'622077174402 '3 428 TRL SPRFL 429 TRX PRI1*3*2 430 TRU INST 431 HDG TAB * 1500120012' 432 ALPHA 5 MAGNITUDE PHASE 433 INST WAT INSTQU*4 434 TRU READ 435 INSTQU TAB '1500120012* 436 ALPHA 3 NEXT INSTRUCTION? 437 INDEX TRL SINDEX* 3* * 438 TRU INST 439 r e a d : ■MOV ■CPCS)*PCSR 440 R1 TRL SREAD*1* BUF 441 TRL SEX EC 442 CLA BUF 443 SHR 30 444 SUB C 33 445 TRZ CAL 446 SUB C 13 447 TRZ DEG 448 SUB C 53 449 TRZ INDEX 450 SUB C 53 450 SUB C 53 451 TP.Z NR DAT 452 SUB C 2 3 453 TRZ PRI 454 SUB £23 455 TRZ RUN 456 SUB C 1 3 457 TRZ C 456 TRL SCNVTF*1 *BUF 459 TRUQU 460 MOV PCSR*CPC) 461 PCSR BS 1 462 BUF BS 1 463 QU WAT GUEST*2 464 TRU HI 465 QUEST ALPHA 1 ? 466 TAB '150012* 467 USE DATFL*JON 468 USE ATAN2* LIB ' 469 USE READ*RAY 470 USE READ*JON 471 USE UTIL*LIB 472 USE MATH1*LIB 473 USECMPLX*LIB 474 USE MEAS3*JON 475 USE POINT*LIB 476 USE GRIDR*ROME 477 USE M0VE1*JON 478 END 136

2. FURPL

This program uses ten complex backscattered cross-section values, either typed in or retrieved from a data file , to construct a Fourier series periodic transient response waveform. The approximate im pulse, step, or ramp response can be generated. The output waveform is plotted on the digital plotter. 1 HLT SFOURPL 2 //FOURPL WAT C '1500120012*3* 1 3 WAT INTRO*4 4 TIMINT WAT TIQU* 6 5 TRL READ 6 TRL SFLINT 7 STR TI 8 ;;at DFILQU*4 9 TRL SREADYN 10 TRU DATFL YES 11 TRU NTERM NO 12 DATFL TRL S GET* 3* * 13 WAT FLNOQU* 3. 14 TRL READ 15 TRL SFLINT 16 STR FLFROM 17 TRL SREDATA*3* * 18 HLT V 19 HLT FLFROM 20 CLA C 103 21 STR N 22 TRU TIME 23 FLFROM b s :L 2 4 DFILQU TAB •1500120012* 25 ALPHA 3 DATA FILE INPUT? 26 FLNOQU TAB *1500120012* • 27 ALPHA 2 FILE # • 28 NTERM WAT NTQU* 5 . 29 TRL READ 30 TRL SFLINT 31 STR N 32 WAT FORQU*6 - 33 TRL SREADYN 34 TRU INPUT 35 TRU INPUT1 36 INPUT1 LDX 50*3*0 37 INI 1 CLA E 23 38 MLY N 39 CLA CG> 40 STR NN 41 CLA CIX3) 42 TRC NN 43 TRU IN21 IX3NN 45 TRU TIME IX3=NN 46 IN21 WAT REAQU* 4 47 TRL READ 48 STR V* 3 49 WAT IMAGQU* 4 50 TRL READ 138

51 STR V+l* 3 52 RPT1 TRX INI 1 * 3* 2 53 INPUT LDX 50* 3*0 5 4 INI CLA C23 55 MLYN 56 CLA 57 STR NN 58 CLA C 1X3) 59 TRC NN 60 TRU IN2 IX3NN 62 TRU TIME IX3=NN 63 IN2 WAT MAGQU* 3 64 TRL READ 65 STR MAG 66 WATPHAQU*3 67 TRL READ 68 TRL SFMLY* 1*C *622077341402 *3 69 TRL SFDVD* 1;[ *550000000410'3 70 TRL SSINCOS 71 TRL SFMLY* 1*MAG 72 STR V+l* 3 73 CLA CG) 74 TRL SFMLY* 1*MAG 75 STR V* 3 76 RPT TRX INI * 3* 2 77 TIME CLA TI 78 TRL SINTFL 79 STR TIF 80 CLA C '400000000401*3 81 TRL SFDVD*1* TIF 82 STR DT 83 PLOT WAT PLQU*7 84 TRL READ 85 IMP LDX 50*3* 1 86 IMP1 CLS V*3 87 STR W* 3 88 CLS V-l*3 89 STR W- 1 * 3 90 TRX IMP 1* 3*2 91 TRU PL1 92 SOU LDX 50*3* 1 93 SQU1 CLA C 1X3) 94 ADD c m 95 TRLSINTFL 96 TRL SFDVD*1*C'400000000402'3 97 STR DVD 98 CLS V* 3 99 TRL SFDVD*1 * DVD 100 STR W-l*3 139

101 CLA V-l* 3 102 TRL SFDVD*I*DVD 103 STR W* 3 104 TRX SQU1 * 3* 2 105 TRU PL 1 106 RAMP LDX 50*3* 1 107 RA1 CLA C 1X3) 108 • ADD C 1 3 109 TRL SINTFL 110 TRL SFDVD*1*C *400000000402 * 3 1 11 STR DVD 112 TRL SFMLY*1* DVD 113 STR DVD 114 CLA V* 3 115 TRL SFDVD*1 * DVD 116 STR W* 3 117 CLA V-l* 3 118 TRL SFDVD*1 * DVD 119 STR W- 1 * 3 120 TRX RA1* 3*2 121 PL1 CLA C 13 122 TRL SINTFL 123 STR DL 124 TRL SFPPI*1* DL 125 WAT MULTQU* 5 126 TRLREAD 127 STR YMULT 128 CLS C *400000000400'3 129 STRT 130 PL11 WAT PLQU1* 5 131 TRL READ 132 TRL SFMLY*1* C *400000000402 '3 133 TRL SFLINT * 134 SUB C 153 135 TRZ PLSM 136 SUB C 1 53 137 TRZ PLLA 138 TRU PL 1 1 139 PLLA TRL SGRID1 140 TRL SUP 141 CLA C 5003 142 STR Y 143 CLA C 7503 144 STR X 145 TRL SMOVE* 1*X 146 CLA CZ) 147 STR X 148 STR Y 149 TRL SORIG*1*X 150 TRL SUP 140

151 MOV TI#c1X4) 152 MOV CZ># 153 CLA T 154 PL2 TRL SFMLY# 1#£ *567000000413 '3 155 TRL £FLINT 156 STR X 157 CLS T 158 TRL SFPP 159 TRL SFMLY#1#YMULT 160 TRL SFMLY#1* £'764000000411 *3 161 TRL SFLINT 162 STR Y 163 TRL SPLOT#1 #X 164 CLA T . . 165 TRL SFADD#1#DT 166 STR T 167 TRX PL2# 3#1 168 TRL SUP 169 # CLS £5003 170 STR Y 171 CLS C 7503 172 STR X 173 TRL SMOVE# 1#X. . , 174 CLA Z)QAL3 3RKP STR X 176 STR Y 177 TRL SORIG#1#X 178 TRL SUP. 179 WAT FINGU# 4 180 TRL READ . 181 PLSM TRL SGRIDL. 182 MOV TI# ( 1X4). 183 MOV CZ># <1X3) 184 CLA T 185 PL22 TRL SFMLY,1#C'567000000412'3 186 TRLSFLINT 187 STR X 188 CLS T 189 TRL SFPP 190 TRL SFMLY#1#C *764000000410'3 191 TRL SFMLY#1#YMULT 192 TRL SFLINT 193 STR Y 194 TRL SPLOT#1#X 195 CLA T 196 TRL SFADD#1# DT 197 STR T 198 TRX PL22# 3#1 199 TRL SUP 200 CLS £2503 201 STR Y 202 CLS C 3753 203 STR X 204 TRL SMOVE.. 1*X 205 CLA CZ> 206 STR X 207 STR Y 208 TRL SORI G* 1 * X 209 TRL SUP 210 WAT FINQU* 4 211 TRL READ 212 INTRO ALPHA 4 FOURIER SERIES ROUTINE 213 TIGU TAB ’150012' 214 ALPHA 5 NUMBER OF INTERVALS? 215 NTQU TAB ’150012' 216 ALPHA 4 NUMBER OF FREQUENCIES? 217 MAGQU TAB ’1500120012’ 218 ALPHA 2 MAGNITUDE? 219 PHAQU TAB ’150012' 220 ALPHA 2 PHASE? 221 PLQU TAB ’1500120012’ 222 ALPHA 6 IMPULSE*STEP*OR RAMP RESPONSE? 223 MULTQU TAB *1500120012’ 224 ALPHA 4 MAGNITUDE MULTIPLIER? 225 FINQU TAB '1500120012* 226 ALPHA 3 PLOT FINISHED 227 FORQU TAB '1500120012' 228 ALPHA 5 POLAR COORDINATE INPUTS? 229 REAGU TAB '1500120012' 230 ALPHA 3 REAL PART? 231 IMAGQU TAB ’150012' 232 ALPHA 3 IMAGINARY PART? 233 PL GUI TAB ’1500120012’ 234 ALPHA 4 15 OR 7*5 INCH CHART? 235 TI BS 1 236 MAG BS 1 237 DL BS 1 238 N BS 1 239 W BS 100 240 NN BS 1 241 TIF BS 1 242 DT BS 1 243 DVD BS 1 244 X BS 1 245 Y BS 1 246 YMULT BS 1 247 T BS 1 248 V BS 100 249 USE PLOT*LIB 250 USE MATH1*LIB 251 USE DATFL, JON 252 USE UTIL,LIB 253 USE FOUR,JON 254 USE 6RIDL,JON 255 USEREAD,JON 256 USEREAD,RAY 2 57 USE GRIDR,ROME 258 USE EXRET,LIB 259 READ MOVCPCS),PCS 260 MOV C1X1>,1X1 261 TRL SREAD,1,REBUF 262 TRL 5EXEC 263 CLA REBUF 264 s h r 30 265 SUB £ 2 3 266 TRZ TIMINT 267 SUB C 73 268 TRZ IMP 269 SUB £73 270 TRZ PLOT 271 SUB £23 272 TRZ RAMP 273 SUB £ 1 3 274 TRZ SQU 275 TRL SCNVTF,1,REBUF 276 TRU QUEST 277 MOV 1X1,CIXl) 278 MOV PCS,CPC) 279 QUEST WAT QU, 1 280 TRU READ+2 281 QU ALPHA 1 ? 282 PCS BS 1 283 1X1 BS 1 284 REBUF BS 5 285 END APPENDIX C

COMPUTER PROGRAMS FOR IMAGE GENERATION

Listings for IMAG2, IMAG4, and IMSTRS are presented in this section.

A modified Fortran IV language is'used for these programs.

1. IMAG2

This is the basic imaging program. I t accepts p ro file function data from specified data files for each of three orthogonal look angles and computes the approximate lim itin g surface. A plot simu lating an isometric view of the lim itin g surface is generated using the digital plotter.

143 144

1 DIMENSION;AREAC3*128)#AC128)# NAMEC3)#XAREAC129)*YAREAC129> 2 DIMENSION;TPSHC129)#BTSHC129) 3 RFAL;MAG 4 INTFGER;klC5)#K2C5) 5 NLOOK=3 6 c a l l ;up 7 DISPLAY; 'HYPERBOLA FACTOR " 8 a c c e p t ;HYP 9 do;ioo 1= 1#nlook 10 DISPLAY; 'LOOK ANGLE NUMBER "# I 11 DISPLAY;'DATA FILENAME: " 12 CALL;FLNAKC NAME) 13 CALL;RDATACA#128#NAME) 14 DISPLAY;'SCALE FACTOR= " is a c c f p t ;s c a l e 16 DO;50 K = 1,128 17 ACK) = SCALF.*ACK) 18 50 AREACI#K)=HYP*ACK) 19 CALL;FPLOTC17.#0.) 20 c a l l ;f o r i g c o .#o .) 21 c a l l ;f p l o t c o .#o .> 22 CALL;FPL0TC0.#10.) 23 CALL;FPLOTC0.#5.) 24 CALL;FPLOTC10.24#5.) 2 5 CALL;UP 26 D0;90 L=l#128 27 X= »08*CL-1.> 28 Y=5.+.01*ACL) 29 90 CALL;FPLOTCX#Y) 30 CALL;UP 31 ioo continue; 32 CALL;FPLOTC17.#0.) 33 CALL;FORIGC0.#0.) 34 DO#* 1 1 0 1 = 1# 129 35 TPSHCI 5 = 0. 36 XAREACI) = 0. 37 YAREACI)=0. 38 110 BTSHCI)=128. 39 DO;120 1 = 1# NLOOK 40 DO;120 J=l#128 41 IF;CAREACI#J).GE.O.) AREACI# J)=0• 42 120 IF;CAREACI#J).LT.O.) AREACI#J)=-AREACI#J) 43 DO;130 K=1# NLOOK 44 DO;125 1=1#128 45 IF;CAREACK#I).LE.O.) K1CK)=I 46 125 IF#* CAREACK# I).GT.O.) GO TO; 126 47 126 DO;129 J=I#128 48 IF; CAREACK# «J) • GT. 0. ) K2CK)=J+1 49 129 IF;CAREACK#J).LE.O.) GO TO;130 50 130 c o n t i n u e ; 51 call;up 52 K11=K1(1) 53 K21=K2C1> 54 DO; 600 I=K1 1 * K2 1 55 X= 65•- I 56 K12=129-K2C2) 57 K22=l29-KlC2) 58 DO;550 J=K12^K22 59 Y=J-64. 60 Z=ABSCAREACI t I>/Y> 61 Z1=ABSCAREAC2.> 129-J5/X) 62 IF;CZ1.LE.Z) Z=Z1 63 K13=65-K1(3) 64 D0;200 L=1>K13 65 XY=ABSCX*Y> 66 IF;CAREAC3j 65-L).LT.XY> GO T0;201 67 200 c o n t i n u e ; 68 201 Z 1=L-1• 69 i f ; c z i .l e .z ) Z=Z1 70 XAREACI>=XARFACI>+Z 71 YAREACJ)=YAREACJ)+Z 72 i f ;CZ.GE.TPSHCJ+l)-l.) TPSHCJJ-Z 73 IF;CZ.l t .TPSHCJ+l)-l.) TPSHCJ)=TPSKCJ+1) 74 550 CONTINUE; 75 d o ;590 J=K12*K22 76 IF;CTPSHCJ>.GT.O.) GO TO;560 77 IF;CTPSHCJ+l).GT.O.) GO T0;560 78 IF;CTPSHCJ-1>.LE.O.> GO TO;590 •79 560 Y=J-64* 80 XPL=8.+»08*.866*CY-X) 81 YPL=10.+.08*CTPSHCJ>-.5*CX+Y>> 82 CALL;FPL0TCXPL,YPL) 83 590 CONTINUE; 84 600 CALL;UP 85 Kl1=K1C1) 86 K21=K2 Cl) 87 D0;900 I-Kl1*K21 88 X= 65•-I 89 Kl2=l29-K2C2) 90 K22-129-K1C2) 91 BTSHCK22+1)=128• 92 DO;850 J-Kl2 j K22 93 Y—J-64• 94 Z=-ABSCAREACI*I)/Y> 95 Z1--ABSCAREAC2.*129-J)/X) 96 if ; c z i .g e .z ) Z=Z1 97 Kl3=K2C3>-64 98 DO;700 L = 1>K13 99 XY=ABSCX*Y> 100 IF;CAREAC3*64+L).LT.XY) GO TO;701 146

101 700 continue; 102 701 Z 1= -L+1• 103 i f ; CZ1 • GF.• Z > Z = Z1 104 XAREACI)=XAREACI)-Z 105 YAREAC J)=YAREACJ) -Z 106 IF; CZ.GT.-l.) Z=128 107 IF;CZ.LE.BTSHCJ+l)-l.) GO T0;845 108 BTSHCJ)=BTSHCJ+1)- 1• 109 GO T0;850 110 845 IF;CBTSHC J-ll.GT.O.) 3TSHCJ-1>=0. 111 BTSHCJ)=Z 112 IF;CBTSHCJ+25.GT.1.) BTSKCJ+2>-l. 113 850 c o n t i n u e ; 114 DO;890 J=K12,K22 115 IF; CBTSHC JJ.GT.OO GO T0;890 116 860 Y=J-64. 117 XPL=8.+.08*.866*CY-X> 118 YPL=10.+.08*CBTSHCJ)-.5*CX+Y>> 119 call;fplotcxpl,ypd 120 890 c o n t i n u e ; 121 900 CALL;UP 122 c a l l ; FPLOTC 17 .,0.) 123 CALL;FORIGC0.,0.) 124 c a l l ;f p l o t c 0.,0.) 125 c a l l ;FPLOTC0.*10. ) 126 CALL;FPLOTC0.*5.) 127 CALL,* FPLOTC 10.24, 5.) 128 CALL;UP 129 DO;910 1=1,128 130 X=0.08*C1-1. ) 131 Y=S.-0.0025*XAREACI> 132 910 c a l l ;f p l o t c x ,y ) 133 c a l l ;UP 134 CALL; FPLOTC 17., 00 135 c a l l ;FORIGCO-, 0.) 136 CALL;FPLOTC 0 • , 0 • ) 137 CALL;FPLOTC0.,10.) 138 CALL;FPLOTC0., 5.) 139 CALL;FPLOTC10.24, 5 . ) 140 c a l l ;u p 141 D0;920 1=1,128 142 X=0.08*C1-1.) 143 Y=5.-0«0025*YAREACI> 144 920 c a l l ;f p l o t c x ,y > 145 CALL;UP 146 CALL;FPLOTC0.,0.) 147 call;up 148 EVNX=0. 149 EVNY=0. 150 EVDX=0. 151 EVDY-0• 1 52 d o ;950 J=l,128 153 EVNX=F.VNX+ABS CXAREAf J)-4.*AREA<1> J)/HYP) 1 54 E VN Y = EVNY+ABSC YAREAC J)-4•*AREAC 2* 129“J)/HYP > 155 F.VDX=EVDX+ABS< 4 • *AREA( 1» J) /HYP ) 156 950 EVDY=EVDY+ABSC4.*AREAC2*JJ/HYP) 157 EVX=EVNX/EVDX 155 EVY =EVNY/EVDY 159 DI s p l a y ; * EVX EVX 160 DISPLAY;* EVY ’SEVY 161 s t o p ; 162 u s e ; f l n a m .»l i b 1 63 u s e ;r u d a t a ,l i b 164 e n d ; 148

2. IMAG4

This revised imaging program accepts p ro file function input data as before, and also accepts operator inputs specifying a revised lim itin g contour and approximate target orientation in formation as discussed in Chapter V. The image plot uses the same format as IMAG2. 1 DIMENSION;AREAC3*128),AC 128)* NAMEC3),XAREAC129) s DIMENSION;TPSHC129),BTSHC129) 3 r e a l ;MAG 4 INTEGER;KlC5),K2CS) 5 NL00K=3 6 DISPLAY;'SPHEROID ANGLE" 7 a c c e p t ;p 6 P=3*14159*P/180. 9 FCOS=COSCP) 10 PSIN=SINCP) 11 DISPLAY;'SPHEROID ASPECT RATIO" IS a c c e p t ;a s 13 G=1/CAS*AS) 14 DISPLAY;'SIL. ASPECT LIMIT" 15 a c c e p t ;f 16 F=2.*F 17 SCFAC=PSIN*PCOS*C1-AS*AS) 16 SSFAC-1.-PSIN*PSIN*C1-AS*AS) 19 CCFAC=1 .*-PCOS*PCOS*C 1-AS*AS> 20 CALL;UP 21 DO;100 1=1jNLOOK 22 DISPLAY;'LOOK ANGLE NUMBER ", I 23 DISPLAY;'DATA FILE NAME: " 24 c a l l ;f l n a m c n a m e ) 25 CALL;RDATACA,128,NAME) 26 DISPLAY;'SCALE FACTOR= " 27 ACCEPT;SCALE 28 DO;50 K=1,128 29 ACK)=SCALE*ACK) 30 50 AREACI,K)=.70*ACK> 31 CALL;FPLOTC17., 0.) 32 c a l l ;FORIGC0.,0.) 33 c a l l ;f p l o t c o .,o .) 34 c a l l ;f p l o t c o .,i o .) 35 c a l l ;f p l o t c o .,5.) 36 call;fplotci0 .24,5.> 37 c a l l ;u p 38 D0;90 L=1,128 39 X=•08*CL~1•) 40 Y=5.+.01*ACL) 41 90 c a l l ;f p l o t c x ,y ) 42 c a l l ;up 43 100 continue; 44 call;fplotc17.,0 .) 45 c a l l ;f o r i g c o .,o .) 46 d o ; iio 1=1,129 47 TPSHCI)=0. 48 XAREACI)=0* 49 110 BTSHCI)=128. 50 DO;120 1=1,NLOOK 150

51 D0;i20 J=l,128 52 IF;CAREACI,J).GE.O.> AREACI, J) = 0. 53 120 IFJ CAREAC UJ ) .LT.O. > AREACI,J>=- AREACI, 54 DO; 130 K= UNLOOK 55 D0;i25 1 = U 128 56 IF;CAREACK*I).LE.O-) K1CK)=I 57 125 IF;CAREACK*I).GT.O.) GO TO;126 58 126 ‘ DO; 129 J=l, 128 59 IF;CAREACK,J).GT.O.) K2CK)=J+1 60 129 IF;CAREACK,J).LE.O.) GO to; 130 61 130 continue; 62 c a l l ;UP 63 K 11=K1C1) 64 K21=K2C1) 65 EXN=0. 66 EXD=0. 67 DO;600 I=K11,K21 68 X=65.-I 69 K12 = 129-K2C 2) 70 K22=129-K1C2) 71 DO;550 J=K12,K22 72 Y=J-64. 73 BRIND=Q • 74 GO T0;950 75 195 if;cz.eq.o.) go to; 510 76 K13=65.-K1C3) 77 IF;CK13.GT.Z+1) K13=z+1 78 D0;200 L=1,K13 79 XR 0T=X*P CO S+Y*PSIN 80 YROT=Y*PCOS“X*PSlN 81 IF; CAREAC3*65-L).LT.CXR0T**2+G*YR0T**2)/F) GO 82 IF;CAREAC3j 65-L).LT.ABS(XR0T*YR0T)) GO T0;201 83 200 continue; 84 201 Z 1=L-1. 85 i f ; c z i .l e .z > z =zi 86 XAREAC1)=XAREAC1)+Z 87 510 IF;CZ.GE.TPSHCJ+l>-1 . ) TPSHCJ) -Z 88 i f ; CZ.l t .TPSHCJ+n-l.) TPSHCJ) =TPSHCJ+1)-1. 89 550 c o n t i n u e ; 90 d o ;590 J=K12*K22 91 IF;CTPSHCJ).GT.O.) GO TO;560 92 IF;CTPSHCJ+l).GT.O.) GO TO;560 93 IF;CTPSHCJ-l).LE.O.) GO TO;590 94 560 Y=J-64. 95 XPL=8.+.08*.866*CY-X) 96 YPL=1O.+.08*CTPSHCJ)-.5*CX+Y)) 97 CALL;FPLOTCXPL,YPL) 98 590 continue; 99 600 c a l l ;u p 100 D0;900 I-Kl1,K21 151

101 X= 65•-1 102 K22=129.-K1C2) 103 BTSHCK22+1)=128• 104 D0;850 J=K12*K22 105 Y=J-64. 106 BRIND=1 107 GO T0;950 108 695 IF1CZ.EQ.0.) GO T0;810 109 K13=K2C3>**64 110 IF;CK13.GT.Z+1) K13-Z+l 111 Z=-Z 112 D0;700 L=1*K13 113 XR0T=X*PC0S+Y*PSIN 114 YR0T=Y*PC0S-X*PSIN 115 IF;CAREAC Z* 64+L).LT« CXR0T**2+G*YR0T**2>/F> GO T0;701 116 IF;CAREAC3*64+L).LT.ABSCXROT*YROT)) GO TO;701 117 700 c o n t i n u e ; 118 701 Z 1= - L + 1• 119 if;czi.ge.z> z=zi 120 XAREACI)=XAREACI)-Z 121 810 i f ;CZ.GT.-l.) Z=128 122 IF; CZ.LE.BTSHCJ+n-l,) G0T0;845 123 BTSHCJ)=BTSHCJ+l>-1. 124 GO T0;850 125 845 if;cbtshcj-u.gt.o.) BTSHCJM> = 0. 126 BTSHC J)=Z 127 IF;CBTSHCJ+2).GT.l.) BTSHCJ+2)=l. 128 850 CONTINUE; 129 D0;890 J=K12jK22 130 IF;CBTSHCJ).GT.O.) GO T0;890 131 Y=J-64. 132 XPL=8.+.08*.866*CY-X) 133 YPL=10.+.08*CBTSHCJ)-.5*) 134 CALL;FPLOTCXPL>YPL) 135 890 CONTINUE! 136 EXN=EXN+ABSCXAREACI >-5.71*AREA(1 * I ) > 137 EXD-EXD+ABSC 5.71*AREA(1# I ) ) 138 900 CALL;UP 139 CALL;FPLOTC 0 • * 0 • ) 140 E=EXN/EXD 141 DISPLAY;'E'SE 142 s t o p ; 143 950 YPRIM-SCFAC*X/SSFAC 144 XPRIM=SCFAC*Y/CCFAC 145 ARY=F*AREAC1*1)-CY-YPRIM)**2 146 ARX=F*AREAC2.> 129-J)-CX-XPRIM)**2 147 IF;CARY.LE.O.) GO T0;960 148 IF;CARX.LE.O.) GO T0;960 149 Z=ABSCAREAC1>I>/CY-YPRIM)) 150 Z1=SQRTCARY) 152

151 IF;CZl.LT.Z) Z-Zl 152 Z 1=ABS CAREAC 2.»129-J)/CX-XPRIM>) 153 IF;CZl•LT•Z) Z=Z1 1 54 Z1=SGRTCARX) 155 i f ;c z i .l t .z ) Z=Z1 156 YPL=10.+ .16*CBTSHCJ)-.5*CX+Y>) 157 call;fplotcxpl*ypd 158 850 CONTINUE; 159 900 CALL;UP 160 u s e ;f l n a m ,l i b 161 u s e ;rvjdata.»l i b 162 e n d ; * 3. IMSTRS

This in teractive program modifies ramp response waveforms to obtain virtual profile functions. Scaling, D.C. level shifting, time shifting, and forward blanking of waveforms are provided. 1 DIMENS I ON J AREAC 128),NAMEC3),ARFC 128) 2 REAL;MAG 3 i n t e g e r ;t b l n k ,t s h f t 4 COMPLEX;TFMPC10) 5 DISPLAY;'STORAGE FILE NAME: ” 6 CALL;FLNAMCNAME) 7 CALL;UP 8 DISPLAY;'TYPE IN ZERO IF FILE INPUT” 9 a c c e p t ;IND 10 IF;CIND.EO.O.) GO TO;iOO 11 DISPLAY;'NUMBER OF HARMONICS " 12 a c c e p t ;N 13 10 D0;50 J=1j N 14 IF;CIND.EQ.O.) GO TO;120 15 DISPLAY;'HARMONIC NUMBER ",J 16 DISPLAY;'MAGNITUDE CCM) " 17 a c c e p t ;m a g 18 DI SPLAY; 'PHASE CDEG) " 19 ACCEPT;PHASE 20 PHASE=PHASE/57.2 21 20 DO;50 K = 1, 128 22 ARG=J*K/20-37 23 FACT=COS C ARG )*COS CPHASE>-SINC ARG)*SIN(PHASE) 24 AREACK)=AREACK)+MAG*FACT/CJ*J) 25 50 CONTINUE; 26 c a l l ;FPLOTC17.,0.) 27 CALL;FORIGC0.,0.) 28 CALL;FPLOTC0.,0.) 29 CALL,*FPLOTCO., 10. ) 30 CALL;FPLOTC0.,5.> 31 CALL;FPLOTC10.24,5.) 32 CALL;UP 33 D0;90 L=l,128 34 X=.08*CL-1.) 35 Y=5*+.01*AREACL) 36 90 CALL;FPLOTCX,Y) 37 CALL;UP 38 91 DISPLAY;'DC OFFSET CIN) " 39 ACCEPT;DCOFF 40 DC0FF=DC0FF/.005 41 DISPLAY;'FORWARD BLANKINGCIN)" 42 ACCEPT;TBLNKF 43 DISPLAY;'TIME SHIFT CIN) " 44 ACCEPT;TSHFTF 45 DISPLAY;'SCALE FACTOR” 46 ACCEPT;SCALE 47 TSHFT=2 5*TSHFTF 48 TBLNK=2 5*T8LNKF 49 D0;95 L=l,128 50 IF,* CL.LT.TBLNK) ARFCD-O. 51 IFJCL.LT.TBLNK) GO T0J95 52 M=L-TSHFT 53 IFJCM.LT.O.) M=M+128 54 IF5CM.GT.128) M=M-128 55 ARFCL)=SCALE*CAREACM)-DCOFF) 56 95 CONTINUE; 57 D0;97 L=1t 128 58 AREACL)=ARF CL) 59 X=.08*CL-1.) 60 Y=5.+.01*AREACL> 61 9 7 CALLiFPLOTCX^Y) 62 CALL;UP 63 CALL; VJDATACAREA.. 128.. NAME) 64 GO TO;91 65 100 CALL;GET 66 DISPLAY;'FILE 67 ACCEPT;NUMB 68 CALL;REDATACTEMP>NUMB) 69 N=10 70 GO TO;10 71 120 MAG=CMAGCTEMPCJ)) 72 PHASE=ATAN2CTEMPCJ)) 73 GO T0;20 74 u s e ;f l n a m >l i b 7 5 u s e ;r w d a t a ,l i b 76 u s e ;d a t f l ,. JON 77 e n d ; APPENDIX D

CONTROL COMPUTER CHARACTERISTICSP 63

The purpose of this appendix is to describe the hardware and software associated with the digital computer used to control the measurement system. The description is given in sufficient detail that programs and hardware discussed elsewhere are understandable.’

The basic computer was manufactured by IBM and called the Minimal

Informer. It is a 37-bit parallel-binary stored program computer and uses the Fieldata instruction set.

Registers: The central processor has a total of 12 program mable registers and a core memory of 4096 37 -b it (plus p arity ) words.

The registers and their functions are tabulated in Table 26. Note that register lengths are not all the same. High-order bits are lost when data are transferred from memory or a long register to a shorter register. When data are transferred from a short register to a longer re s is te r, high-order zeros are dummied-in.

Number system: The number system used by the computer is

3 6 -b it binary fractional magnitude with sign as shown below.

Magnitude

156 157

TABLE 26

CPU REGISTERS

Name Uses Length Address zero register source of zero words, always zero, read only 37 bits 70000g index register 1 counting, address modifi- : cation 12 bits 70001g index register 2 counting, address modifi- : cation 12 bits 70002g index register 3 counting, address modifi- : cation 12 bits 70003g index register 4 counting, address modifi- : cation 12 bits 70004g

A register accumulator, addition sub traction multiplication division, shifting, logical operations 37 bits 70010g

Q register quotient register, multipli cation, division, shifting : 37 bits 700118 program counter holds address of next in - : struction to he executed 15 bits 70013g program counter holds return address from 70014b store subroutines 37 bits also mem. loc. 14g loc. 14g display register console indicator lig h t display, write only. 37 bits 70016g switch register 1 console switch register, read only 37 bits. 70020g. switch register 2 console switch register, read only 37 bits 70021 g 158 The largest number is 1-2"^. The smallest is -(1-2"^). Minus zero is a valid number and in fact results when a positive number in the accumulator (A) register is reduced to zero by an addition or subtraction operation.

Addressing and instruction format: Memory and registers can be referenced by 1 5 -b it addresses eith er d ire c tly or by means of indexing. If indexing is specified, the contents of the specified index reg ister are added to the address part of the instruction word to obtain an effective address. The instruction format is shown below.

37 . . .36 . .31 30 28 27 16 15 1

OP Y B a Code

Bit positions 31 through 36 contain a 6 -b it operation code. B it positions 1 through 15 («) contain the 15-bit address of an operand in memory reference instructions. Bit positions 28 through 30 (y) specify the index register (1,2,3 or 4) whose contents are to be added to before the instruction is executed Ay of zero specifies no indexing.

Sense instructions: The 0 part of the instruction word (bits

16 through 27) performs d iffe re n t functions depending on the in structions. One of the functions is to specify an indicator or con dition to be set, reset or tested by the sense instructions. Table 27 gives the sense functions of corresponding 0 codes. The SEN (sense),

SMS (sense and set) and SNR (sense and reset) instructions have operation codes 05Q, 06g and 07Q, respectively. If indexing is TABLE 27

SENSE FUNCTIONS

Octal code Function SNR SNS SEN 2-76 even numbers - I/O converters in use

100 overf1ow alarm X

102 interpret sign mode X X

103 continue on I/O errors X X

110 sense switch 1 X

111 sense switch 2 X

112 sense switch 3 X

113 sense switch 4 X

114 sense lig h t 1 XX X

115 sense lig h t 2 X X X

130 I/O converter alarm X 1

136 break occurred x ;

140 allow interrupts X : X

141 allow I/O interrupts X X

142 allow CPU interrupts X ; X

153 w rite EOF X X

155 memory alarm X

156 bit error X :

144 I/O converter deselect* X

174 generate bit error* X

176 complement memory.parity X X

*Transfer is forced 160 specified by y, the contents of the specified index register are added to a to form an effective address. For the SEN instruction, i f the condition being tested is met or the indicator being tested is set, the effective address is placed in the program counter causing a transfer to occur. Otherwise the program counter is in cremented by 1 and the program continues in sequence. For the SNS and SNR instructions the specified indicators or conditions are set and reset, respectively. For these instructions if a change in state of the specified indicator occurs the computer transfers to the effective address, otherwise it continues in sequence.

Overflow: For instructions where accumulator overflow is possible, that is, the result of executing the instruction is greater than or equal to unity and w ill not f i t in the A register, the action taken by the computer is controlled by the $ part of the instruction word as specified in Table 28. Two exceptions are the add e (ADB) and subtract 3 (SBB) instructions where the equivalent of e = 5q is forced.

Table 29 describes the operation of the central processor in structions. In order to keep the table reasonably short the following conventions have been used:

1) a means the value of the a part of the instruction word.

If the instruction has been indexed, it means the sum of

the a part of the instruction word and the contents of

the specified index register.

2) C(a) means the contents of address cc. 161

TABLE 28

ACTION TAKEN ON OVERFLOW* II B it = 0 w * v r+

B it 18 clear OA before instruction execution no action

B it 17 set OA on overflow no action

B it 16 set OA on overflow continue on and halt overf1ow

* ADB and SBB force equivalent of 1012 for bits 18-16 162

3) C(x) where x is a register name means the contents of the

register x. C(A), for example, means the contents of the

accumulator (A) reg ister.

4) If a register column is left blank the corresponding register

is unaffected by the instruction. For instructions referencing

two index registers, Iy and I( y + 1 ) , i f y is 4 , y+1 is 1.

Several instructions are not completely specified in Table 29.

Three of these, the sense instructions, have already been described.

Another which needs further discussion is the repeat (RPT) instruction.

The repeat instruction causes the instruction immediately following it to be executed a + 1 times. After each execution of the instruction its a is increased by 0 of the repeat instruction, e of the repeat instruction is also placed in index register 4. If the repeated in struction calls fo r indexing, i t is indexed normally before the f ir s t execution. Both instructions remain unchanged in memory. For the sequence RPT, TRC, the TRC (transfer or compare) instruction is repeated until the contents of the accumulator are less than or equal to the contents of address a for a maximum of a (of the RPT) + 1 times. If the TRC is repeated the specified number of times, one instruction is skipped and the computer continues in sequence. I f the contents of address a are equal to the contents of the accumulator, two instructions are skipped. If the contents of the accumulator are less than the contents of address a the computer continues in sequence. The remaining repeat count is placed in index register 3. For the RPT, TABLE 2 9 CPI) INSTRUCTIONS In s t O verflow Index Address Overflow & Code Indexable Repeatable P ossible Function A Q Regs a Conditions Comments

AOS 24 Yes Yes Add Beta C (a) + S C(A) I Y = C{b) + 6 C (a) p o s itiv e and Bits 16-13 do not LC(q) + 1 carry from bit co n tro l a c tio n on 36 of adder overflow, O.A. is s e t and computer continues in sequence.

ADD 12 Yes Yes Yes Add C(A) + C(o) Same sign and Sits 16-18 control 1 carry from a c tio n on o verflo w . bit 36 of adder

ADM 13 Yes Yes Yes Add C(A) + |C(u)| Sign of A posi Bits 16-18 control Magnitude t iv e and 1 c a rry a c tio n on o verfle w . from b it 36 of adder.

CAM 11 Yes • C lear and Add + J C M I . Magnitude

CLA 10 Yes C le a r and Add CCa)

CLS 14 Yes C lea r and Sub 1-36: C(a)i_3s t r a c t 37: Complement • ^{0)37

CSM 15 Yes C le ar and - |C ( a ) | Subt. Magni tude

CYL 35 Yes Cycle L e ft A, Q cycled, Signs included; if long l e f t a mod o = 0, contents of 123 placed A and Q unchanged.

CYS 34 Yes * Cycle L e ft A cycled le ft Sign is not included; Short a mod 128 If o = 0, contents o f A unchanged.

DVD 22 Yes Yes D ivid e Remainder Q uo tien t IC(A)| > |CCa)| C(A) * C(b ); b its (15-18) control o v e rflo w .

CTl CO TARLE 29 CPU INSTRUCTIONS (c o n t in u e d )

In s t Overflow Index Address Overflow I Code Indexable Repeatable Possible Function A Q Regs a Conditions Cements

3VF 26 Yes Yes Divide Fast 22-36: 1 -1 5 : W - i s l i C(A) * C(a)l-15! Remainder Q uotient Bits 16-18 control R a h - i s ) 1 -2 1 : Zero 16-36: Zero o verflow

JVL 23 Yes Yes D iv id e Long Remainder q u o tie n t |C(A) | » lC(o)| C(A,Q) » C(3); bits (16-18) control o verflo w .

HIT 00 H a lt Stop computer; complete I/O con verter operations which are in process.

LDX 53 Load index a l - 12+1 ^ In 4 index register R egisters 6+1 computers T=4, *+ 1=1

L6A 03 Yes Yes Logical Add Logical Sun 0+0=0 0+1=1 C(a) + C(A) 1+0=1 1+1=1 b its 1-37

LS!i 02 Yes Yes Logical Logical Pro 0x0=0 1x0=0 M u ltip ly duct C(a)*C(A) 0x1=0 1x1=1 b its 1-37 i LGS 04 Yes Yes L og ical Nega 1 *s comple B its 1-37 tio n ment of C(a) . t

LCD 51 Yes Load C(a) placed in addressable reg s

RPT 3 i= l Memory te s t C(o2)-»o2 Process is perforr.d twice for each LOO 2 2^ 2 (s p e c ia l C(a2+6l)+ 2+gl sequence) C(o2+2&l)+a2+23l memory lo c a tio n a t e tc . a 16-usec rate for * (oj) times. TABLE 29 CPI' INSTRUCTIONS (continued)

In s t Overflow Index Address Overflow & Code Indexable Repeatable possible Function A Q Regs Q Conditions Comments

HLF 27 Yes M u ltip ly (1-15) High (22-36) Low C(a)i_i5*C(A)i_;5 Fast order bits. order bits. Sign of product (16-35) Zero (1-21) Zero In A and Q

MLR 21 Yes M u ltip ly and High order bits Low order b it C(tr)*C{A) Sign of Round [rounded if product in A and Q. *3 6 " «

KLY 20 Yes M u ltip ly High order bits Low order b it C(a)*C(A) Sign of ■ product in A and Q.

KOV 52 Yes Move I f RPT, KOV C(a) location v3. then contains If RPT =■ 1. modify last a refere ice vS by C D 2]

KSK 55 Yes Yes Mask C(A)'C(Q)+C(a)*C(Q) Q is l's comple ment of Q. * 1 KRH 37 Yes Norm alize Result of shifts 1 -1 5 Numbe r Shift C(A) left with O's inser o f s h if t s . until 1 appears + ted in vacated .1 6 -3 7 : O's in bit 36 if p o s itio n s C(A)=0,N=36, Sign b it unchanged.

RPA 54 Yes Yes Replace • t 1 -1 5 : C(A) 1-15 Address 1 6 -3 7 : ur - changed

RPT 01 Yes Repeat e - i 4 o-*step counter. 13 un changed

533 25 Yes Yes S u btract C (o)-B C(A) l r = C(a) - 5 C(A) are nega Bits (16-18) do not Beta t iv e and 1 c a rry control action on ^ ( ° ) ] - 1 2 ’ ® from b it 36 of overflow; O.A. is adder s e t and computer continues in sequence.

* = Logical "AND" + » Logical “OR" TABLE 2 9 CPU INSTRUCTIONS (continued)

In s t Overflow Index Address Overflow & Code Indexable Repeatable Possible Function A Q Regs a Conditions Comments

SBM 17 Yes Yes Yes S u btract C(A)-|C(a)| A is negative Bits (16-18) contrd magnitude and 1 c a rry overflow action. from b it posi tion 36 of adder

SEN 05 Yes Sense ( 6 )= l,o -P C (S)=0. PC+l-PC

SHI 30 Yes Yes Shift Left C(A) shifted 1 shifted from Sign not shifted; l e f t o mod 126 bit 36 of A inject O's to right r e g is te r of A register; bits (16-18) control over flow action.

SHR 32 Yes Shift Right C(A) shifted Sign not included; r ig h t o mod 12B inject O's to le ft. s a 31 Yes Yes Shift Left C(A.Q) Shifted 1 shifted out Signs not shifted; long le ft a mod 128 of position 36 of inject O's to right • A re g is te r of Q register; bits (16-18) control overflow action

SNR 07 Yes Sense and ( s ) - l ,a-*PC and 0^3 Reset (e}=0,1+PC-PC

{ b H .o -P C and 1 SNS 06 Yes Sense and • 1 Set (S)=l, HPC-PC

SRL 33 Yes Shift Right C(A and Q) Signs excluded; Long Shift right o Inject O's to left mod 128 places of A register.

STR 50 Yes Yes S to re CCA) T

In s t Address Overflow I Code Indexable Repeatable Possible Function A Q Regs Conditions Co—ents

SUB 16 Yes Yes Yes Subtract C (A )-C (o) Different signs and 3its (16-12) 1 carry from bit overflew action. 36 of adder

TRC 47 Yes Yes Compare C(A) I f RPT, TRC C(a)>C(A),PC+l then I’ con C(c)

TRL 41 - Load PCS B- I Y PC+l-PCS R eg is te r and re g .o * PC T ra n sfer

TRii 46 Yes Transfer on Negative 1a )37=0*(PC+1)-?C

TRP 44 Yes Transfer on (A)37=3i;-?- . P o s itiv e (A)37=1,(?C+1)-PC

TRS 42 Transfer to C (PCS) reg PC PCS Register

TRU 40 Yes T ra n s fe r Un I f I ^ V l : 3-»PC conditional n + s-»iT

TAX 43 T ra n s fe r on . • , i f If I( +1M 0, Index l ( T+ l ) - V l ( T+ l ) a-*?C

TRZ 45 Yes Transfer on |Ai=0,=-*PC Zero jA|j>0,PC+l-PC 168

MOV (move) sequence the yb address is indexed by the contents of

index register 2. When the sequence is completed the Q register

contains the last address where data was extracted.

Timing for instructions is given in Table 30.

In te rru p t: A number of conditions can cause an in terru p t. When

an interrupt occurs the contents of the program counter are placed in

memory location 15Q and 00200g is placed in the program counter so

that the computer transfers to location 200g. For an interrupt to

occur the allow— interupts indicator (140g) must be set. When an

interrupt occurs the allow -interrupts indicator is reset to prevent

any further interrupts until the indicator is set again by the program.

In addition, for interrupts to occur, at least one of two other indicators

must be set. The allow-CPU indicator must be set fo r memory p arity

or bit errors to cause interrupts. Setting the allow-I/O indicator

enables a number of I/O conditions to cause interrupts.

Input/Output: Input/output operations are handled by a separate

processor called the I/O converter. The relationship between the I/O

converter, the central processor and the I/O devices is shown in

Fig. 75. When an I/O instruction is recognized by the central processor

i t is transmitted to the I/O converter fo r decoding and processing.

The central processor normally continues with the succeeding in 

structions while the I/O converter independently processes the I/O

instruction. If the I/O converter is already in use when the central

processor encounters an I/O instruction, the central processor is

held up u ntil the I/O converter is fre e. Data are transferred through 169

TABLE 30 CPU INSTRUCTION TIMING

Average Average OP Time OP Time Coda Mnomonic Name tnsoc ) Code Mnomonic Namo U see.}

00 t U J Holt 22.67 m, 40 l a y Unconditional tranifer 17.33 01 R£I Rnooot 21.33 < 41 IBL Load PCS and transfer 25.33 $ 02 LGM* LggiggiMultiply 22.67 U. 42 IBS Transfor >t> PCS 25.33 03 ISA* Logical Add 22.67 DC 43 IM Tronsfer ■so Index 29.67 LL_ 04 L £ ^ * Logical Naaalion 22.67 W> 44 IS £ Tronsfer On 1+1 A 20 t j 05 SEN Sente 24 Z 45 BZ Transfer, on_Zero_A 24 <3 Transfer on f-) A S i 06 &US feme ond Set 24 46 IBN 20 07 SNR Seme ond Reset 24 47 ISC* Tromfer on compare 21.3

10 CLA Clear and Add 22.67 50 SIB* StPJfl 22.67 11 c m Clear and Add 51 LQQ Lflfljj 33.33 Magnitude 22.67 IS> 52 m y ' Move 33.33 12 ADD* Add 24 < 53 LOX Load Indox 18.67 13 Add Magnitude 24 u 54 RPA* Replace Address 28 iJ? AJ2AS* J3 14 0 5 Clear ond Subtract 24 s 55 MSK* Mask 48 O! 15 PSM Clear and Subtract o 56 Spare o M nsnLtudo 22.67 57 Spare • < 16 -5 1 2 3 * Subtract 24 17 SCM* Subtract Moanitudo 24 60 Spare t/1 61 Spare v"! < lS%20 MLY M u ltip ly 392 - j 62 Spare < 21 MLR M u ltio lv and Round 400.7 u 63 Spare u 22 BYD O .'Jtjdj 425 64 Spare 23 DVL 425 65 Spare > P.iyitk-Leay fu Ax 24 A d d B ela 41.33 a. 66 SKB S kip 21.3 U 5 25 SSfl* Subtract Bota 41.33 67 esp Bacltfpocrj 21.3 26 G Y f C.'yid?_fqif 208 27 t e k f M ultiply East 177.3 70 RAN Rnad Alphameric 21.3 71 e k y Rcod Reverse 21.3 30 SHJ, S h iffJ jift 26.67 4n 72 ROK Read O ctal 21.3 in 31 5 U Shift Loft l,9PP 26.67 4a < 73 s e a Ssurcb 21.3 26.67 4n - i 74 WAN Write Alohameric 21.3 32 SHR Shift Right M 33 26.67 4a 75 WWA Rowrite 21.3 i? SSL ShifLRighL Ltmg n 2 34 ££5 Cycle $hort 26.67 4n ^ 76 WOK Write Qetgl 21.3 r_! 35 C ycle Lona 26.67 4a 77 RWD Rewind 21.3 u. 36 Spare X in ■ 37 fciS M Normalize 28 4 (n-1)

• Repeatable instructions. If instruction it repootod, subtract 1.33 H mc from overage rime for each repetition after the first, Indexing, if any, oppliei to first repatition only. Nonindexoble instruction. If Instruction is indexable and it Is indexed, add 2.67 H sec ; average time. 170

the central processor between the core memory and the I/O converter

as 37 -b it words.

DISK MEMORY DISK ADDRESS DATA (8 BIT CHARACTERS] DEVICE CENTRAL I/O SELECTION PROCESSOR CONVERTER (DIGITAL DATA DATA MUX.) TELETYPEWRITER (8-B IT CHARACTERS) DATA PARALLEL CORE j u i r u L — TO SERIAL E3 Q MEMORY CONVERTER PLOTTER ANALOG \f(J TO DIGITAL CONVERTER PAPER TAPE READER

PAPER TAPE PUNCH

Fig. 75—Clock diagram showing the relatio n between the I/O converter, the central processor and the I/O devices.

I/O instruction format: The I/O instruction word format is shown below.

37 36 31 30 22 21 16 15 "1 OP Code KJ a

The a part (b its 1 through 15) specifies the starting memory address for data transfer. The K part specifies the number of words to be transferred. For write (output) instructions, bits 22 through 30 are 171 used. For read (input) instructions bits 22 through 29 are used to specify eith er a word count or block count as determined by b it 30 being a zero or a one. Blocks are made up of arb itra ry numbers of words and are separated by block marks. Block marks w ill be ex plained below. The J part of the instruction word is the device address used by the device-selection multiplexer.

I/O registers: Two registers and a memory location are available for programming. The I/O instruction register contains the op-code and J address of the current or la s t I/O instruction. The K part contains the current contents of the work or block counter and the a part contains the memory address of the next memory location from which data are to be taken or into which data are to be placed. When the I/O instruction is completed the address is one higher than the la s t location accessed. The address of the I/O instruction register is 70030g. The maintenance register (address 70024g) contains in formation on the current status of the I/O converter equipment and is not generally used fo r programming. Memory location 10g contains the current or last I/O instruction executed.

Data character format: Data are transferred between the I/O converter and the address-selection multiplexer as 8-bit characters.

The 8 bits are designated, from high order to low order, as P (parity),

C (control), Ig, Ip Dg, D^, Dp DQ. For output the P-bit is generated by the I/O converter to give the character odd parity. For input the

I/O converter tests for odd parity. A C-bit of 1 indicates a data character. A C -b it of 0 indicates a control character. Meaningful control characters are BLS (block start), BLE (block end), EOF (end 172 of file ) and STOP. The codes for the control characters are given in

Table 31.

TABLE 31

CONTROL CHARACTER CODES

BIT P c l 2 h °3 D2 D1 Do BLS 1 0 1 0 1 0 1 1

BLE 0 0 1 1 0 1 0 0

EOF 1 0 1 1 0 1 0 1

STOP 0 0 1 0 1 1 1 1

Each write instruction causes a BLS character to be transmitted at the beginning of the output operation. Data characters are generated by breaking down the words to be output. The data characters are followed by two BLE's. EOF's can be substituted by BLE's by executing a SNS 153g prior to execution of the output instruction.

For input, 8-bit data characters are assembled into 37-bits computer words. The input data may be divided into blocks for a read-by-blocks instruction (bit 30 of the read instruction word = 1) by

BLS's a t the beginning of each block and two BLE's or EOF’ s a t the end of each block. I f EOF's are used and the I/O in terru p t has been enabled by execution of SNS 140g and SNS 141g instructions, an inter rupt will occur when the EOF's are read. For a read-by-words (bit

30 = 0) instruction, block marks may or may not be present. The specified number of words is read regardless of how the data are divided into blocks. If a STOP character is read, the input.operation is terminated without regard for word or block counts. Data characters are transferred between the I/O converter and the address selection multiplexer in one of three modes; as octal data, as alphanumeric data in the interpret-sign mode, and as alphanumeric data in the not-interpret-sign mode. For octal output 37-bit computer words are broken into thirteen data characters corresponding to the alphanumeric representations of the sign and the twelve octal digits making up the remainder of the word. The alphanumeric represen tation is obtained by setting the I2, 1^ and D3 bits equal to 1102 and the D2, D-j and Dg bits equal to the octal number. Transmission starts at the sign b it and provides to the low order end of the word. For alphanumeric output in the interpret-sign mode the 37-bit word is broken into seven data characters. The sign bit is output as an alphanumeric zero or one as fo r octal output. The remainder of the word is output six bits at a time. Each group of six bits forms I2 through Dg of the corresponding data character. The interpret-sign mode is set prior to the execution of an alphanumeric I/O instruction by the execution of a SNS 102g instruction. In the not-interpret-sign mode the sign bit is ignored and the 37-bit word is broken into six data characters.

For input, the process is reversed and data characters are assembled into 37-b it computer words. For input in the n o t-in terp ret-

sign mode the sign bit is made zero. Blocks of data to be read need not form an integral number of characters. If block mark characters are encountered, the I/O converter completes incomplete words by supplying low-order zeros. Incomplete words are sim ilarly completed

if a STOP character is read. 174

I/O instructions: A lis t of input-output instructions is given in

Table 32. The search instruction performs an automatic search fo r data defined by up to thirty descriptors. It hasn't been used in any of the programs published in this work and w ill not be described.

Magnetic tape instructions have been omitted since the present computer system does not have magnetic tape.

TABLE 32

I/O INSTRUCTIONS

0c’;;al OP code Mnemoni c Function

70 RAN read alphanumeric

72 ROK read octal

73 SCH search

74 WAN w rite alphanumeric

76 WOK write octal

Disk memory: The disk memory has a capacity of 20.5 million

8-bit characters. The data are divided into ten thousand tracks of

2050 characters each. The data are written and read by a single pair of heads which are mechanically positioned to the desired track.

This is accomplished by the execution of a w rite octal instruction with a J address of 30g and a word count of one. The a address specifies the location of a four-digit BCD track address. Access time is be tween 100 and 800 milliseconds. Data can be w ritten by a w rite alpha numeric instruction with a J address of 30g. Old data are e ffe c tiv e ly erased. Similarly, data may be read by a read alphanumeric instruction.

If more data than can be contained on one track is specified by the word 175 or block count the heads are automatically moved to the next sequential track and the input/output operation is continued.

Teletypewriter: The teletypewriter uses a modified ASCII code

(American Standard Code fo r Information Interchange) as shown in

Table 33. The ASCII code bits actually used by the teletypewriter are given as column headings and down the l e f t margin in the tab le. The internal code representation is given in octal along with each character.

For output, bits I 2 through DQ of the output character are used directly to form bits bg through b-j of the ASCII character. B it by is formed by either complementing or duplicating b it bg. The mode is set to

"complement" at the beginning of the output operation and does not change so long as non-zero (b its I 2 through Dq) characters are output.

A zero-character is not transmitted to the printer but switches the mode to "duplicate". The first non-zero character is transmitted to the printer in the duplicate mode and the complement mode is restored.

Trailing zero-characters are effectively ignored. Control characters are ignored.

For input, characters from columns 0 through 5 are converted in a way analogous to the output conversion. Columns 0 and 1 pro duce two input characters for each keystroke, a zero-character and a character having I 2 through Dq equal to bg through b-j. Columns 2,

3, 4 and 5 produce single characters with I2 through Dq equal to b2 through b^. Columns 6 and 7 produce control-characters with I 2 through

Dq equal to bg through b-j. The only characters from columns 6 and 7 that can be generated from the keyboard are the RUBOUT and the STOP, 176

TABLE 33 TELETYPE I/O CODE

Lb?,...... __ °1 °1 °°i lbfi. 'o ‘l \ \ \ ASCII intormer ■ K Control Print ing cl larac ters Control 4u b- Characteirs Characters

% bi 0 1 2 3 4 5 6 7 space 0 @ P 0000 0020 40 60 00 20 (00)40 (00)60 DCI 1 A 0 0001 0001 0021 i i 61 01 21 (00)41 (00)61 DC2 li 2 B R 0010 0002 0022 42 62 02 22' (00)42 (00)62 DC3 # 3 C S 0011 0003 0023 43 63 03 23 (00)43 (00)63 DC4 $ 4 D T BLE 0100 0004 0024 44 64 04 24 (00)44 (00)64 WWRO % 5 E U EOF 0101 0005 0025 45 " 65 05 25 (00)45 (00)65 & 6 F V 0110 0006 0026 46 66 06 26 (00)46 (00)66 1 BELL 7 G W 0111 0007 0027 47 67 07 27 (00)47 (00)67 ( 8 H X 1000 0010 0030 50 70 10 30 (00)50 (00)70 ) 9 I Y 1001 0011 0031 51 71. II 31 (00)51 (00)71 LINE FEED * J Z 1010 0012 0032 52 72 12 32 (00)52 (00)72 “ ESC. + K I BLS ion 0013 0033 53 h 13 33 (00)53 (00)73 < L I 1100 0014 0034 54 74 14 34 (00)54 (00)74 CAR RET. M : 1101 0015 0035 55 75 15 35 (00)55 (00)75 SHIFT OUT > N + m o 0016 0036 56 76 16 36 (00)56 (00)76 "SHIFT RUB- IN / ? 0 STOP OUT n n 0017 0037 57 77 17 37 (00)57 (00)77 177

the la tte r of which is generated by the "CLR KYBD" key. The "CLR

KYBD" key also generates an interrupt pulse and w ill cause an inter rupt i f the I/O interrupt has been enabled by SNS 140q and SNS 141g instructions.

P lo tte r: The p lo tte r has four basic pen motions: 0.01 inches in the plus-x d irectio n , 0.01 inches in the minus-x d irectio n , 0.01 inches in the plus-y direction and 0.01 inches in the minus-y direction. In addition the pen can be raised or lowered. Each data character output to the plotter produces one or more functions as indicated by Table 34. x- and y-motions can be combined to produce 45-degree diagonal motions. Zero-characters and control-characters are ignored.

Parallel/serial converter: In the parallel-to-serial converter, bits I 2 through DQ of the data characters are converted to serial NRZ data at a 500 KHz rate. A clock is provided which makes a one-to- zero transition approximately lys after a change in the data line and at least lys before the next change in the data line. Data are not transmitted continuously but are limited by the maximum character rate of the 1/0 converter which is about 75 KHz. Control-characters are suppressed. 178

TABLE 34 PLOTTER CODE

Bits

Function h h °3 °2 D1 D0 X Pen up

X Pen down

X 1 increment: pius-x

XX 1 increment: 45 degrees

X 1 increment: plus-y

X X 1 increment: 135 degrees

X 1 increment: minus-x

XX 1 increment: 225 degrees

X 1 increment: mi nus-y

X X 1 increment: 315 degrees

A/D converter: The analog-to-digital converter accepts a 0 to

1.0 volt analog signal and converts it to 10-bit binary 0 to 1777g.

The conversion is started when the firs t data character is read.

Four zero-characters are sent followed by a character containing

the two high-order octal digits and a character containing the two

low-order octal digits. Data may be read at approximately a 5 KHz word rate but the input bandwidth has been lim ited to about 50 Hz

to minimize noise. APPENDIX E

THE ASSEMBLER

A. Introduction

The assembly-1anguage programming system used with the IBM

Minimal Informer computer is documented in d etail in an internal publication of the ElectroScience Laboratory, [171] and the description contained in this appendix is only s u ffic ie n t to guide an experienced assembly-1anguage programmer in reading the computer programs contained in this report.

The instruction format in this language is less rig id than in most assemblers in that the various fields of the instructions are not required to start or end in specific columns. The fields are separated by one or more spaces.

B. Instruction Fields

The four fields of an instruction are:

a) Label (optional) - one to six alphanumeric characters

beginning with an alphabetic character

b) Operation (always required) - a two-, three-, or five-

letter alphabetic code specifying either a machine operation,

an extended mnemonic to be interpreted in terms of machine

functions, or an assembler command causing one of the

following actions:

179 180

i) assignment of data storage

i i ) assignment of data storage

iii) linkage to external files

iv) termination of assembly.

c) Operand (required except for op-codes of HLT, TRS, or

END) - a variable length field composed of subfields

separated by commas. The subfields are:

i) Alpha - address

ii) Gamma - index register reference, if used

i i i ) Beta- increment or second address, i f used

iv) K - word or block count

v) J - device number, i f used

vi) textual material

Zeros are supplied fo r any missing subfields of the operand.

d) Comments (optional) - all text material following the third

field on any line.

C. Instruction Types

In the following examples of various types of instruction formats,

the label fie ld , i f used, must not be preceded by a space character.

A central processor instruction has the form:

Label OP Alpha, Gamma, Beta comments

The move instruction is an exception to this form because the length of its second address requires that the gamma and beta portions of the address be taken together as a single subfield. I t has the form:

Label MOV Alpha, Gamma-beta 181

An input or output instruction has the form:

Label OP Alpha,K,J comments

A block storage command assigning N words of storage has the form:

Label BS N comments

A tabulation command assigning values to successive words has the form:

Label TAB N1»N2,N3,*** comments

A command to assign N words of alphanumeric data with six characters per word has the form:

Label ALPHA N XXX*•• comments

A command to designate that an external file is required by a program, where that file is indexed in the disk file directory by file s name and user name, has the form:

USE f i l e , name comments

The command which indicates to the assembler that the end of the symbolic program has been reached has the form:

END

D. Special Symbols

The following special symbols are recognized by the assembler:

* In column 1 - entire line is comment

# In column 1 - entry point for this program

$ Prefixed to address - external routine

* As address - current location

** As address - to be supplied by program 182

D Prefixed to number - d is k address

Unmodified number - decimal constant

" " Enclosing characters - alphanumeric constant

' 1 Enclosing number - octal constant

. [ U Enclosing number - decimal lit e r a l from

literal table

[ ' 'DEnclosing number - octal lit e r a l from lite r a l

table

C" “HEnclosing characters - alphanumeric lite r a l from

literal table

( ) Enclosing characters - machine register or

sense indicator

An address reference may be composed of one of the above addresses plus or minus a constant to reference unlabeled instructions or storage.

E. Hardware Operation Codes

The following mnemonics are recognized as machine operation codes:

Misc. Class Transfer Class

HLT Halt TRU Transfer Unconditional

RPT Repeat TRL Transfer and Load PCS

L6M Logical Multiply TRS Transfer to PCS

LGA Logical Add TRX Transfer on Index

LGN Logical Negation TRP Transfer on {+) A Reg. 183

SEN Sense TRZ Transfer on Zero A Reg.

SNS Sense and Set TRN Transfer on { -) A Reg.

SNR Sense and Reset TRC Transfer on Compare

Add Class M ultiply Class

CLA Clear and Add MLY Multiply

CAM Clear and Add MLR M ultiply and Round

Magnitude DVD Divide

ADD Add DVL Divide Long

ADM Add Magnitude DVF Divide Fast

CLS Clear and Subtract MLF Multiply Fast

CSM Clear and Subtract

Magnitude

SUB Subtract

SBM Subtract Magnitude

ADB Add Beta

SBB Subtract Beta

S h ift Class I/O Class

SHL S h ift Left RAN Read Alphanumeric

SLL Shift Left Long ROK Read Octal

SHR Shift Right SCH Search

SRL Shift Right Long WAN Wri te A1phanumeri c

CYS Cycle Short WOK Wri te Octal

CYL Cycle Long

NRM Normalize

Store Class

STR Store 184

LOD Load

MOV Move

LDX Load Index

RPA Replace Address

MSK Mask

F, Extended Operation Codes

The following mnemonics are recognized as extended operation codes in which additional information such as device number or sense indicators is supplied by the assembler

TBR - Transfer i f break occurred

TIU - Transfer if I/O in use

TL1 - Transfer if sense light 1 on

TL2 - Transfer if sense light 2 on

TOV - Transfer if overflow indicator set

RAB - Read alphanumeric by blocks

RAD - Read alphanumeric from disk

RAT - Read alphanumeric from typewriter

RDB - Read disk by blocks

RTB - Read typew riter by blocks

WAT - Write alphanumeric on typewriter

WAD - Write alphanumeric on disk

WKD - Write octal disk (reposition R/W heads) 185

G. Machine Registers

The following symbols are recognized as machine registers:

(Z) - Zero register

(1X1)- Index register 1

(1X2)- Index register 2

(1X3)- Index register 3

(1X4)- Index register 4

(A) - A register

(Q) - Q register

(PC) - Program counter

(PCS)- Program counter store

(IPCS)- Interrupt program counter store

(DISP)- Display register

(SRI) - Switch register 1

(SR2) - Switch register 2

(M) - I/O maintenance register

(10) - I/O Instruction register

(D) - Disk address register

H. Sense Codes

The following symbols are recognized as sense indicators:

(IU) - I/O in use

(OVA)- Overflow alarm

(ISN)- Interpret-sign mode

(CIO)- Continue on I/O error

(SW1)- Sense switch 1

(SW2)- Sense switch 2 (SW3)- Sense sv/itch 3

(SW4)- Sense switch 4

(SL1)- Sense light 1

(SL2)- Sense light 2

(IOA)- I/O alarm

(BRK)- Break occurred

(AI) - Allow interrupt

(AIO)- Allow I/O interrupt

(ACPU)- Allow CPU interrupt

(WEF)- Write end of f i l e .

I . Data Formats

Floating point numbers are represented as a signed binary fraction with a nine-bit exponent. The least-significant nine bits of the word represent the power of two multiplier plus 400g.

Thus the octal floating point representation of -1.0 would be w ritten as -'4000000004011 where the primes denote octal notation.

ASCII control characters are represented internally as 12-bit characters with zeros for the high-order six bits. This is done to distinguish them from the ASCII printing characters which are repre sented as s ix -b it characters. BIBLIOGRAPHY

1. Proceedings of the GISAT I I Symposium (U), Volume I I , Part 1

(Unclassified), Meeting of 2, 3, and 4 October 1967, Bedford,

Massachusetts. AD 839 700.

2. Develet, J .A ., J r ., "Performance of a Synthetic-Aperture

Mapping Radar System," IEEE Trans, Aerospace Navigational

Electronics, Vol. ANE-11, pp. 173-179, September 1964.

3. "Radar Signature Investigation," Report RADC-TR-70-257,

Rome A ir Development Center, A ir Force Systems Command,

G riffis s A ir Force Base, New York, November 1970.

4. Short Pulse Theory and V e rificatio n Program, Report RADC-TR-

70-133, Rome Air Development Center, A ir Force Systems

Command, G riffis s A ir Force Base, New York, August 1970.

5. Lewis, R.M., "Physical Optics Inverse Diffraction," IEEE

Transactions on Antennas and Propagation, Vol. AP-17, #3,

pp. 308-314, May 1969.

6. Kennaugh, E.M. and C osgriff, R .L ., "The Use of Impulse

Response in Electromagnetic Scattering Problems," I.R.E.

National Convention Record, Part 1, 1958.

7. Shaffer, R., "Transient Currents on a Perfectly Conducting

Cylinder Illuminated by Unit-Step and Impulsive Plane Waves,"

Report 2415-2, The Ohio State University ElectroScience

187 Laboratory, Department of E lectrical Engineering, Columbus, Ohio,

3 May 1968. AD 702 874.

8. C.L, Bennett, "A Technique fo r Computing the Approximate Electro

magnetic Impulse Response of Conducting Bodies," Ph.D. D issertation, .

Purdue University, School of Engineering, June 1968.

9. J.D. DeZorenzo, "A Range fo r Measuring the Impulse Response of

Scattering Objects," NEREM, November 1967.

10. Kennaugh, E.M. and M offatt, D .L ., "Transient and Impulse Response

Approximations," Proc. IEEE, Vol. 53, pp. 893-901, August 1965.

11. Young, J ., M o ffatt, D. and Kennaugh, E., "Time-Domain Radar

Signature Measurement," Report AFCRL-69-0202, A ir Force Cambridge

Research Laboratories, O ffice of Aerospace Research, USAF,

Bedford, Massachusetts.

12. Kennaugh, E.M. and Moffatt, D.L., op c it., pg. 896.

13. Kennaugh, E.M. and M offatt, D .L ., op c i t . , pg. 896.

14. Bojarski, N.N., "Three-dimensional Electromagnetic Short Pulse

Inverse Scattering," Syracuse University Research Corporation,

Syracuse, New York, February 1967.

15. Report 2784-2, The Ohio State University ElectroScience

Laboratory, Department o f E lectrical Engineering, Columbus,

Ohio, May 1971.

16. Svoboda, D.E., "Phased Array Applications of Antennas with

Integrated Electronic Circuits," Ph.D. Dissertation, The Ohio

State University, April 1969. "Informer Assembler Manual," Internal Publication of the

Ohio State University ElectroScience Laboratory, Department of Electrical Engineering, Columbus, Ohio, October 1968.