LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 5\0.84 ZUr w. 582-587 cop. 2 Digitized by the Internet Archive in 2013 http://archive.org/details/colftarrealtimee584sand 0/J UIUCDCS-R-T3-58U /yuL^ii C000-1U69-0237 COLFTAR: A REAL-TIME ELECTRO-OPTICAL SYSTEM FOR TWO-DIMENSIONAL FOURIER TRANSFORMS by Douglas Stuart Sand December, 1973 DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, ILLINOIS TW£ LIBRARY OF THB MAR 2 5 1974 iNoia UIUCDCS-R-T3-58U C000-1U69-023T COLFTAR: A REAL-TIME ELECTRO-OPTICAL SYSTEM FOR TWO-DIMENSIONAL FOURIER TRANSFORMS by DOUGLAS STUART SAND December, 1973 Department of Computer Science University of Illinois Urbana, Illinois 6l801 This work was supported in part by Contract No. US AEC AT ( 11-1 ) 1U69 and was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering, at the University of Illinois. Ill ACKNOWLEDGMENT The author is deeply indebted to his adviser, Professor W. J. Poppelbaum, for his guidance, constant support, and patience (especially during AEC visits); his early and continuing enthusiasm for the electro-optic light valve (Ardenne tube) and the COLFTAR system has been invaluable. The author also wishes to thank Professor Michael Faiman for his continual advice and assistance, as well as Chinlon Lin for early work on the cooled-crystal problem, and Masamichi Sato for many useful discussions and for constructing the photon couplers. The author would also like to thank Mrs. Barbara Bunting and Mrs. Barbara Armstrong for typing the manuscript, the staff of the business office for useful expediting, the drafting group for many of the diagrams, and the staff of the printing group for duplicating the thesis. COLFTAR: A REAL-TIME ELECTRO-OPTICAL SYSTEM FOR TWO-DIMENSIONAL FOURIER TRANSFORMS Douglas Stuart Sand, Ph.D. Department of Electrical Engineering University of Illinois at Urbana-Champaign, 1972 An electro-optical system is described which generates optical Fourier transforms of two-dimensional video images, in real time, at standard video frame rates. This system is designated COLFTAR, which denotes "Cooled On-Line Fourier Transform and Reconstruction". The theory, construction, and Operation of the system and its principal components are described in detail, with special emphasis on the resolution and modulation characteristics of the cooled- crystal electro-optic light valve (or Ardenne tube) which is the central component of the sytem. Several application examples are included, as well as a summary of possible improvements. The essential components of the system are: pulsed laser source, electro-optical light valve, optics including Fourier transform lens, reference beam, vidicon detector, and support electronics. The necessary coherent two- dimensional object is produced by the light valve: the video frame is written as a charge pattern onto the surface of a thin (25 x 25 x 0.1 mm) KD*P crystal maintained at its Curie temperature (-52°C) by thermoelectric elements; a collimated polarized laser beam is directed through the crystal which modulates the beam polarization by the longitudinal electro-optic effect; a crossed polarizer then produces the two-dimensional amplitude-modulated coherent object. The object beam is directed through a lens, and the Fourier transform is detected by a vidicon target located in the focal plane of the lens. The complex amplitude of the transform is retained by detecting the sum of the trans- form and a reference beam. For a standard raster scan the video output then consists of an amplitude-modulated carrier which is synchronously demodulated to to obtain the Fourier transform. The system can produce Fourier transforms of arbitrary video frames with resolution of 500 by 500 line-pairs. Further, the same system can generate inverse Fourier transforms, so that an image can be reconstructed after its Fourier transform has been altered by an electronic "spatial filter". Also, Fraunhoffer holograms and synthetic (computer generated) Fourier transforms be reconstructed. In operation the system can serve as a stand-alone device, as a computer peripheral unit, or - using the advantage of real-time operation - for interactive image processing by Fourier transforms. IV TABLE OF CONTENTS Page 1. INTRODUCTION 1 2. THE LIGHT VALVE . . . . „ ... „ . k 2.1 Basic Configuration of the Light Valve h 2.2 The Light Valve with Room-Temperature Crystal 10 2.3 Temperature Variation of Crystal Parameters 21 2,k Light Valve Resolution „ 32 2.U.1 The Electrostatic Field 32 2. U.2 Surface-Charge Decay 38 2.U. 3 Electro-Optic Mode Rotation h6 2.k.k Recapitulation 52 2.5 The Cooled-Crystal Transmission Light Valve 5^ 3. THE COLFTAR SYSTEM 63 3.1 Theory of System Configuration and Operation 63 3.2 System Configuration 79 3.2.1 COLFTAR Optical System 79 3.2.2 COLFTAR Electronic Configuration 87 3.3 System Operation 103 3.1+ System Applications 107 h. SUMMARY 112 LIST OF REFERENCES 115 VITA 118 LIST OF TABLES Table Page 1. Summary of Conductivity Data, o = a exp(-E /kT) . . 2k U 3l 2. Summary of Electrostatic/Electro-Optic Resolution Characteristics 37 VI LIST pF FIGURES Figure Page 1. COLFTAR. System Diagram 3 2. Longitudinal Electro-Optic Amplitude Modulator .... 6 3. Crystal Axes, Symmetry, and Cuts for KDP and Isomorphs 8 h* Transmission Mode Ardenne Tube 9 5. Reflex Mode Ardenne Tube 9 6« Room-Temperature Light Valve 11 7- Resolution Limit for a 0.38 mm KD*P Crystal at 25°C . 15 8. Resolution Limit for a 0.25 mm KDP Crystal at 25°C . . 15 9* Exemplary Live Television Image for a 0.125 mm KD*P Crystal at 25°C 16 10* Exemplary Live Television Image for a 0.125 mm KD*P Crystal at 25°C 16 11* Successive Bar-Patterns with "Hysteresis" at 25°C . . 18 12* KD*P Crystal Front-Surface Deterioration after 10 Hours of Operation at 25°C 19 13. KD*P Crystal Back-Surface Deterioration after 10 Hours of Operation at 25°C 20 Ik . KD*P Crystal Electro-Optic Response to a Uniform Raster after 10 Hours of Operation at 25°C 20 15. KDP Crystal after about 5 Hours of Operation at 25°C . 21 16. Reciprocal Dielectric Constant l/e versus Temperature, Clamped and Undamped KD*P . . . .° 27 17 . Longitudinal and Transverse Dielectric Constants versus Temperature for KD*P 28 18. Crystal Configuration for the Electrostatic Field . . 33 VI 1 Figure Page 19. Normalized Modulation Transfer Function 36 20. Cooper Heatsink and TEM Mounting Cylinder for Cooled- Crystal Light Valve 57 21 • Resolution Example for the Cooled-Crystal Light 62 Valve, at -50°C 22. Optical Fourier Transform 6k 23. Coordinate Systems for Object and Transform Planes . . TO 2k. COLFTAR Optical System 80 25 • COLFTAE Electronic System Configuration 88 26« Light-Valve Electronic Subsystem 89 27. Temperature Sensor Circuit 92 28. Temperature Control Circuit 93 29. Current Source for Secondary (Colder) Cooling Module . 9^- 30. Current Source for Primary (Warmer) Cooling Module . . 95 31. Power Supplies for Cooling-Unit Current Sources ... 96 32. Video Gate and Field Counter 98 33. Unblank Coupler for Video Isolation Amplifier .... 99 3h. Grid Voltage, Gate, and Lockout Protection Circuits. 101 35* Write-Gun Filament Current Circuit 102 36. Phase Detection Amplifier 104 1. INTRODUCTION For several years there has been a gradual development of concepts and devices related to optical data processing. In particular, there has been considerable interest in image processing in the spatial frequency domain, because, in principle, the two-dimensional Fourier transform of an image can (2) be obtained from a simple thin lens. In practice, the typical experimental spatial filtering system is quite cumbersome, partly because the required coherent image is usually generated by a photographic transparency (modulating a collimated monochromatic beam) , and also because operations on the Fourier transforms itself are confined to the medium of another photographic trans- (l 2 3) parency. ' ' Clearly, the constraints inherent in photographic transpar- encies do not facilitate operational flexibility or speed and, in fact, much of the recent research work has been done by digital computer simulation, even though this requires two large-scale Fourier transforms for each image as well as the time-consuming peripheral operations of image digitizing and reconstruction. The Cooled On-Line Fourier Transform And Reconstruction (COLFTAR) system is a real-time optical image processing system, designed to operate with images in video format (such as television frames), which can generate Fourier transforms and image reconstructions (transform inversions) at video (h, 5) frame rates (30 images per second) • Each such transform or reconstruc- tion is available as an electronic signal in video format, with a system delay of only one frame period. This system is unique in two primary features. First , the coherent images are generated in real time by a Pockels effect light valve of advanced design. Second, the Fourier transform is detected directly by a standard vidicon, using holographic techniques to retain the amplitude and phase components of the transform. Together, these features facilitate the real-time generation of two-dimensional Fourier transforms and inversions. In addition, since "both the transform and image are available (input and output) in the form of electronic signals, one may use sophisticated techniques analog or digital - to operate in the spatial frequency domain. The essential components of the COLFTAR system are shown in Figure 1: pulsed laser source, electro- optical light valve, optics including Fourier transform lens, reference beam, vidicon detector, and support electronics. The necessary coherent two-dimensional object is produced by the light valve: the video frame is written as a charge pattern onto the surface of a thin (25 x 25 x 0.1mm) KD*P crystal maintained at its Curie temperature (-52°) by thermoelectric elements; a collimated polarized laser beam is directed through the crystal which modulates the beam polarization by the longitudinal electro- optic effect; a crossed polarizer then produces the two-dimensional amplitude- modulated coherent object. The object beam is directed through a lens, and the Fourier transform is detected by a vidicon target located in the focal plane of the lens. The complex amplitude of the transform is retained by detecting the sum of the transform and a reference beam. The COLFTAR system is an improved, generalized version of the on-line Fourier transform system proposed by Poppelbauni ' and described by CasasenV . The theory and design details of the COLFTAR system are presented below. The electro-optic light valve is considered in depth because of its essential contri- bution to the real-time capability of the system and because of interest in the use of such devices as television projection systems^ . Potential system applications are also discussed. O 2-5 §S o: > 01 tn O Is 1 I O O 0» w c 01 o tf >- C o o o S- T3 O 0) «> 0) E O U. c c o o o 3 (A k. W *- 0> c o 01 cr 0*0, *» E ^r ■O O © > £ w ■rt -P 01 CO I o o •H o 1 2. THE LIGHT VALVE The electro-otpic light valve, or Ardenne tube, is the central com- ponent of the COLFTAR system. Early work on the light valve using a room- temperature crystal, produced consistantly poor resolution and rapid deterio- ration of the crystal assembly. By cooling the crystal to near its Curie temperature, about -52°C, both resolution and crystal lifetime improve sig- nificantly, so that the present version of the light valve contains thermo- electric cooling elements. The result is a light valve with full resolution of 500 television lines and no observable crystal deterioration. In this section we consider the development of the light valve from the early version with a room-temperature crystal to the present device, which cools the crystal to the Curie temperature. Examples of the deficiencies characteristic of the room-temperature light valve are given. Some of the theoretical factors for resolution and improvement by cooling are presented. Details of the construction and operation of the transmission-mode cooled- crystal light valve are included. Finally, several possible improvements are suggested. 2.1 Basic Configuration of the Light Valve The light valve must amplitude-modulate the cross section of a col- limated beam of monochromatic light. The modulation format is that of stan- dard television, with a frame of about 500 horizontal lines with nearly 500 resolvable points for each horizontal line. In effect the light valve is to serve as a "real-time" photographic transparency, much like a television (7) projector such as the Eidophor system. ' ' Early work on the OLFT system began with an evaluation of available methods for television projection. It (5) was decided to construct a working version of the Ardenne tube (sometimes called the Pockels tube) which uses the linear electro-optic effect to modulate the polarization of the light beam. Electro-Optic Effect . The Ardenne tube uses the longitudinal linear electro-optic effect (the Pockels effect), in which the direction of light propagation is colinear with the major component of the low-frequency (electro- static) electric field. The crystal usually used in Ardenne tubes is KDP (potassium dihydrogen phosphate, KH PO, ) or its deuterated isomorph, KD*P. This material is a uniaxial crystal of the piezoelectric point group ^2m. For the longitudinal electro-optic effect, the light propagates along the crystal- ( R) lographic c-axis (optic axis), and it can be shown that the two allowed modes of propagation are linearly polarized with respect to the (x* , y') axis, where (x' , y' ) are rotated k^° about the c-axis from the crystallographic (a, b) axes. For each mode the index of refraction is given by 3 n a n . = n_ - -— - r^„ E a 2 63 x' a z e>j z 3 n n , = n + — rv E y' a 2 o3 z where n is the ordinary index of refraction, r^_ is the electro-optic coef- ficient, and E the local electrostatic electric field strength. After propa- gating a distance L through the crystal, the electric field vectors E , and E , of the two optical modes are of the form E x , = A x , exp j(k o n x ,L) E yl = A y , exp j(k o n y ,L) where A , and A , are the initial complex amplitudes of the two modes, and x y k = 2tt/X is the free-space wave number. The differential phase delay between E . and E , is called the retardation r and is x 1 y' T = k L(n , - n , ) = k n r. E L o y' x' o a 63 z A simple amplitude modulator is shown in Figure 2. The input polarizer is oriented so that the initial amplitudes are equal: A , = A , = A//2 When the light emerges from the crystal it is circularily polarized with com- ponents E = (E , + E , )//2 x x' J E = (E , - E ,)//2 y y' x 1 Incident light beam Input polarizer (lltox) Output polarizer (II toy) Figure 2. Longitudinal Electro-Optic Amplitude Modulat or The output polarizer selects E , which is v „ A J ( Va L) rjr/2 -jr/g e -e J ( Va L) = jAe ° a sin(r/2) The amplitude has been modulated "by the factor j sin(r/2) = j sin ^(V/Y^) where V = E L, and V , , the "half-wave voltage", is V, /o = Tr/k n r/--, = A /2n 3 zv_ 1/2 o a 63 o a 63 At room temperature the half-wave voltage is UkV for KD*P and 8.2kV for KDP, at A = 633nm. o Ardenne Tube Light Valve . The electro-optic crystal in the Ardenne tube is a 0° - Z cut platelet, as shown in Figure 3. The faces are normal to the optic axis and the face edges are parallel to the a and b axes. This is the arrangement of the amplitude modulator described above. The crystal is mounted on a substrate for support, and the inner face of the crystal is usually covered with a conducting layer or electrode. In the Ardenne tube the modulating voltage is established by an electron beam scanned in a tele- vision raster pattern. The electron beam deposits a charge pattern on the exposed face of the crystal, and the modulating voltage is established between this charge and the conducting electrode (usually grounded). The electron beam requires a vacuum so that the entire assembly is enclosed in a vacuum chamber with windows for the light beam entrance and exit. The components of the Ardenne tube are arranged in one of two basic configurations, the transmission mode (see Figure k) or the reflex mode (see Figure 5). In the transmission mode light valve, the crystal with a 0-XocY b-YorX A. CRYSTAL AXES ROTATION- INVERSION AXIS , " [MO] THE [HO] AND [HO] DIRECTIONS ARE FAST ANDSUOW VIBRATION DIRECTIONS FOR FIELD II 2 SYMMETRY PLANES (m) 2 FOLD AXES B. 4 2m SYMMETRY -»- ELEMENTS 45* Z PLATE (EXPANDER) 0" Z PLATE C. 0°Z AND 45°Z PLATES Figure 3. Crystal Axes, Symmetry, and Cuts for KDP and Isomorphs POLARlZ-ER P, ELECTRON BEAM t: transparemt comooctin& electrode ANALYZER P z TRANSMITTED L1&HT x 5UBSTR.AT 'CRYSTAL. 'HODE / k: catv Figure k. Transmission Mode Ardenne Tube REFLECTION COATIMCt /TRAN'bPA.REMT COMOUCTlON COATiKIC* * electron BEAM 3 N SUBSTRATE 'CRYSTAL To \/ id icon ^CLAN- THOMPSON! POL. AR1Z.IKJ& BEAM SPLITTER S Figure 5. Reflex Mode Ardenne Tube 10 transparent conducting layer is mounted on a transparent substrate located between two parallel windows. This requires the electron beam to be off-axis, typically at about 30°. In the reflex mode the light beam passes through the crystal twice, being reflected by a mirror layer on one crystal face. There are two reflex types: the first is similar to the transmission mode, but the conducting layer is the mirror - this also requires an off-axis electron beam; the second, shown in Figure 5, has a dielectric mirror layer and a transparent substrate, with the electron beam colinear with the optic axis but physically separate from the optical path. A comparison of these modes is given later. 2.2 The Light Valve with Room-Temperature Crystal In this section we consider the Ardenne tube light valve described (5) by Casasent , in which the electro-optic crystal is maintained at room temperature. The components of this transmission mode light valve are described in detail by Casasent, and only a summary of the salient components and operating characteristics is included here. This is followed by a dis- cussion of the deficiencies - low resolution and rapid crystal deterioration - inherent in using a room-temperature crystal. The experimental apparatus of the room-temperature light valve is shown in Figure 6. The components described below are: the electron optics (the write beam and erase beam), and the optics (crystal assembly, pulsed light source, and chamber windows). Electron Optics . The electron optics consists of the write-beam electron gun, which deposits the surface charge pattern for the video frame, and the erase-beam electron gun, used to erase any residual surface charge 11 write: GUM ERA5E <5UW ISOLATED TGT. HOLDER DEMOUUTABLE FLAWGt- O&JECT PLAKJE-' (CRY5TAC) Figure 6. Room-Temperature Light Valve 12 between video frames. Both electron guns are mounted at a 30° angle to the optical axis, and are separated by a rotation of 120° about this axis. The conducting layer of the crystal is grounded so that the cathodes of the electron guns are maintained at negative potentials by high voltage supplies. At room temperature the electro-optic half-wave voltage is UkV for KD*P so that the write-gun cathode potential is typically 15 to 20kV. At this potential the secondary electron emission by the target is negligible, so that the write-beam acts as a current source. The write-beam current is modulated by a cathode-driver amplifier which operates at cathode potential and receives its video signal through a wide-band transformer - this combination, together with voltage supplies for the grids Gl and G2, is referred to as the "video isolation amplifier". The write beam is scanned in a raster pattern by a high resolution magnetic deflection system which includes correction for the "keystone" distortion of off-axis scanning. The erase beam is unfocussed and provides a "flood" beam to cover the entire crystal uniformly. It is pulsed for a period of about lmS between successive video frames. The write gun is a modified cathode-ray-tube electron gun designated WIA903 (Westinghouse , Elmira, New York). This gun is designed for a focussed beam diameter of l6.5ym at a beam current of lyA and a cathode-to-target potential of about 25kV. The focus is electrostatic, with a cathode-to-G3 potential about V ,/3. The maximum beam current is determined by the cathode characteristics. In four samples with standard tricarbonate cathodes, initial beam currents ranged from luA to 20yA at nominal heater power. By increasing the cathode temperature the beam current can be increased by a factor of ten 13 or more with an increase in beam diameter and a reduced cathode lifetime. After an up-to-air cycle of the vacuum chamber (using dry N_ as a backfill) the cathode can be reactivated for operation at reduced beam currents. This can be done several times before beam current is too low. The erase gun is a simple triode structure similar to the flood guns used in storage tubes. It is designed to provide a diverging beam of half-angle approximately 10° at a current of 1mA. The cathode potential is adjustable from to 2.5kV. The cathode material is similar to that of the write gun, but its lifetime is somewhat longer because the design current is more than adequate. Optics . The optics consist of the electro-optic crystal and substrate, the vacuum- chamber windows, and the pulsed, collimated laser beam source. The crystal assembly consists of: a CaF substrate, 1.75" in diameter and 0.375" thick; the KD*P (or KDP) crystal, 0°Z-cut, of size 1.0" square by 0.01" or 0.005" thick, with faces polished to surface flatness of A/5 on each side; the conducting layer, which is a thin film of transparent CdO deposited on the inner face of the crystal and covered with a protective layer of MgF p ; and the transparent assembly epoxy which joins the crystal to the substrate (this epoxy is squeezed to a layer about 15um thick to remove all bubbles). The vacuum chamber windows are quartz interferometer plates of surface flatness A/10 and with single-layer MgF anti-reflection coatings on each face. The light source is a Spectra-Physics 125 HeNe continuous-wave gas laser with typical output power of 70mW at 633nm. The laser beam is passed through an Isomet TFM502 electro-optic modulator to pulse the beam "on" for a lmS period between video frames. The beam is then expanded to a diameter of about Ucm by a Spectra-Physics 331/33*+ Beam Expanding Telescope. lit Room-Temperature Crystal Resolution . The most obvious deficiency of of the light valve with room-temperature crystal is the low resolution. The theoretical resolution is discussed in Section 2.k below, where the two factors of crystal thickness and costal time constant are shown to determine the resolution limit. Samples of room-temperature resolution and image quality are given in Figures 7, 8, 9 and 10. The raster size in each case is 1.5cm x 2.0cm. Figure 7 is an early KD*P crystal (by Clevite Laboratories) of thickness 0.38mm and with a semitransparent gold conductive layer. The bar pattern totals 50 television lines (25 black and 25 white lines) which was the maxi- mum number resolvable for that crystal assembly. The uneven, almost granular, appearance of the image is due to an "orange peel" surface finish and perhaps due to nonuniformity of the conducting layer Figure 8 is a KDP crystal of thickness 0.25mm obtained from the Isomet Corporation, with the CdO conducting layer described above. The bar pattern totals 128 television lines and is at the resolution limit. This photograph was taken after a series of experiments with a cumulative crystal usage of about one hour at 0.25uA target current. The various spots and scratches are caused by external optics and interference of the coherent laser beam (at 633nm) . Figures 9 and 10 are live television, using a 0.125mm KD*P crystal from Isomet. The target current is about l y A and the cathode potential is 22kV. These are the best of about fifty live television photographs. The resolution is approximately 150 television lines. The nonuniform appearance is probably due to crystal nonuniformities , as suggested by Salvo , although 15 Figure 7. Resolution Limit for a 0.38 mm KD*P Crystal at 25°C Figure 8. Resolution Limit for a 0.25 mm KDP Crystal at 25°C 16 Figure 9. Exemplary Live Television Image for a 0.125 mm KD*P Crystal at 25°C Figure 10. Exemplary Live Television Image for a 0.125 mm KD*P Crystal at 25°C IT some areas are "shaded" by the interaction between the electron beam and the high target potentials. Some of the "etch" patterns described below can be seen in these two photographs, and these patterns are much more obvious in most of the other photographs in the series. Finally, Figure 11 is an example of crystal conductivity "hysteresis", which was particularily evident in a series of bar-pattern tests taken with the 0.25mm KDP crystal of Figure 8. Figure 11 is a double exposure of two bar patterns, each at a target current of about 0.15uA. The first, on the left, is of l6 television lines, and was left on the crystal for about 5 minutes. The second, on the right, is of 8 television lines, and this exposure was taken about 1 minute after the pattern was changed from 16 to 8 lines. The right edges of the two central bright bars are shaded. These edges were black in the 8-line pattern, since the bars are derived from a binary counter synchronized to the beginning of each horizontal line (on the left of the raster area; the bright elongated ellipse on the far left of each exposure is epoxy). Crystal Deterioration . The second problem of the room temperature crystal is rapid crystal deterioration. This is evident in two forms: a surface "etching" and destruction of the conducting layer. The cause of both is the conduction mechanism of KDP and KD*P, which is mobility of hydrogen ions in the lattice. The room-temperature light valve can only write a negative charge pattern onto the surface, so that the crystal current is always in one direction - hydrogen ions travel from the conducting layer to the surface and are neutralized by the deposited electrons. The result is a depletion of the crystal lattice and chemical reactions at the conducting-layer interface, and an accumulation of hydrogen molecules at the surface, which eventually 18 Figure 11. Successive Bar-Patterns with "Hysteresis" at 25°C escape in the form of "outgassing" . Experimental evidence for the conduction mechanism is discussed in Section 2.3. The resulting crystal destruction is presented here. Figure 12 is a photograph of the exposed face of a KD*P crystal of thickness 0.125mm, after about 10 hours of operation. The assembly is lighted from behind, and the white areas are surface "etching", measured to he about 15um deep. The resolution bar patterns (Figures 8 and 11) are clearly present,, The pattern which looks like trapezoids is differential etching apparently related to crystal growth characteristics. The circular spot is a large bubble which grew in the epoxy layer. 19 Figure 12. KD*P Crystal Front-Surface Deterioration after 10 Hours of Operation at 25°C Figure 13 is the same crystal as Figure 12, but the back side is illuminated so that the reflection characteristics of the conducting layer are emphasized. Clearly, extensive destruction has also occurred, following the same patterns as the surface etching. In addition, the broad, triangular shaped gray area in the center is severe damage, as indicated in Figure lU, which is the same crystal in place in the light valve with a uniform raster pattern. The central area, the "great black spot", has much lower sensitivity due to the lack of an effective conducting layer. 20 Figure 13. KD*P Crystal Back-Surface Deterioration after 10 Hours of Operation at 25° C Figure Ik. KD*P Crystal Electro-Optic Response to a Uniform Raster after 10 Hours of Operation at 25°c 21 Figure 15. KDP Crystal after about 5 Hours of Operation at 25°C Figure 15 is a KDP crystal of thickness C. 125mm, after about five hours of operation. In this case there is no serious surface damage, but the conducting layer is completely destroyed, as the tiny bubbles indicate. The black area on one side was covered by an SiO coating of \/h thickness. The coating helped to protect this area but the response (brightness) was so low that the raster was usually reduced in size to cover only the uncoated area. The low response may have been caused by capacitive voltage division between the coating and crystal. 2.3 Temperature Variation of Crystal Parameters KDP and KD*P are paraelectric at room temperature but when cooled to below their transition temperatures T (at about -50°C for KD*P) they change from the tetragonal £2m to the orthorhombic mm point group and become ferroelectric. Above T the dielectric constant e and electro-optic coefficient o c 22 r r obey the Curie-Weiss law, attaining values near T values at 63 ° their room temperature values. In addition the conductivity at T is about 0.1$ of the room-temperature value. These factors facilitate a cooled- crystal light valve with high resolution and low crystal deterioration. In this section we discuss reported values of these parameters as temperature is varied, and consider some of the implications and potential difficulties for a cooled-crystal light valve. Further discussion may be found in Lin and the original sources cited. Transition Temperature . The temperature at which KDP changes from the paraelectric to ferroelectric phase is called the ferroelectric transition temperature T . T varies with the deuteration level, from 123° K for KDP to * 00 approximately 22U°K for 95% dueteration (commerical KD*P). Kaminow indicate that KD*P of deuteration level x and chemical formula KH , n xD PO, 2(l-x) 2x k ■ has a transition temperature T s (123 + 106x)°K o There is evidence that for high deuteration levels the above formula under- '-■. estimates T - above 90%, small changes in x give large changes in T . Also, exact values of x are difficult to determine and are lower than the deuteration of the growth solution (the protons are apparently sequestered during the \ (12) growth process). Conductivity . The conductivity of KD*P is due to mobility of deuteron ions (or protons, for KDP). A clear discussion is given by O'Keeffe (13) and Perrino , who conclude that below 100°C the dominant conduction mechanism is the mobility of "L" defects. An "L" defect is the absence of the 23 hydrogen ion which normally bonds adjacent corners of PO, tetragons. Thus, deuteron "holes" propagate from cathode to anode. This agrees with the observations of Schmidt , who found that hydrogen gas was evolved from the cathode face of a KDP plate, while the anode face (in contact with a mercury electrode) blackened from chemical reaction. This also agrees with early reports of "outgassing" of KDP under electron beam bombardment in light valves. (13) O'Keeffe and Perrino measured the conductivity a of various KDP crystals doped so that N , the number of L-defects, could be determined. Li Using the relation a = qN L y L , where q is the charge of a proton, the L— defect mobility u was found to be Li -ID P U T = 6x10 cm /Vs (at 25°C) J_j According to the theory of ionic conductivity, the temperature dependence of o (16, 17) is given by a = a exp -(E /kT) , O o> where k is Boltzmann's constant, E is the activation energy, and T the temperature in degrees Kelvin. This is in agreement with the published data for a, which is summarized in Table 1, where o is the z-axis conductivity and c o is the x or y-axis conductivity. EL From Table 1 it is evident that conductivity is fairly consistant , but certain anamolies are present. For example, at 27°C, U53 (Mason) fo. la = 4 a K " 1+7 (O'Keeffe and Perrino) This may be due to impurity concentration variations. Mason measured c before 1950 and experience in the growth of KDP has increased greatly since then. The 2k , -P On o TJ h •H _* S (3D CO ,G s ir\ l/N O -H O CM t~ vo CO H -p ON CO -=t u^ VO o H o-i VD ,3 o C— ir\ n A LTN H • • t— on «> 4) u o • • C\J H -3- CM H H • • CM D o o o r-4 H H rH CM H l/N -=r * en 8 ^ I d -~-> o ^H Jh CD H D CD +2 ft T + 30°K, o £ S - 66 - 0.1(T - T ) a o for £ T - T ^30, o £ S - 62 a while at T = T - 3°K, £ S - 20 , and at T = T - 10°K, £ S - 10. o a . ' o 'a T S ( 25 ) A set of curves for £ , £ , and £ are given in Figure IT. C C 3, 27 o x Ofe - 4 - Oi - o.o (OOO c/<4 UNCLAMPEO feO «>o -40 -30 -2.0 -10 TEMP (-C) Figure 16. Reciprocal Dielectric Constant 1/e versus c Temperature, Clamped and Undamped KD*P 28 10' 10- io- 10 2 10 -I — I — I — I I I I I ' -50 50 100 °C Figure 17. Longitudinal and Transverse Dielectric Constants versus Temperature for KD*P 29 Electro-Optic Coefficients . For the c-axis small-signal electro-optic m g (21) coefficients r^^ (constant stress) and r^-_ (constant strain), Kanzig states T T that Xr /( e - l) i s temperature independent and that 63 c This is consistant with the results of nonlinear optics theory and with ( 21 2U ) experimental results. ' The theory also indicates that r. /(e - l) is independent of temperature. From Lin, zv = 0.06l(e - l)e (m/V) 63 co -12 where the permittivity of free space e = 8.85^ x 10 farad/m. Room- temperature values are , for KD*P , r^ = 26. U x 10~ 12 m/V rj = 8.8 x 10" 12 m/V Crystal Time Constant . The time constant which determines the charge- pattern decay time in the light valve is a function of the spatial frequency of the charge pattern, as discussed in Section 2.U. However, this time constant is related to the crystal dielectric relaxation time constant t = e e/a. KD*P o is anisotropic for e and a, so that the longitudinal time-constant is c o c c and the tranverse time-constant is t = e e /a a o a a (9) These time constants were evaluated by Lin ' at various temperatures. Selected values are: 30 at T = 25°C, t = 0.111 sec, c t = 0.072 sec; a at T = -50°C, jj ^ c = 2030 sec, x = U8 sec . a Measurements of the crystal time constant t for KDP at room tempera- ture were taken and first evaluated "by Casasent . In a simplified analysis one need only consider the exponential decay during that part of the cycle when the scanning electron team is "off". This yields the following: T = 2uA.> x = 139 mS beam c h 122 6 119 8 llil 10 103 10 91 The two values at lOuA were taken consecutively, the first shortly after the beam current was changed from 8uA to 10yA, and the second several minutes later. These values are in agreement with the room-temperature value calculated by Lin, as cited above. Casasent attributes the decreasing time constant to crystal heating as the surface absorbs the electron beam kinetic energy. A simple analysis indicates that this is unlikely. In the worst case the incident power is about 20kV x lOyA = 0.2W over about h cm . Lin indicates that this power will alter the transverse temperature by 0.2°C. With a crystal thickness of 0.25mm and a thermal conductivity of 2mW/mm°C, the longitudinal temperature change would be 0.06°C. At a mean temperature of 300°K, the equation for c yields 31 a change of about 2.5% for a temperature change of 0.27°K, which is too small for the observed change in the time constant. It is more likely that this change in time constant is caused by non-ohmic conductivity (x is a function of L ), and increasing conductivity defects due to unidirectional ionic current (at constant I, the effective t beam decreases with time as a increases). Half-Wave Voltage and Charge . In Section 2.1, the half-wave voltage V , was defined to be V l/2 = V 2 V63 -3 The temperature variation of n is on the order of 10 over the range from 8. room temperature to the transition temperature, so that V , as a function of temperature would be a linear function of T: V 1/2 (T) r 63 (r) T - T c v^Tr) " T^FT - «• - i e From the values calculated by Lin ' for KD*P and at ^ = 633 nm, o V / ■ - 1/2 ' UU10 volts at 25°C - „ 208 volts at -50°C For an estimate of the charge required to obtain the half-wave voltage at various temperatures, consider a simple parallel-plate capacitor filled with material of dielectric constant e : the capacitance is directly proportional to c e . The half-wave voltage is inversely proportional to £ so that the required charge, being the product of capacitance and voltage, is constant . For the light valve, the anisotropic dielectric constant complicates the analysis, but the result is essentially the same: the required beam current is independent of temperature. 32 2.k Light Valve Resolution The resolution of the light valve can be determined from an analysis of the electro-optical configuration. The problem separates into three areas: the electrostatic field as a function of initial surface charge density; the decay of charge with time due to non-zero conductivity; and the electro-optical effect. Each area is considered below. 2.U.1 The Electrostatic Field The geometry of the electrostatic field problem is shown in Figure 18. The field potential $(x, y 5 z) satisfies the free-space Laplace equation V 2 $ = (l) in the region z < -L, while in the crystal region -L < z < 0, the anisotropic Laplace equation is satisfied: 2 2 P 8 3 % 3 \ (2) 2 2 2 3x 3y e a 9 z The boundary conditions are *(z = 0) = (3) (•)" = ($) + M (il*) " e c(^ ^ = S -^ ^ (5) where (•) is evaluated at z = -L , and (•) at z = -L , and where s(x, y) is the surface charge density as deposited by the electron beam (assuming no charge leakage). For convenience we will use a "mixed-space" representation, which is obtained by Fourier transform over the coordinates x and y: -j(k x x+k y) *(k x ,k ,z) = /jixdy$(x 5 y,z)e * ^^ 33 Free Space e = e = e = l a b c Surface Charge S(x, y) Grounded Conducting Plane Figure 18. Crystal Configuration for the Electrostatic Field This is particularily convenient because the boundary conditions transform directly into mixed-space, and the solutions of the two Laplace equations are simple exponentials. The solution is straightforward and can be found in Sand' the crystal region -L ^ z $ 0, it is sinh(k'z) (27) In S(k ,k ) #(k x ,k y ,z) £ k sinh(k'L) + 6cosh(k'L)" o where = A 2 ♦ k 2 k' = k/e a c 3 = /e e a c If the surface charge pattern S(x, y) is sinusoidal, S(x, y) = A + B cos ax (7) 3>+ where the surface wavelength A = 2ir/a, then it is easily demonstrated that _, » Az _ , v sinh(a'z) £o $(x,y,z) = -— - Bcos(ax) sinh(a , L) + 3 cosh(a . L ) (8) c where a' = I a I /e /e 1 a c The potential $ at any point can be related to the electro-optic effect as follows. Using the terminology of Section 2.1, the differential retardation dr at any point is given by 3 dr = k n iv-E o a 63 z = k n r^_[- ~1 o a 63 L dz It is shown in Section 2 . U . 3 that the cumulative phase front deviation is very small relative to the crystal thickness L and the smallest charge-pattern wave length (A )min, so that a z-directed incident light beam is essentially un deviate^ when it exits the crystal at z - 0. Then the total retardation at any point (x, y) at z = is simply z = r = / dr z =-L = -k n 3 r. / dz f-^-$ o a 63 , \3z —Li = k n r^_$(z = -L) o a 63 From (7) the surface potential is S(k k ) . (k x ,k y ,z=-L) = £ X k y /(l + 3 coth k'L) (9) Note that in the limit k + 0, $(0,0, -L) = S(0,0)L/ e e o c 35 which is the relation between potential and charge for a parallel plate capacitor of separation L and dielectric constant e . The retardation modulation transfer function is easily obtained, since the mixed-space representation is the result of the required two-dimensional Fourier transform, where charge-pattern wave length A is related to spatial s radial frequency k by kA = 2tt. The modulation transfer function is simply a T/S and from Equation (9) is clearly a function of k only. The normalized retardation modulation transfer function is then r(k ,k )/S(k ,k ) M(k) = r!o,o)/s(o^o) y do) e -1 = c [l + /e e coth(kL/e /e )] TV" a c a c kL This is identical to the normalized charge-to- volt age modulation transfer func- tion. For the electro-optic amplitude modulator, where modulation is propor- tional to sin(r/2), the transfer relation is nonlinear, being a function of k and depth of modulation. However, the small-signal approximation sinx ^ x would be the worst-case transfer function since r(k) is smaller than r(o) for the same charge magnitude. In this small-signal case, (10) is also the amplitude modulation transfer function. For KDP and KD*P the factor /e e is found to range from a minimum a c of 30 at 25°C for KDP to about 200 for KD*P at -50°C, so that the inequality tanh(k'L) << /e e a c In this case (10) reduces to M(k) = *«%(>'*■> (11) k'L where k'L = kL/e /e . This simple function is plotted as a "universal" resolu- a c tion curve (tanhx)/x in Figure 19. 36 yj|:i:i ;, .:;|^ii; ! -|^::^).-:|^4:^g l .2 .3 ,k .5 -1.0 2.0 3. U. 5. 7. Figure 19. Normalized Modulation Transfer Function The approximation (ll) clearly indicates that for a given X , the effective crystal thickness is L/e /e , which decreases with temperature to a minimum C SL of 0.316 for KD*P at -52°C. Table 2 is a set of values for wavelength X for various modulation levels, crystal thickness, and temperature. Also included is the equivalent number of television lines for a 15 mm raster, N = &5 mm) x (tt/X ) s It should be emphasized that M is the amplitude modulation transfer function. When the light valve image is viewed by eye, the apparent transfer function is VT . Even so, the high line-numbers indicated in Table 2 do not correspond to the low resolution seen in the examples of Section 2.2. The additional factors affecting resolution are charge decay and the electro-optic effect. 37 KDP KD*P 25°C 25°C o°c -25°C -Uo°c -50°C -52°C E a 1+1+ 60 62 61+ 61* 65 65 C 21.9 U3.5 61.3 109 213 629 650 /e e a c 31.0 1.1*2 51.1 1.17 61.6 1.01 83.5 0.77 117 0.55 202 0.321 206 0.316 /e /e a c / X s 595 1+90 1*23 321 230 131+ 132 M = 1/2, S \ N 5U 61 71 93 131 22l+ 228 / A , 113 93.5 81.0 61. k 1+3.8 25.7 25.2 M = i/io, s \" 26U 322 372 U92 686 1171+ 1190 Ik 985 810 700 530 380 222 218 M = 1//2", S \ N 31 37 1+3 56 79 135 137 M = l//I6~,( X s 360 298 257 195 ll+0 81.5 80.5 \n 83 101 117 15U 211+ 368 371* [L = 127 ym, A in ym, N in television lines across 15 mm] Table 2. Summary of Electrostatic/Electro-Optic Resolution Characteristics 38 2.U.2 Surface-Charge. Decay In the analysis below, the surface charge is shown to decay from a longitudinal current and a transverse surface current. Each current component has its own time constant which is a function of spatial frequency, depth of the surface charge layer, and the relative values of the dielectric relaxation times £ e /a and £^£ /a . Under certain conditions these surface-charge c c a a decay times decrease with increasing spatial frequency, so that overall resolution decreases as time increases. Depth of Surface-Charge Layer . In the electrostatic solution it was assumed that the charge deposited by the electron beam was confined to a surface layer of infinitesimal thickness. However, the electrons penetrate to a finite depth before their kinetic energy is completely absorbed by lattice collisions. Knoll indicates that the penetration range w is given by w = (C / m) (2x10 V) 2 /(l + 2 x 10 V) (cm) where V is the electron beam cathode-to-target potential in volts, m is the target mass density in gm/cm , and C is a slowly varying function of V, equaling 0.6 for V ~ 10 volts. For KD*P, m = 2.36, and Knoll's curve yields V = k 9 7, 10, 15, 20, 25 kV W = 162, 510, 980, 2050, 3530, 5530 nm Most of the incident (primary) electrons should penetrate to nearly this depth, but as each electron is decelerated, it scatters several low-energy electrons in all directions (some of which emerge from the surface as secondary electrons), so that the incident electron beam may be assumed to fill the local volume approximately uniformly to the depth w or greater. Then the initial charge density would be, using the dimensions of Figure 18, 39 p(x, y, z, t=0) = Sixj_yl [ U ( z+L ) _ u ( z+ L-w)] (12) w where u(z) is the unit step-function and where S(x,y) is the charge density as deposited by the electron team. In the limit w -*■ , p becomes a surface charge density. Note that (12) ignores the finite time required for the electron beam to scan the raster pattern. Even so, (12) should be a good approximation over a small area of several resolution elements per side, which is all that is required to evaluate the effect of charge decay on the high spatial frequencies. Diffusion Current . For a simple one -dimensional field the current J is composed of a drift term and a diffusion term: J = nqyE - qDy(dn/dx) where n is the local density of excess carriers of charge q, mobility y, and diffusion constant D, and E is the local electric field. Poisson's equation dE , ^=nq/ £ , the Einstein relation D = ykT/q, and E = -d/dx may be used to reduce the above equation for J to ,2, ii. m \*3 J = e y /dj>\d_J> + /kT\d£l W,v 2 U/,3 dx x ' dx" With the sine-pattern potential (8) the various derivatives of can be evaluated from which one obtains, at z = -L, /kT d^A /feL djt\ a kT/q \* dx 3 )/^ X dx 2 )"* " AL/e ko A similar result is obtained for derivatives with respect to z. Since kT/q ~ 2.5 mV at 300° K, and the local potential is at least several volts, ; the diffusion current is negligible with respect to the drift current. Space-Charge Neutrality . The charge-decay problem is greatly (IT) simplified if we may assume space-charge neutrality. According to Lamb , the current for a single type of carrier becomes space-charge limited if the dielectric relaxation time t, t = e n e /a c c is approximately equal to or greater than the carrier transit time t , V = L 2 / „ V , where V is the voltage across a distance L, and y is the carrier mobility. Assuming the carriers are L-defects , we may use y as given in Section 2.3. Then with V = 1000 volts and L = 0.125 mm, x = 250 sec. at 25° C, which is very much greater than t - 0.1 sec, and we may safely assume space- charge neutrality. Further, t/t should be approximately temperature- independent, since o <* v for a fixed number of defects. Conductivity Relation . We assume the current is ohmic but anisotropic, so that current J is related to local electric field E by J .= a E, J = a E, J = a E (13) x axy ay z cz where a is the transverse conductivity (near the surface) and a is the a c longitudinal conductivity. Over the range of several dielectric relaxation times the conductivities are assumed to be constant. The change of conductivity due to carrier transport and accumulation is important but will be considered to occur over a very long time. Charge-Decay Differential Equations . The complete mechanism for charge decay is quite complicated and since little is known beyond the conductivity data cited in Section 2.3, we will assume that the time rate- ill of-change af charge density p is given by the charge continuity equation 3p 3t = P = - V (lU) We will consider only the initial decay of charge (that is, p at t " Q), at location (x, y) contained in the Gaussian "whisker" of volume wdxdy located in the charge layer. We denote this charge by S(x, y), obtained by integrating p over z: -L+w S( x , y, t) = / dz p( x, y, z, t) -L The rate of change of S is then found from (lU), -L+w S( x , y, t) = - / dz V • J -L a - J -L+w - / dz 3J 3J 3x 3y z=-L+w -L where the first term above occurs because J vanishes in the free-space region z < -L. With the conductivity relation (13) and the anisotropic Poisson's equation 3E 3E 3x 3y ) -..ft)- P / (l6) reduces to (15) (16) (IT) -a E c z a -L+w / 3E + - ~ f dz I f- - e -s*- z =_L+w + e a -L V e C 9Z a a e a S a c e e e a a E a e a c a E c e / z z=-L+w z z=-L With the field-potential relation E = ■■ V , the above equation becomes k2 a S a e a a c S = - — — + - e e^ e dzl z=-L a a as: a e / a c \ 9 c e 3z z=-L+w Note that the above charge-decay equation has the same form in the mixed space representation of (.6), where ( x, y) "t (. k.» k ) . x y Field Potential . The electrostatic field potential inside the crystal ( -L ^ z ^ ) must satisfy the boundary condition cj>( z = ) = and the mixed-space anisotropic Poisson's equation C — 5" - ot ] = - p / e e , d c dz (19) (20) where a = k / e /e a c and / 2 2 k = / k + k The boundary conditions at the free-space interface z = -L are 4> -L + and Tf- -L 3z _= e 91 -L c <()z -L which, using the free-space homogeneous solution of (l), reduces to the single homogeneous boundary condition where . = !£. M. + = 3.91 + -L k 3z -L a 3z -L $ = Zee a c (21) The solution <}>(k , k , z ) is given by x y o ■(z) = / dz' p(z') G(z-z')/e_e . T c — Li (22) where the Green's function G is U3 for z' $ z, i » \ ( sJ-^- as y. / ainh a(jz,'+L) + 3 cosh a(z'+L) \ G[z-z J - - i ■ a - ■ n ■ sinh aL + B cosh aL ; for z' >, z, (23) , , . / sinh az' v / sinh a(z+L) + 3 cosh a(z+L) \ U " Z j " " l a ; ^ sinh aL + 3 cosh aL ' Using (22) and (23) it is easily shown that 3d) . T f , . / . x si nh a( z'+L) + 3 cosh a(z'+L) e^e T I -= - cosh aL J dz ' p ( z ) *-r — * , _ — ; u c 3z T smh aL + 3 cosh aL cosh a(z+L) + 3 sinh a(z+L) r , , / ,, . , . r— r — T _j_ r — ; J dz ' p(z') sinh az 1 sinh aL + 3 cosh aL z from which we obtain, using (12) 3 c or i i \ t i j. tanhaLx t = (e.e /a ) ( 1 + j c c B Since B is large, the limiting x is simply t . Note that a small value of B implies that the time-constant increases with spatial frequency. The same limit holds for a -* (with tanh aL = 0). The time constant defined "by (25) is not a simple function, but it readily reduces to a more amenable form by assuming L >> w and aL >> 1, so that sinh aL = cosh aL = ^e and cosh a(L-w) - e cosh aL V - w (26) Then (25) becomes e S/S = - (-£) + e "" e a ow(l + B) X \fe- - a -£) (1 - cosh aw - B sinh aw) + (— ) (e aW - l) Lea a J Again, the large - B approximation is valid, with which (26) reduces to , S/S . - (!SL) - (i. - ^) e " aw sinh av (27) see aw a c a The above equation has the same limit as aw -*■ as the original (25), and also clearly indicates that the limit as aw ^ » is t=t . a A numerical example will serve as a good analysis of (27). For w = 2 ym, L = 127 Urn, 2tt ■{: 122 (25° C) a = - — / e /e S a C I 0.033T (-50° C) where X = 15 mm/ 250 cycles = 60ym, and / e /e is from the calculations b a c (9) of Lin , for KD*P. The calculated values of t and t are listed in a c Section 2.3. Evaluation of (27) then yields 99 mS (25° C) t (250 cycles) = « 20U S (-50° C) These values are very close to a mean value of 1/x and 1/x , and are too a c large to he the source of the poor resolution observed at room temperature. However, by considering defect accumulation the value of t changes significantly. A steady current of 1mA for 1000 sec. (~ 15 min.) yields an accumulated number of neutralized deuterons N, as d N d = It/q = 6.25 x 10 15 If these deuterons are concentrated within the layer of depth w, the density n would be, for a 15 mm x 20 mm raster, n, = N./vA = 1.0U x 10 19 /cm 3 d d ( 1 ft ) From the data of 0'Keeffe and Perrino , the density of L-defects is n T = o/quL = 8.85 x 10 1T /cm 3 which is about n,/l2. Without specifying the conductivity mechanism, it is reasonable to assume the conductivity might increase by a factor of 10 inside the charge layer. This would change a by the factor of 10, but in (25) and (27), o is the conductivity at z = -L + w , Just outside the charge layer, and so should not be increased by defect accumulation. Then, with a -*■ 10 a , the same set of values in (27) yields a a h6 26.8 mS (25° C) x (250 cycles) = 21.9 S (-50° C) The charge is considerable, and is enough to account for the low resolution at room temperature, since information at 250 cycles (the television limit) decays about four times faster than the dc -level. If we assume a larger value of w, the disparity is even greater. We have considered only the initial charge decay. The decay of charge would be slightly different after a short time, since the charge, which was initially a uniform distribution, would tend to drift to the '"top" and "bottom" of the region of enhanced conductivity. A more complete analysis would be interesting. 2.1*. 3 Electro-Optic Mode Rotation The third factor which determines resolution in the light valve is the electro-optic effect. Specifically, the polarization of the allowed modes of propagation is a function of the magnitude and spatial frequency of the local electrostatic field. For high spatial frequencies and slight angular displacement of the optical phase front, the polarization is considerably different from that of the simple amplitude modulator of Section 2.1. The index ellipse is defined by the intersection of the index ellipsoid and a plane intersecting the origin and parallel to the constant- phase surfaces of the D vector (this plane is normal to the wave vector k ) . ( 8 ) It can be shown that for any k there are two allowed polarizations of D which are orthogonal and in the direction of the major and minor axes of the index ellipse. For the point-group F2m the index ellipsoid is 1 = \ (a 2 + b 2 ) + -% + 2r Ul bc E a + 2^0 ^ + 2^ E ( hi (28) n n a c where a, b, c are coordinates in the crystallographic orientation and E , E , E are the associated components of the electrostatic field. The ordinary and extra-ordinary indices of refraction are n and n , and the a C electro-optic coefficients are r, and *V . By a rotation of ^5° about 6 the index ellipse becomes 1 ■ * 2 ( ^2 + r 63 E c> + >? ( -T " r 63 E c» + *T + 2l \l* <* E y + xE x> (29 > n n n J a a c where x, y, z are related to a, b, c by 'W (- 1 x °) ( b ) (3o) \0 /2/ \ c / The phase front is assumed to propagate in the direction s which is a small angle from z and rotated from x by the angle , so that § = (s , s , s ) - (0 cos , sin , l) (31) x y z This defines a new coordinate system x' = (x' } y*, z') where z' = s and cos sin -0 \ / x \ -sin sin cf> 1/ \z/ The condition z' = defines the plane normal to s . By transforming the index ellipsoid (29) into x' coordinates and using the condition z' =0, we obtain an equation of the form 1 = A x' 2 + By' 2 + 2Cx'y' This transforms into the canonical form 1 = a (x") 2 + 6 (y M ) 2 48 by a rotation \J> about z'. The factors in the two equations are related by a, 3=|(A + B)+| /(A - B) 2 + 4C 2 and the rotation angle is tan 2\\> = 2C/(A - B) By performing the indicated (and tedious) operations we obtain, for small , |{A + B) * -~ - O r Ul (E x cos * + E sin <\>) i-(A - B) - iv E cos 2 - r, (E cos + E sin (j>) C * -r^E sin 24 + r, . (E sin $ - E cos ) 63 c 41 x y and r. E sin 2d> + r, _ (E cos $ '+"E sin +) pil; 63 c 41 x Y y tan r. E cos 2cf> - © r, (E sin <\> - E cos ) If the direction angle is zero, then tan 2\\i = - tan 2 and the axes do not change from those of the simple light modulator. However, (33) indicates that \\i is quite different from <(> under certain circumstances, considered below. Misalignment . The first problem is optical misalignment, giving a non-zero for any field E. This is similar to the problem of aperture angle for the amplitude modulator of Section 2, which is discussed by ( ft ) Yariv . Alignment to within an error of about 1 mrad is possible but requires very careful adjustment. This is below the order of the spatial frequency effect considered below, so we will assume alignment is correct. Phase Front Modulation . The second factor which determines is the angular deviation of the phase front as it is modulated by the electro- optic effect. For an applied charge pattern in the form sin is at the same angle as the sinusoidal charge pattern, so that tan , k = k sin x y From the form of the electrostatic potential, given by (8), it is clear that <">" E x' ' & k E S Then E cos + E sin = E , = E x T y x' S and -E sin -,/£ " 0.06l e. = 0.5k x 10 63 c 12 and r^ * 8.8 x 10 -12 Also, tanh x - 1 for x > 2, which is true for L = 127 ym and A ^ U65 ym s at 25° C and A $ 123 ym at -50° C. Then with A = B, these factors yield s R - 16.3 max approximately independent of temperature. For = 11 mrad, (0E) * 0.18 max To observe the effect of 0E we will consider two special cases. First, for a rotation angle cj> = 6 + mir/2, where m = 0, ±1,..., and where 6 is small. Then the mode rotation equation (33) becomes 51 For 6 = 0, tan 2i/j = tan 2(iJ; ± nnr/2) sin 26 + 6R cos 25 = - tan 26 - 0R i\> * - |- tan -1 0.18 - -5° Similarly, for = 6 + (2hi+1)ttA, where m = 0, ±1,..., we have tan 2\\i = tan 2(^* - (2m+l )it/U) = - cot 2ijj' cos 26 + (-l) m 0R = + sin 26 or \m tan 2x/j f - - tan 26/(1 + (-1) ©R) For small 6 , ip' = - 6 /(l + 0.18) and the difference is ij;' + 6 = ± 0.2 6. These mode-rotation angles are small, but the possible effect on amplitude modulation is large. For example, to obtain 100% modulation, the incident light beam must be at U5° to the axes x' , y* of the allowed propagation modes. For an incident light beam with E = a E , the two EL amplitudes are E , = E cos (u + tt/U) x a E , = E sin (w + tt/U ) y a where a) is the angular deviation from the x-axis. Then the unmodulated component would be E , - E , x' _y_ min (E TT E . ) x' y ' ' = 2 tan w 52 This equals O.I65 for w = 5°. This is the same order of magnitude as the relative electrostatic field response at high spatial frequencies. In the transmission light valve, this mode rotation problem gives clear preference to directing the incident "beam to enter the exposed face of the crystal. For negligible misalignment, the entrance mode rotation would be zero, since 3 = at this face, while the exit mode rotation would also be zero since E = E = at the conducting layer. The modes may x y rotate smoothly inside the crystal, but the entrance and exit conditions are correct. The opposite condition, with the entrance beam at the conducting-layer face, would have no difficulty with entrance-mode rotation (including c-axis misalignment), but the exit-mode rotation would be severe The reflex-mode light valve is the worst case, since it is equivalent to two transmission -mode light valves in series, with the conducting layer of the first facing the conducting layer of the second. It would be of interest to compare the experimental resolution for the two entrance -beam directions of the transmission -mode light valve, particularly since mode rotation should be approximately t emperature -independent . 2 . U . U Recapitulation The three factors affecting resolution of the light valve have been considered in detail. The results are summarized here. Electrostatic Field . The relative amplitude modulation as a function of the electrostatic field for a given charge pattern is found to obey a (tanh x)/x curve, where x = 2ttL , A c , with A the spatial wavelength of a sinusoidal charge pattern, and L' is the effective crystal thickness related to the true crystal thickness L by L' = L /e /e . For amplitude a c ~~" response, X = 3.37 L 1 at the 50% point, and 0.72 L 1 at the 10$ point; while 53 for intensity response, A = 6.5^ L 1 and 2.0 L' for 50% and 10%, respectively, The effective thickness is a function of temperature, being 1.17 L at 25° C and 0.32 L at -50° C for KD*P. For L = 127 ym and a 15 mm raster, the 50$ amplitude response is 6l television lines at 25° C and 22U lines at -50° C, while the 10% response is at 322 and 117U lines, respectively. The electrostatic field response can "be improved "by increasing the crystal area, reducing crystal thickness, or cooling the crystal to its transition temperature. Cooling the crystal is equivalent to reducing thickness "by the factor 3.65. Charge -Pattern Decay Time . The charge pattern decays by a longitudinal current and a transverse surface current. The time-constant of the longitudinal current is essentially constant as spatial frequency is varied. The transverse time constant is strongly dependent on spatial frequency but in a new crystal the longitudinal time constant is the dominant factor. If the transverse conductivity increases relative to the longitudinal conductivity, possibly by an accumulation of defect centers transported by a one-way current, then the transverse time constant dominates. If a increases by a factor of ten, the highest spatial a frequency decreases about four times faster than the d.c. term. This effect agrees with the experimental observation that resolution decreases somewhat after the first minute or so of beam current . The best method of reducing the loss of resolution due to charge decay is to cool the crystal. By cooling to about -50° C the conductivities are decreased by about 1000. Other methods, such as alternating positive and negative charge patterns to reduce the cumulative one-way longitudinal current do not eliminate the possibility of crystal lattice destruction due to excess deuteron transport, or non-reversible chemical reactions with the conducting layer. Further, the room-temperature time constant of about 0.1 sec is too short for a real- 5k time Fourier transform system, which requires the entire pattern to be present and stationary while the light beam is pulsed to generate the Fourier transform. Electro-optic Mode Rotation . The index ellipse indicates that the polarization of the allowed modes of propagation is a function of phase front direction and the relative values of the transverse and longitudinal components of the electrostatic field. The analysis is rather complicated but indicates that the polarization of a mode can rotate by several degrees for high spatial frequencies or small optical misalignments, Mode rotation agrees with the experimental observation that resolution is slightly dependent on the angle of polarization of the incident light beam. The effect is minimized for the transmission-mode light valve with the light beam incident on the exposed face of the crystal. The effect should be relatively temperature independent and is best reduced by a careful alignment of a well-collinated incident light beam. A converging or diverging beam is a strong possiblity for low resolution. Summary . The light valve resolution is affected by many factors of which crystal thickness and conductivity are the most important. The best method of improving resolution is to cool the crystal to the ferroelectric transition temperature, about -50° C. This also eliminates the problem of crystal deterioration due to ionic conductivity. 2.5 The Cooled-Crystal Transmission Light Valve The room-temperature light valve has been modified for cooled- crystal operation by incorporating a cooling unit as an integral part of the 55 vacuum chamber and crystal mount. The essential modifications are descrihed in this section. A summary of operational characteristics and problems is also included. Cooling Unit . The major modification is the cooling unit, which consists of a set of four two-stage thermoelectric elements (TEMs), and a large copper "block with integral cooling fins for forced-air cooling by a fan. Also required is a set of current sources to power the TEMs, and a set of temperature sensors and amplifiers to control the current sources . The electronic circuits are described in Section 3. (9) Part of the cooling problem was considered in detail by Lin . He analyzed the temperature distribution over the crystal face assuming the present CaF substrate and assembly as described in Section 2.2, but cooled 2 to -52° C by heat pumps around the substrate periphery. For a (25 mm) crystal mounted on a substrate 9.5 mm thick, and a thermal input of about 2 watts (from thermal radiation and electron-beam kinetic energy), the maximum temperature variation over the crystal face would be 0.6° C. This is small enough to operate very near the transition temperature with approximately uniform crystal conditions. Lin also considered the thermal compatibility of the various materials used in the assembly, and found no reason to modify the basic assembly. The transit ion -mode light valve requires a transparent substrate, so that the periphery of the substrate is cooled by four thermoelectric modules of custom design. Cooling to T (about -52° C) requires a temperature difference of about 85° C, which is near the limit for a two- stage thermoelectric unit . Standard two-stage TEMs are designed to operate in series electrically which is simple but somewhat difficult to control. For the precise temperature control required here, it was decided to select 56 two different single stage TEMs to be operated in thermal series with independent electronic control. Each two-stage unit is composed of a 920-31 main stage (1.2" x 1.2" x .22", 19 watts at 8.5A, 3.5V) and a 930-35 secondary stage (0.51" x 1.2" x 0.21", 9.U watts at 3-7A, U.2V), each with BeO end-plates for high efficiency. Both stages are standard units and were soldered together "by the manufacturer (Borg-Warner Thermoelectrics , Des Plaines , Illinois) at a cost of $65 per assembly (a comparable standard two-stage unit costs several times this figure). The four main-stage (warmer) units are connected electrically in series. The four secondary (cooler) units are controlled by four independent current sources. The TEMs operate better than the manufacturer's specifications indicate, but there is a large variation in characteristics between the various single-stage units. The cold-side of each TEM is bonded to the crystal substrate edge with Eccobond 56C silver-loaded epoxy, which is also used to bond the TEM hot-side to the copper heatsink. The copper heatsink is composed of a cylinder and a plate, fastened together by electron -beam welding for good thermal continuity. A photograph of the heatsink is given in Figure 20. The cylinder has an outside diameter of 82 mm and a length of k'J mm, with the inside hollowed out to an octagonal shape approximately 60 mm across, to fit the four TEM hot sides. The copper plate is 230 mm square and 23 mm thick with a 60 mm hole in the center and two 0-ring grooves machined into the faces. On each edge of the plate are 37 slots, cut by a bandsaw, about 1 mm thick with 3 mm spacing and a depth of 37 mm. The heatsink is bolted 57 Figure 20. Cooper Heatsink and TEM Mounting Cylinder for Cooled-Crystal Light Valve 58 between the exit-window flange and the body of the light-v&lve vacuum chamber, as shown in Figure 6. The heatsink is cooled by forced-air convection through the slots . One side of the plate is covered by an aluminum sheet cowling which is connected to a Rotron PF-R fan by a k inch diameter flexible plastic appliance duct. The cooling characteristics can be estimated as follows. To extract 2 watts at -55° C, the four TEMs require 50 to 100 watts to be extracted from the hot-side, which must be maintained at about 30° C (the cooling capacity drops drastically if the hot-sides rise above 35° C). An approximate analysis indicates that the temperature rise along the copper cylinder is 35° C at about 100 watts, and the total temperature difference between the TEM hot-side and the heatsink slots should be about 5° C If the fan operates at about 100 ft /min, the air velocity in the slots is about 1000 ft/min. The approximate heat-transfer coefficient (29) 2 for these conditions is found to be 6.1 mW/cm C. The slot area is 2 2 5000 cm , so the heat transfer is 30 mW/cm ° C, and at 100 watts the temperature rise from air to slot-face would be 3.3° C. With a total temperature rise of 8.5° C, the room temperature must be kept at about 22° C for efficient TEM operation. These temperatures were verified in operation by a temperature sensor located on the hottest part of the copper cylinder. When the cooling unit was designed, several cooling methods were considered and TEMs with forced convection seemed optimal. In practice, the bulk of the copper heatsink is a problem. Recently developed high-efficiency water-vapor heat-pipes (Heat Pipe Corporation of America, Watchung, New Jersey) would help to reduce the size of the heatsink, at least in the vicinity of the light valve. A possible replacement for the entire TEM-heatsink unit would be a recently available mechanical refrigeration unit capable of 59 reaching -60° C (FTS Systems, Inc., Briarcliff Manor, New York) — previously, such units were limited to -U0° C. Crystal Assembly . The major modification of the crystal assembly is entirely optical, to minimize interference fringes with the monochromatic coherent laser source. This is discussed in Section 3. A further planned modification was to increase the crystal edge from 25 mm to 30 mm and to replace the round substrate (as in Figure 8) with a square substrate, (38 mm) x 13 mm, which would fit inside the "nest" formed by the four TEMs, and thus conform to the geometry of Lin's temperature analysis. However, due to various economies, the original substrate design has been retained, and the TEM nest extended by small copper plates 3 mm thick which are bonded with Eccobond 5&C to the back side of the substrate. This has the effect of increasing the heat load, with a slight increase in temperature difference over the crystal face. The copper plates introduce a thermal contraction problem: the first substrate installed cracked along one corner when a temperature of about -10° C was reached. In addition, there is some cracking of the crystal along the edges which are bonded at the conducting layers to the parallel copper strips visible in Figure 12. It is not known if the continuity of the conducting layer circuit is damaged by this cracking. Electron Optics . The electron guns have been modified by substituting a "coated-powder-cathode" ("cpc") for the old tricarbonate units. The cp-cathode is reported to have less unit-to-unit variation, a longer lifetime at higher temperatures, and much better resistance to up-to-air cycles of the demountable vacuum system. The possibility of using (31) the "ultimate" cathode — known as the Philips or barium-dispenser cathode " " — was considered, but the Westinghouse electron gun people could not include it at this time. Both the write-gun and erase-gun work very well with the reduced target potentials and reduced conductivity near T , but the long time 6o constants require write-gun frame gating and other circuit modifications which are described in Section 3. A secondary-electron collection electrode is also required. The present version of this electrode is a thick copper wire "bent into a 25 mm square "ring" which is mounted on the substrate so that it surrounds the outside edge of the crystal. During the erase gun pulse, secondary electron emission charges the crystal face in a positive direction to approximately the potential of the secondary- electron collection electrode. This potential seems to be optimal at about +25 volts with respect to the crystal conducting layer (and the surrounding vacuum chamber) which is grounded. The erase-gun cathode-to-target potential is not critical, and good secondary emission is obtained in the range of 1 to 2 kV. The write-gun cathode-to-target potential is typically 15 to 20 kV, where an increase in potential tends to decrease the minimum focussed beam diameter, particularly at enhanced beam currents, such as 10 to 100 yA. Electronics . The required modifications to the light-valve electronics are described in detail in Section 3. The obvious change is the addition of the TEM drivers and temperature sensing and control circuits. Also, an adjustable current source was added to have better control of the write-gun filament power. Less obvious is the need for write-gun frame- gating and protection circuits. The high write-gun cathode potential makes it exceedingly easy to "overwrite" the crystal, with target potentials quickly reaching 1 kV or more after three or four successive video frames (say, 0.2 sec). This is above the erase-gun potential so that erasing is impossible, and the only method of eliminating this surface charge is to allow the crystal to warm up to about -20° C, where the time constant is on the order of ten minutes. Further, such high surface charges either induce field strengths in the range of crystal breakdown or generate large inverse piezoelectric forces because the first crystal used cracked in several places 6l each time an "overwrite" occurred (the cracks were all in the [110 ] direction). These "overwrites" were not caused "by normal experimental operations "because the write-gun frame gating is well controlled. Line- voltage transients or high-voltage arcing of the write-gun power supplies is the likely source of catastrophic "overwrite." The possibility and duration of such transients has been reduced by including a grid- voltage gate in the video isolation amplifiers, as described in Section 3. Operation . The operation of the cooled-crystal light valve is similar to that of the room-temperature version. The differences are the need for careful procedures (including more regular cleaning of the high- voltage equipment) to reduce the possibility of catastrophic transients, and the operation of the temperature control system. The cool-down and warm-up cycles should be about one hour each to minimize thermal stresses. The crystal should be maintained at about 1° C or more warmer than the transition temperature. Below the transition temperature, ferroelectric domains form which appear as bright or dark areas with a [100] incident polarization and [010] -directed analyzer. The shape and size of these domains can be changed by depositing charge with the write- beam. In addition to the domains, there are very bright irregular lines which have no apparent relation to nearby domains and which do not disappear when the crossed polarizers are rotated to the [110] and [110] (21) directions, even though the domain patches disappear. Kanzig attributes these bright lines to boundaries between two different types of domain groups, saying that the domain walls themselves are only a few angstroms thick and should not be visible. A photograph of a typical video frame is given in Figure 21. Storage time at this resolution is approximately one hour, 62 Figure 21. Resolution Example for the Cooled-Crystal Light Valve, at -50°C 63 THE COLFTAR SYSTEM The COLFTAR* system is a combination of the high-resolution cooled-crystal light-valve (discussed in detail in Section 2), a standard vidicon camera detector, Fourier transform optics, and support electronics. The system is designed to accept an input object in video frame format, and generate the optical Fourier transform of this object after a time delay of one video frame (in "real-time" or "on-line") . The transform output is also in video format and, if desired, may serve as the next input frame so that the subsequent transform is an inverse transform, and the output is the reconstructed object. This section discusses the theory, design, operation, and application of the COLFTAR system. 3.1 Theory of System Configuration and Operation The COLFTAR system must be able to generate the optical Fourier transform of a coherent two-dimensional object, and , if desired, be able to reconstruct the object by inverse transform (a second pass through the COLFTAR optics). This requires that the size and resolution of object, transform, and reconstructed object are all compatible with the size and resolution limitations of the COLFTAR components. Also, to preserve the complex value of the transform, it is necessary to include a coherent reference beam with the transform incident on the vidicon target. These various considerations are discussed below. The Optical Fourier Transform . A thin lens can be used to obtain (2) the optical Fourier transform of a coherent object. A simple example is illustrated in Figure 22. A characteristic of a thin lens is that all * "COLFTAR" designates "Cooled On-Line Fourier Transform and Reconstruction" 6k H i) M cd d o o CO cd o H PA k. PM o W Is fl H CO H Pn ts 65 parallel light rays incident on the lens at an angle from the optical axis z must pass through the point P located in the back focal plane of the lens at x 1 = f tan 0, where f is the focal length of the lens. In the Huygens construction, neglecting various corrections such as the obliquity factor, the amplitude G(x') of the light reaching P is given by oo G(x') = B / dx g(x) e"J kA (35) _oo where g(x) is the wavefront amplitude in the coherent object plane, B is a complex number, k = 2tt/A is the wave number, and A is the optical path difference, relative to some reference point in the x-plane. All of the rays are parallel, so that A = x sin - x tan = xx'/f (36) for small angles (which is the same type of approximation used to obtain the above integral for G) . Clearly, the function G/B is the Fourier transform of g, with distance x' in the Fourier transform plane related to pattern-wavelength A in the object plane by Ax' = Af (37) (This becomes obvious by substituting g = sin 2tt(x/A) into (35) » to obtain a delta-function with (37) as its singularity point.) A more rigorous derivation begins with the diffraction integral in the far-field or Fraunhofer region (for which an elegant derivation can (32) be found in O'Neill ' , where a Green's function solution is obtained which obviates one of the approximations commonly used), and, approximating 2 2 the thin lens by a phase factor of the form exp( -jkf/2 ) (x + y ), concludes with the complete expression for the optical Fourier transform of a two- dimensional pattern g(x, y): 66 2jkf » - &r (xx'+yy 1 ) g(x', y «) = y=- ff dxd y g( x > y) e (38 j For this expression the object g must be located in the front focal plane of the lens (in Figure 22, the object-to-lens distance is f ) . Minimum Transform Area . In the equation (38) for the two- dimensional optical Fourier transform, the object function g(x, y) can be complex-valued. From the discussion in Sections 2.1 and 2.U, the output of the light valve is an amplitude -modulated function of essentially constant phase. With this phase factor absorbed into the complex factor multiplying the integral of (38), we may consider g(x, y) to be real -valued . In this case, it is easy to show that the transform function G(x', y') is redundant: Let F(uO be the Fourier transform of g(x) , 00 i FU) = // dxdy g(x) e"^**- (39) _co Then for real -valued g, the complex conjugate F*U) = F(-u L ) (kO) and F is known in all four quadrants if it is known in any two adjacent quandrants , say, I and II. From the form of (38) we have pG(x') = e J6 F(x'k/f) (Ul) where 6 is real -valued, slowly -varying (and is eliminated by the detection process discussed below) and y is a real constant. Then all the information of G is contained in two adjacent quadrants. The constraint that the object function g be real -valued is not restrictive for most video objects, such as photographs, which are real- valued to begin with. However, for "synthetic" objects (say, computer- generated, or from some other non -visual source) and for object-reconstruction by inverse transform, this constraint on g is of interest, and this case will be examined in the discussion on reconstruction below. 67 Object -Trans form Relations . The dimensions and spatial frequency content of the object pattern in the (x, y) plane determine the spatial frequency content and dimensions of the transform pattern in the (x' , y') plane. The object is generated by a video-format raster scan, while the transform is detected by another raster scan. This combination imposes constraints on the parameters of object and transform. If the same system is to be used to reconstruct the object by a second (inverse) transform, additional constraints are imposed. For a given direction in the two-dimensional plane, the minimum spatial wavelength A is related to the maximum dimension L and number of cycles N by A Q = L/N (1+2) (N is one-half the number of "television lines"). For the object plane, the parameters of interest are (L , N , A^ ) in the x-direction, and x x Ox (L , N , A. ) in the y-direction. y y Oy Dimensions for the transform plane (x', y 1 ) are related to those in the object plane by (37) • If x' denotes the maximum distance from the transform center x' = to the outer edge (in the x direction), it is related to the smallest object wavelength A by x' = Af/A Qx , (U3) and if K n , is the smallest x' -directed wavelength in the transform plane, Ox' it is related to x_ (the maximum x-distance measured from x = in the object plane) by A„„, = *f/x„ (MO Ox' ' A similar pair of relations relates y' -dimensions to y -dimensions . If we let IT be the number of cycles from x = to x~, then from above, Ox 68 M 0x " V*0» = W = H 0x' so that the number of cycles is constant in both planes . Video Format of Object and Transform . The object is generated in the light valve from an input video signal and raster scan of standard broadcast format: there are 30 frames per second, and 525 horizontal lines for each f rams , of which 1*82 lines compose the two-dimensional object and k3 lines are ignored (during vertical retrace); the duration of each horizontal line is 52.5 yS followed by 11.0 yS of blanking during horizontal retrace, for a total of 63.5 yS (or 15,750 lines per second); the object aspect ratio is k:3, so that the length L of a horizontal line is U/3 times the length L of the vertical scan; (each frame is composed of two fields with controlled interlace, so that field #1 contains all odd-numbered lines and field #2 contains all even-numbered lines ) . The vertical resolution of the object pattern is, from the sampling theorem, one-half the number of samples so that the minimum vertical wavelength is h n = 2A = L /2l+l Oy scan y and N = 2^1 . Because of the finite length of the sampling sequence (the vertical scan length) the usable vertical resolution is often reduced by the (7) so-called "Kell factor' which is usually taken to be 0.7 or 0.85, depending on various conditions. The horizontal resolution of the object pattern is limited by the bandwidth of the video amplifiers (and, of course, the resolution of the light valve). A typical value is N = N = 2 la cycles, for which the bandwidth required is 2 Ul cycles/52.5 yS = U.6 MHz, which is well inside the limits for the light valve and vidicon video amplifiers. With N = 2Ul, A_ = (U/3) A„ • Horizontal resolution is x 'Ox Oy not affected by the Kell factor. 69 The coordinate systems (x, y) for the object plane and (x' , y') for the transform plane are given in Figure 23. The raster scan for the object is of dimensions L by L , is centered in the x-direction, and displaced x y by y = a > L /2 in the y-direction. This displacement is necessary for the reconstruction sequence, and a displacement in the direction of the shortest object length is preferred to minimize the increase in transform-plane resolution. The transform of the displaced object g(x, y-a) is related to that of the original by ^-jw a / __^ [g(x, y-a)] = e X \J- [g(x, y)] (U 5 ) where oj = x'k/f, as in (39) with (38). In the object plane we have L = (U/3) L , N = N , x y x y' so With x = L /2 x and y = a + L /2 - L , y y the transform-plane relations become A n , = 2Af/L Ox' x t A Qy , = Xf/L y = (3/2) A 0x , *0 " Xf/A 0x " (N x /2) A 0x' K ' «/ A 0y " "y A oy If the transform plane is scanned over quadrants I and II, the transform aspect ration is 3:2, which is very close to the standard format of U:3 in the object plane. At least the object format must conform to standard specifications, so that the change in aspect ratio is accommodated by an TO A 0x /2 A rt /2 Resolution Element Obj ect Plone < >y' Vo i 1 3 9 1 U, _. Scan H ^ Ly I < r Ci h "Xo nr z rsz: *0 -y; A 0y , /2 Ao.,/2 Resolution Element Transform Plane Figure 23. Coordinate Systems for Object and Transform Planes 71 electronic change of the raster size in the transform plane, or_ the two aspect ratios can be made equal "by changing the number of cycles N slightly, by adding more blanked lines to the vertical retrace period. This latter procedure is preferable for two reasons: first, the electronic system is less complicated because the two aspect ratios are the same, and second, the above calculations do not include the reduction of vertical resolution expressed by the Kell factor. Since the Kell factor is partly a subjective evaluation, the appropriate aspect-ratio modification should be determined experimentally. In the light valve, the maximum dimension is about 20 mm so that L = 20 mm, L = 15 mm, x y N = N = 2*41, x y A 0x = 83 ym ' A 0y = 62 - k m - The focal length of the Fourier transform lens is 720 mm (not optimal), and with A = 633 nm, the transform-plane dimensions become A 0x' = k5 ' 6 Mm > A 0y' = 3 °* U Um ' x^ = 5-5 nm, y^ = 7-3 mm, L , = 11 mm, L , = 7.3 mm. x' y' The standard l" vidicon has a nominal raster of 1/2" by 3/8" with diagonal 0.625", and usually this can be increased to a maximum usable diagonal of 0.70". The transform plane dimensions are slightly smaller than the standard size so that the focal length of the transform lens could be increased slightly. Complex-Value Detection by Reference Beam . The optical Fourier transform is "generated" by a pulse of light passing through the object transparency (the light valve) and the Fourier transform lens. The 72 transform is "detected" by the photoconductive target of a vidicon. Most light detectors, including the vidicon target, respond to the intensity of incident light so that it is necessary to use a reference beam — much like that used in photographic holograpy — to retain the amplitude and phase content of the optical Fourier transform. The reference beam incident on the target is of the form A e J*U, y) where A is a real constant (or, possibly, with small, smooth variations over the target area) and (x, y) is the relative phase difference between the reference beam and F e , which by (U5) is the transform of the offset function g(x, y-a), and F is the "true" Fourier transform of g(x, y) . Note that the phase 6 in (kl) is absorbed into . The reference beam and Fourier transform are added together by passing through a beam- splitter, and the vidicon target detects the intensity O' of the sum, 3 = |A e^ + F e"J ay | 2 (U6) = A 2 + FF* + 2A Re[F e" J {aJ+ ^ ] where Re[»] denotes "the real part of ...." The reference beam is "on- axis" so that 4> is nearly a constant (the variations of <(> should be much smaller than those of A). Then the third term on the right of (U6) becomes 2A Re[F] cos(ay +<(>)+ 2A Im[F] sin(ay + cf>) (U7) where Im[»] denotes "imaginary part of ...." Clearly (1+7) is an amplitude- modulated sinusoidal carrier of spatial wavelength 2Tr/a. If = , the in-phase and quadrature components are Re[F] and Im[F] , respectively, which can be obtained in parallel by synchronous demodulation of {h'j). The value is very temperature-dependent and must be monitored in real-time by a phase -sensitive detector, as discussed in Section 3.2. The value of a is constant and is determined by alignment and calibration. 73 The form of (^6) and (Ut) is essentially the same as expressions for detected intensity in photographic holography, for which the reference "beam is off -axis and the object is on-axis . Here the opposite arrangement is used, to facilitate reconstruction, as discussed below. Also, in holography with an off-axis beam, the linear term (U7) is separated from 2 the quadratic terms A and FF* by a carrier of spatial frequency sufficiently high so that at least the "upper sideband" of {hj) does not overlap the spatial frequency range of the quadratic terms. This requires a high resolution detector to resolve spatial frequencies at least three times the highest spatial frequency of F. This is beyond the limit of the standard l" vidicon. Special high-resolution vidicons are available* but their cost is too high (~$10K) to be included in the present COLFTAR system, (if a high resolution vidicon is available, it can be "retro-fitted" into the present system by tilting the reference beam off -axis slightly and increasing the bandwidths of the video amplifiers.) In the "economy" version of the COLFTAR system, the resolution limitation requires the linear term (U7) to occupy the same spatial frequency range as the quadratic term FF*. By making the reference beam amplitude A large relative to the highest amplitude of F, the term FF* is small relative 2 to A and {h r j) i so that the overlap effect is minimal. Unfortunately, the 2 magnitude of (U7) is small relative to A so that the signal-to-noise ratio will not be ideal. This and other considerations make the high-resolution vidicon system preferable to the "economy" version. * For fast scanning, there is a 2" vidicon from Westinghouse or a 3" FPS vidicon from General Electric; and for slow scanning, there is the family of return-beam vidicons. Reconstruction "by Sequential Transform . The video object may be reconstructed from its detected Fourier transform by a second pass through the COLFTAR system: the transform is transferred electronically from the vidicon to the light valve, and after the next light pulse, the vidicon detects the reconstructed object. That is, the object undergoes two optical Fourier transforms, sequential in time. The effect of two sequential transforms is analogous to that of an optical system composed of two thin lenses separated by the sum of their focal lengths: an object located in the front focal plane of the first lens is imaged to the back focal plane of the second lens with a magnification of -M, where M is the ratio of the focal length of the second lens to that of the first. In the COLFTAR system, the s.ame lens serves twice, by an electronic transfer from vidicon to light valve. Note that during this transfer the Fourier transform may be easily modified by simple electronic circuits, so that the COLFTAR system can function as a real-time spatial filter. The analysis of the sequential -transform reconstruction is considerably more complicated than that of the optical analogue described above. First, consider the result of the two sequential optical Fourier transforms without the detection process and offset rasters. In one dimension, the original object is g(x) and from (38) its optical Fourier transform is G(x') = D / dx g(x) e " JxX ' k/F (1*8) where D = |b| = l//Af - 1.5 x 10~ 3 m" 1 . Recall that the phase of B will be absorbed by the detection process, so it is ignored here. During the electronic transfer, G(x') becomes the second "object" h(x) by the coordinate transformation 75 h(x) = G(x' -> wx) (U9) where w = L ,/L is the ratio of the vidicon raster length, to the light valve raster length. From (U8) and (k9) 3 the optical Fourier transform H(x') of h(x) is rr/ ,\ ^2 r , ii / n\ r j -jx(x'+wx")k/f H(x') = D J dx g(.x ) J dx e = D 2 (Af/V) g(-x7w) (50) since the integral over x becomes a delta function. In two dimensions (50) is H(x', y') = (D 2 A 2 f 2 /w x w y ) g(-xVw x , -y'/w ) (51) where w = L ,/L and w = L ,/L . Clearly, (51) is the original object, xx'x yyy o> inverted and with a coordinate scale change which converts light-valve- raster dimensions to vidicon-raster dimensions. The vidicon raster has been positioned to detect only the upper half of the Fourier transform, quadrants I and II, for which y 1 > relative to the x', y' origin defined by the optical axis. The light-valve raster is also confined to quadrants I and II , y £ in the x,y-plane. It is easily demonstrated that this truncation of the Fourier transform does not prohibit the reconstruction of a real object function. If G(x' ) is the transform of g(x), then the truncated transform is \ [1 + sgn(y')] G(x') (52) where the sign function sgn(x) = x/|x| for x ^ and sgn(0) = 0. It can be shown that -j sgn(a)) is the Fourier transform of l/fTt, which is the kernel of the Hilbert transform. Then sgn(y') = / dyUf/uyk) e " Jy ' yk/f (53) By substituting this into (52), the truncated-transform equivalent of (51) is found to be where 76 H(x\ y») =(D 2 A 2 f 2 /w w ). ft(-x'/w , -y'/w ) (5M x y x y g(x, y) = [g(x, y) + jg t (x, y)]/2 (55) and g+ is the y-axis Hilbert transform of g, given by g + (x, y) - / dt ^^y (56) If g is a real -valued function, then g is also real, and the reconstructed object is simply the real component of (5*0- The complete two-dimensional expression for the reconstructed object is quite complicated, because of the many terms generated by the two successive intensity detections. To simplify, assume for the first transform that = in the intensity equation (U6). Further, assume that the detected intensity of the first transform has been reduced by the factor A and that the term FF* in (U6) may be neglected. Then the transform function which is transferred to the light valve is of the form ^1 /A 1 B \ + 2 Re[G e" jay ' k/f ] (57) where G(x ! ) is the optical Fourier transform of centered object function g(x) , and the parameter a is the offset of the light-valve raster in the y-direction. (in operation it is desirable to reduce the term A on the right of (57) so that (57) is only "slightly" positive-definite.) Then the detected intensity of the second transform is given by J 2 = A 2 + |H| 2 + 2A 2 Re[H e' J *] (58) where H is the optical Fourier transform of the half-plane trunction of (57), as in (52). As in (55), H = [H + j H + ]/2 (59) 77 where H(x' ) is the optical Fourier transform of (57) and H is related to H by the Hilbert transform (56). Then (58) becomes .2 J 1 i TT |2 J 1 |„ti2 J 2 = A 2 + IT |h| + IT ' h I + 2A H cos (j) + 2A H + sin = , we have ^2 = A 2 + 2A 2 H (63) Examining the terms of (6l), it is clear the only the last term on the right is nonzero in the upper half-plane; and, in fact, this is the reconstructed object, shifted to the position of the vidicon raster which scans the upper half-plane. With the offset-constant a slightly greater than the maximum y-dimension of the object, the reconstructed object is shifted far enough from the x'-axis to reduce the effect of the terms near the x'-axis. Note that a by-product of the sequential-transform reconstruction process is the y-direction Hilbert transform, which can be obtained by setting <\> = tt/2. 78 Summary . The COLFTAR system generates Fourier transforms and reconstructions of two dimensional objects in video format. A coherent object is obtained by directing a collimated beam of pulsed laser light through the cooled-crystal light valve. The light beam then passes through a simple thin lens and the optical Fourier transform is found in the back focal plane of the lens. The optical Fourier transform (38) is equal to the "true" Fourier transform multiplied by a complex factor, as in (Ul) . This complex factor is absorbed by the detection process, in which the sum of the Fourier transform and a reference beam are detected as the intensity (46) by the photoconductive target of a standard vidicon. The object may be reconstructed from its Fourier transform, by a second pass through the COLFTAR system. The input object format is that of a standard broadcast video raster, of about U8l horizontal scan lines (nominally), with an equal number of resolution elements in both horizontal and vertical directions, and with the vertical scan length equal to 0.75 times the horizontal scan length. To facilitate reconstruction, the object raster is offset from the center of the object plane into the positive-y half-plane (vertically). Then the detected intensity contains a linear term which is the product of the Fourier transform and a sinusoidal carrier, so that the real and imaginary parts of the transform are present as the in-phase and quadrature components of the amplitude-modulated carrier. Because of the redundancy of the Fourier transform, only two adjacent quadrants (I and II) are scanned by the vidicon raster. For reconstruction the Fourier transform, either directly from the vidicon or as modified or synthesized by some external source such as a general -purpose computer, is written onto the light valve as a new "object." The subsequent optical Fourier transform produces the 79 reconstructed object as the real component of the linear term in the detected intensity (60). 3.2 System Configuration A general block diagram of the COLFTAR system was given in Figure 1. This represents the configuration of an operational system designed for any of three modes of operation: Fourier transform of video input; Fourier transform, modification by "spatial" filtering, and reconstruction of input video; and "reconstruction" of synthetic (computer generated) Fourier transform input. This system -would interact with a video source and a general -purpose computer. In this section, the experimental configuration is described, which would form the basis of the system of Figure 1. Because of the experimental status of this system, many components have been designed for maximum parameter adjustability, while certain operational components and interconnections are simulated by manual control. In consequence, the description of the system configuration consists of a collection of seemingly disparate items, which are amalgamated by the .experimenter during system operation. There is a useful dichotomy of optical components and electronic components, and each group is described below. 3.2.1 COLFTAR Optical System The basic configuration of the COLFTAR optical system is given in Figure 2k. The major components are the collimated pulsed laser source, the light valve (represented by the crystal "X"), the Fourier transform lens, and the vidicon target. There is also an interferometric phase detector, which is not indicated in the diagram. These various components, as well as the mirrors and beamsplitter, are discussed in detail below. 8o c o o > > CM -J -t: x E (0 c _ «) p -I o o .2 2 Oh I I N O a> o « «> • a> o — o £ cd a. in u_ o n M it ii •S CD a. X -J UJ h- ■p CO (/) i>5 >- CQ CO H o ■H J -P < O a a »- EH a. i-q o O o a: • CM -J o 3 M •H o . Pn 10 o 81 The operation of the optical system is simple. The optical path is folded by the two mirrors so that the beamsplitter serves twice: first, to generate the reference beam and the input beam for the light-valve; and second to combine the reference beam and Fourier transform as input to the vidicon detector. To satisfy the Fourier transform condition, distance XM L = LM V = f , the focal length of the transform lens. Also, so that the reference beam has the proper "sphericity", distance BV = BX. There are three polarizers. The first, P x , defines the polarization of the input beam for the light valve, and also blocks the reflected component of the Fourier transform. The second polarizer, P ( | , extracts the cross-polarized amplitude-modulated output of the light valve. The third, P , converts the reference beam and the Fourier transform to the same polarization (required for for proper detection), and is rotatable to allow adjusting the relative balance between the reference amplitude and that of the transform. The optical system in Figure 2k is designed so that the vidicon normally detects the Fourier transform of the light-valve object. However, during system alignment it is useful to have a simple method of viewing the light-valve object itself. This can be done by placing a lens of focal length -f/2 (where f is the transform lens focal length) about halfway between the transform lens and the vidicon. This combination images the light-valve crystal to the vidicon target with a magnification of about +1/2, which is approximately the ratio of the raster size of the vidicon to that of the light valve. Recall that for reconstruction, the light-valve raster is offset to the upper half-plane and the vidicon scans only the upper half of the transform plane. The magnification of +1/2 will correctly image upper half-plane to upper half-plane. 82 Pulsed Light Source . As mentioned in Section 2, the light valve operates with a pulsed light source obtained from the combination of a Spectra- Physics 125 HeNe laser and 331/33 1 * Beam Expanding Telescope, and an Isomet TFM502 electro-optic modulator. The beam is pulsed "on" during the interframe period (vertical blanking time) of the video signal, by applying a 300 volt pulse to the TFM502, used as a "beam shutter". Unfortunately, even very careful alignment of the TFM502 produces an "on" to "off" ratio of about 300 to 1, which is too small: for a 33 mS frame, a 1 mS "on" time results in an effective "on" to "off" ratio of 100 to 11, so that 10% of the transform power (integrated by the vidicon) is obtained from the incomplete object (as the light-valve raster is scanned). This "beam shutter" should be replaced by one of three alternate possibilities: a beam chopper, such as a piezoelectric bender-bimorph or a tuning-fork chopper; a piezoelectrically-scanned Fabry-Perot etalon filter (Model UlO, Coherent Optics, Inc., Fairport , NY); or by direct pulsing of the laser excitation current. The third possibility is the simplest from the optical-component viewpoint , since only the laser and collimator are required. If a new laser can be obtained, a pulsed version would be adequate. Other- (2h) wise , the drive circuits of the continuous-wave laser could be altered to provide a satisfactory solution. The quality of the expanded laser beam is of interest. The laser has an output beam diameter of 2 mm (to the e intensity point) and a far- field divergence angle of 0.7 mrad. The telescope contains an expanding lens of focal length 182 mm, so the beam is expanded (by the ratio of the two focal lengths) to a diameter of Ul.7 mm with a divergence angle of 0.037 mrad (which is well within the collimation requirements of the light valve, for high resolution). The collimation is within A/8 on axis within the central 83 kG mm aperture, and coma is corrected to A/8 over a +10 mrad field. The telescope also contains a spatial filter assembly (a pinhole of diameter 6.8 \im) to produce a very smooth Gaussian amplitude distribution. At a radius of 12„5 mm (the outer corner of the light-valve raster) the Gaussian amplitude has a relative value of 0.93^, which represents a small but possibly significant "pattern" multiplying the "true" light-valve object. If necessary, this (35) can be corrected by an apodization filter to flatten the beam amplitude. Beamsplitter and Mirrors . The beamsplitter is an fused-silica inter- ferometer flat of diameter 50.8 mm and thickness 9.5 mm (a 25 mm cross section requires a 38 mm aperture at U5 and at this thickness), with sides flat to V20 (each) over a kl mm aperture and parallel to 1 sec. The splitter side is coated with a single-layer "achromatic beamsplitter" dielectric coating, with approximate reflection coefficients (intensity) of R.. = 0.15, R • = 0.U2, and transmission coefficients of T = 0.85, T^ = O.56, for polarizations parallel and perpendicular, respectively, to the plane of incidence. The opposite side (facing the light valve) is coated with a "peaked antiref lection" multi- layer dielectric coating, of transmission > 99-8% at 633 nm, U5 incidence, and polarization parallel to the plane of incidence - this eliminates multiple reflections of the Fourier transform. The two mirrors are Pyrex substrates of diameter 51 mm and flat to A./20 over a Ul mm aperture and are coated with a multilayer dielectric coating of reflectance > 99 >9% for polarization parallel to the plane of incidence, at 22.5°. Both beamsplitter and mirrors were obtained from Oriel Optics Corp. , Stanford, Conn. Polarizers . The present polarizers are Polaroid HN32 film laminated between glass sheets of X/1+ flatness. HN32 is a good polarizer, transmitting about 6h% of the power of polarized light oriented for maximum transmission, and about 0.007% of the cross-polarized power, for an extinction ratio of 0.005%. Also, the acceptance angle is large. Unfortunately, it is difficult to obtain 8U a laminated assembly without interference fringing due to mismatch of the various indexes of refraction. There are few alternate possibilities, because of the large aperture required. Birefringent polarizers are prohibitively expensive at the required 25 mm aperture, as are dielectric multilayer cube polarizers. A possible solution is an interferometer flat with light incident at the Brewster angle: the reflected component will be very well polarized, perpendicular to the plane of incidence, if multiple reflections from the opposite face are eliminated (by an AR coating, or a wedge of about 2° between the two faces). Unfortunately, the reflected power is only about 15$« This might be improved by a dielectric multilayer coating, at higher cost. Light-Valve Windows and Crystal Assembly . The two windows of the light valve are quartz interferometer flats, with each face of flatness X /10 , coated with a single-layer (MgF ) ant ire fleet ion coating. These should be recoated with peaked multilayer antire flection coatings to reduce interference fringes. The crystal assembly consists of the crystal with its thin- film conducting layer bonded to the CaF substrate by a transparent epoxy layer, with crystal and substrate faces of A/5 flatness. By itself, this assembly produces terrible interference fringes. Most of the interference can be eliminated by coating the exposed face of the substrate with a good multilayer antireflection coating. The remaining variation due to interference of ( ~\f\ \ multiple reflections can be estimated as follows. Heavens gives an expres- sion for the relative amplitudes of reflected and refracted light for a com- bination of two thin- film dielectric layers on a substrate. This is equivalent to the crystal assembly, ignoring the conductive layer. The worst case is for indexes of refraction »-,_ = n - 1.U65 (crystal extraordinary index), 85 n = I.567 (epoxy), and n = I.U3U (CaF ) which yields a mean transmitted ampli- tude of 0.82 relative to the incident amplitude, with a maximum peak-to-peak variation of 1.6$. This is small enough to "be negligible if the interference ripple is at a low spatial frequency. If the ripple is at a high spatial fre- quency, it will tend to distrub the Fourier transform. This is a multiplying error in the object plane, which is a convolution error in the transform plane, making error compensation in the transform plane difficult. Fourier Transform Lens . The Fourier transform lens is an air-spaced aplanatic telescope objective (Clave, Paris), of focal length 720 mm and diameter 60 mm, obtained from Special Optics, Cedar Grove, NJ. The objective is composed of two elements, with all surfaces coated with broadband antireflec- tion coatings, for a cumulative loss of about 1/2$ at 633 nm. The lens is dif- fraction limited, having essentially no spherical aberration or coma over a +1° field of view. This corresponds to a diameter of 25 mm in the transform plane, which is slightly larger than the 23 mm diameter required by the offset vidicon raster. As mentioned in Section 3.1, this focal length is slightly less than the optimum value for maximum vidicon raster size. Unfortunately, custom focal lengths are expensive, and 720 mm was the closest known stock value. It is possible to increase the effective focal length by using a diverging spherical wave as the input beam for the light valve, but the change is quite limited because of the stringent collimation requirement for high resolution, as dis- cussed in Section 2.U.3. Vidicon Target . The vidicon target is a photoconductive layer supported by a thin glass window which closes one end of the vacuum envelope. The layer 86 is about 2 to 10 urn thick, and located between the layer and the glass is a transparent conducting layer. The glass face which is exposed to atmospheric pressure is covered with a high-efficiency broadband antireflection coating. The optical characteristics of this assembly are not too important, because optical imperfections, such as non-flatness, will affect transform and reference beam equally. Interferometric Phase Detector . In the equation for detected intensity (U6), the reference phase is the phase difference between the reference beam and the optical Fourier transform. The transform optical path is about 1.5 m longer than the reference path. The ambient temperature variation is on the order of 0.5°C, so that, using a typical thermal expansion coefficient of about 16 um/m°C for carbon steel, the reference phase will vary by about 13 wavelengths over a temperature cycle. This requires a phase-sensitive detector to obtain the current value of for proper interpretation of the Fourier transform. The arrangement of the optics as in Figure 2k is a variation of a Twyman- Green interferometer, with unequal path lengths. The collimated laser beam is round and the rasters are rectangular, so that part of the reference beam and light-valve input beam can be used to form a sum, for which the intensity is a function of phase. This can be detected by a simple phototransistor. In addi- tion, because the output power of the laser drifts with time, it is necessary to know the current beam amplitude, which can be obtained by another phototran- sistor monitoring the reference beam alone. The two phototransistor outputs then determine both amplitude and phase of the reference beam. 87 For reconstruction it is desirable to have an integer multiple of it. Rather than wait for the proper value during the temperature drift cycle, the phase can be controlled dynamically by using the phase detector to control a piezoelectric translator which moves, say, mirror M to compensate for thermal drift. Suitable translators are available from several sources although some require rather high input voltages (several kilovolts) for a few microns of displacement, while others are on the order of 100 volts per micron. 3.2.2 COLFTAR Electronic Configuration The electronic configuration of the COLFTAR system is indicated in Figure 25, in which blocks represent major components or subsystems. The input consists of a video signal containing the video frame in raster-synchronized format, and a synchronization signal. The block labeled "Sequencing" controls the proper sequence and timing of operations such as write-gun gating, erase- gun pulsing, laser-beam pulsing, and vidicon scanning; in the experimental system, "Sequencing" is a set of manual controls. The output is either the (demodulated) Fourier transform or the reconstructed video from a transform- reconstruction sequence. During a trans form- reconstruct ion sequence the Fourier transform from the vidicon is sent back to the light-valve after being modified in some manner by the "Reconstruction Processor", which, in the experi- mental system, is essentially a buffer amplifier. The blocks appended to the "Reconstruction Processor", such as "Video Frame Store", are suggested sub- systems to facilitate Fourier transform modification by spatial filtering or reconstruction of synthetic, computer-generated transforms. The various experi- mental electronic components and circuits are described below. Light-Valve Electronics . A block diagram of the electronics of the light- valve subsystem is given in Figure 26. Most of the components are 88 k o 41 *- Si to in o & ° -5 o +~t O © w •D O Ol c-se co^o 544 O £ V> V. 3 O ° -2. c c >. o> CO Q D 4-, at < E o a> (D at u c at 0) 01 w. 3 O o w «t c a o 6 o at h- ;«!=► E W W |/> at o u — at at o S> -5 at s o. c 2" E ** 3 o at o 8 » I " CL at O |3 .? o _i > f-4- H=^, at at J2 at 3 °i llV c o u o 3 s *- a* v> u c o u a. at (E c at 3 tr at CO o c >» CO at il o o a CO o « a> at c w ■o o o > £ co a o •H 3 •H fl O O » w ■3 CO o •H 8 -P o i -p ■a •H 90 described in detail by Casasent , including the drive circuits for the electro-optic he am- shutter, which is part of the block "Pulsed Laser" in Figure 25. Changes and additions required for cooled-crystal operation are described below, and include: temperature sense and control circuits; write- gun frame gating; write-gun and erase-gun transient protection; write-gun filament current source. Temperature Sense and Control Circuits . The temperature of the crystal and substrate is sensed by four calibrated pn junctions and controlled by a set of thermoelectric elements. The temperature circuits consist of four temperature sensor amplifiers, four temperature difference amplifiers, and five voltage-controlled current drivers. These are described below. The temperature sensors are 2N3128 transistors. Each transistor is contained in a small ceramic-and-epoxy case about 0.05" x 0.05" x 0.03", which allows fast thermal response and requires negligible space when bonded to the substrate near the crystal edge. From the Ebers-Moll equations, the base-to-emitter voltage V is a linear function of temperature at constant I BE and V = 0. All four junctions were calibrated simultaneously against a thermocouple and two precision thermistors , over the temperature range of -60°C to -20°C, with increments of 1°C, and over the range -20°C to +25°C with 2°C increments. At I £E = 10.00 yA, the measured V BE each fit the curve V BE = E " AT » with B ~ 5 ?° mV and A - 2 -^ mV/°C. There are four different sets of A and B, and for each curve, the standard deviation is less than 0.05°C. The 2N3128 transistors are apparently no longer available. A good replacement would be the MMT70 , which is contained in an all-epoxy case of diameter 0.09" and height 0.06". It should be remarked that pn junctions sensors are not ideal, for several reasons: the units must be calibrated after all 91 high-heat treatments, such as lead soldering; the junctions detect stray rf radiation, which raises the junction temperature as much as 1°C above ambient as the detected power is dissipated in the junction; finally, the junctions are susceptible to destructive breakdown if high-voltage arching occurs nearby,, The temperature sensor circuit of Figure 27 consists of a current source to bias the junction, and a precision amplifier with adjustable bias and gain to -produce V = T/10 volts, where T is the sensor temperature. The & * out overall variation between all four sensors and associated circuits is less than 0.1°C over the calibration range -60°C to -20°C. Each secondary (cooler) thermoelectric module is driven by a voltage- to-current power amplifier, shown in Figure 29. The voltage input V . is determined by the circuit shown in Figure 28. The desired temperature T is selected by setting a precision potentiometer, for which voltage follower A generates V = T/10. Emitter- follower Q sets a limit for the maximum operating current, which is controlled for each module by voltage-comparator C, with visual indication given by the light-emitting diode MV50. Amplifier A. i generates the current-control voltage V_. , in the form V - 22(V - V ) - 0.2(V + V ) Ii K Ti T0 y l TO Ti ; At the normal operating temperature, about -50°C, the thermoelectric modules require about 2 amps each; the above equation gives V . - 2 with V = V = -5. The primary thermoelectric modules are connected electrically in series, and require about 6 amps during normal operation. This current is provided by the power current source shown in Figure 30, which is essentially a scaled version of the circuit in Figure 29. The circuits for the unregulated power supplies for all five current sources are given in Figure 31. 92 +> •rl O u •H O u o CQ 5j CO 3 0) CM P-4 93 w\ |h o u o H O -P § 13 V. 4) E-i OO C\J e •H &4 9h o s to a •H H O O o to V H O O d o o 0> CQ o o CQ O OS CM to 95 4) 3 o a £ •H H 8 o Oh o o CO cj o no •H Cm 96 'VMnryvv^ o CO -p a v o I bO Pi •H H O O O o CO O CM 97 Write-Gun Frame Gating . The input video to the light-valve write-gun isolation amplifier must he gated to select the desired video frame to he stored on the crystal surface. For the experimental system, this circuit consists of an integrated-circuit video gate (MC11+U5L) controlled hy a field-pulse counter, as shown in Figure 32. The hinary counter is loaded with a field count set hy manual switches during the gate "off" time. Timing is initiated by the "start" switch. After "start", the first vertical synch, pulse opens the gate. The count is decreased hy one for each vertical synch. pulse (one per field, two fields per frame), until zero is reached, when the gate is closed and the circuit reset. By itself, this circuit works well. However, the video isolation amplifier is essentially ac-coupled and cannot handle the sudden change in dc-level caused hy video gating. For reliable operation, clamping circuits must be added to the high-level (isolated) part of the isola- tion amplifier. Transient Protection Circuits . For transient protection the duration and repeatability of the write-gun and erase-gun beam currents is controlled by one-shot timing circuits. The erase gun modifications are described else- (37) where . The modifications for the write gun include a photon-coupler to supply "unblank" pulses to the high-level (isolated) video amplifier, and a grid-voltage gate with lockout. The "unblank" photon coupler circuit is given in Figure 33. The photon coupler, described in detail elsewhere "' , consists of an infrared light-emitting diode coupled to a photodiode by a light pipe, and is tested for 30kV isolation. The LED is driven by a logic-controlled current switch. The photodiode output current appears as a voltage change, of about lOmV across the IK resistor and with a risetime of 50 nS, and is detected by the high-gain comparator. The comparator output, called "unblank", is a logical one only during the unblanked period of each horizontal line which occurs during the desired video frame. 98 o (3 4. > I > + I \*\ A o IX) 7\ * 17 3 ^-t-AVvr 1 > + 4 H"' CD 6 z » to P ; I _ u c 3 O + CM o CD + ■o .« < u. ii 8 z CO CM* sr -« US OJ on •H P-4 99 z eg O 2 O *H 0) H O o H ■H IO O 100 The grid- volt age gate and lockout circuit is given in Figure 3^. The first "unblank" pulse initiates the "Gate" oneshot, with duration 100 mS. The termination of "Gate" triggers "Lockout", which prevents further "Gate" periods for a "protection" period of about 60 sec. This is required when the erase gun is controlled manually, so that transient "overwrites" do not damage the crystal, as discussed in Section 2.5. The write-gun grid voltage is controlled by the "Gate" signal as follows: Normally the grid-voltage is held near isolated-ground (about -20 kV) by current sink 0,3. When the "Gate" goes high, current source Q2 is turned on by QU, and the grid voltage rises to the clamp level of Ql. When "Gate" is off, Q2 is also off, so the grid voltage falls to the saturation level of Q3. This grid voltage (relative to the cathode, which is about +200 volts above isolated-ground) is deep into cutoff, so the write-gun beam current is thoroughly off. Filament Current Sources . The beam currents required for the write gun and erase gun are obtained by operating the cathodes at temperatures con- siderably higher than normal. To reduce variations caused by line-voltage changes, the filament currents are supplied by direct- current regulated sources. Figure 35 is the circuit for the write-gun filament current , and the circuit for the erase gun is similar. These current regulators have a "standby" mode of U00 mA, and can be switched manually to the "operating" mode, where the current may be adjusted from ^50 to 550 mA. This "standby" mode is necessary in the experimental system, so that the high-temperature conditions - which shorten cathode lifetime - are held to a minimum. Phase Detection Amplifier . The reference-beam phase detector con- sists of two phototransistors, one of which detects the (amplitudes) of the reference beam, while the other detects the intensity of the sum of the reference 101 cm cj -o — * ° J" rt" CM c 2 O O 3 W -P •H CJ fH •H o o •H P CJ 0 cd p H o > ■H O 0) §> ■H Eh ° c 102 pi o u •H O ■P a u u pi o -p a o I CD -P •H 00 •H P-4 103 beam and a reference "ray" which traverses the optical path of the Fourier transform optics „ In both phototransistors the collector current is approxi- mately proportional to the incident light power (intensity), so that a voltage proportional to the intensity can he obtained from an operational amplifier used as a transresistance amplifier. Then the reference phase can be obtained, as cos , from a simple summing amplifier. These circuits are given in Figure 36. The magnitude A of the reference beam can be obtained by a simple square-root circuit. The phase and amplitude vary quite slowly (on the order of 1 Hz), so that the only design difficulty is d.c. drift in the various amplifiers. 3.3 System Operation The configuration of the COLFTAE system is arranged to provide a general-purpose facility for two-dimensional Fourier transforms of images in video format, and/or reconstruction of images by inverse Fourier transform. There are three basic modes of operation: l) Fourier transform, 2) inverse Fourier transform, and 3) Fourier transform and reconstruction. The third mode is essentially mode one alternating with mode two. For all modes the optical system is unchanged. However, because it is necessary to retain the complex value of the Fourier transform, the electronic system of mode one differs slightly from that of mode two, with changes between modes controlled by the sequencing logic. The three modes of operation are described below. In the experimental COLFTAR system certain components cannot operate at maximum video frame rates, although sequential operation at slower rates is possible. Specifically, the "standard vidicon camera" is designed for live television scenes, which change relatively slowly from frame to frame. If the illumination is rapidly removed from the vidicon, several frames of beam-scanning are required to fully "erase" the electronic after-image ioU o o C\J cc A u (£> 0C + "< O o QQ C\J + QQ + CSJ < II O H u 4) •H 0) O en On 00 CVJ > CVJ t t N < o M 105 (39) (decay is hyperbolic!). This is called vidicon "lag" and is a combination of photoconductor carrier-recombination delay and the dependence of effective electron beam current upon local surface potential. This requires a "vidicon- lag delay" between successive Fourier transforms, so that the vidicon target can be scanned for several frames to "erase" the previous target image. This is not a problem for manual operation, but a high-speed COLFTAR system would require a low-lag vidicon (such as a plumbicon). Fourier Transform Operation . In the Fourier transform mode, the sequence of operations for a single transform is as follows: a) Erase Light-Valve Crystal Surface; (l mS) b) Write Object onto Crystal Surface; (30 mS) c) Pulse Light-Beam; (l mS) d) Scan Vidicon Target for Fourier Transform Output; (30 mS) e) Coincident with (d), Use Synchronous Demodulation to Obtain, in Parallel, the Real and Imaginary Parts of the Fourier Transform. At this point the Fourier transform operation is complete. A subsequent trans- form operation can occur after the "vidicon-lag delay", which is about 0.5 sec, Inverse Fourier Transform Operation . To obtain an inverse Fourier transform, the upper half-plane of the transform is written onto the light- valve crystal, as described in section 3.1. The video signal sent to the light valve must be of the form of a sinusoidal carrier amplitude -modulated by the Fourier transform. This is required so that both real and imaginary parts of the transform can be written onto the crystal surface as a charge pattern - recall that the light valve can only generate a real object. The io6 carrier frequency must be such that the reconstructed object is offset into the upper half-plane, as scanned by the vidicon. The proper transform format can be obtained by including a synchronous modulator in the COLFTAR electronic system. Then the sequence of operations is a) Erase Light-Valve Crystal Surface; (l mS) b) Write Modulated Transform onto Crystal Surface; (30 mS) c) Pulse Light-Beam; (l mS) d) Scan Vidicon Target for Reconstructed Object. (30 mS) At this point the inverse Fourier transform operation is complete. A subsequent operation again requires a "vidicon-lag delay". The reconstruction of a real object is a one-step operation, as above. The reconstruction of a complex-valued object requires a two-step process, based on the detected-intensity equation (60). For the real part, the transform is symmetrical, as in (^0), while for the imaginary part, the transform is ant i symmetrical. By reconstructing only the upper half-plane, both parts are automatically reconstructed, although the relative magnitude of the two parts is unity (the actual relative magnitude is, of course, the same as that for the symmetrical and antisymmetrical parts of the transform). The real part, from ( 60 ) is obtained with the reference phase § = 0, while the imaginary part is obtained with (j> = tt/2. The four sub-steps, above, result in the real part; after a "vidicon-lag delay", the imaginary part is obtained by changing the reference phase (with the phase-control feedback loop), then repeating steps (c) and (d) - the transform has been retained on the crystal because of the long time-constant at -50°C. 107 Fourier Transform and Reconstruction . This mode of operation essen- tially requires a Fourier-transform operation (mode one) followed "by an inverse- Fourier-transform operation (mode two). The sequence is as follows: a) Erase Light-Valve Crystal Surface; (l mS) t>) Write Object onto Crystal Surface; (30 mS) c) Pulse Light-Beam; (l mS) d) Erase Light-Valve Crystal Surface; (l mS) e) Scan Vidicon Raster for Fourier Transform; (30 mS) f) Coincident with (e), Modify Fourier Transform In Time (if Desired), and Write Transform onto Crystal Surface; g) Wait for "Vidicon-Lag Delay"; (?) h) Pulse Light-Beam; (l mS) i) Scan Vidicon Raster for Reconstructed Object^ (30 mS) Note that (f) allows arbitrary operations on the Fourier transform (although in "coded" format, because the transform is still in the form of an amplitude- modulated sinusoidal carrier), using electronic circuits - this is a " real-time spatial filter" of great versatility. If the modified Fourier transform results in a complex- valued object, the imaginary part can be obtained, as before, by shifting the reference phase and repeating steps (g), (h) and (i). 3.^ System Applications The distinguishing characteristic of the COLFTAR system is its ability to generate two-dimensional Fourier transforms and reconstructions of video images at video frame rates , in real time . Thus the COLFTAR system is particularily suitable for high-speed or large-volume image processing, or as part of an interactive processing facility. Some potential applications 108 of the COLFTAR system are discussed below. These areas are: very fast Fourier transforms; image processing and enhancement by spatial filtering and recon- - struction - particularly interactive image processing; and specialized applica- tions such as crystal-lattice reconstruction from x-ray diffraction patterns, and acoustic hologram displays. Fast Fourier Transform . The Fast Fourier Transform (FFT) is one of the basic tools of two-dimensional image processing and of one-dimensional time-series analysis. The FFT is an all-digital technique applied after the data has been prepared by analog-to-digital conversion. Usually the FFT is done twice, once for the transform and once for image construction, after which the data undergoes digital-to-analog conversion for video display or output as a microfilm frame. The processing time for the FFT is a great improvement over the time required for a "slow" Fourier transform, but for two-dimensional images the time required is still quite large. Hunt considers various methods, all based on the FFT timing equation, t = AMN(log M + log N) for a two-dimensional array of size M by N, where A is a constant for a given computer (and programming method). Hunt found that a radix-2 FORTRAN FFT on a CDC6600 requires 120 mS for a 102^ one- dimensional array. By extrapolation, with the above equation, the time for a 512 by 512 two-dimensional array - equivalent to the COLFTAR raster resolution - requires 55 » 3 seconds . There are various methods to reduce this time - such as machine-language coding for high efficiency, and specialized hardware - but even so, the above extra- polated time does not consider the increased data-management problems in handling an array of over 250,000 points (Hunt suggests that a (lOOO) array is the maximum feasible under optimal conditions). Obviously, for high-speed, 109 real-time Fourier transforms, the digital FFT is not in the same class as the COLFTAR system, which generates video transforms in 33 mS , at maximum rates. In the area of one-dimensional Fourier transforms, the COLFTAE system also provides a high-speed, real-time facility. In this case, the data (usually a time-series) are written onto the light-valve crystal as sequential groups, one group for each horizontal line. There is then a one-to-one mapping of points in time, t., to points on the light-valve raster: f(t.) * f(n.Ax, rn^y) It is easily demonstrated that the one-dimensional Fourier transform of the set of data {f(t.)} is found in the two-dimensional plane along a line passing through the transform origin at an angle equal to the light-valve scan angle. Thus, a one-dimensional time-series array of 250,000 points requires 33 mS to generate its Fourier transform, while the comparable FFT time is the same as that for the two-dimensional array, 55 seconds. Clearly, the COLFTAR system has a tremendous speed advantage over the digital FFT. The only disadvantages are fixed format (the video raster is determined by the electronic deflection equipment - random-access scanning could be used) , and the relatively low dynamic range available in the analog transform representation (the standard vidicon would typically be limited to less than 6k levels of gray, depending on various factors such as noise, while the digital computer usually has a floating-point format covering many decades) . Image Processing . With the popularization of the digital FFT around 1965, the processing of images by spatial- frequency operations became feasible, and the intensity and scope of image processing research increased tremendously, 110 as readily indicated "by the hyper- exponential growth of image-processing "biblio- graphies. Yet the available facilities for such research - notably, the FFT ' as implemented on a general-purpose digital computer - are essentially in the ( Uo kl) primitive stage. Again, the reports of Hunt are of interest. He indicates that 90$ or more of the computer time is used by the FFT process, and that an optimized routine for an array of 102U by 502U, on a CDC 6600 requires about k minutes of central processor time, but 30 to k^ minutes of elapsed job time, because of memory processing requirements - this is for a single transform and reconstruction sequence. Obviously image processing by this method cannot be part of an interactive system (that is, a real-time image- processing system which allows user interaction). Again, the COLFTAR system can provide the Fourier-transform facility for a real-time system. The availability of interactive image-processing facilities should prove to be of signal value for research in the area of image enhancement, where experimental results are often evaluated by highly subjective criteria. The high-speed capability of the COLFTAR system should be suitable for image-processing applications involving large numbers of images. Some typical possible applications of recent interest are: inspection of integrated circuits by spatial filters ; positional character-recognition by matched spatial filters' ; photo-reconaissance processing by sampling the Fourier (3) transform ; and fingerprint recognition by matched spatial filter. Special Applications . There are several areas which are not normally considered "image-processing" but where the abilities of the COLFTAR system may be useful. One such area is the determination or "reconstruction" of crystal lattice structure from x-ray diffraction information. Here, the Ill x-ray diffraction pattern is recorded as an intensity , so that all phase information is lost. By applying various symmetry rules to construct hypothetical lattices, one can eventually find a structure which reproduces the recorded diffraction pattern (which is the Fourier transform of the lattice) Obviously, this is a "cut-and-try" method which should he ideally suited to an interactive Fourier transform system (using, of course, the COLFTAR system). Another area involves the use of a real-time Fourier-transform (kh) system for the reconstruction and display of far- field acoustic holograms , for, say, underwater imaging. In this case, a cooled-crystal light valve similar to that of the COLFTAR system is already part of a research effort in this direction. 112 k. SUMMARY The COLFTAR system is a real-time two-dimensional Fourier transform generator which operates with images and transforms in video format. The con- figuration of the COLFTAR system includes an electro-optic light modulator of advanced design, a compact Fourier-transform optical system, and a vidicon detector with phase information preserved "by a holographic reference beam. Together with support and control electronics, the system can generate Fourier transforms, inverse Fourier transforms, and transform-reconstruction sequences, all in real-time, at video frame-rates of 30 transforms per second, and with video images of up to 500 by 500 television-lines of resolution. The central component of the COLFTAR system is the electro-optic light valve, or Ardenne tube, which amplitude-modulates the wavefront of a coherent incident light-beam by the longitudinal linear electro-optic effect in a thin KD*P crystal cooled to its Curie temperature (-52°C). This is the "cooled- crystal" version of the light valve, which has evolved from an earlier version using a room-temperature crystal. Section 2, above, thoroughly con- siders the primary factors which are deleterious to the operation at room- temperature, but are advantageous for operation near the Curie temperature. Included is a theoretical analysis of resolution and time constant which presents three original approaches: the anisotropic electrostatic field; the anisotropic, in homogeneous surface charge decay; and the electro-optical mode rotation. The theoretical results are shown to be consistant with experimental observa- tions of resolution and operation at room temperature and near the Curie tempera- ture. Included is a description of the light-valve modifications required for cooled-crystal operation, which are primarily the addition of thermoelectric 113 cooling elements, temperature sensors, and temperature control electronics. In addition, protection circuits are required to prevent transient "overwrites", which deposit sufficient surface charge to cause crystal cracking. The COLFTAR system is built around the light valve. The optical system is a modified interferometer arrangement, with a beamsplitter which generates the input light beam for the light valve and also combines the Fourier transform with a reference beam for detection by a standard vidicon target. The optical path is folded, and because the reference beam path and Fourier transform path are of different lengths an interferometric phase detector is required to monitor (and control) the reference phase as the ambient tempera- ture changes. A Fourier transform is generated as follows: the light-valve crystal is erased and the video object is written onto the crystal, which is located in the upper-half of the back focal plane of the transform lens; the coherent light beam (generated by a laser and be am -expanding telescope) is pulsed "on" for about 1 mS , during which time the vidicon target detects the intensity (magnitude squared) of the sum of the reference beam and the Fourier transform; the vidicon target, located in the upper-half of the front focal plane of the transform lens, is then scanned, and the output signal includes the real and imaginary parts of the Fourier transform as the in-phase and quadrature components of an amplitude-modulated sinusoidal carrier. An inverse Fourier transform is slightly more complicated, because of the possible com- plex value of the reconstructed object, but the sequence of operations is essentially the same as for the Fourier transform - the only system changes are a re- arrangement of the electronics to accommodate the format changes. Finally, the video object can be modified by real-time spatial filtering . liU which is a two-step process: the Fourier transform is the first step, which results in a video signal for the Fourier transform; this signal is transferred to the light valve after which the inverse transform is generated, which is the reconstructed object; during the transfer process, the Fourier transform may he modified by electronic "spatial filters" which are the equivalent of transform-plane filters in an all-optical spatial filtering system. There are several potential applications for the COLFTAR system, pri- marily in the areas of image processing and enhancement by spatial-frequency operations. The principal characteristic of the COLFTAR system is its high speed and real-time capability. The COLFTAR system can generate a Fourier transform of a (500 by 500) — element video object in 1/30 second, with no delay, while a digital computer, using an optimized "Fast Fourier Transform: routine, would typically require about 50 seconds of central-processor time and several minutes of memory-processing time for an object of the same resolu- tion. The high speed and real-time capability of the COLFTAR system are ideally suited to interactive and/or high- volume image processing applications. 115 LIST OF REFERENCES 1. A. Vander Lugt , Optica Acta, 15, 1, 1968. 2. J. W. Goodman, "Introduction to Fourier Optics", McGraw-Hill, New York, 1968. 3. G. G. Lendaris and G. L. Stanley, Proceedings of the IEEE, 58, 198, 1970. k. W. J. Poppelbaum, M. Faiman, D. Casasent, and D. Sand, Proceedings of the IEEE, 56., 17UU, 1968. Also, W. J. Poppelbaum, "Adaptive On-Line Fourier Transform", in "Pictorial Pattern Recognition", ed. by G. C. Cheng, Thompson Book Company, Washington, D. C, 1968. 5. D. P. Casasent, "An On-Line Electro-Optical Video Processing System", (Ph.D. Thesis), Report No. 331, Department of Computer Science, University of Illinois, Urbana, Illinois, May, 1969 . 6. C. J. Salvo, IEEE Transactions on Electron Devices, ED-18 , 7^8, 1971. 7« W. J. Poppelbaum, "Computer Hardware Theory", The Macmillan Company, New York, 1972. 8. A. Yariv, "Quantum Electronics", John Wiley and Sons, New York, 1967. 9. C Lin, "Design Factors for a Transition Temperature Pockels Tube", (M. S. Thesis), Report No. Hl3, Department of Computer Science, University of Illinois, Urbana, Illinois, August, 1970 • 10. I. P. Kaminow, Physical Review, 138_, A1539, 1965 . 11. G. M. Loiacono, Materials Research Bulletin, _5> 775 > 1970. 12. Conversation with T. Nowicki, Isomet Corporation, Oakland, New Jersey, October 12, 1970. 13. M. 0'Keeffe and C. Perrino, J. Phys. Chem. Solids, 28, 211, 1967. Ik. V. H. Schmidt, J. Sci. Instrum. , U5, 889, 1965. 15. R. S. Stites, W. E. Meyer and C. L. Buddecke, "Electro-Optic Projection Study", AD617087, Autonetics, Anaheim, California, 1965. Rome Air Develop- ment Center Technical Report No. RADC-TR-65-25. Also, W. E. Stoney, "Electro-Optic Projector Study", C6-1256/3 1 *, Autonetics, Anaheim, California, 1966. Final Report on Rome Air Development Center Contract No. AF30(602)-3720. 16. W. P. Mason, "Piezoelectric Crystals and Their Applications in Ultrasonics", Van Nostrand, New York, 1950. 116 17. D. R. Lamb, "Electrical Conduction Mechanisms in Thin Insulating Films", Methuen and Company, London, 1967- 18. M. O'Keeffe and C. Perrino, J. Phys. Chem. Solids, 28, 1086, 1967, 19. V. H. Schmidt and E. A. Uehling, Physical Review, 126 , i+UT , 1962. 20. W. R. Beam, "Electronics of Solids", McGraw-Hill, New York, 1965. 21. W. Kanzig, "Ferroelectrics and Antiferroelectrics" , in Solid State Physics, Volume k 9 ed. by F. Seitz and D. Turnbull, Academic Press, New York, 1967. 22. F. Jona and G. Shirane , "Ferroelectric Crystals", Pergamon Press, New York, 1962. 23. R. M. Hill and S. K. Ichiki, Physical Review, 130 , 150, 1963. 2k. I. P. Kaminow and G. 0. Harding, Physical Review, 129 , 1562, 1963. 25. G. Marie, Philips Technical Review, 30, 292, 1969. 26. I. P. Kaminow and E. H. Turner, Proceedings of the IEEE, 5k, 131 k, 1966. 27. D. S. Sand, "A Theoretical Analysis of the Modulation Characteristics of an Electro-Optic Light Valve", (M. S. Thesis), Report No. 303, Department of Computer Science, University of Illinois, Urbana, Illinois, January, 19 69. 28. Max Knoll, "Materials and Processes of Electron Devices", Springer-Verlag, Berlin, 1959- 29. F. W. Gutzweiler, Ed., "Silicon Controlled Rectifier Manual", 3rd Ed., General Electric Company, Auburn, New York, 196k. 30. Conversation with Leslie Vaughn, Storage Tube Division, Westinghouse Electric Corporation, Elmira, New York, July 21, 1972. 31. W. H. Kohl, "Handbook of Materials and Techniques for Vacuum Devices", Reinhold Publishing Corporation, New York, 1967. 32. E. L. O'Neill, "introduction to Statistical Optics", Addi son-Wesley, Reading, Massachusetts, 1963. 33. A. Papoulis , "Systems and Transforms with Applications in Optics", McGraw-Hill, New York, 19 68. 3U. R. K. Lomnes and J. C. W. Taylor, Rev. Sci. Instr., k2_, 766, 1971. 35. D. Casasent and D. Sand, Quarterly Technical Progress Report, Section 2.1, Department of Computer Science, University of Illinois, Urbana, Illinois, April, May, June, 1967. 117 36. 0. S. Heavens, "Optical Properties of Thin Solid Films", Dover Publications, New York, 1965. 37. D. Sand, Quarterly Technical Progress Report, Section 2.1, Department of Computer Science, University of Illinois, Urbana, Illinois, June, July, August, 1969. 38. D. Sand, Quarterly Technical Progress Report, Section 2.2, Department of Computer Science, University of Illinois, Urbana, Illinois, January, February, March, 1972. 39^ L. M. Biberman and S. Nudelman , Eds., "Photoelectronic Imaging Devices", Vol. 2, Plenum Press, New York, 1971. 1+0. B. R. Hunt, "Computational Considerations in Digital Image Enhancement", in "Proceedings, Two-Dimensional Digital Image Processing Conference", University of Missouri, Columbia, Missouri, October, 1971. kl, B. R. Hunt, Proceedings of the IEEE, 60_, 88U , 1972. 1+2. L. S. Watkins, Proceedings of the IEEE, 57., I63U , 1969. 1+3. H. Lipson and C. A. Taylor, "X-Ray Crystal-Structure Determination as a Branch of Physical Optics", in Progress in Optics, Vol. 5, ed. by E. Wolf, North-Holland Publishing Co., Amsterdam, 1966. 1+1+ . G. G. Goetz, "Sound Holograph Real-Time Display Tube", Report No. 1+601, Bendix Corporation, Research Laboratories, Southfield, Michigan, August, 1968 (First Interim Report, ONR Contract No. N00011+-68-C-0338) . Also, G. G. Goetz, Applied Physics Letters, 17, 63, 1970. 118 VITA Douglas Stuart Sand was born on July 7» 19^3, in Minneapolis, Minnesota. As an undergraduate, he attended Princeton University, was a University Scholar from 196l through 1963, and graduated with a B. S. E. in Electrical Engineering in June, 1965. During 1963 and 196U he was a summer intern at the Western Electric Engineering Research Center, Princeton, New Jersey, in the areas of computer hardware design and programming. From 196k through 1966 he was a research assistant in computer programming and time-series analysis for the Biology Department of Princeton University, with an NSF undergraduate grant during the summer of 1965 . In September of 19&5 ne "began graduate work at the University of Illinois, Urb ana-Champaign, and since that time he has been a graduate research assistant of the Circuit and Hardware Systems Research Group of the Department of Computer Science, under Professor W. J. Poppelbaum. He received the M. S. in Electrical Engineering in January, 1969, and has continued to work under Professor Poppelbaum toward a Ph.D. in Electrical Engineering, with minors in physics and mathematics. He is a member of the IEEE. Form AEC-427 U.S. ATOMIC ENERGY COMMISSION iSTSoi UNIVERSITY-TYPE CONTRACTOR'S RECOMMENDATION FOR A DISPOSITION OF SCIENTIF C AND TECHNICAL DOCUMENT f See Instructions on Reverse Side ) 1. AEC REPORT NO. C000-1U69-0237 2. TITLE COLFTAR: A REAL-TIME ELECTRO-OPTICAL SYSTEM FOR TWO-DIMENSIONAL FOURIER TRANSFORMS 3. TYPE OF DOCUMENT (Check one): ETI a. Scientific and technical report |~| b. Conference paper not to be published in a journal: Title of conference Date of conference Exact location of conference Sponsoring organization □ c. Other (Specify) 4. RECOMMENDED ANNOUNCEMENT AND DISTRIBUTION (Check one): CTI a. AEC's normal announcement and distribution procedures may be followed. ~2 b. Make available only within AEC and to AEC contractors and other U.S. Government agencies and their contractors. ~2 c. Make no announcement or distribution. 5. REASON FOR RECOMMENDED RESTRICTIONS: 6. SUBMITTED BY: NAME AND POSITION (Please print or type) W. J. Poppelbaum Professor and Principal Investigator Organization Department of Computer Science University of Illinois Urbana, Illinois 618OI Signature //. Z7. A-7-'- ;7 :,v. « Date December, 1973 FOR AEC USE ONLY 7. AEC CONTRACT ADMINISTRATOR'S COMMENTS, IF ANY. ON ABOVE ANNOUNCEMENT AND DISTRIBUTION RECOMMENDATION: 8. PATENT CLEARANCE: □ a. AEC patent clearance has been granted by responsible AEC patent group. LJ b. Report has been sent to responsible AEC patent group for clearance. LJ c. Patent clearance not required. ilBLIOGRAPHIC DATA iHEET 1. Report No. UIUCDCS-R-73-581+ 3. Recipient's Accession No. Title and Subtitle COLFTAR: A REAL-TIME ELECTRO-OPTICAL SYSTEM FOR TWO-DIMENSIONAL FOURIER TRANSFORMS 5. Report Date December, 1973 6. , Author(s) Douglas Stuart Sand 8- Performing Organization Rept. N °'UIUCDCS-R-73-581+ Performing Organization Name and Address Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 6l801 10. Project/Task/Work Unit No. 11. Contract /Grant No. US AEC AT (ll-l)ll+69 2. Sponsoring Organization Name and Address US AEC Chicago Operations Office 98OO South Cass Avenue Argonne, Illinois 60^39 13. Type of Report & Period Covered 14. 5. Supplementary Notes 6. Abstracts An electro-optical system is described which generates optical Fourier transforms of ;wo-dimensional video images, in real time, at standard video frame rates. This system Is designated COLFTAR, which denotes "Cooled On-Line Fourier Transform and Reconstruc- :ion." The theory, construction, and operation of the system and its principal compo- nents are described in detail, with special emphasis on the resolution and modulation :haracteristics of the cooled-crystal electro-optic light valve (or Ardenne tube) which Is the central component of the system. Several application examples are included, as rell as a summary of possible improvements. The system can produce Fourier transforms of arbitrary video frames with resolution )f 500 by 500 line-pairs. Further, the same system can generate inverse Fourier trans- forms, so that an image can be reconstructed after its Fourier transform has been alter- ed by an electronic "spatial filter." Also, Fraunhoffer holograms and synthetic (com- pter generated) Fourier transforms be reconstructed. In operation the system can serve is a stand-alone device, as a computer peripheral unit, or — using the advantage of real ■ imp njprat . inn-.f or i nteractiv e imago proooooing by Fourier transforms, /. Key words and Document Analysis. 17a. Descriptors 'ockels Cell -ight Valve f ideo Fourier Transform Electronic Spatial Filter Electro-Optical Processor 7b. Identifiers/Open-Ended Terms 7e. COSATI Field/Croup B. Availability Statement Unlimited distribution 3RM NTIS-38 (10-70) 19. Security Class (This Report) UNCLASSIFIED 20. Security Class (This Page UNCLASSIFIED 21. No. of Pages 128 22. Price USCOMM'OC 4032S-P7! *>. #* JUL Z 5 \tf 4