LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN cop. 2 The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN SEP 2 W; SEP 12 RECfO N 2 2 7 L161 — O-1096 Digitized by the Internet Archive in 2013 http://archive.org/details/onlineelectroopt331casa p/o-vr )w;.33/ REPORT NO. 331 ~)tl^lX^ coo-1^69-0120 ■S\ AN ON-LINE ELECTRO- OPTICAL VIDEO PROCESSING SYSTEM by David Paul Casasent JUN 1 6 1963 MAY, 1969 DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, ILLINOIS COO-ll+69-0120 DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF ILLINOIS URBANA, ILLINOIS 6l801 ERRATA to AN ON-LINE ELECTRO-OPTICAL VIDEO PROCESSING SYSTEM by David Paul Casasent Report No. 331 May, 1969 ERRATA FAGE 58 CORRECTED FIGURE Figure \h. Q) KEYSTONED PICTURE b) INITIAL RAMP c) LEFT SIDE CORRECTION e) FINAL PICTURE d)BIAS LEVEL MODULATED RAMP f) BIAS AND AMPLITUDE MODULATED RAMP Figure Ik. Keystone Waveforms Report No. 331 AN ON-LINE ELECTRO-OPTICAL VIDEO PROCESSING SYSTEM* David Paul Casasent May, 1969 Department of Computer Science University of Illinois Urbana, Illinois 61801 * Submitted in partial fulfillment for the Doctor of Philosophy Degree in Electrical Engineering, at the University of Illinois, May, 1969. AN ON-LINE ELECTRO-OPTICAL VIDEO PROCESSING SYSTEM David Paul Casasent, Ph.D. Department of Electrical Engineering University of Illinois, 19&9 An electro-optical system is described which is capable of staticizing a video image, reading it, processing it. and erasing it on-line. The image is formed as a charge pattern on an electro-optical crystal -which serves as the target for an off-axis electron gun. This charge distribution, by means of the linear- longitudinal electro-optical or Pockels effect, is used to modulate a laser beam. The laser beam is pulsed on and off by a separate electro-optical modulator with variable duty cycle and output light intensity and with an extinction ratio in excess of 300:1. Either the image or its Fourier Transform can be projected onto a pick-up tube via an optical system and dis- played on a monitor. The charge pattern can then be erased by a second off-axis electron gun using secondary emission. The time constants and secondary emission characteristics of the crystals are investigated. An extensive discussion of the methods employed to circumvent divergence, natural birefringence and thermal problems in electro-optic crystals is presented. The electron-optics capable of depositing 1 mil spots of charge at kilo volt potentials, with beam currents in excess of 10u.A, from an off-axis electron gun with keystone and dynamic focus correction are described. A method of obtaining comparable crystal resolution is suggested. A system as described above has the potential capability of processing over one million bits of information in parallel. Appli- cations in the field of spatial filtering and television projection are experimentally verified and a possible adaptive spatial filtering system for use in deep space exploration is presented. Ill ACKNOWLEDGMENT The author is deeply indebted to Professor W. J. Poppelbaum for suggesting the project and for his constant support and counsel. He would also like to thank Professor Michael Faiman, Doug Sand and Al Irwin for their advice and assistance. The author would also like to thank Miss Carla Donaldson and Mrs. Elinor Peterson for typing the manuscript. IV TABLE OF CONTENTS ACKNOWLEDGMENT . . . iii LIST OF FIGURES v LIST OF TABLES vi 1. INTRODUCTION 1 2. LIGHT SOURCE „ 3 2.1 The Optical Fourier Transform 3 2.2 The Light Source 5 3. ELECTRO-OPTICS 10 3.1 The Electro-Optic Effect 10 3.2 The Beam Shutter . . Ik 3.3 The Target Crystal . <> 35 3.^ Crystal Assembly k6 k. ELECTRON- OPTICS . 50 4.1 Write Gun . 50 k.2 Deflection 52 km 3 Focusing o.. 56 h.k Coupling Amplifier „ 60 h. 5 Vacuum System „ . . . 6l k.6 Erase Gun 62 5. APPLICATIONS o . . . . 7^4 5-1 Spatial Filtering ...... „ „..■>.. jh 5*2 Reconstruction <> 77 5.3 Television .... c .... 79 5.4 Adaptive Spatial Filtering 79 5.5 Resolution „ . . . 82 6. CONCLUSIONS . . Qh REFERENCES „ 86 VITA 88 V LIST OF FIGURES Figure Page 1. System Diagram 3 2. One Dimensional Fourier Transform 3 3« Illumination from a Non- Coherent Source .000.... 6 h. The Intersection of the Normal Surfaces with the Sz Plane 13 5. Calculation of "Walk Off" 2k 6. Beam Shutter Driver and Erase Gun Trigger 33 7. Configuration for Potential Distribution Analysis ... k2 8. Relative Charge Leakage Through the Crystal k-5 9. Relative Transmission Due to Charge Spreading Across the Crystal h^ 10. Electronics 51 11. Electrostatic Deflection 53 12. Magnetic Deflection 53 13. Keystone Correction ..... 57 1^. Keystone Waveforms . o .......... 58 15- Erase Gun Drive Circuitry ..... 66 16. Secondary Emission Curve 68 17. The Chamber 73 18. Spatial Filtering 75 19* Reconstructed Image 75 20. Spatially Filtered Image 76 21. Experimental Apparatus ..... 78 22. Timing Diagram 8l VI LIST OF TABLES Table Page 1. The Electro-Optic Tensor r. 18 2. Thermal Properties of Crystal Assemblies 48 3. Measurement of RC Time Constants ..... o ... . 65 1. INTRODUCTION The Circuit Research Group, under Professor W. J. Poppelbaura, at the University of Illinois , Department of Computer Science is currently investigating various methods of bandwidth reduction, digital filtering and three dimensional displays. This system is a novel approach to these and other problems. Such applications are discussed further in Chapter 5- The purpose of this system is the generation and processing of video pictures on-line. The pictures are staticized electro-optically. The processing involves either projection, Fourier Transforming, or eventually adaptive spatial filtering of the picture . The heart of the system, shown in Figure 1, is a chamber housing two off-axis electron guns. The write gun transforms the in- coming video signal into a charge pattern on a transparent electro-optic crystal. A collimated laser beam is then flashed through the chamber and by means of the linear-longitudinal electro-optic effect the beam becomes modulated point by point. A lens system can then project this charge pattern as a picture or form the optical Fourier Transform of it. The charge pattern is then erased from the target crystal by the second electron gun using secondary emission. This write, read, erase sequence is achieved in one television frame. Creating a high resolution transparency on-line and thus modulating a collimated laser beam with over 100,000 points of infor- mation which can be processed in parallel at the speed of light is useful in investigating other uncommon forms of information processing. w co w o. CO o H o C3 \ O E-i O o g -p CO H CO I o CO 2. LIGHT SOURCE 2.1 The Optical Fourier Transform The choice of light source as well as the fabrication and selection of many other components was determined by the fact that the system must be capable of generating the Fourier Transform of a picture This enables optical data processing and spatial filtering to be done. Figure 2. One Dimensional Fourier Transform The Fourier Transform property of a lens can be shown for the simple one dimensional case using Figure 2. The planes or rather lines of interest are the left and right focal planes. The left one contains the object and the right one the image. Let P be a point in the image plane a distance w below the optical axis. Its illumination or amplitude is determined by the brightness and phase of all beams coming from the object. Since P is in a focal plane, all beams are parallel on the left side of the lens and form an angle 9 with the optic axis, tan = w/f. The beam from the section between x and x + dx con- tributes an amplitude a(x)dx cos%£ X where a(x) is the modulating function or transmissivity in x and the path delay with respect to some reference point. The crux of the analysis is that tan = s/x or s is a linear function of x. w s = ft By setting the cos term in equation 2 equal to the real part of the exponential, and then assuming an image of infinite extent, the total illumination in P is p oo ,.00 2rrw x / a(x)dx cos - — = / a(x) cos ^ X = ./ A- n ./ f\ n -oo -00 p 00 p 00 / a(x) cos w xdx = Re / a(x) exp(jw x)dx = — oo —oo RE (F[a(x)]] (3) Or, the image in the back focal plane of a lens is the real part of the Fourier Transform of a transparency placed in front of the lens . Even from this simple construction, many points can be seen. Equation 1 is not general unless the incident light is monochromatic. Equation 2 also is general only if the light is spatially coherent. In order for the time dependence in equation 3 to cancel, a temporally coherent source is required. Finally, the intensity of the illuminating light for a given position x multiplies the transmissivity a(x) for that point, hence a uniform amplitude incident plane wave is also needed. It was found from tests performed with a high resolution 35mm slide that this requirement could be relaxed. A truncated collimated Gaussian distribution proved to be an adequate approximation to a plane wave. (2) A two dimensional analysis yields the result f(x',y' , l = J f(x,y)exp j [wx + w y]dxdy (k) 2.2 The Light Source o A continuous wave He-Ne gas laser with a 70mw line at 6328A is used as the light source. The previous section discussed the need for a coherent source. Coherent light suitable for optical data processing can be produced from an incoherent source. The two methods (3) are compared below. A laser beam has a Gaussian intensity distribution across its aperture given by I(p) = -^ e^/^ 2 (5) 2*0! A uniform intensity across a circle of radius p = p is obtained by passing the above radiation through a filter of transmission ( P 2 - p 2 )/2a 2 T = e U p < p Q T = p > p (6) 2 By differentiating with respect to a and maximizing I laser " ^ ' ' An incoherent source of diameter 8 spaced a distance g from a lens will be assumed to have sufficient spatial coherence if the difference in path length to the edge of the lens is no greater than X/2 for the nearest and farthest points of the source. Thin -S shown in Figure 3. The aperture of the lens and the distance fr r source are assumed to be much larger than the source diameter, a >^ g » 6, d = \/2. The diameter of the source can thus be appr .ed from tan 9 X]2 B giving for the source diamter 5 = g\/2a SOURCE LENS Figure 3. Illumination from a Non-Coherent Source An incoherent source of area da and total power b placed at the source point of Figure 3 will transfer an amount of power through the lens given by Lambert ■ s Law . . / cos e dfi P. = bd (10) mc cos 6 dfi where surface r, is a small solid angle and r is a half sphere. Cos in r, can be approximated as 1 and the half sphere integral evaluated as below / dfi 2 ■'r x P. mc - bd a \\r\ ,-r ? prt/2 p 2n — ua.0 Jt / / cos 6 sin 9 d6 d$ ■'o '0 (11) Substituting for da the coherence value from equation 9 P. = ^- (12) mc 16 Comparing equation 12 and 7 gives laser 1, P 2 inc b\ (13) o Using a 70mw laser at 6328A compared to a PEK 500 Mercury Arc lamp with a brightness b = 17 watts/cm equation 13 becomes p laser « 10 6 (11+) inc Thus a 70mw laser furnishes one million times the two dimensional coherent power of a 500 watt incoherent source. A continuous wave laser is used due to the duty cycle < system. At the outset of the project pulsed lasers could provide neither the pulse duration nor the repetition rates necessary at adequate power levels . The necessary power level was determined by approximating the expected power losses in each element of the system. Element Transmission Beam Shutter .80 Lens .95 Analyzer . 90 2 Mirrors .90 Collimator .70 Chamber .50 Analyzers . 16 Optics .80 D.C. Spot .20 This gives an overall transmission efficiency T = 0.005- A vidicon -h 2 camera with a photosurface area A=k x 10 m is used as the pick up device. With a duty cycle f = 0.03 and a 50mw light source, the intensity incident on the vidicon would be I = 50 T f/A = O.I875 mw/m (15) This is at the low end of the acceptance level for the camera. Higher powered lasers with lines closer to the visible peak of the spectrum and closer to the maximum vidicon sensitivity would improve this efficiency. Longer read times obviously improve the incident light level enormously. The continuous wave He-Ne gas laser has proved useful and most versatile in this present system. 3. elect; - ics 3.1 The Electro-Optic Effect Both the pulsing and point by point modulation of the lac beam are done electro-optically. The limitations of the system are due to the electro-optic crystals used. The electro-optic effects ha. been presented and derived many times in the literature. /, '^- ? '' The discussion below is presented to unify those aspects of the theory pertinent to this and similar applications. The selection of crystals was based on present crystal technology capabilities. Those areas in which future crystal technology hopefully can provide new avenues of research will become apparent. The electro-optic effects are non-linear phenomena present in materials in which an electric field and the polarization caused by it are not parallel. All crystals exhibit this but to varying degrees. Thus in many cases the linear approximation D = eE is valid within one percent or less and can be used. In anisotropic crystals £ is a dielectric tensor defined by D, = e ,E». This assumption that instantaneous values of D and E are related by a single constant is valid only when the medium is optically lossless. The symmetry of e „ can be shown from a power analysis using the Poynting vector, only with the doubtful assumption that the Poyntin^ vector in anisotropic crystals corresponds to the flux of the energy as it does in isotropic crystals. This reduces the number of independent elements of e . from nine to six. After a transformation to a new coordinate system in which the tensor is diagonal, the number of n independent elements becomes three e .(k = i = x,y,z). The surfaces of constant energy, w , in D space then become ellipsoids . 2 2 2 D D D 2(jJ = _2L_ + _X_ + _L_ (!6) e e e € xx yy zz Maxwell's equations are solved for E for the case of a mono- chromatic plane wave of frequency w propagating in the above crystal with a phase factor exp{iw[— (r • S) - t]} where S is a unit vector normal to the wavefront and n is the index of refraction of the crystal. The solution for K has the form k n S (S • E) \=— k = x,y,z (17) n " ^ e kk — * — > Forming S • E = yields Fresnel's equation 2 2 2 s s s n - ^e n - ue n - \ie n xx yy zz There are two solutions for this equation. We shall call them — * +n and +n . Thus, for a given direction of propagation S, there are two independent linearly polarized plane wave propagations allowed with phase velocities +(c/n, ) and +( c /n p ). This effect is known as the birefringence of anisotropic crystals. The equation for the constant energy density surfaces is normally written as 2 2 2 n n n x y z 2 where n , n , and n are the principal indices of refract: = x' y' z Gj, (k- = x,y,z). This equation is that of a general ellipsoid with major axes parallel to the xyz directions with lengths 2n , 2n . 2n . x y z Equation 1'j is called the index ellipsoid and is useful in finding the — * two allowed directions of D corresponding to the two indices of re- fraction n, and n . From n and n the two independent plane waves which can propagate along an arbitrary direction S in a crystal can be found. The geometric construction is simple: pass a plane through the origin of the ellipsoid perpendicular to the direction of propagation S, this intersects the ellipsoid in an ellipse. The two axes of this ellipse are equal to 2n, and 2n and the direction of these two axes are the allowed directions of D. In uniaxial crystals two of the indices of refraction are equal. With the z axis as the axis of symmetry or the optic axis, equation 19 becomes 2 2 2 H + -h + —2 - 1 < 20 * n n "e where n is the ordinary index of refraction and n the extraordinary index of refraction. This is the equation for an ellipsoid. The inter- section of this ellipsoid with a plane through the origin normal to the direction of propagation is an ellipse. The length of the major axis of this ellipse is n (0) and the extraordinary ray is polarized along it. The ordinary ray is polarized along the minor axis of length n (0 ) where 13 is the angle between the optic axis and the direction of propagation (7) n (0) is plotted in Figure k. As changes, the direction of polarization of the ordinary ray remains fixed while the direction of polarization of the extraordinary ray changes, n also changes with 0, n (0 ) = n while n (90 ) = n since e e 1 2„ • 2„ cos sin 2 ^n 2 n (0 ) n_ n e e (2i; Figure h shows the curves formed by the intersection of the Sz plane with the normal surfaces; the values of n and n can be read directly. — > — * Note D is perpendicular to D . n o (0) Figure h. The Intersection of the Normal Surfaces wi-Hn t.hp R7 Plnnp ^) In considering the many different classes of crystals it is more useful to write the index ellipsoid in general x,y,z coordinates (%i x2 + (-^) 2 y 2 + (-W 2 + 2 ^V Z + 2 ^ } 5 xz + 2 ^6 xy = x (22) n n n°n n^n where in the contracted Voigt subscript notation xx - 1, yy - 2, zz = yz = zy = h, zx = xz = 5, xy = yx = 6. In thii the eJ applied electric field on the propagation characteristics can be se These effects are the linear and quadratic electro-optic effects. The linear electro-optic effect, also called the Pockels effect, is described by the electro-optic tensor r. . as a change in the index of refraction which is proportional to the first power of the electric field A(40. = r. .E. (23) n 2 i ij J In the case of a crystal exhibiting the quadratic electro-optic effect, often called the Kerr effect, the index ellipsoid constants are proportional to the square of the electric field It is more useful to express this change with the tensor g. ., „ in terms of the polarization components 3.2 The Beam Shutter Since the charge pattern on the target crystal is a coordinate representation while the optical Fourier Transform is a frequency representation, the entire charge pattern must be written before the read cycle can start. For interference experiments, this information must thus be processed in parallel. This necessitates a beam shutter for pulsing the laser on and off. Similarly, the erase cycle must not 15 start until the information on the crystal has been processed and the laser is off. The write cycle is 31- 3msec long, the read cycle 1msec and the erase cycle 1msec. The three thus total 1/30 sec or standard video frame rate. The read and erase cycle occur during vertical blanking time which is normally 900(j.sec. This is increased to 2msec to allow safer operation. The amount of charge on the target crystal determines the relative light intensity out. Thermal considerations (sections 3*3 and h.6) make it advisable to increase the erase time and reduce the charge on the crystal thus increasing the read time. This increased vertical blanking results in a loss of about 16 lines from one field. As section 3^3 demonstrates, this is beyond present resolution limits and hence presents no problems. When crystals capable of higher resolution become available, suitable protective coatings can be applied to permit faster erase, higher charges and lower read time, then standard blanking signals can be used. The requirements for the beam shutter seem simple but a survey of commercially available ones proved none to be applicable without modifications. The beam shutter must allow either 0% or 100^ of the incident light through. The extinction ratio (maximum light transmitted divided by minimum light transmitted) must be greater than 300:1 if a contrast ratio of 10:1 on the vidicon is to be obtained. The minimum light level is incident on the vidicon for 31ms during which time the vidicon integrates it, the maximum light level is only incident on the vidicon for 1ms, thus the effective contrast ratio becomes [300/(31-1) ] :1. Warm-up time and the DC and RF systems involved \ "ed turning the laser on and off directly as a means of modulation. At tl outset of the project neither the erase time nor the laser power neec during the read time were known. No pulsed laser seemed to have a sufficiently variable pulse width and duty cycle to be useful in the prototype system. Theoretically an image orthicon pick-up tube could be employed and its target, accelerating grid, or second emission grid potential pulsed to prevent photocathode electrons from reaching the target thus modulating the light. However, recovery time for focus and deflection as well as the possibility of damaging the target seemed to prevent such modifications. Thus an outer cavity electro-optic light modulator with two stable output light levels, a low driving potential, an aperture adequate to contain the laser beam, and an extinction ratio of 300:1 was sought. The beam shutter chosen was the TFM502 produced by Isomet. Its aperture was 5^m and a driving voltage of only 300V was needed to switch from to 100% modulation. As extinction ratio of over 300:1 was achieved. This could only be done by external modifications. The techniques involved in achieving such performance characteristics involve a detailed analysis of both lasers and electro-optic materials. These principles are outlined below. The modulator uses a transverse electro-optic effect where the directions of the incident light and applied voltages are perpendicular. The crystals used are a proprietary compound, which for the sake of the discussion below, can be assumed to be of ^2m point group symmetry. 17 All crystals fall into one of the 32 possible point groups, each characterized by different symmetry operations which reduce the number of independent elements of r. .. The results of these symmetry operations on r. . are summarized in Table 1 for the 32 possible point groups . For a crystal with ^+2m point group symmetry equation 22 becomes 2 2 2 - + -^-o + "^-o + 2r )n E yz + 2r,,Exz + 2r._E^xy = 1 (26) 2 T 2 T 2 T "laY* ^ly T "63 z n o n o n o where z is the optic axis and x and y are the other two crystals axes in the basal plane. If the electric field is applied along z, equation 26 becomes 2 2 2 ^2~ + —2 + 2r 63 E z Xy = n o 1 „ * .2 , 1 „ v„ .2 z 2 (— + r 6 3 V x ' + ( — " r 63 E z } V + — = 1 (27) n n where the new principal dielectric axes are obtained as before by 1., 2 diagonalizing the 3x3 matrix for (—5). In this case x' and y' are n rotated U5 from x and y about z. In this diagonalized form the change in the index of refraction is readily seen to be 1 3 x 2 63 z n ' = n + iiA.-E (28) y 2 63 z v n = n z e n 1 1 where it has been assumed that An = - -^- A{— ~) and r^-.E « — =. 2 2 63 Z 2 n o CENTROSYMMETRlCAL CLASSES (ALL MODULI VANISH) RICLINIC CLASS 1 • NONCENTROSYMMETRICAL CLASSES ORTHORHOMBIC CUBIC CLASS 222 CLASS mm 2 CLASS 432 CLASS 43m ft 23 • • • :: CLASS 2//X? CLASS 4 x: MONOCLINIC CLASS 2//X3 CLAS S mlX2 CLASS mlX3 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • TETRAGONAL CLASS 4 CLASS 422 CLASS 4mm • • • • • o X • • • y.\ CLASS 3 TRIGONAL CLASS 32 CLASS JmlmlXj) CLASS 3m(mlX 2 ) :n i:i CLASS 6 HEXAGONAL CLASS 6mm CLASS 622 CLASS 6 CLASS 6m2(mlX 1 ) CLASS 6m2(m±X 2 ) : : I : : I • • • • • • • • • D • ZERO MODULUS • NONZERO MODULUS EQUAL MODULI MODULI NUMERICALLY EQUAL BUT OPPOSITE IN SIGN. • A MODULUS EQUAL TO MINUS 2 TIMES THE HEAVY DOT MODULUS TO WHICH IT IS JOINED. Table 1. The Electro-Optic Tensor r (h) ij 19 With a field in the z direction and light propagation in the z direction polarized in the x'y' plane at 4 5 to the axes, the retardation between components along x' and y' is from equation 28 3 r = * S 6 | z z (29) However if the light is propagating in the y' direction, polarized in the x'z plane at 4 5 to z, the retardation between components along x' and z becomes from equation 28 n n 3 r._E r = c (n " n e 2 )L y (3 °' where L. is the length of the crystal in the i direction. At sufficiently high fields this retardation equals rt, interference occurs, and the relative light transmitted through a crossed analyzer can be controlled from to 100% by the applied field. A comparison of equations 29 and 30 explains why most commercial modulators use the transverse effect. In the longitudinal case, r « E L or V and is independent of the crystal length, while in the transverse case r « E L ' and much lower applied voltages are z y required as the length of the sample is increased. The modulator uses a type of 4 5 y cut crystal. The input o laser light is at 6328A. The modulator has four crystals each of length L = 50mm and square cross section b = ^mm. With -E applied, equation 26 becomes ^T~ + 4 - 2r kiY z ' x (31) n n J e 30 Diagonalization of the (—5) matrix shows that the new x ' and z ' -ire n ' rotated by an angle a about y where a is given by 2 2 2r,.E n n Tan 2a m ^lyO « (32 n " n e Note that here the rotation is dependent on the applied field and is very small. The new indices for x and z become n -n = ^—7 + ^S (33) x z 1 3 2 2 (— + — g) (— + —5) n n e n n e The phase retardation between light in the y and x - z = directions for a length of crystal L becomes 3 1 l 2 T = 2tnT2 r 4l E L/\(-^ + — -) (34 n n e In such transverse modulators, numerous problems must be considered. First, in i+2m materials, the change in index of refraction due to natural birefringence depends on the direction of beam propagation as in Figure k. For an input light beam with a divergence of 0.7 milliradians , the change in n due to the natural birefringence is o c 2 x 10 while the electrically induced change is only 10 (50 times the previous valued. This is due to the fact that since propagation is at 45 to the optic axis , the change in birefringence for small variations in this angle is a maximum. 21 Second, such transverse modulators have the required half -wave voltages reduced by the factor L/b where L is the crystal length in the direction of light propagation and b is the crystal width across which the voltage is applied. However, the power loss in the long conductors and in the electro-optic material can produce minute temperature gradients which can produce strains in the crystal altering the phase relationships and deflecting the beam. Born and Wolf have shown that a gradient in the index of refraction in the direction perpendicular to the beam path, ^si, where n is the index of refraction, cause a deflection of the beam with a radius of curvature given by R = -n/yn. In terms of a deflection angle a, a - — \7n.. For small temperature variations n = n + W where n^ is the n quiescent value, N a constant and the temperature referred to the quiescent value. Then a = -(— )N(— ) which shows that a linear tempera- ture variation deflects the beam uniformly with no change in its collimation properties. If the only heat is the loss in the conductors dfl to which the voltage is applied, then — = P /a A where P is the power flowing through the crystal, a is the thermal conductivity and A is the cross section area of heat flow. This gives LNP Heat generated within the electro-optic material produces a worse effect. Assuming both conductors at y = +b/2 and y = -b/2 to be at temperature 0=0 and a uniform heat generation P then P 2 n D f b 2 ^ and <* - TT (36) Thus the deflection suffered by any ray in the beam depends on its distance from the center of the beam shutter. This produces both a deflection and a decollimation of the beam. A temperature variation from one end of the beam shutter to the other produces a change in the retardation given in radians by £T = f 1 Lke (37) where k is the thermal retardation coefficient in radians per C. Peters has obtained a value of N = -1.5 x 10 / C and k = 1.1 x 10~ 5 /°C for KDP and k = 4.7 x 10 _5 /°C for ADP. Equation 37 shows that a temperature difference of only 0.01 C between the ends of the modulators could produce a retardation of over 30 . Using equation 35, the effect of heat dissipated in the conductors P produces an a = 2P while the effect of the total heat generated in the crystal P from equation 36 gives a = -^P y where y is the distance from the center of the crystal. These thermal effects are minimized by the selection of a 45 y cut crystal using r, modulation. For this case the required half- wave voltage and power are minimized. The temperature differences between parts of the mdoulator are cancelled by matching the temperature coefficients of the various crystal sections and rotating the axis of the second pair of crystals 180 with respect to the first. Further 23 improvement is obtained by reducing the beam size in which case y in equation 36 becomes very small and the beam, even with a deflection angle, can more easily be contained in the transverse b dimension of the shutter . A third problem in transverse modulators using r, is that of "walk off". In anisotropic materials in general, the direction of propagation of the wave normals is different from the direction of — » — * propagation of the rays. This is a consequence of the fact that D and E are not in the same direction. Only when the input light is parallel to or normal to the optic axis do the directions of propagation coincide. The situation for a k-5 y cut crystal is shown in Figure 5. The input light travels in the x - z = direction, with polarization at 45 to the xz plane when amplitude modulation is desired and in the xz plane or normal to it for phase modulation. The ordinary ray continues in the x - z = direction polarized normal to the xz plane. The extra- ordinary ray travels at an angle 3 in the xz plane with its polarization in the xz plane. The wave normals for both rays still travel in the x - z = direction. p is given by p = tan [( — ) cot a] + a - — e where a is the angle between the light direction and the optic axis. For a 45 cut crystal and normal incident 1 P - cos~ 1 [(n 2 + n e 2 )/(2n 4 + Si^) ] (38) The direction p is the tangent to equation 21 at the point of inter- section of the crystal surface as in the figure. The extinction ratio of such a device is determined by the amount by -which the ordinary and extraordinary rays overlap. To improve J OPTIC AXIS je RAY f DIRECTION j WAVE NORMAL DIRECTION *- // * // */ X, o/>^ 8 X 2 £ z - ♦ - ' 1 i^/ o e Lie > X ' \ . n INPUT LIGHT ■°^ *fc %> Figure 5. Calculation of "Walk Off" the extinction ratio two such identical cyrstals are oriented so that the ordinary ray in the first crystal travels as an extraordinary ray in the second crystal, while the extraordinary ray in the first crystal propagates as an ordinary ray in the second crystal. Besides cancelling "walk off", thermal effects are also reduced. Such an arrangement requires extremely precise matching of crystal lengths and orientations. The tolerances and performance can be greatly improved by narrower beams since beam paths need be matched only over small cross sections. 25 The existence of a large natural birefringence was experimentally verified. A laser beam was passed through the shutter and appeared as a single bright spot on a target. As voltage was applied to the shutter, a black line appeared in the bright spot and moved as the voltage was varied. This verified the fact that even with a laser beam there are amny different rays traveling though the shutter at many different angles . Each beam has its own transfer characteristic depending on its angle. As a particular voltage is applied the natural retardation for one particular angle or path is compensated but not for the others . The black line sweeping the laser spot is a plot of the polar retardation as a function of the path through the crystal. If all light traveled at one angle and the crystal were uniform, the black spot would grow not move. A pin hole inserted at the output or input enhanced the performance since as the voltage increased the black spot swept across the pinhole and all light was modulated. The extinction ratio was measured for two laser beams one with one -half the diameter and twice the divergence angle of the other. Much larger ratios were obtained with the smaller laser beam, implying that the divergence angle is not the important parameter and thus that the two crystal compensation effectively removes this problem. Operation with a collimated laser beam with a beam divergence 1/50 of its previous value also failed to improve the performance. Much higher extinction ratios than either diameter laser beam could provide were needed. Also a high power beam was needed, thus the larger diameter one. Further tests were thus performed to determine techniques for improving the ratio. The difference in beam paths was first proven to be mainly due to crystal non- uniformity and alignment. Using a small laser beam the bias voltage necessary to obtain a minimum was recorded for various positions of the entrance beam. The voltage varied from 20 to 150 volts. Thus worse extinction ratios should be expected with a larger laser b f , Part of the DC retardation was due to the laser, however. Using a photometric microscope and x-y recorder, the intensity pattern 7" from the output window of the laser was plotted. It showed inter- ference and diffraction, its non-Gaussian nature was due to diffraction from the finite aperture of the plasma tube as well as dirt, dust, and plasma noise but not from higher order mode competition. 58" from the laser the plot was highly Gaussian as expected since the only beam that will propagate unaltered is a Gaussian beam; it is the principal solution to Maxwell's equations in a laser cavity. Physical reasons prevented placing the beam shutter this far from the laser. At this point several beam parameters are worth recalling. One solution to the scalar wave equation is the Gaussian distribution i|/- = exp(-2r 2 /a 2 ^ (39' 2 2 2 where r = x + y and the beam travels in the z direction, a is the distance at which the amplitude is l/e its value on the axis, and 2a is called the diameter. One final parameter d is defined by i = -2j\/na 2 ( h0) Substitution shows that d' = 0, hence d = d + z relates d in an out- 27 put plane to d, in an input plane a distance z away. A Gaussian beam contracts to a minimum diameter 2a at a point called the beam waist where the phase front is plane, z is measured from this waist where 2 d = jjta /2X and d = d + z. Then a can be written as a 2 (z) = a Q 2 [l + (2Xz/«a 2 )] (kl) The beam contour a(z) is a hyperbola with asymptotes inclined to the axis at an angle G = 2\/jta , this angle is called the beam divergence. This Gaussian profile is not the only solution but it is the most important and called the fundamental mode as compared to higher order modes. A proper understanding of these parameters and their manipulation is imperative in the optical steering of Gaussian beams. A plane parallel beam incident on a lens is focused to a waist one focal length away. However, this is not true for a Gaussian beam. To match the modes of one structure onto another involves transforming a given Gaussian beam into another beam of prescribed properties. Consider two beam waists a and a located distances z and z from a lens. The required parameters to achieve such a transformation are derived below. 2 The complex beam parameters at the waist are d = jira /2X 2 and d = jna J2X. For a lens of focal length f one knows that l/d = 1/cL - l/f where d is measured at the lens. For d measured distances Z-. and z from the lens d becomes d - z and d, becomes d + z . In terms of a characteristic focal length of the system f = ita a /2A., the distances z and z become a 2 r^ 2^ z, = f + — / f - f * 2 - a V Thus it is noted that f must be larger than f . For a laser with a long radius resonator L = l80cm characterized by an output beam diameter of 2mm at the 1/e points, equation kl gives a = .88mm at l/e points, this beam waist occurring at the center of the resonator. An obvious consequence of these equations is the fact that for a Gaussian beam passing through a cylinder of length L and cross section b, b will be minimized when the length L is equal to the con- focal parameter of the beam which is defined in terms of the beam waist 2 as nna /\. In this case the waist occurs in the center of the cylinder and the diameter of the beam at each end face is equal. If the waist diameter is 2a , the entrance and exit diameters become 2j2a. . The importance of these previous calculations can now be seen. Consider the He-Ne laser used with a 2mm diameter beam and a divergence of 0.7mrad incident on four 5 mm x 5mm x 50mm 4 5 y cut crystals. The values of the beam diameter D, divergence 5, and crystal width b determine the maximum length of each crystal l - ^e m max S Initial calculations yield a value for D of h. 965mm apparently well above the value for the laser used. However, if one considers "walk off" with p = 1° 10' for KDP and p = 1° J47 ' for ADP,. the displacement of the 29 extraordinary ray for a 50mm long crystal is 0.85mm for KDP and 1.55mm for ADP. This reduces the useable aperture to about 4mm. When high extinction ratios are desired, and for ease of alignment since the entire shutter is 250mm long, the aperture is divided by a safety factor of from 3 to 8. Using 5, the effective aperture becomes 0.8mm. The beam must thus be contained in this diameter and any rays outside this area will be assumed to strike the walls and appear as an unmodulated DC background level limiting the obtainable extinction ratio drastically. The 2mm beam diameter used in equation 43 is defined at the l/e points and from equation 24 only 86$> of the power is contained in this diameter. Since extinction ratios of 300:1 are desired, less than 1/300 of the beam power must be outside the 1mm area. This means that the 4.0mm diameter must be reduced to at least 0.8mm. Thus the beam size must be reduced by a factor x > 5- The effect of x on equation 43 is L = (b - D/x)/ox. Using L = 50, b = 0.8, D = 4.0, the acceptable values for x are about 10 > x > 75 b which checks with the above calculation. The allowable input beam diameter to the l/e points is thus 0.24 < D < 0.48. With D less than the upper limit the power is contained in an adequate area and with D greater than the lower limit the beam is prevented from striking the sides of the crystal. Thus it becomes necessary to reduce the beam size. As noted this is best done by a single lens which images the waist of the laser to the center of the beam shutter, a is 0.88mm for the laser, the confocal beam parameter for the shutter is 200mm since there are four crystals. Thus a^ = .l6mm assuming an index of 1.5 for the shutter. 2 The entrance beam diameter to the l/e points is thus 0.450mm which is within the acceptable limits of D calculated above. Equation 42 t- becomes ; ! = f 1 5-5 -Jf 2 - 350 2 z 2 = f + .182 ^T - 350 2 w Solving these equations for z , z and f with the conditions z > 900nm, z_ > 100mm, f > 350rnm, one solution is f = 375mm, d = 1090mm, d 2 = 433mm. Besides reducing the beam diameter, the single lens brings the far field (Gaussian distribution) closer while removing much of the noise present on the beam. The extinction ratio is further enhanced by spatial filtering during collimation. The aperture stop passes only the fundamental laser mode should others be present and the resultant energy distribution is a smooth Gaussian when a pinhole nearly equal to the diffraction limited spot size is used. The first collimator lens of focal length f, focuses the laser beam of radius a and wavelength X to a spot of radius a„ = 1 \f../jra. An aperture equal to twice the focused spot size provides an excellent degree of filtering with less than 0.1$ power loss in the fundamental Gaussian beam. The pinhole diameter is microns is thus given by A = 1.6f-,/2a where both a and f, are measured in mm. The second collimator expanding lens of focal length f gives a parallel Gaussian output beam of diameter 2f a/f . The 2mm diameter laser beam could be collimated to 0.48mm or less before entering the shutter and then recollimated to 50mm after passing through the shutter with spatial filtering done during both 31 collimations. With no spatial filtering whatsoever an extinction ratio of 100:1 can be achieved. The second collimation which must always be done increases the extinction ratio to 300:1. The first collimation only slightly increases this ratio. The associated loss in power introduced by the extra collimation does not warrant the slightly increased extinction ratio. Should crystals of the cubic class of sufficient size and homogenity for use in modulators become available, many natural bire- fringence problems would be overcome since from Table 1 n = n for crystals of class ^3m« Single crystal modulators coupled with a collimating condensor with a spatial filtering pinhole might also become available if crystals with electro-optic coefficients of sufficient magnitude in directions where "walk off" does not occur can be found. A third future possibility would be a design where crystal orientation and alignment are not as critical and where accurate equal compensating crystal lengths can be obtained. One particular cubic class crystal CuCl appears very suitable. It has an electronic polarization, not ionic as KDP, thus it is useful at higher frequencies. KDP since it has an optic axis requires input light to be collimated within three minutes or less. CuCl is isotopic and can contain divergences of 30 . KDP is fragile and shatters easily with handling or a temperature change; CuCl can be handled roughly, is unaffected by temperature, and can be more easily polished. Also the Q of CuCl can be controlled since its resistivity is sensitive to doping. KDP is an insulator; doping was found to affect its color but as yet not its electrical properties. An in depth analysis of present beam shutter Is presented in reference 10. Special modulators using optically active crystals i dual transverse Pockels effect have been investigated. But these, t have alignment and extinction problems . The beam shutter drive circuit must be capable of driving 10 feet of ^lfi coax into a capacitive load (95pf, > 10 U) . The be shutter drive circuit is shown in Figure 6. A negative vertical sync pulse is the trigger. The output is a 300 volt pulse whose amplitude and width can be varied. The second output pulse occurs after the beam shutter pulse and controls the erase gun. There are two BNC connectors on the beam shutter. The output of the drive circuit of Figure 6 is applied to one and a bias level from a 50V supply to the other. The bias voltage removes most of the natural birefringence not cancelled by the crystal geometry. Neither supply voltage need be well regulated. The light transmitted, T, is related to the applied voltage by p T = sin x (45) where x oc v. Taking a small increment, e, about V 2 T . sin 2 (| + 6 ) = 1 - € 2 = 1 - ^- 8 2 (h6) where p + e=-r(l + o) and 6 « v. Since T = 1 at - = x 33 Figure 6. Beam Shutter Driver and Erase Gun Trigger 2 dT = 1 - (1 - \ o 2 ) = fiV/k = 2.5 Thus if v is regulated to 1%, T will be regulated to 0.02; . The rise and fall times of the output pulse need not be extremely fast. The only thing that is important is that the power contained in each pulse of light and the repetition rate be nearly constant. For a 1ms light pulse, the power lost due to an 0.5^sec rise time is 0.05%. If this were improved by a factor of 5 the resultant power gained, 0.0U%, is negligible. With longer read times the per- centage drops very rapidly. A constant repetition rate is insured by synchronizing the shutter to the video by the vertical sync pulse trigger. The beam shutter drive circuit consists of a monostable multi- vibrator which drives a fast high power switching transistor. The trigger pulse is formed from the vertical sync pulse. The pulse width is variable from 0.5 to 6 msec, independent of the input trigger width, by means of the potentiometer in the current sink. This flexibility is pulse width is useful for test purposes. The current sink transistor isolates the potentiometer from the timing circuit and permits the use of a smaller potentiometer with less capacitance. Also, for a given potentiometer value, more pulse variation is possible than in the case of a single potentiometer to ground. The rise time of the output pulse driving 12 feet of coaxial cable into a lOOpf load is 5i-J.sec; the fall time is lOOnsec. The off state (no light, ~ 300V) occurs most of the time. Hence the NPN output power transistor returned to ~ +300V was used. Its collector resistor thus dissipates power only when the light is on 35 (V = OV, 12ma) . The beam shutter's analyzer is thus oriented so out that the input and output beams are vertically polarized. The trailing edge of the multivibrator's output pulse is used to produce a 200^sec pulse to start the erase cycle as soon as the read cycle has ended. The pulse is transformer coupled to the high level erase gun section. A fast rise time drive pulse is thus required. A 5nsec rise time is achieved by the emitter coupled logic output section. 3.3 The Target Crystal Decisions on the electro-optic target crystal in the chamber and its associated design factors require considerations of many factors. A charge pattern of sufficient resolution, magnitude, and persistence to modulate a laser beam must be placed on the target crystal in the chamber on-line. This places severe restrictions on the electron gun and its associated electronics as well as on the crystal. The longitudinal electro-optic effect is necessary for parallel processing of information. Without this the Fourier Transform cannot be produced. The physical size of the crystal target is the determining factor in both crystal selection and system performance. The size of the spot of charge that is deposited on the crystal must be of sufficient magnitude to develop very large voltages point by point across the crystal and yet sufficiently small to permit high resolution. -5 The minimum spot diameter capable of this is 2.5 x 10 m (l mil). For television resolution this requires a target at least 1" x 1". This spot size is measured on a fine grain phosphor target. The resolution obtainable on a crystal target is very different and . iy the width of the crystal divided by its thickness. All crystals exhibiting the quadratic electro-optic effect cannot be grown this large nor polished as thin as is necessary. From equations 23 and 2k, it is seen that all crystals exhibiting the quadratic electro-optic effect are characterized by a center of symmetry while those crystals which do not posses a center of symmetry all exhibit the linear electro-optic effect. It is for this reason that r. . in Table 1 for the centrosymmetrical classes has all zero elements. From Table 1 and symmetry conditions, it can be seen that a longitudinal effect free of background birefringence and optical activity can be obtained only with crystals of the classes ^+3^ of the cubic system and 42m of the tetragonal system. Strains, faults, and impurities present in many of these crystals make them unsuitable for use. Also the magnitude of the electro-optic coefficient for many substances is too low to make them usable. When large crystals are desired the selection reduces to those of class ^2m namely, KDP (Potassium Dihydrogen Phosphate"! and its isomorphs, KD*P (Potassium Dideuterium Phosphate) and ADP (Ammonium Dihydrogen Phosphate). Since the advent of the laser, these have been the most widely used crystals primarily because large samples of the necessary optical quality could be produced. As will be seen shortly, this is no longer so; either improved polishing techniques for crystals of the class "5 2m or improved growing techniques for crystals of the other classes is needed to enhance the available resolution in novel applications such as this. 37 This ^2m class of crystals has been extensively discussed. Billings showed that the most useful crystal section is a z-cut or basal plane with the applied field in the z direction and the light propagation in the same direction polarized at k^ to the x' and y' crystallographic axes. This was analyzed in equations 27 through 29- Equation 29 is commonly written as r = it rz where V = E L is the V l/2 Z applied voltage and V / is the half -wave voltage or that value of V for which the retardation equals jr. From this v 1 = — =2- (k8) 2 2n r 63 where X = 2nc/oo is the free space wavelength. For V = 0, r = and the components along x' and y' are in phase at the output face of the crystal thus leaving the polarization of the beam unchanged. There is no projection of this wave along the axis of a crossed analyzer and the output light is zero. As V is increased, the projection of the output wave along the analyzer's axis increases until at V = V, /„, T = n, the output polarization is parallel to the axis of the analyzer, and the output light is equal to that at the input . The values of half-wave voltage for the two commonly used crystals of class ^2m are V , (KDP) = 875OV and V , (KD*P) = 3^80v. They are calculated from equation 48 using experimentally determined o values of r^ at the 6328A wavelength used in this system. The high values of V, / have little effect on the choice of crystal or electron gun. The electron gun and its associated electronics are capable of generating discrete points of charge of sufficient magnitude to reach V , and of sufficiently small size to attain 500 line I itlon 01 1" x 1" target. As the analysis below shows, it is not the large required voltage which limits the obtainable results but rather the crystal thickness. The necessary beam current can be calculated to sufficient accuracy by assuming the crystal to be a parallel plate capacitor with c = -2-2L± (49) b where e is the relative dielectric constant for the particular r orientation of light and voltage chosen, d is the diameter of a spot of charge, and b is the crystal thickness. The charge on one plate of this capacitor is Q, = CV where V is the voltage of the particular spot of charge under question with respect to the conducting grounded back face. This can also be written in terms of the beam current, I. the time At required to write one spot, and the secondary emission ratio 8 as Q, = -At(l - b) . Writing the line time as T = NAt where K is the number of spots of charge per line or the resolution, the above two values of Q may be equated and solved for I € e nd 2 NV 1 ■ Ml- & )T < 5 °> The values for these various parameters are € Q = (36* x 10 9 )" 1 f/m € = 21 (KDP), ^8(KD*P) d = 1 mil = 2.5 x 10" 5 m 39 -h b = 10 mils = 2.5 x 10 m T = 52.1 x 10 sec 6=0 N = 185 V ■ 8750v(KDP) 3^80v(KD*P) giving I(KDP) - ll.H u A, l(KD*P) = ll.OuA. This calculation ignores the interaction of fields due to neighboring charge spots on the incoming electron beam; this has been shown to produce a defocusing of a 2 x 10 m diameter beam by 17$ • This effect is very minor since the value of N used was only 185. This analysis also ignores the very high yet finite resistivity of the crystal which may cause diffusion and spreading of the spot. The persistence tests of section k.6 and the analysis below show this also to be a very minor factor. The line time used in equation 50 is the horizontal scan time of commercial television minus the horizontal blank time. It is the time the electron beam must take to write one line. The value for resolution N is derived below. The values of e are e~-,/e~ since both r 33' the field and the light are applied in the z or 3 direction, the value for KD*P is for a 90$ deuterated sample. The values of V are the half- wave voltages calculated from equation kQ; this gives the maximum necessary beam current. 6 is chosen as zero since the accelerating potential is very high; the experimental determination of the secondary emission curve is presented in section k.6. The resolution obtainable from a crystal sample of area A and thickness b is derived below. By applying a curvilinear square analysis to a parallel plate crystal capacitor where one plate is a uniform conducting layer and the other plate is a sp . i of diameter d creating a voltage V across the crystal, the di the spot to the V/2 point is found to be a = d + .M+b (5J This is the spacing that must be allowed between spots of charge. From this the resolution N for a square raster is given by N = A/c . For a 1" x 1" x .01" crystal the maximum obtainable resolution is 185. O.kUb is much larger than d due to the problems and techniques involved in polishing these crystals. For a square raster of face width u the resolution is N ~ 2oo/b. It should be noted that only the crystal's dimensions were involved in the above calculation, the spot size and half- wave voltage have no effect. Several important conclusions can now be made: First, the required beam current for KDP and KD*P is nearly the same since it is proportional to the e V , product. Second, the electron gun is capable of depositing spots of charge of sufficient voltage to generate V, /„ for any electro-optic crystal. Third, defocusing and charge diffusion effects need to be quite large before an appreciable difference is caused since the spots are five times smaller than the required spacing. Thus the limiting parameter in all cases becomes the crystal thickness as noted previously and there seems to be no reason for selecting one ^2m crystal over another since none can be polished thinner -h than 2.5 x 10 m and still maintain sufficient optical quality to be useful. kl A more detailed analysis of the charge distribution further verifies the conclusion concerning crystal thickness and shows that KD*P is a slightly better choice in many respects, laplace's equation is solved in a crystal slab on which parallel bars of uniform charge of width d separated by d are placed, each bar having sufficient charge to generate V / . Figure 7 shows a cross section of such a crystal with the bar pattern chosen parallel to Z to make the resulting potential distribution independent of z for a fixed x and y. The pattern is thus periodic and only a 2d width of the crystal need be considered. The thickness of the crystal is b and I is the beam current. The potential distribution in the crystal is given by some V(x, y, t) and the surface distribution by V'(x, t) = V(x, b, t) while V(x, 0, t) =0. The current charging a surface element of width Ax is / v r < x < d/2 ± W - ± Q i 3 y 2 d < x < 2d i, = l(x)Ax where (52) l(x) =0 {d/2 < x < 3/2d Due to the finite resistance p of the crystal there is a current which leaks through the target thus discharging the surface given by lim V(x,b,t) - V(x,b - Ay,t) = dV, Ax , , X 2 Ay^O Ay cy' p W) P AX * where Ax is the width of the surface element under consideration and Ay is a small distance below the crystal surface. Due to the net current CRYSTAL SURFACE CRYSTAL Y 4 t t Io 1 1 1 1 f I I I -►* GROUND PLANE d/2 d 3d/2 2d Figure 7. Configuration for Potential Distribution Analysis I = i - i the charge on the surface element changes according to lAt = C Ax{V(x,b,t + At) - V(x,b,t)) (5*0 where C is the capacitance of the crystal. Substituting for I leads to ax, bt ] y=b ' i(x) _ av, 1 dy'y=b pC (55) Given the surface distribution V'(x,t) at any time, V(x,y,t) inside the crystal can be calculated from the boundary conditions at y = and y = b. Thus V(x,y,t) must satisfy Laplace's equation 4-4 = ° dx dy (56) h3 with boundary conditions V(x, 0, t) = V(x, b, t) = V'(x,t) (13) Schagen has solved equations 55 and 56 with the result I o R n " t / R o C o I n R o V'(x,t) = (V ' - -|^)e ° ° + -^ + 2 co ( _ x) n {1 - exp[-(2n + l) jtb/d]coth[ (2n+l) jtb/dJt/R^} n I R nio 2n+T [ (2n+l)jtb/d]coth[(2n+l)jtb/d] ,jtx- cos[(2n+l)^] (57) where V ' is the initial value of V'(x,t) for t = and R n C is the time constant of the crystal. After one frame time t, the potential difference between the center of the charged strip and the center of the uncharged strip is V(0,t) - V'(d, T ) (58) If the target were an insulator this difference would simply be I t/c q (59) This rather formidable potential equation describes the effects of charge leakage both along the crystal surface and through the crystal. The relative potential difference V (x,t) is obtained by dividing equation 58 by equation 59 giving ^ oo , .n (1 - exp[-(2rnl;nb/d]coth[(2n+lMtb/d]T/ V 'r (x ' T) : n n=0 2n+I [ (2n+l)nb/d]coth[ {2n+V nb/dJT /;-/;, i ~^~ The charge leakage to ground through the crystal causes a lo picture charge but does not necessarily involve a loss of resoluti' rather it results in a loss of sensitivity. When b/d -> 0, the target is uniformly illuminated and equation 60 becomes the familiar exponential decay . - T / R o c o V 'r^lb/a=o' " T /R rj C < 6l > which is plotted in Figure 8. The charge leakage across the crystal from charged areas to uncharged areas most definitely affects the resolution. In the case of crossed polarizers, there is ideally 100% transmission beneath each strip of charge. Dividing equation 60 by equation 6l gives a relative modulation figure M. In Figure 9, M is plotted versus b/d for various time constants t/R C It is seen that for various values of t/ELC the relative modulation between those areas of maximum charge and those areas of minimum charge depends only on the ratio b/d. The relative modulation is also seen to increase rapidly for lower values of t/R„C ; this is to be expected since the larger R n C n becomes the more stable the charge pattern becomes. For b/d = k, the relative modulation is 67% for t/R C q =0.1 while it drops to 2k% for t/R q C =0.5- In section k.6, the R n C n time constants are experimentally determined to be 100msec. t is the standard television vertical scan k5 ';f 1.00 o.eo 0.60 040 0.20 °0 2 4 0. 6 8 1 1 2 1.4 1.6 1.8 2 • V, R C Figure 8. Relative Charge Leakage Through the Crystal t ' 0.8 0.6 0.4 02 £/ R. C^O. .19 0.28 s 1 ? b/ d Figure $. Relative Transmission Due to Charge Spreading Across the Crystal time t = 30msec. Thus t/R q C = 0.3- From Figure 8, the the charged strip is about 85 r /c of its initial value. For a 1.0" x 1.0 0.01" crystal with 500 line pairs, the intensity of tr.e light tl at the center of the uncharged stip is from Figure 9 over 8of of the initial intensity of the charged strip and thus not resolvable. For 200 line pairs the intensity is only kofo of the initial value of the charged strip and is thus resolvable. As the above analysis shows, the charge pattern must remain as stationary as possible during the 33ms write cycle. Since the retention time of the crystal is proportional to the product of crystal resistivity and dielectric constant, KD*P with its much larger dielectric constant is better. With either crystal, erasure must still be used. The lower V , of the KD*P does not affect the required beam current but the defocusing effects due to spots of charge are considerably reduced by the lower voltages required on a KD*P crystal. 3.^ Crystal Assembly The crystal assembly consists of a KD"*P crystal with a conducting layer of CdO, cemented via silicone rubber to a calcium fluoride substrate. The conducting layer is connected via the circumferential edge of the substrate to an insulated terminal that may be grounded or any reference desired. The entire assembly is demountable, For rapid and clean exchange of crystal assemblies during airings, the crystal assembly is mounted in a snap-in image orthicon target holder. There are four paramount considerations in this assembly: cleanliness, homogeneity, thermal conductivity,- and thermal expansion. hi (Ih) Preliminary tests indicated that optical flatness was not necessary since the retardation was differential. As long as the flatness and cleanliness are such that they introduce a sufficiently low degree of scattering, they are only of secondary importance. The scattered light produced by thermally unstable assemblies breaking down generally over- shadows that due to flatness. The thermal considerations arise from the heat dissipated in the assembly. The electrical power supplied to the crystal capacitor is the product of the average voltage on the surface (V, i = 3750 volts in worse case) and the beam current (i = llua. from equation 50) . The chief problem is one of the heat generated by stopping these high energy electrons. This is roughly the product of the accelerating potential (30KV , I and the beam current (llua) . These figures for a 1.0" x 1.0" x 0.01" crystal yield 0.3 watts of power. This heat is dissipated by radiation and conduction. Using Stephan's Law for the small temperature change produced, the heat dissipated by radiation is seen to be negligible. Thus this 0.3 watts must be dissipated by conduction in the crystal assembly. The 20mw of optical power absorbed is negligible. To conduct this power away as quickly as possible, a high thermal conductivity for each element in the crystal assembly is desired. Likewise the thermal ex- pansion coefficient for each element should be matched. Table 2 lists available values of these two parameters for various assembly elements investigated. A glance at Table 2 shows that most of the power will be dissipated at the glue interface as its thermal conductivity is so low. Much work is needed in improving this. The cement besides being Material Thermal Condu cal/cm/sec/ Li)!' 2.9 x 10 KD*P 2.9 x 10 BeO 0.69 CaE 2.3 x 10 Quartz 0.02 Glass 0.002 Sylgard . L82 Cement 0.00035 Silicone Cement 0.003 CdO 0.80 Gold 0.70 -3 -3 Thermal Expansion Coefficient 23 x 10 21 x 10 -6 -6 22 x 10 .9 x 10 .9 x 10 -6 -6 -6 20 x 10 -6 10 x 10 (15) -6 Table 2. Thermal Properties of Crystal Assemblies transparent, non-polarizing, and bubble free, should be rigid as the crystal thickness is reduced after it is positioned on the substrate. Attempts at using conductive loaded cements and finding higher thermal conductivity ones have not yet produced good results . Since the conductive layer is in contact with the glue, it also is affected by the heat dissipation. Even though the glue is not in the electrical circuit (being on the far side of the conductive coating "> , it is most definitely in the thermal circuit. Gold electrodes are commonly used but for higher resolution they have proved inadequate. The uniformity of the crystal is much higher than that of the gold layer due both to thickness and thermal properties of the gold. This results in a non-uniform electro-optic effect as well as a non-uniform relaxation time and charge spreading. The deposition of uniform coatings of gold is quite difficult; they also prove unstable under electron beam bombardment. During deposition the h9 metal atoms appear to nucleate at steps and imperfections in the surface. Even with a clean, uniform, smooth surface, the gold has been found to boil up. Thicker layers of gold improve the uniformity at a cost of light transmission and resistance. A microscopic examination after sustained electron bombardment revealed that the gold layer had become granular islands and discontinuities which degraded resolution since the charge spots had no reference. This was felt to be due to the thermal dissipation occurring and the poor linear expansion coefficient match. A CdO layer was found to work quite well. Gold is amorphous while CdO is crystalline. Thermal stability is added to the layer by a three step deposition process. First a SiO coating is sputtered onto the crystal. The CdO doped with metallic cadmium is then sputtered and diffused through the SiO . A second SiO layer is then applied. The resistance of the conducting layer is 100,000fi/square. Care must be taken that this layer be much lower in resistance than the crystal. When this layer becomes heated, the metallic cadmium oxidizes and the resistance of the layer permanently increases. The SiO protectorate insures the uniformity, continuity, and stability of this layer. The thermal conductivity of CdO is high and its expansion coefficient matches that of KD*P much better than does gold. Quartz is a conventional substrate used quite often and quite well in many applications. However, many types are optically active. Also, its thermal properties as well as its index match are very poor for this use. CaF is inert, hard and possesses an excellent temperature match and a high thermal conductivity. k. ELECTRON-OPTICS k.l Write Gun A block diagram of the electronics is shown in Figure 10. The severe conditions on beam current and spot size make the choice of the write gun and its associated electronics very difficult. A high accel- erating potential is necessary both for zero secondary emission during the write cycle and for good spot size. The fact that certain portions of the crystal target may be near 8,000 volts necessitates an accel- erating potential well above this. The higher beam current in a small spot is best achieved by increasing the velocity of the electron beam rather than its density. The mutual repulsion of electrons in a dense beam prevents sharp focusing in the later case. The electron gun which was found to be best had a beam current of 20>_ia in a 1 mil spot. It has electrostatic focus and magnetic deflection. Due to the repeated airings that the gun would have to undergo, various cathodes were investigated. Thorium dispenser, tungsten matrix and various impregnated cathodes appeared to be very promising, but the cost of modifying the gun prohibited their use in the prototype system. The thermionic cathode material on the gun is a barium, strontium, calcium carbonate compound. The initial activation converts the carbonates to oxides by a thermal decomposition process and some of the oxides to free metal by a combined thermal, electrolysis and chemical process. Emission is obtained from a mono-molecular layer of free barium. During airings, the chamber is backfilled with nitrogen gas and one volt is kept on the filaments to reduce oxidation. 51 115 VAC -t> 10KV ISOLATION TRANSFORMFP. — H" ERASE GUN POWER SUPPLY (>ERASE GUN DYNAMIC FOCUS -i 30KV ISOLATION TRANSFORMFR M 1 FOCUS POWER SUPPT.Y HIGH VOLTAGE POWER SUPPLY 30KV ISOLATION TRANSFORMER HIGH VOLTAGE AMPLIFIER METER PANEL T> CRYSTAL BACK T y* WRITE GUN VIDEO AMPLIFIER 5 vujeh SYNC IN SYNC TRIGGER OUT C DEFLECTION YOKE DUAL SAWTOOTH GENERATOR 115 mi HORIZONTAL I VERTICAL on DRIVER KEYSTONE CORRECTION r DRIVER POWER SUPPLY U VACUUM SYSTEM Figure 10. Electronics U.2 Deflection The type of deflection used appreciably affects the gur performance. Both electrostatic and magnetic deflection are compared on the basis of the deflection sensitivity, S, defined as the amount deflection per given field. For electrostatic deflection where the parameters are shown in Figure 11. The corresponding equat- (l6) for magnetic deflection from Figure 12 is S R -± = U/-/J2V (63) B B v rn V a By comparing these sensitivity factors it becomes obvious that magnetic deflection is preferrable. In both cases if V is increased to increase a the electron speed, the spot becomes brighter but deflection sensitivity drops. The change, however, is much less in the magnetic case. Thus magnetic deflection is less sensitive to defocusing due to a change in beam current, accelerating potential and electron speed. Other arguments could be advanced such as the fact that the magnetic field, besides being more uniform, imparts no energy to the electrons during deflection and hence with no velocity change images are sharper. The insulation requirements are also less severe in the magnetic case. The magnetic deflection system chosen consists of a E to I driver amplifier whose input is taken from a dual ramp generator and whose output drives a yoke load. The necessary yoke current for a (17) given beam deflection half-angle, 0, is given by 53 _J * Figure 11. Electrostatic Deflection ,J t Y J I Figure 12. Magnetic Deflection = k FTJl sin G where V is the effective anode potential, L the yoke inductance and k s. a constant dependent on the geometry. The horizontal retrace time is given by^°' T = 1.25LI/V (65) where V is the yoke driver voltage. This retrace time must be kept less than lCysec for deflection at standard video rates. Similarly, the duty cycle of the ramp generator must be kept high enough for operation at video rates. Dual ramp generators are used to produce the voltage ramps which control the scanning and deflection of the electron beam. These generators produce a to 10V peak to peak ramp, with + 5 volt biasing and 0.50^ linearity into a 10K load. The ramps are generated by charging up a capacitor with a constant current source. A rotary switch selects the capacitor value, a potentiometer controls the magnitude of the current, and a stop pulse activates a clamp whicn returns the ramp level to ground. Three stages of gain with high negative feedback linearly amplify the ramp and adjust its DC level. The x-y deflection drivers are direct coupled feedback amplifiers which convert the voltage ramp into a current ramp suitable for driving a yoke load with 0.25$> linearity. The current ramps range from -3 to +3 amperes. They are generated by sensing the voltage across lfi resistor placed in series with the yoke and comparing it to 55 the input voltage and reducing the resultant voltage difference to zero. The bias control on the ramp generator enables the current ramps to be symmetrical. The deflection yokes are uniformly wound, high Q, ferrite cores, The inductance of the vertical coil is 6k\iE and for the horizontal coil the inductance is flyH. Keystoning is produced by the geometry of the deflection system. Instead of the rectangular pattern, a keystone shape results. The reason for this lies in the fact that the amount of current produced by the driver determines the angle of deflection as measured looking down on the crystal. is proportional to I as is the amount of deflection. But for a given horizontal position, that is for anywhere on a given vertical line, V and thus I are the same and so is . As the scan moves down the crystal, however, the distance from the center of deflection to the screen, D, increases due to the off- axis geometry. must remain constant since it is controlled by I, thus as D increases, so must the deflection. This produces an increasing width as the beam scans down the crystal. This effect is called keystoning. It can be corrected by modifying the horizontal ramp so that the amplitude for the bottom line is less than for the top line, thus keeping the deflection constant. The modulation necessary is linear and directly proportional to the vertical position on the target. The circuit of Figure 13 achieves this modulation. It is accomplished in conjunction with the generation of the horizontal ramp. Figures lU a and b show the initial keystoned picture and its horizontal ramp. The horizontal centering potentiometer of Figure 13a varies the DC reference for the ramp generator of Figure 13b and thus the Jf current produced by the E to I amplifier and hence the centering the picture on the target. By modulating this horizontal ramp bias level at the vertical rate, the waveform of Figure lUd and the picture of Figure 14c result. The starting point for each horizontal line has shifted over slightly. However, each ramp is still of equal amplitude, thus the right side error becomes doubled. The amplitude of each horizontal ramp is controlled by modulating the constant source charging the capacitor bank. The start and stop of the ramp are determined by the horizontal sync pulses. This charging time remains constant but the charging current is modulated to produce less and less current for each successive horizontal line hence less ramp amplitude as in Figure lUf. The left side correction is a positive going ramp at the vertical rate controlled by the vertical sync pulse. The right side correction is a negative going ramp again at the vertical rate. These ramps are generated in a manner similar to that of Figure 13b. Their amplitude and hence the amount of correction available are controlled by two potentiometers . 4.3 Focusing The choice of focusing system was dictated by different considerations. An off axis gun geometry was needed. This lengthened the throw of the gun (the distance from the center of focus to the screen") . Electrostatic focusing plates could be placed inside the tube 57 Hi 1 z -wv- H<3- O-*- H(r ■Ifc i ~iQr^ te ^ + ^ OK z o i — VW — l|l n .> o !?* 2 j— I— ■CI o a: b. Horizontal Ramp Generator Figure 13. Keystone Correction . fNI ( (jNTBOi K* CAMERA 1 1 _^ BEAM SHUTTER 1 J ♦ OPTICS SELECTIVE SCAN NINO 75uT- Figure lk. Keystone Waveforms while magnetic focusing necessitated a still longer throw. With the very high accelerating potentials envisioned, magnetic focusing required a very large flux density. Although magnetic focusing does in general give somewhat sharper images and a more uniform field, more than adequate results were obtained with the electrostatic system chosen. Both systems have the same aberrations. Another reason for the selection was that all magnetic systems show some defocusing due to field inter- 59 actions although soft iron shields reduce this. Defocusing is generally small in tubes with mixed systems. A well regulated high voltage supply, insulated "by Plexiglass and with Plexiglass knobs, fed through a high voltage isolation trans- former, was floated on the high voltage cathode supply. The focus current and regulation requirements were too severe to tap the cathode supply. The focus supply is continuously variable to 10KV at 8ma with 0.01% regulation. The unit consists of a power circuit and a regulator circuit. The power circuit is simply an autotransformer driving a high voltage transformer whose output is rectified and doubled in a full wave doubler. This waveform is fed to the series regulator section where a difference amplifier controls the voltage applied to the grid of the regulator tube. The change in plate resistance of this tube absorbs the variations in the voltage from the power circuit producing the 0.01% regulated output . Due to the target size and off axis geometry, the throw of the gun changes considerably. The throw of the gun is proportional to the necessary focus voltage. A plot of focus voltage versus throw is a parabola. A plot of the change in focus voltage versus the deflection distance on the screen was calculated on a computer and found to be approximately linear with a 150V focus voltage change necessary for a 1" x 1" target. This correction is known as dynamic focus. It can be accomplished by applying a 150V ramp at the vertical rate instead of a constant voltage to one end of the difference amplifier in the series regulator section of the focus supply. The high volt ■ the m Identic design to the focus supply except that the ;e is c variable to 30KV at 20ma. 4 . k Coupling Amplifier The video input signal modulates the cathode through a high- voltage coupling amplifier. The amplifier generates the filament voltage, the grid voltage and the grid acceleration voltage bias for the gun as well as amplifies the incoming video signal (up to 150 tim< raises it to cathode potential (up to 30KV) and uses it to modulate the cathode voltage for the write gun. It provides 30KV isolation, a band- width of lOmHz and a regulation of 0.01$. It consists of a low-level video preamp with video and trigger inputs and a high voltage section with the cathode supply input. In the low- level section, the video is AC coupled to the base of an emitter follower whose DC level is set by a constant current sink transistor with RC time constants such that an input pulse (keyclamp pulse sets the current drain and thus the DC level. This is very important and will be discussed further later. The video is then DC coupled to a video modulator transistor with RF from a lOOmc oscillator capacitively coupled to the emitter. The video thus modulates the lOOmc RF carrier producing a double sideband amplitude modulated signal at the collector of the modulator which is inductively coupled to the high voltage section. 61 Since a KDP crystal is used as the target instead of a phosphor care must be taken to keep the electron beam moving to prevent burning of parts of the. crystal. This can be done by controlling the keyclamp pulse which sets the DC level of the cathode of the gun. The keyclamp pulse is formed from the horizontal sync pulse by means of wave shaping and delays. The keyclamp pulse is 2.2|isec long and delayed by 1msec with respect to the U.5u.sec long horizontal sync pulse. This keyclamp circuit is a type of sample and hold circuit where the coupling amplifier samplies the DC level of the video signal while the keyclamp is present and uses this as a DC reference level for one horizontal line. The central portion of the horizontal sync pulse, being the most negative portion of the video signal, must be used as the reference level to insure a negative reference of the cathode to the grid. In the absence of this pulse, there is no DC level, and the cathode goes positive with respect to the grid and becomes cut off. Rectified horizontal and vertical ramps are used as DC inputs to two asymmetric flipflops whose outputs drive a NOR. This is used to gate the horizontal sync pulse off and thus the gun, if sweep is lost. U.5 Vacuum System The vacuum system requires special consideration. It must be -9 capable of producing 10 torr in one hour. Higher pumping speeds than normal are required due to the outgassing of the crystal and the frequent airings of the chamber. No oil is used since backstreaming can change the crystals ' properties . No vibration of the pumps can be tolerated due to the critical optical alignment necessary. Water cooling is inconvenient. A 601/sec ion pump with a 40001/:;'^ tit,'. . ob- limator and liquid nitrogen sorption pump met all of the above requirements . Continuous pumping is necessary since the target crystal, due to heating, gives off vapors during electron bombardment. By 'baking out" the crystal assemblies for a day, this effect can be reduced and a sealed system would require only a small appendage pump to maintain vacuum. h.G Erase Gun A crystal time constant larger than one frame time is necessary if parallel processing is to be done. Likewise, an RC time constant less than one frame time is necessary if on-line television rate pro- cessing is to be done. Both of these seemingly contradictory objectives can be achieved by a write-erase cycle. Widely varying values for RC have been experimentally obtained by diverse reseachers. An accurate measurement technique for RC is necessary to evaluate the effectiveness of erasure and to optimize the various electron gun parameters. Two discharge times must be considered: the time t for discharge through the crystal target and the time t ' for transverse discharge across the surface of the plate. These are given by r (66) T' = € € r p' where e is the relative dielectric constant in the direction of the r 63 optic axis, p the resistivity in that direction and p' the resistivity in a direction normal to the optic axis. These parameters are very temperature dependent i o 3100 r T'-T c p = io 1 - 27 + W°l* n . cra (67) 1.85 + 2^70/T 1 _ 10 ' ■ ' 0, - cm where T" is the operating temperature, T is the absolute operating temperature and T the Curie temperature: T = -150 C for KDP and -50°C for KD*P. The measurement technique chosen consists in writing continuously two bars on the crystal, shining the laser beam through one of the bars, picking up the resultant intensity variation on a calibrated photovoltaic cell and displaying the output on a scope. From the maximum and minimum intensity readings, the time constant can be determined. A point on the crystal which is bombarded by current pulses of amplitude I and time duration T, every T, + T seconds has a resultant steady state voltage after a current pulse given by -T /RC V 2= RI (1 "-(T 1+ T g )}RC < 68 > 1 - e where R and C are the resistance and capacitance of the point in question, -T /RC T seconds later, its value is V, = V e ' . If the initial intensity is I and the intensities corresponding to the voltages V and V are I and I , then RC= T — sin" 1 I 2 /I log [ ^ —J sin Ij^/Iq The RC time constants of Table 3 were measured in this manner for various values of beam current I. The Table also the experimentally determined values of crystal voltage to the val, calculated from equation 68. The agreement is excellent. The decrea, in t with increasing beam current is due to the corresponding rise in crystal temperature which lowers both e and p. The three readings for ICVa beam current show this effect quite well. The first reading was taken immediately after the previous four readings and the second ten minutes later. The third reading was taken immediately after increasing the beam current from to lOua. The first reading is greater than the second since the crystal had not heated up completely. The third was highest of all since the intermediate current increases and the time required for recording their data was omitted. This type of measurement gives an accurate estimate of the time constant to be expected in an on- line system. A second electron gun inclined at 35° serves as the erase gun. Its drive requirements are much less severe than for the write gun. No deflection or focusing is required, also regulation is not critical. The cathode and grid voltages are obtained from a bleeder circuit across the output of a high-voltage power supply as shown in Figure 15- Gl controls the beam current and G2 the beam size. The monostable multi- vibrator floats at cathode potential. Its output drives Gl. It is 65 Beam Current RC V Calculated V 2\ia. l45msec 57^ 600 4^a 125msec 1110 1118 6\ia 121msec 1580 1572 8ua 112msec 20^+0 2036 lO^a 95 r nsec 2360 2330 10ua 92msec lOtxa 101msec Table 3- Measurement of RC Time Constant normally 250V below the cathode and the gun is off. When the monostable pulse occurs, Gl is driven close to cathode potential turning on the gun. The difference between Gl and the cathode and hence the beam current can be controlled by R . R controls the beam size at the crystal. The erase time is controlled by the 50K potentiometer in the multivibrator. It is variable from 0.6 to 2msec. The multivibrator is transformer coupled to ground level to allow the pulse shaped from the trailing edge of the beam shutter pulse to serve as a trigger. This coupling also prevents the multivibrator from triggering on the 20 volt, 120 cycle power supply ripple. The primary has 15 turns of #30 teflon insulated wire and the secondary 5 turns on a — " Ferrite core. Only a pulse with a rise time less than 0.5M-sec can trigger the transformer. The emitter coupled differential amplifier at the output of Figure 6 achieves this rise time and the current necessary to drive the 50ft load. The current drain of the multivibrator is kept very low so that a battery floated at cathode potential can be used as the supply. The 2 bank llposition rotary switch permits the cathode potential to be varied while keeping Gl and G2 fixed relative to the cathode and the power supply load constant. The switch is shorting to prevent open -3KV Figure 15 . Erase Gun Drive Circuitry 67 circuits in the gun, its isolation is over 3000 volts. The resistors R are h'JKQ 2 watt. A 3000 volt isolation filament transformer with its center tap referenced to the cathode provides the filament voltage and current for the gun and allows standby operation. The gun thus emits a defocused spray of electrons toward the target. The accelerating potential of these electrons is determined by the difference between the crystal voltage and the cathode voltage. When this accelerating potential is chosen so as to yield a secondary emission ratio greater than one, the electron beam removes charge from the crystal surface and thus erases. The erase operates on the principle of secondary emission. Electrons can be freed from materials by many methods. In KDP and KD*P the particular method of interest is bombardment by other electrons. The electrons emitted are called secondary electrons and the process secondary emission. The ratio of secondary electrons to primary electrons for a given material is a function of the accelerating potential of the incident electrons. A typical curve is shown in Figure 16. The only points of actual importance are the two points at which the secondary emission is one, these are called respectively the first and second crossover . The only two stable points are V and V . This can be seen by assuming the cathode potential V to be fixed and the target potential K V_ to be such that the accelerating potential V. = V m - V v = V, . If 1 A 1 K. 1 the target potential rises slightly V increases beyond V , a becomes A _L greater than 1, the target thus charges more positively increasing V further until it reaches V^. If the surface potential then rises, V 2 * 'A Secondary End ssion Ratio Accelerating Potential Figure 16. Secondary Emission Curve a becomes less than 1, the surface thus decreases, and V A decreases back to V . Likewise if the surface potential decreases, V A decreases, becomes greater than 1, the surface becomes charged more positively and V increases back to V again. Thus V g is a stable point. Similarly if V is fixed at V and the target potential decreases slightly, V A 1 decreases, a becomes less than 1, and the surface potential continues to decrease until V A = V Q = 0. Thus the equilibrium voltage for all target voltages greater than V ± + \ (recall V R is negative) will be V £ . This equilibrium voltage will be obtained if the beam current 1 and its duration t are sufficient. An analysis similar to that of E E section 3-3 for the case of the write gun yields the relation T = 7 _L W here I is the current in mA required to erase the crystal E * ' T E charged to an average voltage V in KV in a time T £ in msec. The erase gun used is capable of depositing a 2ma beam over the 1.5" optical diameter. 69 If the cathode potential is set at -V , then the equilibrium target voltage will be ground, a seemingly desirable condition. This however requires both that crystal potentials be kept more positive than -V which must be the case in any system and that V be determined. Experimental attempts to rigorously determine this value were not successful. An exact measurement for an insulator dielectric is extremely difficult. V and a vary drastically as a function of numerous parameters: crystal cleanliness, crystal flatness, doping, surface state, temperature, conductivity, etc. An alternate method by which the equilibrium target potential can be fixed was thus employed. A collector ring was mounted around the crystal and fixed at a potential V between V and V . Although neither V nor V is known exactly, V is typically low (less than 100V) while V is much larger (greater than 1500V) . Operation of the gun has verified these ranges of voltages. The effect of this is to shift the secondary emission curve to a as shown in Figure 16. The new second crossover point V is only several volts less than V . Thus a variable cathode voltage, beam current and on-time adapt erasure to all crystals of the KDP family. This alternate approach has several advantages in that some collector for the secondary electrons is necessary to prevent their redistribution across the target surface. This collector voltage must be greater than the target voltage to ensure removal of all secondaries emitted. This method also allows excellent monitoring of primary or crystal current and secondary or collector ring current. ("■ ) '• ' us ;., 'loted, the verified by the experimental set up used in the t The voltage across the crystal before erasure wa:. d after erasure was nearly 300V. The c< >r ring was fixed at +300V and the cathode at -l^OOV. As Vp was varied the resultant equilibrium voltage . red it. At V K = -1500V or V ~ 500V, o was apparently quite large nly lmsec = T_ was required for erasure. At other values of V„ larger tirr. T„, were needed. Similarly with a V = +300V, V\ ~ V while the E c 3 c difference increased as V was decreased since a also decreases and thus c the slope. Crystal resolution is also improved by erasure since charge is removed before it can spread laterally across the crystal or longitudinally through it. At this point it is worth noting that landing coils to force the beam to impinge normal to the crystal surface were considered but erase gun considerations prevented their incorporation. The only advantage gained by them would be an effective beam current which was higher by a factor of — where 9 is the angle of inclination of the COS u gun, and thus better shaped spots smaller by the same factor. However, sufficient beam current and spot size were obtained without using these coils. Resolution is limited by the crystal thickness and beam currents higher than lCvia cannot be used from power dissipation considerations. The defocusing effect is approximately the same with and without coils since the path difference between edges of the crystal and the top and bottom are nearly the same in both cases. 71 The field required in the landing coils depends on the velocity of the electrons and hence the cathode potential. The field of these coils must be considered static since their inertia is too large to consider them otherwise. They assume that all electrons have the same energy and they also affect both the write and erase guns. Thus the cathode potential of the write gun must be fixed, and this would limit the versatility of the system. When the effect on the flood gun electrons is considered, the results are disastrous. The flood gun electrons are at very low energy, traveling very slow, and are in the correcting field for a long time. As a result they are deflected much further than the write gun electrons. Preliminary calculations indicated that the angle of inclination of the erase gun would have to be nearly l80 . The control of the electron beam thus becomes extremely difficult but worse yet all of the flood gun electrons are at different velocities since the target voltage can vary by thousands of volts. Thus the electrons would be deflected through a large number of different angles making erasure nearly impossible. Also a more efficient final system would operate in a reflex mode where the light would travel through the crystal twice, thus reducing the necessary voltage and current by 50$. In this case, the electron gun would be mounted normal to the crystal on the side coated with a multidielectric mirror and the incident light would enter from the opposite side of the crystal through a beam splitter. As a result of various write and erase gun tests, several effects of sustained electron bombardment of KDP were discovered. After writing a static picture at an accelerating potential of 25KV and l\ie. beam current for Lght hours, the pattern became etc tal surface. A microscopic i indicated the dept about 15-20 microns. This depth is most likely a func\ accelerating potential since the higher it becomes the higher tl electrons ' velocities and the further their penetration into the ciyat target. The erosion appears only after sustained writing for many with no erasure. This effect has not appeared when on-line picture:: are written and erasure is used. Also the accelerating potential has sub- sequently been kept below 20KV and the beam current below 5\i&. Another worthwhile point is the fact that this etched area can be written over with a new picture. In this case, there is some small background scattering which the write gun with sufficient current can overcome. This further indicates that optically flat crystals are not necessary. On several occasions, crystal overheating occurred: once during writing with 25KV accelerating potential and 10^a beam current for one hour and once during erasure with 2.5KV accelerating potential and lma beam current for ten minutes. The crystal heated considerably and as it cooled expanded and cracked. The newer assemblies with matched temperature coefficients, high thermal conductivities and protective layers surrounding the glue and conductor have not exhibited these effects. Should these problems appear after sustained use a protective coating could be applied to the front crystal surface, thus preventing the electron beam from striking the crystal directly. With the collector ring method of erasure, the secondary emission properties of the material are not too important since both I , T and V are variable over a 73 sufficient range to accomodate most materials. A coating with a high secondary emission ratio could be selected thus reducing both I and 1L,, lii hi The expense of the crystal assemblies and the decrease in available beam current after airings prevented more detailed investi- gation of these problems. Figure 17 is a photograph of the chamber showing both guns. This chamber is an extensive modification of a light valve first (20 21) developed in 1939 smd. attributed to several authors. ' Figure 17. The Chamber 5. [CATIONS 5 . 1 Spatial Filteri: The principle of 1 filtering is wel- rn, it I masking out certain portions of the frequency plane representation (22) a picture. Figure l8 v ' explains the principle in one dimensior. . was proven in section 2.1, a lens forms in its back focal plane the frequency representation of a transparency placed in its input plane. A diffraction grating is placed in the input plane. If only first order interference is considered, three plane waves a, b, and c propagate and produce the three images A, B, and C shown. These three points corre- spond respectively to the dc value and to the positive and negative spatial frequencies of the grating. A second lens can reconstruct an image of the grating, the operation being to take the Fourier Transform of a Fourier Transform. A different input image would result in a different frequency representation, so that masking out A, B, and C would filter out the diffraction grating but not other portions of the picture . This principle was demonstrated by focusing a camera on a screen on which the letters AEC (Atomic Energy Commission") with vertical bars superimposed were placed. The output of the camera provided the video and synchronization for the electron gun which deposited a charge pattern on a KDP crystal. Using an optical system as in Figure 18, the image was reconstructed on a vidicon placed in the back focal plane of the final lens. The resultant image, appearing on a monitor is shown in Figure 19. A microscope slide with ink spots corresponding to the 75 □irFRacnoN CRATING INCIDENT LIGHT OF WAVELENGTH X FOURIER TRANSFORM Figure 18. Spatial Filtering Figure 19- Reconstructed Image frequency representation of the grating was bhen pli Transform plane. The resultant reco: image is shown in Figure 20. Figure 20. Spatially Filtered Image If overlapping signal and noise are to be separated, this can be done most efficiently in their spectra, and the advantage of this optical filtering is that two dimensional images can be handled, the processing can be done in parallel and on-line, and the spectra separation occurs automatically by diffraction. Another advantage can be seen by referring back to Figure 18. If the grating is translated in the input plane, the points A, B, and C do not move or change. This is due to the fact that they are in a frequency domain while the input 77 plane has spatial coordinates. These points are produced by wavelets which are parallel on the left side of the lens. This property is known as the translational invariance of the Fourier Transform. The resolution is limited by the 0.01" thick crystal used to about 100 lines. The crystal thus acts as a low pass filter and most of the picture content is confined to the central portion of the frequency plane. The central spot contains so much as the incident intensity that the higher order frequencies become deemphasized when the spectrum is displayed on a pick-up device. This can be corrected and gradients in the picture emphasized either by blocking out the dc spot or by emphasizing the higher frequencies in the video coupling amplifier. Such a spatial filtering technique can be used for character recognition. In this case, masks of the frequency representation of the desired characters can be placed in the Fourier Transform plane and the resultant image will be transmitted only when the desired character appears in the input plane. Another use could be as a method of applying pictorial in- formation on-line to a computer. The computer input could have the form of the spectrum of the picture. It can be formed on-line and possess the minimum information density mecessary to describe the picture. Figure 21 shows the equipment used in the experiment. 5.2 Reconstruction A Fourier Transform on a pick-up tube suitable both for computer input and for use in reconstruction must contain both the phase and amplitude information of its image. This presents problems Figure 21. Experimental Apparatus since all light detectors are intensity or square-law devices. The class of functions which can be reconstructed from only the amplitude portion of their spectrum is quite limited. The Fourier Transform must be of constant phase and the input picture the mirror image of itself. One obvious way to preserve the phase is to add a constant bias term to the Fourier Transform. A constant bias transforms as a delta function at the origin. The latter is easier to implement. An unfortunate necessity is that this delta function pulse must contain as much power as the picture itself to successfully bias the transform (23) positive. 79 5.3 Television On-line pictures have also been transmitted through the system, the input video signals being picked up from commercial tele- vision stations. Each frame is written on the crystal and during the vertical blanking time it is read and erased. Noise may be added to the video signal and spatially filtered on-line. The video picture can also simply be focused onto the vidicon and displayed on a monitor. Even more important, they can be projected onto a larger screen. In this case the reading and erasing would occur simultaneously to avoid flicker and retention. Such a system, to be most efficient, would employ an arc lamp as the light source. Since the Fourier Transform is not needed neither is coherent light. A large screen television system is a prime desire of the military. Such television projection systems are much more efficient than present ones since the picture brightness is no longer determined by the energy of an electron as it strikes a phosphor, but rather is independent, being determined by the intensity of a separate light source. ^.h Adaptive Spatial Filtering A future project of the Hardware Research Group will be to create the filter as well as the spectrum on-line. Video transmissions in the presence of noise, such as in deep space exploration, can be accomplished or at least the picture to noise ratio enhanced consid- erably by an on-line spatial filtering system as described below. A nod i cli the camera lens) and arier Trai spatial filter for the . frame durin _d be open and both picture and noise transmitted. Such i of the translational invariance of the Fourier Tr noise which was periodic, constant or slowly varying. analysis of the types of noise spectra produced should iertafc before proceeding. Both the types of noise spectra expected they are additive or multiplicative needs to be determined. A color center crystal may be a possible transfer medi serve as the filter. Its advantage, besides its high resolutic. . that the filtering could be done optically and the phase content of t reconstructed picture thus preserved. An alternate system (should the light levels, read times and laser Q-switching required for the color center crystal prove unobtainat would be an electronic spatial filtering scheme in which the video signals of two Fourier Transforms are subtracted. The timing diagram for such a system is shown in Figure 22. In this case the Fourier Transform of the first or "noise frame" would be formed on the vidicon, stored, and its video signal subtracted from the video of the Fourier Transform of the second or "picture plus noise" frame. The resultant spatially filtered Fourier Transform would then be written on the electro-optic crystal and the spatially filtered image reconstructed by the same optical system that transformed it. Pursuant to this latter system as well as to provide the most versatile experimental system possible for exploring these diverse 81 NOISE WRITE NOISE OFF OFF SEE NOTE (in) SYNC I i I i < UJ I I I I I I OFF PICTURE PLUS NOISE SYNC RECONSTRUCTION (a)INCOMING VIDEO WRITE WRITE (b)OPERATING MODES PICTURE PLUS NOISE OFF FILTERED FT. (c) WRITE GUN OFF OFF OFF (d) LASER-BEAM SHUTTER I f i i OFF (e) ERASE GUN ' I I i SEE NOTE (i) SEE NOTE (ii) (f)VIDICON I I l 1 i STORE FT READOUT 0F N0| SE FT OF NOISE (g) STORE SYNC OFF (i) SCAN OFF FT OF NOISE AND PUT IN STORE (ii) SCAN OFF FT. OF PICTURE PLUS NOISE USING FT OF NOISE AND PUT RESULTANT VIDEO ON WRITE GUN Hli) SCAN OFF FILTERED RECONSTRUCTED PICTURE AND DISPLAY IT NOISE WRITE NOISE OFF OFF SEE NOTE (iii) SYNC 1 1 111 o < < Ld cr (£ UJ OFF M i i " i l i J IN STORE AS MASK Figure 22. Timing Diagram research areas, a spc: La] :torage tube was cc bed. tt ended, non-destructive readout device with video in] video information frame can be read in, stored for over t non-destructively read out and erased. These three operational can be selected by pulsing appropriate grids in the tub sync signals . This device was used in the experiment .to display selected television frames. Further detail., . storage tube, known as the Alphecon, will appear in future department quarterly reports . 5.5 Resolution Late in the project 0.005" thick crystals v;ere obtained, the resolution was notably improved to over 200 lines but was still not comparable to that of television. Higher resolution can be obtained with yet thinner crystals but these do not seem obtainable for many years. Larger crystals would also enhance the resolution, but the nonuni- formities present in the larger crystals grown to date as well as the increased thickness required to support them does not look promising. KD*P samples have consistently provided better resolution than comparable KDP assemblies. This can be attributed to the larger time constant of KD*P which permits less charge spread and to the lower voltages involved which tend to defocus the electron beam less. (2k) However, a detailed analysis of the electro-optic effect proves that the effective electrostatic crystal thickness is determined by the ratio of the dielectric constants. T' = ^J^iAoo where T' is the effective thickness and T the measured thickness. For KD*P /€-,-,/£-,-, = 1.1, while V H 7 33 83 for KDP /e,,/e.__ = l-^- This realization opens up new avenues of research and is the reason for the inclusion of the rather detailed electro-optic discussion of Chapter 3- Should KDP and KD*P crystals f~~ "I (25) be operated near their Curie temperature where l^ii/ e oo ~ 0.033 ', the effective crystal thickness would be reduced by a factor of 30 enabling thicker crystals to be used with a theoretical resolution of better than 1000 lines . The fantastic related advantages of ' • should be fully exploited. The crystal volta; by a factor of nearly 100. The theoretical time constant (using 66 and 67) for KDP at the Curie temperature (-1^0°C) is The vistas possible in such operations are unparalleled. By using the techniques described in section . . -ptical activity, natural birefringence, and thermal problems can be circui - vented and numerous other crystals made operable. Table 1 is a good reference for such selection. Protective coatings such as chiolite, chriolite, SiO and ZnS should be applied to the front surface to permit higher voltage gradients and to prevent the etching and overheating noted in section k.6. The dielectric constant of the coating should be such that most of the voltage is developed across the crystal, the time constant should be similar to that of the crystal used, the thickness should be X/^ to prevent reflections, and the secondary emission curve should be known or at least similar to that of the crystal used. The properties of these above four compounds are compatible with KDP crystals and their isomorphs. These investigations have produced a most versatile system. It is capable of writing, reading and erasing a target crystal on-line. The write gun current, the read time as well as the light intensity, and the erase time as well as the flood gun current are all separately variable. The chamber is demountable which increases its complexity but makes for a more versatile system. The system is designed to modulate either coherent or incoherent light and hence enable Fourier Transforms 85 to be generated on-line. As a research tool it is useful in the in- vestigation of the uncommon forms of information processing noted in section 5 as well as newer methods that future technology might dictate REFEREHl 1. W. J. Poppelbaum, "Computer Applications of Electr- Proceedings spring Joint Computer Conference , Yf 2. K. Preston, "Use of the Fourier Transformable Properties of lenc for Signal Spectrum Analysis, " Optical and Electro-Optical Information Processing, J. T. Tippett et al., Eds. Cambridge, Mass. Technology Press, 1965, Chapter h. 3« Spectra- Physics, Inc., Laser Technical Bulletin No. 1, "Optical Properties of Lasers as Compared to Conventional Radiators, " by Ac L. Bloom, Mountain View, Calif. k. A. Yariv, Quantum Electronics, John Wiley and Tons, New York, 1967 5« P. Butcher, Non-linear Optical Phenomena , Ohio State University, 1965- 6. M. Born and E. Wolf, Principles of Optics , Macmillan, New York, 7. G. Ujhelyi, Novel Electro-Optical Light Modulators, Report No. 170, Department of Computer Science, University of Illinois, October 26, 1964 c 8. Mo Born and E. Wolf, op. cite 9. C. Peters, "Gigacycle Bandwidth-Coherent-Light Traveling -Wave Amplitude Modulator, " Proceedings IEEE, Vol. 53, pp. ^55-^+60, May 1965. 10. Io Po Kaminow and E. Ho Turner, "Electro- optic Light Modulators, " Applied Optics, Vol. 5, pp. l6l2-l628, October 1966. llo Bo Billings, "The Electro-Optic Effect in Uniaxial Crystals of the type XH 2 P0, , " JOSA , Vol. 39, pp. 797-808, October 19^9- 12. W. Stoney, Electro-Optic Projector Study, Auto'-ietics Report C 6-1253/3^, June, 1966. 13. P. Schayer, "On the Mechanism of High-Velocity Target Stabilization and the Mode of Operation of Television-Camera Tubes of the Image- Iconoscope Type, " Phillips Research Reports , Vol. 6, pp. 135-153, 1951. 14. W. J. Poppelbaum, M. Faiman, D. Casasent, and D. Sand, "On-Line Fourier Transform of Video Image, " Letter in Proceedings IEEE, Vol. 56, pp. 17^-17^6, October 1968. 8 7 15- Personal Communications with Isomet Corporation, 1968. 16. J. Rider and S. Uslan, Encyclopedia of Cathode-Ray Oscilloscopes and their Uses , Rider, New York, 1959* 17. D. Casasent, Specifications for a Demountable Pockels Effect Tube, File No. 550-91> Department of Computer Science, University of Illinois, March 13, 1967. 18. CELCO, Inc., Conversion Computation for Deflection Yokes and Deflection Amplifiers, Data Sheet Y 2G, Celco, Mahwah, New Jersey. 19* W. Konzig, Solid State Physics , Academic Press, New York, 1957* Vol. h, pp. 14-16. 20. M. Von Ardenne, Tabellen der Electronenphysik, Ionenphysik, und Uebermikroskopie , Vol. 1., Berlin: Deutscher Verlog der Wrisenshapten, 1956, p. 202. 21. C. F. Pulvari, Letter in Electronics , February 28, 1964. 22. W. J. Poppelbaum, "Adaptive on Line Fourier Transform, " Pictorial Pattern Recognition , Thompson, 1968, p. 387-39^« 23. Quarterly Technical Progress Report, Section 1, Department of Computer Science, University of Illinois, Urbana, Illinois, April, May, June 1967. 2k. D. Sand, A Theoretical Analysis of the Modulation Characteristics of an Electro-Optic Light Valve, Report No. 303, Department of Computer Science, University of Illinois, Urbana, Illinois, to be published. 25. G. Bush, Helvetica Physica Acta, Vol. II, p. 269, 1938. VITA David Paul Casasent was born on December 8, 19^2, Washington, D.C. He received his B.3. in Electrical ring, ffr the University of Illinois in l'j6h, graduating with higl re and placing second as the Outstanding Senior in Electrical Engineering. Since then he has been a research assistant at the Department of Computer Science of the University of Illinois . In _ he obtained his M.S. He has assisted in the teaching and grading of many courses as well as in the establishment of a new demonstration course in Computer Science. He is a member of Eta Kappa Nu, Sigma Tau, and the IEEE. Form AEC-427 (6/68) AECM 3201 U.S. ATOMIC ENERGY COMMISSION U ^™o SITY_TYPE CONTRACTOR'S RECOMMENDATION FOR DISPOSITION OF SCIENTIF'J AND TECHNICAL DOCUMENT 1. AEC REPORT NO. coo- 146 9- 0120 I See Instructions on Reverse Side ) 2. TITLE AN ON-LINE ELECTRO-OPTICAL VIDEO PROCESSING SYSTEM 3. TYPE OF DOCUMENT (Check one): □ 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 Oc- Other (Specify) Ph.D. Thp,