Evaluation of PROM characteristics

George J. M. Aitken and Randolph Balaberda

Sensitometry and the spatial-frequency response of a PROM SLM are evaluated with special emphasis onpositive-mode operation. Spatial uniformity, the effects of crystal strain, and the readout decay character-istics are examined. The positive mode is 100 times more sensitive and has better linearity than the negativemode, but the spatial bandwidth is less by a factor of 0.17. Spatial variations of crystal strain cause devia-tions in y of as much as 42% of its strain-free value.

1. IntroductionA Pockels readout optical modulator (PROM)1-3 was

experimentally evaluated for use in a coherent opticalcomputer which processes Doppler-shifted emergencysignals in a satellite-based crashed-aircraft locationsystem.4 The spatial light modulator (SLM) is theoptical input device onto which a set of 1-D signals iswritten in parallel by a modulated laser beam. The ItekPROM evaluated in this study has a 2.5-cm diam crystal800 Am thick coated with 6-,um thick parylene layers oneach face. The surfaces of the bismuth silicon oxide(BSO) crystal have a wedge angle of 0.250 and a flatnessof X/10 rms. Results reported here were obtained withwriting and reading wavelengths of 0.458 and 0.633 ,um,respectively. The PROM was operated as an amplitudemodulator with a polarizer-analyzer combination in thereadout path. Only readout in transmission wasstudied in detail because of the rather severe astigma-tism found in reflection.2 In all measurements in-volving spatial sampling or scanning of the output, thePROM was moved past the aperture or probe so thatthe optical path external to the PROM was constant.Positive-mode operation, which has not received at-tention in the literature, was measured along with theusual negative mode.

II. Sensitometry DataSensitometry data were gathered by measuring the

zero-order intensity in the Fourier output plane with:a fiber-optic probe of diameter ten times the radius ofthe first zero in the diffraction pattern. A 5-mm diam

The authors are with Queen's University, Department of ElectricalEngineering, Kingston, Ontario K7L 3N6.

Received 26 September 1983.0003-6935/84/060901-04$02.00/0.C) 1984 Optical Society of America.

aperture corresponding to 4% of the total PROM areawas used to define local regions on the surface of thePROM. The solid lines in Fig. 1 are measured sensi-tometry curves for positive and negative modes of op-eration in a strain-free and a strained region of thePROM with an applied voltage of 2000 V. In principle,the curves of one mode can be obtained from those ofthe other; however, the two sets of curves show clearlyhow imperfections such as crystal strain can causeperformance to depart from the ideal.

Because BSO exhibits the piezoelectric effect, crystalstrain creates an internally generated voltage V, acrossthe crystal. The output intensity from a strained areareceiving a uniform unit exposure is

I = (1 - X) sin2 ((7r/2Vh)jVd[D(E) - B] + Vj) + X, (1)

where X is the extinction ratio of the polarizer-analyzercombination, Vh is the half-wave voltage, Vd is theinitial voltage across the crystal, D(E) is the relativedistribution of voltage across the crystal as a functionof exposure E, and B is the base-line subtraction factor.The factor B is 0 for the negative mode and unity for thepositive mode. V will have a noticeable effect whenVd [D (E) - B] is small, that is, for high exposures in thenegative mode and low exposures in the positive mode.In the exposure ranges where [D(E) - B] is zero, Eq. (1)gives

IV I = (2

Vh/7r) sin-l[(I - X)/(1 - X)]112 (2)

The value of X in the strained region is the output at thedip in the positive-mode curve, while I is the value atzero exposure in the positive mode or at infinite expo-sure in the negative mode. In the example shown, theestimated strain voltage is 75 ± 24 V. Strain voltage hasbeen defined with the same polarity as Vd; thus, positiveV, adds to crystal voltage in the negative mode andsubtracts from it in the positive mode. When D(E),estimated from the strain-free sensitometry data, andVS = 75 V are combined in Eq. (1), the calculated curves

15 March 1984 / Vol. 23, No. 6 / APPLIED OPTICS 901

200C

il ~ ~ ~~~I il IIfill

-I 0 __ 2aW

10 10 10 10

EXPOSURE (ILJ/cm2)

Fig. 1. Positive- and negative-mode sensitometstrain-free and strained regions of a PROM: circltriangles, strained; dashed curves, computed for a st:

the same magnitude but opposite polaril

input modulation indices, the fractional output inten-sity is proportional to y times the fractional input in-tensity,5 it is clear that variations in y due to crystalstrain can be a significant source of variation in thePROM's transmittance.

VOLTS Spatial uniformity of the transmittance and the strainvoltage were examined by scanning the minimum out-put and zero-exposure output in the positive mode witha 3-mm aperture. Note that nonuniformity of thecrystal structure limits the minimum output by causinga spatially variable permanent Pockels effect. Theminimum output, normalized with respect to the max-

- a_... * imum under the same conditions, varies gradually andsmoothly from 2 X 10-4 on one side of the crystal to 9X 10-4 at the other side, where it rises abruptly to 1.4

1Lw±L 3 11i4 X o-3 at the edge. For comparison, the operating0' 10, point defined as the inflection point in the strain-free

curves of Fig. 1 is at 10-2 of maximum, and in the centerry curves for of the aperture the minimum is 0.5 X 10-4. Estimatedes, strain-free; strain voltage varied from essentially 0 to 75 V and wasrain voltage of always positive, with the highest values occurring in the;y. central area of the crystal. The maximum strain volt-

age creates a phase shift of 1.70.

10-2

UzL'IV

U-

U.UI

lo-4

I-Ua:IcU.

01-5

FIRST ORDER---- SECOND ODER

i b- s s ' X

" \

,I .1I 10 100

FREQUENCY (cycles/mm)

Fig. 2. Positive-mode diffraction efficiency as a function of exposure.Curves a, b, c, and d correspond to modulation indices 0.85, 0.71, 0.47,and 0.24, respectively. Dashed curves are the second-order

intensities.

for the strained region are in good agreement with themeasured ones, which suggests that the principal factorcausing the sensitometry variations is crystal strain. InFig. 1, the curves computed for a strain voltage of po-larity opposite to that found in the PROM studied hereare shown as dashed lines. For the regions whosemeasured curves are depicted in Fig. 1,7y at a positive-mode bias of 2 itJ/cm 2 is 1.9 in the strain-free region and2.7 in the strained one. At a negative-mode bias of 200yuJ/cm

2, is -1.7 and -1.3 in the strain-free andstrained regions, respectively. Recalling that, for small

Ill. Spatial-Frequency ResponseBecause evaluation tests should be conducted under

conditions that approximate as closely as possible thoseof the intended application, the exposure biases in ourtests were constant at the values which yielded y asclose to 2 as possible, that is, 2 1uJ/cm 2 in the positivemode and 200 ,gJ/cm2 in the negative mode. A Mach-Zehnder interferometer in the write-light path provideda sinusoidal exposure. with variable spatial frequency,bias, and modulation. Zero, first, and, where strongenough, second orders were measured in the Fourierplane and corrected for the zero-order scatter, whichwas determined experimentally. Diffraction efficiencyi7 in a strain-free region was computed as a function ofspatial frequency.6 In the negative mode the resultswere similar to those reported by others: the 50%bandwidths f.5 were 6, 11, 12, and 14 cycles/mm formodulation indices m of 0.85, 0.71, 0.47 and 0.24, re-spectively. Only for m = 0.24 was the second-orderterm <1% of the first over a significant band offrequencies. Figure 2 shows the positive-mode re-sponse. All the curves have /O.5 = 1.8 cycles/mm. Thelinearity inherent in a positive replica of the input ex-posure is clearly demonstrated with second-order termsof <1% of the first-order terms at all values of m except0.85. It is interesting to note that the ratio of second-to first-order diffraction terms increases with spatialfrequency in the negative mode, while the reverse is truefor the positive mode. Above 11 cycles/mm in thenegative mode and above 2 cycles/mm in the positivemode, -q is proportional to f4 as predicted by Owechkoand Tanguay.7

An apparent increase in MTF width with increasingexposure has been noted in a number of articles on thePROM. To gain some insight into this phenomenon,the PROM's output was observed during exposure toa sinusoidal intensity. A narrowband interference filter

902 APPLIED OPTICS / Vol. 23, No. 6 / 15 March 1984

-II'10

I-

Z

N

a:

2

o0tL3

0-3[

10

101

blocked the write light so that writing and reading couldtake place simultaneously. The first diffracted orderwas recorded as a function of time, while the source in-tensity was held constant. These observations werecorrected for the exposure-dependent zero scatter andfor the (sine)2 function relating crystal voltage to outputintensity. The correction factor is

dA 2 ir (C VdD(E)]2 (3)

dV I2Vh

which on normalizing with respect to its value at E = 0and inserting the values for Vd and Vh reduces tocos2[1.22 D(E)]. The first-order diffraction, normal-ized with respect to this factor, is shown in Fig. 3 as afunction of E for input spatial frequencies of 1-64 cy-cles/mm and input m = 0.47. At low spatial frequenciesthe general behavior with increasing exposure is a rapidrise to a peak followed by a gradual decline. In the casesof 16, 32, and 64 cycles/mm the peak had not beenreached in the exposure range of the experiment. Forthe curves exhibiting a peak, the maximum diffractionefficiency is directly proportional to f-1. The spatialfrequency response of the device can be visualized atany exposure by cutting vertically across the curves. Atlow exposure of the order of 20 ,uJ/cm 2, it is clear thatthe frequency response will be poor, since the lowest-frequency components have reached their peaks but thehigher-frequency components are quite weak. At arelatively high exposure of, say, 200,uJ/cm2, the low-frequency components have declined in strength, whilethe high-frequency ones have increased.

An explanation of this phenomenon may be found inthe effect of longitudinal charge distributions throughthe BSO crystal as described in Ref. 7. When photo-generated charges are swept to the faces of the crystalby the electric field, the sinusoidal spatial distributionof crystal voltage V(f) exhibits a gradual roll-off pro-portional to f'1. If the charge layers are located within

_ ~~~~~~~~~FREOUENCY cyclAW..)

I0

°J 10- 6

10-7L l I l l l l l l l l l l l l l l

0 50 100 150 200BIAS EXPOSURE (/CM2)

Fig. 3. Normalized first-order intensities as functions of exposurewith spatial-frequency as a parameter. The modulation index is

0.47.

Table I. Spatial Variation of Diffraction Efficiency

Frequency Mod. Zero order q MTF(cycles/mm) index A% A% A%

4 0.71 22 15 411 0.71 18 14 332 0.71 12 19 11

4 0.47 22 26 1111 0.47 13 17 532 0.47 11 10 10

the crystal a small distance from the faces, V(f) is de-creased somewhat, and the roll-off approaches f-4. Anasymmetric distribution of charge also decreases V(f),and when the distribution extends past the midpointof the crystal, V(f) is depressed a greater amount at thelow frequencies than at the intermediate or highfrequencies. Thus, as the exposure increases and theaverage voltage across the crystal decreases, the fieldinducing the charge separation decreases. The pho-togenerated charges gradually form a longitudinal dis-tribution extending well into the BSO. As this occurs,the low-frequency components of the voltage patternare diminished, while the components at higherfrequencies are not as greatly affected. The overalleffect is a broader MTF function.

The uniformity of the spatial-frequency response waschecked by measuring -j for five 5-mm diam regionslocated at the center, 8 mm to either side and 8 mmabove and below center. Table I gives the results ofmeasurements at 4, 11, and 32 cycles/mm with modu-lation indices of 0.71 and 0.47. The variation in j overthe PROM surface is typically +15% of the averagevalue. The zero-order variation is consistent with a±20% variation observed in scans of the maximumtransmission with uniform exposure.

IV. Readout Time ConstantsIt is well known that the small but not negligible

photoconductivity produced in the BSO by the readlight causes the stored image to decay slowly duringreadout. In our tests it was observed that the decaytime increased with increasing spatial frequency. Thisis not surprising, because the readout decay mechanismis fundamentally the same as the recording process.Thus, high spatial frequencies which require thelarger-exposure energies to achieve a given in re-cording also need relatively larger readout energies tocause the recorded image to decay to a given level. Forexample, read-light energies at 633 nm which cause theoutput amplitude of the recorded sinusoidal pattern todrop by exp(-1) are 5 X 103, 9 X 103, and 28 X 103AuJ/cm 2 at spatial frequencies 1, 10, and 40 cycles/mm,respectively, in the negative mode. In the positivemode, the corresponding result is read-light energies of0.6 X 103 and 2.6 X 103 1uJ/cm 2 at 1 and 10 cycles/mm.This phenomenon raises the interesting possibility ofincreasing the MTF width of the PROM by a postre-cording exposure to the read light before actuallyreading the output information. A modest sharpeningof detail in a USAF resolution chart was observed dur-ing readout. However, the read-light energy also lowers

15 March 1984 / Vol. 23, No. 6 / APPLIED OPTICS 903

the output signal level which, if carried too far, causesa decrease in the SNR contrast. On the other hand,readout must take place in an interval short comparedwith decay time constant if the recorded image is not tobe altered.

V. DiscussionStrain causes important spatial variations in the

sensitometry response which, through a spatiallyvarying y, will introduce significant fluctuations intransmittance. Deviations from the strain-free valueof y have been observed to range up to 42 and 23% in thepositive and negative modes, respectively. Positive-mode operation offers good sensitivity and a high degreeof linearity. Unfortunately, the spatial frequencybandwidth is -0.17 of the negative-mode bandwidth.With improved PROM construction, a useful posi-tive-mode bandwidth may be possible. Nevertheless,it is clear that high spatial resolution requires light en-ergy. Thus, a low-level mode of operation will always

be a lower-resolution mode. In readout, the differentialspatial-frequency response manifests itself as a fre-quency-dependent decay time constant. Continuousor repeated reading, as might be required of a recordedfilter function in a pattern recognition system, will alterthe spatial-frequency content of the stored image.

This work was supported by grants from the IBMCorporation and the Natural Sciences and EngineeringResearch Council.

References1. S. L. Hou and D. S. Oliver, Appl. Phys. Lett. 18, 325 (1971).2. S. G. Lipson and P. Nisenson, Appl. Opt. 13, 2052 (1974).3. B. A. Horwitz and F. J. Corbett, Opt. Eng. 17, 353 (1978).4. G. J. M. Aitken and D. T. Cassidy, Appl. Opt. 19, 2490 (1980).5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill,

New York, 1968).6. D. Casasent, Appl. Opt. 18, 2445 (1979).7. Y. Owechko and A. R. Tanguay, Jr., Proc. Soc. Photo-Opt. Instrum.

Eng. 218, 67 (1980).

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904 APPLIED OPTICS / Vol. 23, No. 6 / 15 March 1984