Phase stabilization system for holographic opticaldata processing

Clark C. Guest and Thomas K. Gaylord

Routine passive techniques such as temperature and air current control are frequently not adequate to pro-vide interference fringe stabilization in holographic optical data processing experiments. A successful ac-tive phase stabilization system that can be adapted to a variety of experimental configurations is described.It utilizes a synchronous lock-in amplifier and an electrooptic phase modulator to provide real-time stabili-zation of the interference fringe pattern. Both a video detection method and a direct optical detectionmethod are experimentally evaluated in conjunction with the phase stabilization system.

1. Introduction

A problem common to all coherent systems that uti-lize the interference of two or more beams is fringestability. Interference fringes can exhibit short-termjitter, long-term drift, or both. Such effects may merelybe a nuisance, or they may, for example, obscure a ho-lographic recording or confound an interferometricmeasurement. Sources of fringe instability includethermal expansion of optical components, laser wave-length drift, mechanical vibration, and fluctuating aircurrents. Each of these sources can be controlled tosome extent by appropriate passive means; e.g., use ofthermally insensitive designs and materials, optical pathlength equilization, vibration isolation techniques, andshielding from air currents. However, aspects of theoptical system may inhibit use of these common meth-ods, or residual fringe instability may remain in spiteof the best efforts for elimination.

In such cases, use of an active fringe stabilizationsystem should be considered. Neumann and Rose'reported one of the first such systems. They used amagnified image of the holographic fringes to providean optical feedback signal. This was converted to anelectronic signal that controlled a piezoelectricallydriven mirror to alter dynamically the path length ofone of the beams. Rose and Pruett 2 subsequently re-

C. C. Guest is with University of California at San Diego, Depart-ment of Electrical Engineering and Computer Science, La Jolla,California 92093. T. K. Gaylord is with Georgia Institute of Tech-.nology, School of Electrical Engineering, Atlanta, Georgia 30332.

Received 1 February 1985.0003-6935/85/142140-05$02.00/0.© 1985 Optical Society of America.

ported a variation on this system by using the feedbacksignal to control the laser wavelength. MacQuigg3

presented a more sophisticated system using a speciallyfabricated phase control grating and a lock-in amplifier.The active fringe stabilization system to be consideredin this paper combines aspects of the previous methodswith novel methods of obtaining a feedback signal andprocessing it electronically. Experimental results willbe presented, and a comparison with previous systemswill be made.

11. Fringe Stabilization System

The need for an optical fringe stabilization systemarose during the experimental investigation of an opticalholographic digital parallel processor.4 The processoris designed to perform a truth-table lookup operationby detecting matching patterns between binary opticalinput data and truth-table information recorded asthick phase holograms in lithium niobate crystals.Matching patterns are detected by causing destructiveinterference to create an optical Boolean EXCLUSIVEOR operation between the direct image of the input dataand the holographically reconstructed image of thestored truth-table data. The bit error rate (BER) of theprocessor is optimized when the contrast between brightoptical true outputs and dark optical false outputs isgreatest. This requires that the amplitudes of the in-terfering wave fronts be equal and that their phasesdiffer by 180°. Producing a constant amplitude ratiois relatively easy, but maintenance of the proper phaserelationship is susceptible to all the effects listed in theprevious section. Passive measures proved to be in-adequate to obtain satisfactory phase stability, neces-sitating the incorporation of an active fringe stabiliza-tion system.

This phase stabilization task differed from commoncases in that the angle between the paths of the inter-

2140 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985

Fig, 1. Optical experimental system for EXCLUSIVE OR optical dataprocessing and fringe stabilization experiments. Arrangement shownis for video signal output detection: AL, argon laser; BS, beamsplitter; CA, compensated attenuators; E, electrooptic crystal; EA,electronically controlled amplitude modulator; EP, electronicallycontrolled phase modulator; ES, electronically controlled shutters;L1 , focusing lens; L2 , collimating lens; L 3 , L 4 , Fourier transform lenses;M, data mask; M1 , M2, M3, mirrors; 0, object beam path; P, pinholeaperture; PR, polarization rotator; R, reference beam path; V, video

camera.

BeamsptitterElectrooptic

Lens ~~~~~~Vide C-.r

H Optical P.., Meter

ChartRecorderOutput

Fig. 2. Detail of modification to optical system for using direct op-tical detection.

fering beams was nominally 00. Optimizing the BERof the processing system was equivalent to producinga single uniform dark fringe across the extent of theoutput plane. Therefore, a phase control feedbacksystem that maintained the minimum total power in theoutput plane was needed. Methods of applying thefeedback system to more conventional problems withmany light and dark fringes will be presented in a sub-sequent section.

The optical system used in the experiments is shownin Fig. 1. An electrooptic phase modulator was alreadypresent in the reference beam path to provide a 1800

NONCOMPOSITEVIDEOSIGNAL

phase shift between the imaged and reconstructed wavefronts. The phase control feedback signal was summedto the dc voltage applied to this modulator. Two dif-ferent methods of detecting the output of the optical'system were investigated. Figure 1 shows the systemused for the video signal feedback method; Fig. 2 showsthe system for the direct optical detection method. Forthe video signal method, the video camera alreadypresent as the data collection device at the output planeof the processing system was used. The noncompositevideo signal from this camera was tapped to provideinput to the low-pass filter present on the input of thelock-in amplifier. By selecting a time constant for thefilter that was longer than the video frame time, 1/30thsec, the spatial average of the intensity over the entireimage was obtained. Problems encountered with thisarrangement included a large video noise componentmasking the signal of interest and the upper bound onthe frequency response of the stabilization system im-posed by the video frame rate. With a slight compli-cation of the optical system, the integrated intensityoutput could be measured more directly. A beamsplitter diverted a portion of the output image to a fo-cusing lens and onto the photodetector of an opticalpower meter. The chart recorder output of the powermeter was then used as the input signal for the stabili-zation system. This alleviated to a large extent thefrequency response restrictions on the system but de-creased optical power available to the video camera,took up valuable optical table space, and, due to thebeam splitter, produced a distortion in the output imageseen by the video camera. The results obtained witheach method will be compared in a later section.

The electrical portion of the active phase stabilizationsystem consisted of a synchronous lock-in amplifier(Princeton Applied Research model 186A), a speciallydesigned integration and summing circuit, and a high-voltage operational amplifier (op amp) power supply(Burleigh model PZ-70); these are shown in Fig. 3. Thesumming circuit, which Fig. 4 shows in detail, alloweda dc bias voltage to be set to give the nominally correctphase retardation by the modulator. A sinusoidalreference signal provided by the lock-in amplifier wasconverted by the summing circuit to a square wave andthen added to the bias voltage as a dither signal. The

DITHERAMPLITUDE DC

100K OFFSET

10K

TOPHASE

MODULATOR

Fig. 3. Block diagram of the phase stabilization system.

15 July 1985 / Vol. 24, No. 14 / APPLIED OPTICS 2141

TOOTHERVIDEO

EQUIPMENT

Fig. 4. Electronic integration and summing circuitry for the interference fringe stabilization system.

amplitude of the dither signal was adjusted to providea h15' phase shift about the nominal setting. Visually,this produced a barely perceptible variation in the ob-served optical intensity. The dithering technique wasrequired since the purpose of the system was not tocontrol the output intensity to one particular value,which a common negative feedback system would do,but to control the output to the minimum possiblevalue, whatever that might be. The dither is a way ofsearching for values lower than the one presently ob-tained. The modulated output intensity was detectedby one of the two means discussed above, and the re-sulting electrical signal was applied to the input of thesynchronous lock-in amplifier. The function of a syn-chronous lock-in amplifier is to detect and amplify onlythe portion of its input signal that is in phase with (apossibly phase-shifted version of) its reference signaloutput. This can be expressed mathematically as

tV(t) = A fo Vi(T) cos(cLrr + or) exp[-B(t - r)]dT, (1)

where V(t) is the output voltage of the lock-in amplifierVi (t) is the input voltage of the lock-in amplifier, COr isthe radian frequency of the reference oscillator, and A,B, 0

r are adjustable constants. In a practical sense, thisallowed the stabilization system to recover only theoscillations in the optical output intensity due to thedither signal, even in the presence of a very largeamount of noise. The magnitude of the output of thelock-in amplifier was proportional to the phase errorbetween the two beams of the optical system. Fur-thermore, the output was positive for an error in onedirection and negative for an error in the other direction.The principle leading to these properties is demon-strated in Fig. 5. The output of the lock-in amplifier

may be thought of as the time average of the product ofVosc and V. If the bias voltage is far from producingthe minimum output intensity [Fig. 5(a)], V, has astrong positive lobe. As the bias is corrected toward theminimum intensity condition [Fig. 5(b)], the asymmetryof V, decreases. When the minimum intensity isachieved [Fig. 5(c)], V, has twice the frequency of Vosc;therefore, the output of the lock-in amplifier would bezero. If the bias deviated from the minimum in theopposite direction, V, would become increasingly neg-ative.

The output voltage of the lock-in amplifier was in-tegrated before being summed to the phase modulatorbias voltage. The integration provided compensationfor the finite gain of the feedback system. Withoutintegration, some small error would exist at steady state;integration allowed even small errors to be compen-sated. Other useful functions served by the summingcircuitry were adjustment of dither signal amplitude,adjustment of feedback gain (including a switch foropen-loop operation), and a switch for resetting theintegrator.

In operation, the initial conditions for the feedbacksystem were dither signal off, open loop operation, andintegrator reset. The bias voltage control was adjustedto produce a visually good null output. Then the ditherwas turned on, the feedback loop closed, and the inte-grator started. The system was able to follow bothshort-term phase fluctuations and long-term drift.Occasionally, the phase drift would require a feedbackvoltage beyond the capability of the high-voltage powersupply. At these times it was necessary to reset thesystem to produce a phase 2r rad from the one it wasfollowing. The time response of the system to short-

2142 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985

v IV

vps

vosc

vv

vps

vosc

(a) (b) (c)

Fig. 5. Fringe stabilization sequence. The average video signal voltage V, shown as a function of phase shifter voltage Vp, with a dithervoltage present for an average voltage (a) far away, (b) slightly away, and (c) at the minimum video signal voltage level.

term fluctuations vs the feedback stability of the systemcould be adjusted with the feedback gain control.

Ill. System Performance

The system performance using the video detectionand the direct optical detection methods describedabove was measured and compared. The lock-in am-plifier output signal, proportional to phase error, anda signal proportional to the spatially integrated opticaloutput intensity were plotted for each arrangement.These plots are shown in Fig. 6. The superiority of thedirect method is evident. In terms of the experiment,both systems were able to eliminate the very undesirablelong-term phase drift that had been observed previ-ously. Of the two methods, direct feedback producedexperimental results with less statistical deviation.

IV. Application to Other Optical Systems

The conditions described above, where the optimumphase relationship corresponds to the minimum totaloutput itensity, should find application in imagesubtraction and optical information processing but isnot the most common arrangement for interferometricsystems, Usually the interfering beams intersect at anonzero angle producing many bright and dark fringes.The relative phase of the beams affects the position ofthe fringes but not the total output intensity. Thephase stabilization feedback system described in thispaper can be adapted to work with these more commoncases as well. Obviously, what must be done is to limitthe region of output detection to the desired positionof a dark fringe.

One such application occurred in a subsequent opticalprocessing experiment. Again, it was important tostabilizethe relative phase of two beams. In this case,one beam was a plane wave and the other a convergingspherical wave. A portion of both beams was split off,and they were brought together at a zero relative angle

PHASE ERROR SIGNAL1.0- (Volts)

0.5-

0.0 \

CHANGE INOPTICAL OUTPUT INTENSITY

10 sec

2 - (arbitrary units)

14

(a) I-1 110 sec

1.0-

0.5-

0.0-

2-

ii-

PHASE ERROR SIGNAL(Volts)

IA10 sec

CHANGE INOPTICAL OUTPUT INTENSITY

(arbitrary units)

lb)10 sec

Fig. 6. Comparison of output intensity and phase error signals for(a) video feedback method and (b) direct optical feedback method.

with a beam splitter, as shown in Fig. 7. The resultinginterference pattern of concentric circles was magnifiedusing a traveling microscope. The central spot of themagnified pattern was selected with a round aperture,

15 July 1985 / Vol. 24, No. 14 / APPLIED OPTICS 2143

Prismed Light

PHOTODETECTOR

1..RTRAVELLINGMICROSCOPE

Fig. 7. Arrangement for monitoring the relative phase of object andreference beams when circular interference fringes are produced.

Deep in the heart of the crystal

a facet--five, a thousand--

throw back a thousand prismed glows

in a thousand golden tones.

Each one sent forth takes life,

then whirling and leaping,

sings in shouted disharmony

as it bounds from mirrored wall

to window pane. to door, to passage,

and the photodetector of an optical power meter wasplaced behind the aperture. Otherwise, the feedbacksystem was unchanged and controlled the relative phaseof the beams to produce a minimum intensity in themonitored spot. Stabilization of a linear fringe patterncould be affected in a similar way by replacing the cir-cular aperture with a slit and possibly a focusing lens toperform spatial integration.

V. Comparison and Summary

The active phase stabilization system that has beenpresented was developed to meet the needs of a par-ticular optical data processing experiment. The systemdesign, however, is quite general and can be applied toa range of experimental situations. It utilizes the sen-sitive synchronous detection scheme presented byMacQuigg3 but adopts the simpler approach to condi-tioning the optical feedback signal used by Neumannand Rosel of using a slit aperture or, when the inter-fering beams are coaxial, no preconditioning at all.Most notably the monitoring grating in MacQuigg'sscheme that must be specially fabricated for each op-tical arrangement is avoided. In this latter case, thesame detector used to collect experimental data can beused for fringe stabilization. Experiments were con-ducted to evaluate the stability achieved alternatelyusing a video camera and an optical power meter as theoutput detector. The power meter arrangement, whileadding slightly to the complexity of the optical system,was shown to provide the best stability results.

References1. D. B. Neumann and H. W. Rose, "Improvement of Recorded Ho-

lographic Fringes by Feedback Control," Appl. Opt. 6, 1097(1967).

2. H. W. Rose and H. D. Pruett, "Stabilization of Holographic Fringesby FM Feedback," Appl. Opt. 7, 87 (1968).

3. D. R. MacQuigg, "Hologram Fringe Stabilization Method," Appl.Opt. 16, 291 (1977).

4. C. C Guest, M. M. Mirsalehi, and T. K. Gaylord, "EXCLUSIVEOR Processing (Binary Image Subtraction) Using Thick FourierHolograms," Appl. Opt., 23, 3444 (1984).

and back again.

The air is filled with darting beams

seeking out the hidden corners,

slipping behind the mirrors,

under lamps and through the curtains

till nothing is undiscovered,

nothing hides in darkness.

Then slowly settling,

each finds its spot;

Some slip through the window,

others round the door;

one settles in the curtain.

another on a golden head.

And there they wait

for a breeze, a curtain lifted.

an open door,

to set them wildly dancing

in another weaving ecstasy

of prismed light.

Peggy Hale Bilbro

4/81

2144 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985