Diffraction efficiency dependence of holographicsubtraction interferometry in Fe:LiNbO3

R. Magnusson, X. Wang, T. D. Black, and L. N. Tello

Experimental results on holographic subtraction interferometry in photorefractive lithium niobatecrystals are presented. The dependence of the subtraction operation on the hologram diffractionefficiency has been measured for both single holograms and angularly multiplexed holograms. Exampleresults from heat transfer and acoustics are presented.

Key words: Holographic subtraction, interferometry, photorefractive materials.

Introduction

In 1965 Gabor et al. showed that optical imagesubtraction can be accomplished holographically byintroducing a wr phase shift in the reference beambetween the two exposures.' Their holograms wererecorded on holographic plates. Ten years laterHuignard et al. employed this technique to imple-ment coherent subtraction of images by using photo-refractive crystals.2 The procedure is first to recorda Fourier-transform hologram of a given scene in aphotorefractive crystal and then to record a superim-posed Fourier transform with similar amplitude ofanother scene but with a phase shift of r in thereference beam. The result is the production of arefractive-index grating complementary to the grat-ing that constitutes the first hologram. Reconstruc-tion reveals that parts that are common to bothscenes have been erased. On binary data this corre-sponds to the exclusive OR logic operation. Also, ithas been demonstrated that any given hologram (oreven a specific part of that hologram) in a stack ofangularly multiplexed holograms can be selectivelyerased. This is called coherent selective erasure.2Using the same basic principle, Trolinger has demon-strated that holographic subtraction interferometrycan work well.3 He used a system with two referencebeams and applied the phase shift during reconstruc-tion. Guest et al. have successfully employed similar

The authors are with the University of Texas at Arlington,Arlington, Texas 76019; R. Magnusson and X. Wang are with theDepartment of Electrical Engineering; T. D. Black and L. N. Telloare with the Department of Physics.

Received 9 October 1991.0003-6935/92/ 173350-04$05.00/0.i 1992 Optical Society of America.

ideas for binary image subtraction or exclusive ORprocessing.4 A real-time approach to optical imagesubtraction has been presented by Yeh et al. 5

Here we present experimental results that wereobtained for holographic subtraction interferometryin photorefractive crystals. The efficiency of theholographic subtraction is quantified with respect tothe diffraction efficiency of the superimposed holo-grams. It is found that good subtraction is realizedeven for diffraction efficiency exceeding 5%. As ex-pected, the best results, namely, cancellation of thegratings, are found for diffraction efficiencies of theorder of 1% and lower. The results pertain to singleholograms as well as to angularly multiplexed holo-grams. As an example of the use of subtractioninterferometry for practical applications, results fromheat transfer and acoustics are given that indicate anenhanced signal-to-noise ratio that is realized by thesubtraction operation, with Fourier-transform holo-grams used in this case.

Experimental Results

The experimental arrangements that we used areshown in Fig. 1. The system in Fig. 1(a) is used toevaluate the quality of the erasure. An argon-ionlaser operating at 0.514 [km is used to write holo-grams in the lithium niobate crystal (crystal size 10mm x 10 mm X 2 mm; 0.05-mol % iron doped). Thebeam is divided into the object beam S and thereference beam R, and the reference beam passesthrough a phase modulator that can introduce a rphase shift. The angle between the recording beamsis 300. A beam from a He-Ne laser incident at itsBragg angle is used to monitor the diffracted power ofthe photorefractive-index grating. All beams arepolarized orthogonal to the plane of incidence. For

3350 APPLIED OPTICS / Vol. 31, No. 17 / 10 June 1992

10ELECTRONICSHUTTER

U

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Fig. 1. Experimental arrangements used: (a) to evaluate thequality of the erasure, (b) for holographic subtraction interferome-try.

practical applications with real objects the system ofFig. 1(b) is employed.

Figure 2(a) shows the measured diffraction effi-ciency -q (diffracted light power divided by inputpower less power reflected off the crystal) for fiveindividual holograms that are recorded in differenttransverse crystal locations with different exposuretimes. Each hologram exposure is followed by anequal period of subtraction (i.e., a second recordingwith a Tr phase shift). Ideally, the diffraction effi-ciency should return to zero, and the straight linesthat connect the initial point (at t = 0), the peak valueof -q (at t = T), and the final value of -j (at t = 2T)should form an isosceles triangle. Initially the dif-fraction efficiency q increases as a function of theexposure time in accordance with the expression fromKogelnik's theory 6 that is given by q = sin2 y, withy = rnld/ cos 0, where n, is the amplitude of thesinusoidal-index modulation, d is the thickness of thecrystal, X is the free-space wavelength, and 0 is theinternal readout angle. As the material saturates,these oscillations are found to dampen out.7 In Fig.2(a) only one data point per hologram is shown for therecording step, which results in the line segmentsshown. However, each of the data points for the fiverecorded holograms lies on the sin2 y curve. 6 Attime T, given in the Fig. 2 insets for the variousholograms, the second exposure is applied. Since a ,r

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Fig. 2. Hologram diffraction efficiency characteristics during thefirst exposure followed by the rr phase shift and the secondexposure: (a) holograms in different transverse crystal locations,(b) angularly multiplexed holograms. T is the hologram recordingtime before phase shift is applied, and e is the crystal rotation anglein degrees.

phase shift is supplied by the modulator, a refractive-index grating complementary to the grating thatconstitutes the first hologram is produced. There-fore the diffraction efficiency drops from the peaklevel to a minimum value. The smaller this mini-mum value is, the more effective the subtraction.In Fig. 2(a) holograms 1 and 2 are seen to beidentically canceled, whereas holograms 3 and 4 arewell erased but with some residual diffraction effi-ciency remaining. Hologram 5 is reduced only by- 50% by the second exposure.

In Fig. 2(b) the erasure efficiency is similarlyquantified for angularly multiplexed holograms (allholograms in the same transverse crystal location)that are spaced at 10 angular intervals. Again the

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holograms are recorded for T seconds with a r phaseshift applied at that time. The angle + is the crystalrotation angle referenced to the angle that corre-sponds to hologram 1. The hologram angular spac-ing is chosen to be quite large (AX = 1); indeed, nocross talk between the holograms is observed. Notethat saturation is beginning to affect the results forthe two holgrams with the highest diffraction effi-ciency, which were written last.

In Fig. 2 the subtraction exposure that we used isthe same as that used to record the initial hologram.Additional exposure was not found to improve thesubtraction appreciably. The total recording beampower incident upon the crystal (split 50/50) for theseexperiments [Figs. 2(a) and 2(b)] was 2.88 W/cm2.

The analytical expression = sin2 y can now beused to estimate the maximum modulation amplitudeof the refractive index that permits good subtraction.Taking the maximum efficiency for effective subtrac-tion to be 5% as supported by these experiments,we see that the corresponding maximum index modu-lation amplitude is nma, = 10-3.

The experimental arrangement for holographic sub-traction interferometry is shown in Fig. 1(b). Forthe heat transfer example the test object is a short-length coil that is heated up between the two expo-sures with a 20-V applied voltage. If two equalexposures are made, the first exposure for a coldobject and the second exposure after the object isheated, the reconstruction will give a heat transferpattern [Fig. 3(a)]. If a r phase shift is introduced(with the phase modulator) between the two expo-sures, the background and the parts that are notchanged by the heating will be erased, and only

(a)

(a)

(b)Fig. 3. Holographic subtraction interferometry: (a) without irphase shift between the two exposures; (b) with r phase shiftbetween the two exposures, and thus the background iserased. The object is a heated coil.

(b)Fig. 4. Holographic subtraction interferometry: (a) without Tphase shift between the two exposures; (b) with Tr phase shiftbetween the two exposures, and thus the background iserased. The object is a standing acoustic wave in a water tank.The acoustic transducer (at the left) is driven at 450 kHz with a50-V signal.

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(a)

(b)Fig. 5. Same as Fig. 4, except the applied voltage is 80 V.

differential information is reconstructed, as shown inFig. 3(b). In Fig. 4 the object is a standing acousticwave in a water tank, and it is produced by apiezoelectric ceramic transducer that is driven at 450kHz. The acoustic wavelength is 3.3 mm. In thiscase the signal is greatly improved by erasure of theobscuring background. The result shown in Fig. 5 is

similar to that in Fig. 4, except that the strength ofthe acoustic signal has been increased. In Fig. 5(a)the acoustic wave is clearly seen without use ofholographic subtraction. However, the result in Fig.5(b) is produced by holographic subtraction andreveals additional detail such as the sidelobe struc-ture in the acoustic wave field.

Conclusions

Photorefractive crystals are useful as recording mate-rials in holographic subtraction interferome-try. These crystals can be used conveniently ininterferometry since they are self-developing andeasily erasable by heating them to 200C. Thediffraction efficiency of the holograms should be lowto produce a good subtraction, and the current re-search was performed to ascertain what low means.It must be noted that a phase stabilization systemwas not used in these experiments. Such a system isrequired for objects that cause vibration during record-ing (as in aerodynamics) and can be easily incorpo-rated into the experiments.

This paper is based in part on research supportedby the Texas Advanced Technology Program undergrant 003656-045 and by the U.S. Army ResearchOffice under grant DAAL03-86-KO149. Laboratoryassistance by A. Hafiz is acknowledged.

References

1. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, and D.Brumm, "Optical image synthesis (complex amplitude additionand subtraction) by holographic Fourier transformation," Phys.Lett. 18, 116-118 (1965).

2. J. P. Huignard, J. P. Herriau, and F. Micheron, "Coherentselective erasure of superimposed volume holograms in LiNbO3,"Appl. Phys. Lett. 26, 256-258 (1975).

3. J. D. Trolinger, "Application of generalized phase controlduring reconstruction to flow visualization holography," Appl.Opt. 18, 766-774 (1979).

4. C. C. Guest, M. M. Mirsalehi, and T. K. Gaylord, "EXCLUSIVEOR processing (binary image subtraction) using thick Fourierholograms," Appl. Opt. 23, 3444-3454 (1984).

5. P. Yeh, T. Y. Chang, and P. H. Beckwith, "Real-time opticalimage subtraction using dynamic holographic interference inphotorefractive media," Opt. Lett. 13, 586-588 (1988).

6. H. Kogelnik, "Coupled wave theory for thick hologram gratings,"Bell Syst. Tech. J. 48, 2909-2947 (1969).

7. R. Magnusson and T. K. Gaylord, "Use of dynamic theory todescribe experimental results from volume holography," J.Appl. Phys. 47, 190-199 (1976).

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