Otjpist

Coherence-based imaging through turbid mediaby use of degenerate four-wave mixing in thinliquid-crystal films and photorefractives

Denise Brown, Vladimir B. Fleurov, Paul Carroll, and Chris M. Lawson

We describe a coherence-based imaging technique based on degenerate four-wave mixing in two mate-rials. First, a 45°-cut BaTiO3 crystal was used as a self-pumped phase conjugator to obtain depth-resolved images through a 4 mean-free-path ~mfp! scattering media. In addition, an HITC dye-dopedK15 liquid-crystal layer was used to provide single-shot image acquisition through a 2 mfp scatteringmedia. This technique can be used to provide instantaneous ~single-pulse!, depth-resolved, two-dimensional images of the internal structure of scattering materials. Potential applications of thistechnique include subsurface imaging of biomedical tissue and nondestructive evaluation of compositematerials. © 1998 Optical Society of America

OCIS codes: 110.1650, 110.7050, 160.3710.

n

mfs

1. Introduction

Noninvasive optical imaging of the internal structureof objects that are obscured by diffusive media hasrecently attracted interest for characterizing the in-ternal porous structure of certain types of compositematerials and for diagnostic imaging of medical orbiological tissue.1–4 The major problem with usinglight to image objects embedded in highly scatteringmaterials involves the difficulty in differentiating be-tween the minimally scattered image-bearing pho-tons and the strongly scattered background photons.One possible solution to this problem involves the useof optical low-coherence reflectometry ~OLCR!. In

LCR, a Michelson interferometer with a low-emporal coherence-length light source is used in con-unction with some type of coherence filter. Theath length of the reference arm of the interferometers then scanned to map out the backscattered inten-ity versus the depth, with a resolution that can be inhe submicrometer range.5 However, with these

D. Brown, V. B. Fleurov, and C. M. Lawson are with the De-partment of Physics, University of Alabama at Birmingham, 310Campbell Hall, 1300 University Boulevard, Birmingham, Ala-bama 35294-1170. P. Carroll can be reached at 507 North CraigStreet, Victoria, Texas 77901. C. M. Lawson can be reached bye-mail at lawson@uab.edu.

Received 24 November 1997; revised manuscript received 5March 1998.

0003-6935y98y225306-07$15.00y0© 1998 Optical Society of America

5306 APPLIED OPTICS y Vol. 37, No. 22 y 1 August 1998

OLCR methods, the sensor head must be scannedtransversely so that two-dimensional ~2-D! imagescan be obtained.

Other approaches for imaging through diffusive me-dia eliminate the need for transverse scanning. Thiscan allow rapid or instantaneous image acquisition,which can be important for medical applications re-quiring dynamic analysis. These approaches includeholographic coherence-filtering techniques6–8 and

onlinear-optical ~NLO!-based time-gating tech-niques, such as stimulated Raman scattering,9 para-

etric amplification,10 frequency upconversion,11 andast holographic storage in multiple-quantum-welltructures.12,13 Specifically, time-gated, two-wave

mixing processes in photorefractive crystals have beenused for 2-D imaging in turbid media.8,14 In this case,the image could only be reconstructed when blockingthe object beam and subsequently when the referencebeam is used as a readout beam.14 This approach,however, is applicable mainly for NLO materials withslow response times and may be inappropriate for real-time applications requiring instantaneous, single-shotimage acquisition.

For applications requiring single-shot image acqui-sition, we have studied dye-doped liquid-crystalfilms, which can exhibit strong nonlinearities15,16 andhigh phase-conjugate reflectivities.17–19 Further-more, we have recently reported a coherence-filteringtechnique based on degenerate four-wave mixing~DFWM! in these films, which can be applicable forsingle-shot 2-D imaging through turbid media.20,21

p

lbhtpwtqafipbB

fo1f

Awsspr

Fc

In this paper, we report 2-D imaging experimentsin which we compare two types of NLO materials: aBaTiO3 photorefractive crystal and a thin dye-dopedliquid-crystal layer. We also describe the beam-walk-off effects connected to low-coherence holo-graphic methods and discuss ways to improve theresolution and the field of view ~FOV! of the methodwith liquid-crystal-based NLO films.18 Our imagingexperiments were performed in the near-infraredspectral region, which is attractive for biomedical im-aging applications.22

2. Degenerate-Four-Wave-Mixing-Based Imaging withBaTiO3 Crystals

A Ti:Sapphire self-mode-locked laser ~Lexel LaserInc., Model 480! operating at 780 nm with a temporal

ulse width of ;120 fs was used as a low-coherencelight source for the photorefractive-crystal-based ex-periments. The average output power of the 100-MHz, mode-locked pulse train was approximately40 mW. The laser beam was expanded with a tele-scope to a spot size of ;4 mm. As a NLO media weused a 1-mm-thick, 45°-cut Rh-doped BaTiO3 crys-tal23,24 ~Deltronic Crystal Industries, Inc.!.

The experimental setup is shown in Fig. 1. Theaser beam is split into a forward pump and a probeeam by the polarizing beam-splitter cube PBC1. Aalf-wave plate adjusts the splitting ratio of the in-ensities of the pump and the probe beams. Theolarizing beam splitter cube PBC2 and the quarter-ave plate form the backscattered signal from the

est object. The translation stage behind theuarter-wave plate holds the test object and serves asn optical delay line. Backscattered light from dif-erent depths of the test object forms the probe beamn the DFWM scheme. The probe beam at the out-ut of PBC2 has the same polarization as the pumpeam ~extraordinary polarization with respect to theaTiO3 crystal orientation, parallel to the plane of

Fig. 1!.As the insert of Fig. 1 shows, the photorefractive

crystal was used as a self-pumped phase conjugator.The backward pump beam for the DFWM process isformed from Fresnel reflection ~17% reflection coeffi-

Fig. 1. Experimental DFWM imaging setup. Self-pumpedphase conjugation in the BaTiO3 crystal is obtained by means of

resnel reflection of the pump beam from the internal face of therystal.

cient! of the forward pump beam from the back sur-ace of the crystal. The front and the back surfacesf the photorefractive crystal were slightly tilted at a° angle with respect to each other to avoid cross talkrom multiply reflected beams.25 Usually, these

multiple reflections can wash out the two-wave mix-ing hologram and contribute to the incoherent back-ground noise.8 In contrast, our self-pumpedconfiguration takes advantage of the Fresnel reflec-tion from the back surface of the crystal to generatethe backward pump beam. This allows reconstruc-tion of the image by means of real-time holography.

In our first experiments, we measured the inten-sity of the conjugate signal by replacing the CCDcamera shown in Fig. 1 with a silicon photo detector.A probe beam in that case was formed with a flatmirror ~which served as a test object! and without thefocusing lens in the probe beam arm. Figure 2 illus-trates the NLO properties of the photorefractive crys-tal and the performance of the self-pumped phaseconjugator described above. Measurements of theintensity of the conjugate signal as a function of theangular separation of the pump and the probe beamswere performed with a Ti:Sapphire laser operating ina long-coherence-length or cw regime. As Fig. 2shows, the phase-conjugate reflectivity for the 45°-cutBaTiO3 crystal decreases from 17% to approximately6% when the angle a is decreased from 30° to 7°.

dditional measurements, which were performedith a 633-nm He–Ne laser as a pumping source,

how that the maximum gain of the phase-conjugateignal was observed at an angular separation of ap-roximately 40°. When DFWM is compared witheal-time holography,26 the optimal wave-mixing ge-

Fig. 2. Conjugate reflectivity as a function of angular separationof the probe and pump beams is measured with Ti:Sapphire laser,WpumpyWprobe ;1.2. The insert illustrates the accuracy require-ments for proper alignment of the photorefractive crystal in self-pumped phase-conjugation geometry at 780 nm.

1 August 1998 y Vol. 37, No. 22 y APPLIED OPTICS 5307

vm w

c

qp2

rcob

5

ometry for the self-pumped phase conjugator corre-sponds to a grating spacing of L ;1.2 mm. Thisalue for the optimal grating spacing is in good agree-ent with other reported two-wave mixing results.27

The optimal signal gain for the BaTiO3 crystal isobtained with a large angular separation ~a ;52° at780 nm!. As is discussed below, the use of such largeangles in low-coherence imaging results in undesir-able beam-walk-off effects in the NLO filter.

The conjugate signal is quite sensitive to the align-ment of the crystal relative to the input pump beam.The insert of Fig. 2 shows that even a small angularmisalignment, D, of the back face of the crystal fromthe optimum orientation leads to significant de-creases in the phase-conjugate signal ~a decrease of afactor of 2–3 for D ;5–60!. Because of this sensitiv-ity to the alignment of the pump beam ~but not to theimage-bearing probe beam!, this type of self-conjugator is very sensitive to vibrations of the pho-torefractive crystal and is different from thevibration-resistant passive phase conjugators ana-lyzed elsewhere.28

The real-time holographic images shown in Fig. 3were obtained with a Ti:Sapphire laser used as apumping source but operating with different tempo-ral coherence lengths in each case. An Air Forceresolution chart was used as a test object, and theresolution chart patterns were imaged with a 5-cmfocal-length lens onto the photorefractive crystal witha magnification of approximately unity. A COHU4800 CCD camera with a lens in front was used tomonitor the phase-conjugate image.

In accordance with the optical scheme in Fig. 1, theconjugate image of the test object is only formedwhenever the difference in the path lengths of theobject beam ~for given depth! and the ~forward! pumpbeam is less than the coherence length, lc, of the lightsource. Thus the coherence length of the lightsource establishes the depth resolution of this tech-nique. Figure 3 shows two images of a resolution

Fig. 3. Real-time holography by means of DFWM on BaTiO3. Coand ~b! depth-resolved image obtained with self-mode-locked regimbeams is ;9°.

308 APPLIED OPTICS y Vol. 37, No. 22 y 1 August 1998

chart: one depth-resolved ~i.e., small value of lc! andone non-depth-resolved ~i.e., large value of lc!. Thenon-depth-resolved image of Fig. 3~a! was obtained

ith the Ti:Sapphire laser operating in a cw, long-oherence-length ~lc ;2 cm! regime. In contrast, the

depth-resolved image in Fig. 3~b! was obtained withthe self-mode-locked regime of the laser ~120-fstransform-limited pulses!, which is characterized bya very small coherence length ~lc ;40 mm!. Conse-uently, in this case we can acquire a depth-resolvedrofile with a depth resolution of approximately0 mm.As Fig. 3 shows, the imaging FOV for the depth-

esolved image of Fig. 3~b! is significantly narrowedompared with that of the non-depth-resolved imagef Fig. 3~a!. This FOV narrowing is explained byeam-walk-off effects,29 which occur in low-coherence

holographic DFWM imaging systems. The interact-ing beams in this system are coherent only in a nar-row area of their intersection. Therefore theworking volume of the NLO material is reduced asthe angle between coupling beams is increased.Hence the effective area of the NLO coherent filter inthat case is determined by the angular separation ofthe coupling beams, rather than by the beam crosssection or by the thickness of the NLO material. Inparticular, for thick photorefractive crystals, the ex-posed volume of the crystal can increase undesirablebeam-fanning effects. Thus to increase the FOV inlow-coherence-based imaging systems, it is necessaryto decrease the angular separation between thebeams.

Figure 4 shows experimental results that demon-strate low-coherence reflectometry through turbidmedia obtained with a self-pumped phase conjugatoron BaTiO3. Image subtraction techniques wereused in this case to decrease the contribution of thebackground. We achieved this by recording thebackground noise after blocking the probe beam.The recording time of the image was approximately

ate images of the resolution chart are obtained with ~a! cw regimeTi:Sapphire laser. Angular separation between pump and probe

njuge of

S

FrqsllTfrpfmpcS

ns

ac

SUs

i

30 s. The resolution chart in this case was placedbehind a 1-mm-thick scattering cell containing asuspension of polystyrene microspheres in water~0.460 mm at 0.15% concentration!. Using a Mie-

cattering computer program,30 we calculated thenumber of mfp’s that correspond to a given concen-tration of polystyrene microspheres in water. Theimages of Fig. 4 were obtained through a scatteringmedia corresponding to 4 mfp for the double passthrough the 1-mm-thick scattering cell.

3. Coherence Filtering with Dye-Doped Liquid-CrystalFilms

A. Experimental Conditions

Figure 5 shows the DFWM setup used to carry outthe dye-doped liquid-crystal-based imaging experi-ments. A Q-switched alexandrite laser ~Light Age,Inc.! served as our light source. The laser power was250 mW, the repetition rate was 20 Hz, and the spotsize was 3.2 mm, which yields an energy density ofapproximately 0.16 Jycm2. The probe beam is

Fig. 4. Self-pumped phase conjugation on BaTiO3 crystal is ob-tained by means of Fresnel reflection of the pump beam from theinternal face of the crystal. Bars correspond to 3.56 lpymm.

Fig. 5. DFWM imaging setup for nematic liquid-crystal experi-ments. Angle between probe and forward pump beams is ;6°.

formed as a result of reflection off the object ~an Airorce resolution chart!, which is attached to the mir-or M1. A translation stage holds M1 and theuarter-wave plate. The translation stage alsoerves as an optical delay line. A 125-cm focal-ength lens ~L1! was used to focus the object onto theiquid-crystal film with 1.3 times demagnification.he beam splitter BS1 splits the laser beam into a

orward and a backward pump beam. The energyatio of the probe to the forward and the backwardump beams was 7:10:10. The angle between theorward pump and the probe beam was approxi-ately 6°. Beam splitter BS2 was used to direct the

hase-conjugate image to the imaging system, whichonsisted of an aperture A1, a focusing lens L2, and aONY CCD camera.For our thin NLO films, we used dye-doped

ematic liquid crystals, which have recently beenhown to exhibit strong nonlinearities15 and high

DFWM phase-conjugate reflectivities.17–19 Specifi-cally, for our NLO media we used a planar-alignedK15 liquid crystal ~EM Industries! doped with an IRdye ~HITC from Exciton!. These K15 liquid crystalsre similar to the well-known and studied 5CB liquidrystals.15 Coating the interior surfaces of two mi-

croscope slides with polyvinyl alcohol and then uni-directionally buffing the surfaces serves to achieveplanar alignment. We used a mylar spacer and thenarranged the liquid crystal between the two slides,giving a film thickness of approximately 100 mm.

pectrophotometer measurements ~Shimadzu ModelV-3101PC! yielded an absorbance of 1 ~linear ab-

orption coefficient of 230 cm21! at the working wave-length ~797 nm! of the alexandrite laser. Like 5CB,K15 has no central linkage group, making it amongthe most stable of the nematic liquid crystals. Also,K15 is largely birefringent and positively anisotropic,with an optical anisotropy of Dn 5 0.21 and a dielec-tric anisotropy of De 5 12. In the isotropic phase~above the nematic-isotropic transition temperature,Tc!, liquid crystals have less scattering than in thenematic phase, posing another advantage. Also, inthis phase the molecules are randomly oriented andare highly susceptible to external fields; thus theytend to align themselves in the direction of the opticalfield.18

B. Performances of the Liquid Crystal

As was the case for the photorefractive-crystal-basedNLO imaging technique, the FOV of the liquid-crystal-based NLO technique depends on the angulardependence of the phase-conjugate signal, as shownin Fig. 6. It can be seen that Rc increases sharply asa decreases from 26° to 6°. The maximum phase-conjugate reflectivity was approximately 0.5%. Foran angle of 6° between the forward pump and theprobe beam, we had a diffraction grating with a pe-riod ~L 5 ly2 sin a! of 3.8 mm. This sharp increasen Rc at small angles is in good qualitative agreement

with the dependence of the first-order probe-diffraction efficiency of liquid-crystal films observedelsewhere.31 In accordance with similar two-wave

1 August 1998 y Vol. 37, No. 22 y APPLIED OPTICS 5309

pm

2ptwr8ws1

twItbbpsciito

pmbdaaylwsafltt

tm

5

mixing measurements performed elsewhere, the op-timal diffraction efficiency of the NLO film corre-sponds to a grating spacing of Lopt ;50–70 mm.This grating spacing contrasts significantly with theLopt ;1-mm value for the BaTiO3 crystal. By com-paring the data for the liquid-crystal films ~Fig. 6!and the photorefractive crystal ~Fig. 2!, it can be seenthat the maximum phase-conjugate reflectivity forthe liquid-crystal films occurs at much smaller beamcrossing angles. Since larger FOV’s are obtainablefor smaller beam-crossing angles, NLO images basedon dye-doped liquid-crystal films may potentially ex-hibit wider imaging FOV’s than those based on pho-torefractive crystals.

C. Imaging through Turbid Media

First, we determined the possible resolution of ourliquid-crystal-based imaging technique using the al-exandrite laser as our light source. The result inFig. 7 shows an image of the resolution chart pat-terns, which were taken with a single laser pulse.The crossing angle between the probe and the for-ward pump beams was 6°. The finest bars corre-spond to 14.3 lpymm and demonstrates an achievabletransverse resolution of approximately 70 mm. Thedepth resolution, however, was relatively low ~ap-

roximately 5 mm!, since we used the long-pulseode of the alexandrite laser.Next, we used liquid-crystal films to investigate the

-D imaging resolution through a turbid media. Torovide a scattering media, a 1-mm-thick cell con-aining a suspension of polystyrene microspheres inater was inserted between the object ~an Air Force

esolution chart! and the quarter-wave plate. Fig.~a! shows an image of the resolution chart acquiredith a single shot of the laser beam without the

cattering media present. The bars correspond to.41 lpymm ~approximately 700 mm! on the resolu-

Fig. 6. Intensity of the phase-conjugate signal versus the anglebetween probe and forward pump beams. DFWM was performedon dye-doped liquid-crystal film. Energy density of the laserbeam was 0.5 Jycm2.

310 APPLIED OPTICS y Vol. 37, No. 22 y 1 August 1998

ion chart. The NLO media used for this experimentas the same HITC-doped K15 liquid crystal ~EM

ndustries! mentioned earlier. The ratio of the in-ensities of the probe beam to the forward and theackward pump beams was 0.7:1:1, and the laseream spot size on the liquid-crystal surface was ap-roximately 3.5 mm. The image in Fig. 8~b! corre-ponds to a scattering media with a 0.09%oncentration ~2 mfp’s! of polystyrene microspheresn water. As Fig. 8~b! shows, we have demonstratednstantaneous imaging on a liquid-crystal layerhrough a weakly scattering turbid media by usingur DFWM approach.

4. Summary

We have demonstrated two-dimensional ~2-D!, in-stantaneous, coherence filtering through turbid me-dia by means of a degenerate four-wave mixing~DFWM! process in the near-infrared spectral regionin which two types of NLO materials are used, aBaTiO3 photorefractive crystal and a dye-dopedliquid-crystal layer. In the first case, a 45°-cut Ba-TiO3 crystal was used as a self-pumped phase conju-gator ~pumped with femtosecond Ti:Sapphire laser

ulses! to obtain depth-resolved images through a 4fp scattering media. In the second case, DFWM-

ased coherence filtering was performed on a dye-oped liquid-crystal film ~with nanosecondlexandrite laser pulses! to provide single-shot imagecquisition through a 2 mfp scattering media. Anal-sis of the materials as NLO filters showed thatiquid-crystal-based NLO filters could be used forave-mixing geometries that require small angular

eparations of the interaction beams. These resultslso show that liquid-crystal films exhibit high dif-raction efficiencies at small angles, and thus providearge-imaging FOV’s. Hence they may serve as po-ential candidates for NLO filters in various applica-ions that involve 2-D noninvasive imaging.

Fig. 7. An image of the resolution chart demonstrates an achiev-able resolution of approximately 70 mm ~i.e., finest bars correspondo 14.3 lpymm!. The energy density of the probe beam was 50Jycm2.

c

wccmFcd

We have observed very strong thermally inducedorientational optical nonlinearities in our dye-dopedliquid-crystal films at the range of the energy densityof approximately 0.5 Jycm2. To increase the sensi-tivity of the liquid-crystal-based NLO filters, moreresearch is needed to obtain materials with higherNLO responses. Significant NLO sensitivity im-provements ~i.e., improvements in the phase-onjugate reflectivity of the DFWM process! may be

possible with laser-induced molecular reorientationaleffects in liquid-crystal-based films obtained whenexternal dc electric fields are applied.18 With thesedc-field-assisted optical nonlinearities, the optical in-tensity required18 for nonlinear wave mixing is ap-proximately 0.2 Wycm2. Without the dc fieldapplied, the optical intensity needed to generate sim-ilar diffraction efficiencies is approximately 6 Wycm2.This 0.2 Wycm2 threshold intensity is comparable

ith that required for wave mixing in photorefractiverystals. Using laser sources with shorter-oherence lengths can also make significant improve-ents in the depth resolution of our techniques.inally, new photorefractive polymers have also re-ently been used for 2-D imaging through turbid me-ia with DFWM experiments,32 and these may

represent alternative NLO candidate material for ourimaging technique.

This work was partially supported by National Sci-ence Foundation grant OSR-9553348 and NASAgrant NAGW-813.

References1. J. G. Fujimoto, S. De Silvestri, E. P. Ippen, C. A. Puliafito, R.

Margolis, and A. Oseroff, “Femtosecond optical ranging in bi-ological systems,” Opt. Lett. 11, 150–152 ~1986!.

2. L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic2-D imaging through scattering walls using an ultra-fast op-tical Kerr gate,” Science 253, 769–773 ~1991!.

3. S. Andersson-Engels, R. Berg, S. Svanberg, and O. Jarlman,“Time-resolved transillumination for medical diagnostics,”Opt. Lett. 15, 1179–1181 ~1990!.

Fig. 8. Image of a section of the Air Force resolution chart thatimaging through a scattering media of 0.09% concentration of pol

4. M. R. Hee, J. A. Izatt, E. A. Swanson, and J. G. Fujimoto,“Femtosecond transillumination tomography in thick tissues,”Opt. Lett. 18, 1107–1109 ~1993!.

5. B. Danielson and C. Boisrobert, “Absolute optical ranging us-ing low coherence interferometry,” Appl. Opt. 30, 2975–2979~1991!.

6. E. Leith, C. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd,P.-C. Sun, J. Valdmanis, and G. Vossler, “Imaging throughscattering media with holography,” J. Opt. Soc. Am. A 9, 1148–1153 ~1992!.

7. A. Rebane and J. Feinberg, “Time-resolved holography,” Na-ture ~London! 351, 378–380 ~1991!.

8. S. Hyde, N. Barry, R. Jones, J. Dainty, and P. French, “Highresolution depth resolved imaging through scattering mediausing time-resolved holography,” Opt. Commun. 122, 111–116~1996!.

9. M. D. Duncan, R. Mahon, L. L. Tankeresley, and J. Renties,“Time-gated imaging through scattering media using stimu-lated Raman amplification,” Opt. Lett. 16, 1868–1870 ~1991!.

10. F. Devaux and E. Lantz, “Ultrahigh-speed imaging by para-metric image amplification,” Opt. Commun. 118, 25–27 ~1995!.

11. C. Yan and J. C. Diels, “Two-dimensional imaging and three-dimensional reconstruction of low reflectivity surfaces by usingthe range-gating upconversion second-harmonic method,”Appl. Opt. 34, 2993–2997 ~1995!.

12. R. Jones, S. C. W. Hyde, M. J. Lynn, N. P. Barry, J. C. Dainty,P. M. W. French, K. M. Kwolek, D. D. Nolte, and M. R. Melloch,“Holographic storage and high background imaging using pho-torefractive multiple quantum wells,” Appl. Phys. Lett. 69,1837–1839 ~1996!.

13. R. Jones, N. P. Barry, S. C. W. Hyde, P. M. W. French, K. W.Kwolek, D. D. Nolte, and M. R. Melloch, “Direct-to-video ho-lographic readout in quantum wells for three-dimensional im-aging through turbid media,” Opt. Lett. 2, 103–105 ~1998!.

14. S. Hyde, N. Barry, R. Jones, and P. French, “Depth-resolvedholographic imaging through scattering media by photorefrac-tion,” Opt. Lett. 20, 1331–1333 ~1995!.

15. L. Li, H. J. Yuan, G. Hu, and P. Palffy-Muhoray, “Third ordernon-linearities of nematic liquid crystals,” Liq. Cryst. 16, 703–712 ~1994!.

16. I. C. Khoo, S. Slussarenko, B. D. Guenther, M.-Y. Shih, P.Chen, and W. V. Wood, “Optically induced space-charge fields,DC voltage, and extraordinarily large nonlinearity in dye-doped nematic liquid crystals,” Opt. Lett. 4, 253–255 ~1998!.

sponds to 1.41 lpymm. ~a! No scattering media present and ~b!ene microspheres in water.

correystyr

1 August 1998 y Vol. 37, No. 22 y APPLIED OPTICS 5311

17. F. Simoni, O. Francescangeli, Y. Reznikov, and S. Slussarenko,

1

waves in self-pumped phase conjugation with doped

2

2

2

2

3

3

5

“Dye-doped liquid crystals as high-resolution recording me-dia,” Opt. Lett. 22, 549–551 ~1997!.

8. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlin-ear Optical Phenomena ~Wiley-Interscience, New York, 1995!Chap. 10.

19. I. C. Khoo, “Orientational photorefractive effects in nematicliquid crystal films,” IEEE J. Quantum Electron, 32, 525–534~1996!.

20. V. Fleurov, D. Brown, and C. Lawson, “Low-coherence reflec-tometry through scattering media with degenerate four-wavemixing in a thin nonlinear optical layer,” J. Nonlinear Opt.Phys. and Mater. 6, 95–102 ~1997!.

21. V. Fleurov, C. Lawson, D. Brown, A. Dergachev, S. Mirov, andR. Lindquist, “Low-coherence reflectometry based on DFWMin a thin liquid layer,” in Nonlinear Optical Liquids, C. Law-son, ed., Proc. SPIE 2853, 126–134 ~1996!.

22. S. K. Gayen and R. R. Alfano, “Biomedical imaging tech-niques,” Opt. Photonics News, March, 1996, p. 17.

23. J. E. Ford, Y. F. Fainman, and S. H. Lee, “Enhanced perfor-mance from 45°-cut BaTiO3,” Appl. Opt. 28, 4808–4815 ~1989!.

24. B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz,“Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate,” Opt. Lett. 19, 536–538 ~1994!.

25. J. Zhang, X. Lu, L. Zhang, X. Mu, Q. Jiang, Z. Shao, H. Chen,and M. Jiang, “Conjugate fidelity and multiple reflection

312 APPLIED OPTICS y Vol. 37, No. 22 y 1 August 1998

~K0.5Na0.5!0.2~Sr0.75Ba0.25!0.9Nb2O6 crystals,” Opt. Commun.132, 574–582 ~1996!.

6. A. Yariv, “Phase conjugate opticals and real-time holography,”IEEE J. Quantum Electron. QE-14, 650–660 ~1978!.

7. N. Barry, R. Jones, S. C. W. Hyde, J. C. Dainty, P. M. W.French, S. B. Triverdi, and E. Diegues, “Evaluation of photore-fractive holographic imaging through turbid media,” in Con-ference on Lasers and Electro-optics, Vol. 11 of OSAProceedings Series ~Optical Society of America, Washington,D.C., 1997!, pp. 42–43.

8. M. Cronin-Golomb, J. Palaski, and A. Yariv, “Vibration resis-tance, short coherence length operation, and mode-lockedpumping in passive phase conjugate mirrors,” Appl. Phys.Lett. 47, 1131–1133 ~1985!.

9. N. Abramson, Light in Flight ~SPIE Press, Bellingham, Wash.1996!, Chap. 4.

0. C. F. Bohren and D. R. Huffman, Absorption and Scattering ofLight by Small Particles ~Wiley, New York, 1983!, Chap. 8.

1. I. C. Khoo, “Holographic grating formation in dye-doped andfullerene C60-doped nematic liquid-crystal films,” Opt. Lett.20, 2137–2139 ~1995!.

32. D. D. Steele, B. L. Volodin, O. Savina, B. Kippelen, N. Pey-ghambarian, H. Rockel, and S. R. Marder, “Transilluminationimaging through scattering media by use of photorefractivepolymers,” Opt. Lett. 3, 153–155 ~1998!.