Abstract

We propose and demonstrate experimentally a method for utilizing a dynamic phase-encoded photorefractive memory to realize parallel optical addition, subtraction, and inversion operations of stored images. The phase-encoded holographic memory is realized in photorefractive BaTiO3, storing eight images using Walsh–Hadamard binary phase codes and an incremental recording procedure. By subsampling the set of reference beams during the recall operation, the selectivity of the phase address is decreased, allowing one to combine images in such a way that different linear combination of the images can be realized at the output of the memory.

© 1996 Optical Society of America

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1995 (1)

J. Lembcke, C. Denz, T. TschudiOpt. Mater. 4, 428 (1995).
[CrossRef]

1994 (3)

1993 (3)

D. Psaltis, K. CurtisJ. Opt. Soc. Am. A 10, 2547 (1993).
[CrossRef]

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

F. MokOpt. Lett. 18, 915 (1993).
[CrossRef] [PubMed]

1992 (2)

1991 (3)

1977 (1)

H. KurzOpt. Acta 24, 463 (1977).
[CrossRef]

1975 (1)

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Aharoni, A.

Alves, C.

Amodei, J. J.

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Barnes, T. H.

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

Bashaw, M. C.

Burke, W. J.

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Curtis, K.

Denz, C.

J. Lembcke, C. Denz, T. TschudiOpt. Mater. 4, 428 (1995).
[CrossRef]

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

C. Denz, G. Pauliat, G. Roosen, T. TschudiOpt. Commun. 85, 171 (1991);Appl. Opt. 31, 5700 (1992).
[CrossRef]

Dunning, G. J.

Fainman, Y.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. LeeOpt. Lett. 16, 1744 (1991).
[CrossRef]

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

Ford, J.

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

Ford, J. E.

Heanue, J. F.

Hesselink, L.

Kirby, K. W.

Klein, M. B.

Kurz, H.

H. KurzOpt. Acta 24, 463 (1977).
[CrossRef]

Lee, S. H.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. LeeOpt. Lett. 16, 1744 (1991).
[CrossRef]

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

Lembcke, J.

J. Lembcke, C. Denz, T. TschudiOpt. Mater. 4, 428 (1995).
[CrossRef]

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

Leyva, V.

Ma, J.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. LeeOpt. Lett. 16, 1744 (1991).
[CrossRef]

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

McCahon, S. W.

Mok, F.

Mok, F. H.

Pauliat, G.

C. Alves, G. Pauliat, G. RoosenOpt. Lett. 19, 1894 (1994).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, T. TschudiOpt. Commun. 85, 171 (1991);Appl. Opt. 31, 5700 (1992).
[CrossRef]

Philipps, W.

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Psaltis, D.

Rakuljic, G. A.

Roosen, G.

C. Alves, G. Pauliat, G. RoosenOpt. Lett. 19, 1894 (1994).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, T. TschudiOpt. Commun. 85, 171 (1991);Appl. Opt. 31, 5700 (1992).
[CrossRef]

Sasaki, H.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. LeeOpt. Lett. 16, 1744 (1991).
[CrossRef]

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

Staebler, D. L.

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Stoll, H. M.

Tackett, M. C.

Taketomi, Y.

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. LeeOpt. Lett. 16, 1744 (1991).
[CrossRef]

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

Tschudi, T.

J. Lembcke, C. Denz, T. TschudiOpt. Mater. 4, 428 (1995).
[CrossRef]

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

C. Denz, G. Pauliat, G. Roosen, T. TschudiOpt. Commun. 85, 171 (1991);Appl. Opt. 31, 5700 (1992).
[CrossRef]

Valley, G. C.

Walkup, J. F.

Yariv, A.

Appl. Phys. Lett. (1)

D. L. Staebler, W. J. Burke, W. Philipps, J. J. AmodeiAppl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (1)

J. Lembcke, C. Denz, T. H. Barnes, T. Tschudiin Digest of Topical Meeting on Photorefractive Materials, Effects and Devices (Ukrainian Academy of Science, Kiev, 1993), paper SaCO2.

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Acta (1)

H. KurzOpt. Acta 24, 463 (1977).
[CrossRef]

Opt. Commun. (1)

C. Denz, G. Pauliat, G. Roosen, T. TschudiOpt. Commun. 85, 171 (1991);Appl. Opt. 31, 5700 (1992).
[CrossRef]

Opt. Lett. (7)

Opt. Mater. (1)

J. Lembcke, C. Denz, T. TschudiOpt. Mater. 4, 428 (1995).
[CrossRef]

Other (1)

Y. Taketomi, J. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Leein Integrated Photonics Research, Vol. 8 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 212.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup. M, mirror; L’s, lenses; BS, beam splitter; BE’s, beam expanders; ASLM, amplitude spatial light modulator; PSLM, phase spatial light modulator; CGH, computer-generated hologram.

Fig. 2
Fig. 2

Images stored with binary phase codes during readout with the complete set of reference beams.

Fig. 3
Fig. 3

Examples of addition and subtraction of pairwise images: a, |A5 + A7|; b, |A7 + A8|; c, |A5 + A6|; d, |A5A7|; e, |A7A8|; f, |A5A6|.

Fig. 4
Fig. 4

a–c, Three images stored in the phase-coded memory, readout with the complete reference beam set, and their addition and subtraction by addressing the memory with subsets of the phase codes: d, |A1 + A2|; e, |A2A3|; f, |A1 + A2A3|.

Fig. 5
Fig. 5

For inversion of images, a plane wave is stored together with the images to be inverted in the phase coded memory (a). The inversion of the image in Fig. 4c is then equal to |ApwA3|) (b).

Equations (5)

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Δ n ( r ) j N k N Δ n ¯ k j ( r ) exp [ i ( k s k j ) r ] exp ( i φ k j ) ,
A j diff = R j Δ n Bragg selectivity k N exp [ i ( φ k j φ k j ) ] ,
k = 1 N exp [ i ( φ k j φ k j ) ] k = 1 N χ k j χ k J ^ ! = { 0 for j j N for j = j .
k = 1 N exp [ i ( φ k j φ k j ) ] k = 1 N χ k j χ k j ! = { 0 for j j N / m for j = j ,
χ k j = { χ k j for equal ( different ) phase factors 0 other cases .

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