Abstract

We demonstrate one-way image compensation for a thin and polarization-sensitive aberrator by the use of optical lock-in detection. Optical lock-in detection is accomplished by dual-phase modulation in four-wave mixing in a holographic medium. In our scheme, both the image-bearing beam and the reference beam copropagate through the aberrator under the same polarization condition. The holographic grating that reconstructs only the corrected image was generated by selective recording in optical lock-in detection. The phase aberration is subtracted out in the holographic process. This scheme permits image correction through the polarization-sensitive aberrator.

© 2002 Optical Society of America

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  1. J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of lens aberrations by means of holograms,” Appl. Opt. 5, 589–593 (1966).
    [CrossRef] [PubMed]
  2. H. Kogelnik, K. S. Pennington, “Holographic imaging through a random medium,” J. Opt. Soc. Am. 58, 273–274 (1968).
    [CrossRef]
  3. M. E. Marhic, A. Pan, “Matched filtering for efficient cleanup of strongly distorted beams,” Opt. Lett. 13, 817–819 (1988).
    [CrossRef] [PubMed]
  4. G. Andersen, J. Munch, P. Veitch, “Compact, holographic correction of aberrated telescopes,” Appl. Opt. 36, 1427–1432 (1997).
    [CrossRef] [PubMed]
  5. K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
    [CrossRef]
  6. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
    [CrossRef]
  7. A. Yariv, T. L. Koch, “One-way coherent imaging through a distorting medium using four-wave mixing,” Opt. Lett. 7, 113–115 (1982).
    [CrossRef] [PubMed]
  8. O. Ikeda, T. Suzuki, T. Sato, “Image transmission through a turbulent medium using a point reflector and four-wave mixing in BSO crystal,” Appl. Opt. 22, 2192–2195 (1983).
    [CrossRef] [PubMed]
  9. M. A. Kramer, C. J. Wetterer, T. Martinez, “One-way imaging through an aberrator with spatially incoherent light by using an optically addressed spatial light modulator,” Appl. Opt. 30, 3319–3323 (1991).
    [CrossRef] [PubMed]
  10. J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
    [CrossRef]
  11. K. R. MacDonald, W. R. Tompkin, R. W. Boyd, “Passive one-way aberration correction using four-wave mixing,” Opt. Lett. 13, 485–487 (1988).
    [CrossRef] [PubMed]
  12. T. G. Alley, M. A. Kramer, D. R. Martinez, L. P. Schelonka, “Single-pass imaging through a thick dynamic distorter using four-wave mixing,” Opt. Lett. 15, 81–83 (1990).
    [CrossRef] [PubMed]
  13. M. A. Kramer, T. G. Alley, D. R. Martinez, L. P. Schelonka, “Effects of thick aberrators on one-way imaging schemes,” Appl. Opt. 29, 2576–2581 (1990).
    [CrossRef] [PubMed]
  14. J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
    [CrossRef]
  15. J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
    [CrossRef]
  16. D. Statman, J. C. Puth, C. E. Sunderman, B. W. Liby, “One-way imaging with an aberrated reference beam,” Appl. Opt. 39, 3044–3049 (2000).
    [CrossRef]
  17. S. H. Chakmakjian, M. T. Gruneisen, K. Koch, M. A. Kramer, V. Esch, “Time-multiplexed real-time one-way image compensation for high-spatial-frequency aberration correction,” Appl. Opt. 34, 1076–1080 (1995).
    [CrossRef] [PubMed]
  18. T. Ogasawara, M. Ohno, K. Karaki, “One-way image transmission with a pair of multimode optical fibers and a phase-conjugate mirror,” Opt. Lett. 20, 2435–2437 (1995).
    [CrossRef] [PubMed]
  19. T. Y. Chang, J. H. Hong, “One-way image transmission and reconstruction through a thick aberrating medium by use of volume holography,” J. Opt. Soc. Am. A 11, 3206–3211 (1994).
    [CrossRef]
  20. F. Zhao, K. Sayano, “Compact read-only memory with lensless phase-conjugate holograms,” Opt. Lett. 21, 1295–1297 (1996).
    [CrossRef] [PubMed]
  21. T. Honda, H. Matsumoto, “Aberration correction of acousto-optically modulated laser beams by phase conjugation,” Opt. Lett. 15, 308–310 (1990).
    [CrossRef] [PubMed]
  22. J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, “Photorefractive optical lock-in detector,” Opt. Lett. 16, 1442–1444 (1991).
    [CrossRef] [PubMed]
  23. J. Khoury, J. S. Kane, J. Kierstead, C. L. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. 33, 2909–2916 (1994).
    [CrossRef] [PubMed]
  24. J. Khoury, V. Ryan, M. Cronin-Golomb, “Photorefractive frequency converter and phase-sensitive detector,” J. Opt. Soc. Am. B 10, 72–82 (1993).
    [CrossRef]
  25. N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
    [CrossRef] [PubMed]
  26. J. Joseph, T. Oura, T. Minemoto, “Optical implementation of a wavelet transform by use of dynamic holographic recording in a photorefractive material,” Appl. Opt. 34, 3997–4003 (1995).
    [CrossRef] [PubMed]

2000 (1)

1998 (3)

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (3)

1994 (3)

1993 (1)

1991 (2)

1990 (3)

1988 (2)

1983 (1)

1982 (2)

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

A. Yariv, T. L. Koch, “One-way coherent imaging through a distorting medium using four-wave mixing,” Opt. Lett. 7, 113–115 (1982).
[CrossRef] [PubMed]

1968 (1)

1966 (2)

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of lens aberrations by means of holograms,” Appl. Opt. 5, 589–593 (1966).
[CrossRef] [PubMed]

Alley, T. G.

Andersen, G.

Andersen, G. P.

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Aruga, T.

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

Boyd, R. W.

Chakmakjian, S. H.

Chang, T. Y.

Cronin-Golomb, M.

Esch, V.

Fischer, B.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

Goodman, J. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

Gruneisen, M. T.

Gurley, K. S.

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Hara, T.

Hemmer, P.

Honda, T.

Hong, J. H.

Huntley, W. H.

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

Ikeda, O.

Jackson, D. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

Johnson, M. D.

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Joseph, J.

Kane, J. S.

Karaki, K.

Khoury, J.

Kierstead, J.

Knize, R. J.

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Kobayashi, Y.

Koch, K.

Koch, T. L.

Kogelnik, H.

Kramer, M. A.

Lehmann, M.

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

Leith, E.

Liby, B. W.

MacDonald, K. R.

Marhic, M. E.

Martinez, D. R.

Martinez, T.

Matsumoto, H.

Minemoto, T.

Mukohzaka, N.

Munch, J.

Ogasawara, T.

Ohno, M.

Oura, T.

Pan, A.

Pennington, K. S.

Puth, J. C.

Ryan, V.

Sato, T.

Sayano, K.

Schelonka, L. P.

Statman, D.

Sunderman, C. E.

Suzuki, T.

Tompkin, W. R.

Toyoda, H.

Upatnieks, J.

Vander Lugt, A.

Veitch, P.

Wang, H.

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

Wetterer, C. J.

White, J. O.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

White, W. R.

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Woods, C.

Woods, C. L.

Yariv, A.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

A. Yariv, T. L. Koch, “One-way coherent imaging through a distorting medium using four-wave mixing,” Opt. Lett. 7, 113–115 (1982).
[CrossRef] [PubMed]

Yoshida, N.

Yoshikado, S.

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

Zhang, J.

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

Zhao, F.

Appl. Opt. (10)

J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of lens aberrations by means of holograms,” Appl. Opt. 5, 589–593 (1966).
[CrossRef] [PubMed]

G. Andersen, J. Munch, P. Veitch, “Compact, holographic correction of aberrated telescopes,” Appl. Opt. 36, 1427–1432 (1997).
[CrossRef] [PubMed]

O. Ikeda, T. Suzuki, T. Sato, “Image transmission through a turbulent medium using a point reflector and four-wave mixing in BSO crystal,” Appl. Opt. 22, 2192–2195 (1983).
[CrossRef] [PubMed]

M. A. Kramer, C. J. Wetterer, T. Martinez, “One-way imaging through an aberrator with spatially incoherent light by using an optically addressed spatial light modulator,” Appl. Opt. 30, 3319–3323 (1991).
[CrossRef] [PubMed]

M. A. Kramer, T. G. Alley, D. R. Martinez, L. P. Schelonka, “Effects of thick aberrators on one-way imaging schemes,” Appl. Opt. 29, 2576–2581 (1990).
[CrossRef] [PubMed]

D. Statman, J. C. Puth, C. E. Sunderman, B. W. Liby, “One-way imaging with an aberrated reference beam,” Appl. Opt. 39, 3044–3049 (2000).
[CrossRef]

S. H. Chakmakjian, M. T. Gruneisen, K. Koch, M. A. Kramer, V. Esch, “Time-multiplexed real-time one-way image compensation for high-spatial-frequency aberration correction,” Appl. Opt. 34, 1076–1080 (1995).
[CrossRef] [PubMed]

J. Khoury, J. S. Kane, J. Kierstead, C. L. Woods, P. Hemmer, “Real-time holographic baseband frequency demodulator,” Appl. Opt. 33, 2909–2916 (1994).
[CrossRef] [PubMed]

N. Mukohzaka, N. Yoshida, H. Toyoda, Y. Kobayashi, T. Hara, “Diffraction efficiency analysis of a parallel-aligned nematic-liquid crystal spatial light modulator,” Appl. Opt. 33, 2804–2811 (1994).
[CrossRef] [PubMed]

J. Joseph, T. Oura, T. Minemoto, “Optical implementation of a wavelet transform by use of dynamic holographic recording in a photorefractive material,” Appl. Opt. 34, 3997–4003 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “One-way image transmission through a thick dynamic distorter without a reference beam,” Appl. Phys. Lett. 72, 630–632 (1998).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, “Real-time phase conjugate window for one-way optical field imaging through a distortion,” Appl. Phys. Lett. 41, 141–143 (1982).
[CrossRef]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311–313 (1966).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Commun. (1)

K. S. Gurley, G. P. Andersen, R. J. Knize, W. R. White, M. D. Johnson, “Wavelength dependence of wavefront correction using holography in a saturable absorber,” Opt. Commun. 152, 16–18 (1998).
[CrossRef]

Opt. Lett. (9)

M. E. Marhic, A. Pan, “Matched filtering for efficient cleanup of strongly distorted beams,” Opt. Lett. 13, 817–819 (1988).
[CrossRef] [PubMed]

K. R. MacDonald, W. R. Tompkin, R. W. Boyd, “Passive one-way aberration correction using four-wave mixing,” Opt. Lett. 13, 485–487 (1988).
[CrossRef] [PubMed]

T. G. Alley, M. A. Kramer, D. R. Martinez, L. P. Schelonka, “Single-pass imaging through a thick dynamic distorter using four-wave mixing,” Opt. Lett. 15, 81–83 (1990).
[CrossRef] [PubMed]

F. Zhao, K. Sayano, “Compact read-only memory with lensless phase-conjugate holograms,” Opt. Lett. 21, 1295–1297 (1996).
[CrossRef] [PubMed]

T. Honda, H. Matsumoto, “Aberration correction of acousto-optically modulated laser beams by phase conjugation,” Opt. Lett. 15, 308–310 (1990).
[CrossRef] [PubMed]

J. Khoury, V. Ryan, C. Woods, M. Cronin-Golomb, “Photorefractive optical lock-in detector,” Opt. Lett. 16, 1442–1444 (1991).
[CrossRef] [PubMed]

A. Yariv, T. L. Koch, “One-way coherent imaging through a distorting medium using four-wave mixing,” Opt. Lett. 7, 113–115 (1982).
[CrossRef] [PubMed]

J. Zhang, H. Wang, S. Yoshikado, T. Aruga, “Image transmission through a thick dynamic distorter by the photorefractive fanning effect,” Opt. Lett. 23, 585–587 (1998).
[CrossRef]

T. Ogasawara, M. Ohno, K. Karaki, “One-way image transmission with a pair of multimode optical fibers and a phase-conjugate mirror,” Opt. Lett. 20, 2435–2437 (1995).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic setup for one-way image correction by use of optical lock-in detection. N-PBS1 and N-PBS2 are nonpolarizing beam splitters. Polarization states of the image-bearing beam O and reference beam R are the same.

Fig. 2
Fig. 2

Experimental setup. Po, polarizer; PZT1 and PZT2, piezoelectric transducers; PAL-SLM, parallel-aligned nematic liquid-crystal spatial light modulator.

Fig. 3
Fig. 3

Images of number 5 in the absence of an aberrator: (a) unreconstructed image, (b) reconstructed image without phase modulation, (c) reconstructed image with phase modulations by PZT1 and PZT2.

Fig. 4
Fig. 4

Images of number 5 in the presence of the aberrator: (a) unreconstructed image, (b) reconstructed image with phase modulations by PZT1 and PZT2, (c) reconstructed image with phase modulations by PZT1 and PZT2 when a λ/4 plate was inserted just after the aberrator.

Fig. 5
Fig. 5

Intensity variation of part of the reconstructed image when the frequencies of the two phase modulators (PZT1 and PZT2) were different. The difference between the two frequencies was 2 Hz.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

Oa  OD expiΦD,
Ra  RD expiΦD-δ1 sinω1t+ϕ1,
Ob  OD expiΦD-δ2 sinω2t+ϕ2,
Rb  RD expiΦD-δ1 sinω1t+ϕ1-δ2 sinω2t+ϕ2,
IH=OaOb*+Oa*Ob+RaRb*+Ra*Rb+OaRb*+Oa*Rb+RaOb*+Ra*Ob+|Oa|2+|Ob|2+|Ra|2+|Rb|2.
IH+=OaOb*+RaRb*+OaRb*+RaOb*, =ODOD* exp-iδ1 sinω1t+ϕ1+RDRD* exp-iδ1 sinω1t+ϕ1+ODRD*+OD*RD exp-i2δ1 sinω1t+ϕ1.
τ GH+t +GH+=γIH+,
EH+  PGH+  J0δ1PODOD*+J0δ1PRDRD*+PODRD* +J02δ1POD*RD,
EH+  PODRD*.
EH-  POa*Ob+Ra*Rb+Oa*Rb+Ra*Ob  POD*RD.
IH+ =OaOb*+RaRb*+OaRb*+RaOb* =ODOD* expiδ1 sinω1t+ϕ1+RDRD* expiδ1 sinω1t+ϕ1+ODRD* expi2δ1 sinω1t+ϕ1+OD*RD.
EH+  POD*RD,
EH-  PODRD*.
IH+ =OaOb*+RaRb*+OaRb*+RaOb*, =ODOD* expiδ2 sinω2t+ϕ2+RDRD* expiδ2 sinω2t+ϕ2+ODRD* expiδ1 sinω1t+ϕ1+δ2 sinω2t+ϕ2+OD*RD exp-iδ1 sinω1t+ϕ1-δ2 sinω2t+ϕ2.
EH+  PGH+,  J0δ2 PODOD*+ J0δ2PRDRD *+PODRD* n=-n=Jnδ1Jnδ2inΔωτ+1expinΔωt+Δϕ+π +POD*RDn=-n=Jnδ1Jnδ2inΔωτ+1 ×expin Δωt+Δϕ,
EH+  PODRD* n=-n=Jnδ1Jnδ2inΔωτ+1expin Δωt+Δϕ+π +POD*RDn=-n=Jnδ1Jnδ2inΔωτ+1 ×expinΔωt+Δϕ.
IH+=OaOb*+RaRb*+OaRb*+RaOb*,=ODOD* exp-iΩ2t+RDRD* exp-iΩ2t+ODRD* exp-iΩ1+Ω2t+OD*RD×expiΩ1-Ω2t.
EH+  PGH+,  POD*RD1iΔΩτ+1expiΔΩt,

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