Abstract

We present a real-time holographic interferometer for which two reference waves of different phases are created by two-wave mixing with a stationary signal wave in a photorefractive crystal. These waves are reconstructions of the stationary signal wave and interfere with the momentary (changing) signal wave in the manner of a holographic real-time interferometer. A fast change (phase or intensity) of the signal wave leads to different intensity changes in both interferograms that are jointly used for evaluation. With an electric dc field applied to the crystal, a high sensitivity for measuring phase changes (down to λ/50, λ = 633 nm) is found, and the sign of the phase change can be determined.

© 2000 Optical Society of America

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  1. P. K. Rastogi, Holographic Interferometry: Principles and Methods, Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994).
    [CrossRef]
  2. T. Kreis, Holographic Interferometry: Principles and Methods, (Akademische Verlagsgesellschaft, Berlin, 1996).
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  4. M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  5. D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
    [CrossRef]
  6. J. P. Huignard, J. P. Herriau, T. Valentin, “Time average holographic interferometry with photorefractive electrooptic Bi12SiO20 crystals,” Appl. Opt. 16, 2796–2798 (1977).
    [CrossRef] [PubMed]
  7. J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
    [CrossRef] [PubMed]
  8. H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Act. 29, 463–470 (1982).
    [CrossRef]
  9. A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
    [CrossRef]
  10. X. Wang, R. Magnusson, A. Haji-Sheikh, “Real-time interferometry with photorefractive reference holograms,” Appl. Opt. 32, 1983–1986 (1993).
    [CrossRef] [PubMed]
  11. L. Labrunie, G. Pauliat, G. Roosen, J. C. Launay, “Simultaneous acquisition of π/2 phase-stepped interferograms with a photorefractive Bi12GeO20 crystal: application to real-time double-pulse holography,” Opt. Lett. 20, 1652–1654 (1995).
    [CrossRef] [PubMed]
  12. L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
    [CrossRef]
  13. J. P. Huignard, J. P. Herriau, “Real-time double-exposure interferometry with Bi12SiO20 crystals in transverse electrooptic configuration,” Appl. Opt. 16, 1807–1809 (1977).
    [CrossRef] [PubMed]
  14. R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
    [CrossRef]
  15. G. von Bally, F. Rickermann, S. Riehemann, “Application of photorefractive crystals in stroboscopic double-exposure holographic interferometry,” in Proceedings of Conference Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 527–530.
  16. D. Dirksen, G. von Bally, “Holographic double-exposure interferometry in near real time with photorefractive crystals,” J. Opt. Soc. Am. B 11, 1858–1863 (1994).
    [CrossRef]
  17. G. S. Ballard, “Double-exposure holographic interferometry with separate reference beams,” J. Appl. Phys. 39, 4846–4848 (1968).
    [CrossRef]
  18. D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
    [CrossRef]
  19. M. P. Georges, Ph. C. Lemaire, “Real-time interferometer with BSO crystal using phase-shifting for quantitative deformation measurement,” in Proceedings of Conference on Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 403–407.
  20. H. Rehn, M. Esselbach, R. M. Kowarschik, K. H. Ringhofer, “Photorefractive novelty filters for transient phase evaluation,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 730–737 (1996).
    [CrossRef]
  21. D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).
  22. M. P. Georges, Ph. C. Lemaire, “Phase-shifting real-time holographic interferometry that uses bismuth oxide crystals,” Appl. Opt. 34, 7497–7506 (1995).
    [CrossRef] [PubMed]
  23. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  24. D. L. Staebler, J. J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
    [CrossRef]
  25. G. Cedilnik, A. Kiessling, R. Kowarschik, “Intensity controlled shaping of the beam profile using three-wave mixing in photorefractive Bi12TiO20,” Opt. Commun. 151, 196–202 (1998).
    [CrossRef]
  26. S. I. Stepanov, “Adaptive interferometry: a new area of applications of photorefractive crystals,” in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), pp. 125–140.
    [CrossRef]
  27. E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
    [CrossRef]
  28. M. Mann, E. Shamonina, K. H. Ringhofer, “Modelling of two wave mixing experiments in sillenite crystals,” Comp. Phys. Comm. 96, 61–86 (1996).
    [CrossRef]
  29. N. S.-K. Kwong, Y. Tamita, A. Yariv, “Optical tracking filter using transient energy coupling,” J. Opt. Soc. Am. B 5, 1788–1791 (1988).
    [CrossRef]
  30. K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
    [CrossRef]

1998 (1)

G. Cedilnik, A. Kiessling, R. Kowarschik, “Intensity controlled shaping of the beam profile using three-wave mixing in photorefractive Bi12TiO20,” Opt. Commun. 151, 196–202 (1998).
[CrossRef]

1997 (3)

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
[CrossRef]

1996 (1)

M. Mann, E. Shamonina, K. H. Ringhofer, “Modelling of two wave mixing experiments in sillenite crystals,” Comp. Phys. Comm. 96, 61–86 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (1)

1990 (1)

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
[CrossRef]

1989 (1)

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

1988 (1)

1987 (1)

R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
[CrossRef]

1985 (1)

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

1982 (1)

H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Act. 29, 463–470 (1982).
[CrossRef]

1981 (1)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1977 (2)

1972 (1)

D. L. Staebler, J. J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1968 (1)

G. S. Ballard, “Double-exposure holographic interferometry with separate reference beams,” J. Appl. Phys. 39, 4846–4848 (1968).
[CrossRef]

Amodei, J. J.

D. L. Staebler, J. J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Ballard, G. S.

G. S. Ballard, “Double-exposure holographic interferometry with separate reference beams,” J. Appl. Phys. 39, 4846–4848 (1968).
[CrossRef]

Black, T. D.

R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
[CrossRef]

Cedilnik, G.

G. Cedilnik, A. Kiessling, R. Kowarschik, “Intensity controlled shaping of the beam profile using three-wave mixing in photorefractive Bi12TiO20,” Opt. Commun. 151, 196–202 (1998).
[CrossRef]

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Dirksen, D.

D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
[CrossRef]

D. Dirksen, G. von Bally, “Holographic double-exposure interferometry in near real time with photorefractive crystals,” J. Opt. Soc. Am. B 11, 1858–1863 (1994).
[CrossRef]

Esselbach, M.

H. Rehn, M. Esselbach, R. M. Kowarschik, K. H. Ringhofer, “Photorefractive novelty filters for transient phase evaluation,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 730–737 (1996).
[CrossRef]

Feinberg, J.

D. Z. Anderson, J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
[CrossRef]

Georges, M. P.

M. P. Georges, Ph. C. Lemaire, “Phase-shifting real-time holographic interferometry that uses bismuth oxide crystals,” Appl. Opt. 34, 7497–7506 (1995).
[CrossRef] [PubMed]

M. P. Georges, Ph. C. Lemaire, “Real-time interferometer with BSO crystal using phase-shifting for quantitative deformation measurement,” in Proceedings of Conference on Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 403–407.

Haji-Sheikh, A.

Hall, T. J.

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
[CrossRef]

Herriau, J. P.

Huignard, J. P.

Kamshilin, A. A.

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, (Springer-Verlag, Berlin, 1991).
[CrossRef]

Kiessling, A.

G. Cedilnik, A. Kiessling, R. Kowarschik, “Intensity controlled shaping of the beam profile using three-wave mixing in photorefractive Bi12TiO20,” Opt. Commun. 151, 196–202 (1998).
[CrossRef]

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kowarschik, R.

G. Cedilnik, A. Kiessling, R. Kowarschik, “Intensity controlled shaping of the beam profile using three-wave mixing in photorefractive Bi12TiO20,” Opt. Commun. 151, 196–202 (1998).
[CrossRef]

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Kowarschik, R. M.

H. Rehn, M. Esselbach, R. M. Kowarschik, K. H. Ringhofer, “Photorefractive novelty filters for transient phase evaluation,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 730–737 (1996).
[CrossRef]

Kreis, T.

T. Kreis, Holographic Interferometry: Principles and Methods, (Akademische Verlagsgesellschaft, Berlin, 1996).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Kwong, N. S.-K.

Labrunie, L.

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

L. Labrunie, G. Pauliat, G. Roosen, J. C. Launay, “Simultaneous acquisition of π/2 phase-stepped interferograms with a photorefractive Bi12GeO20 crystal: application to real-time double-pulse holography,” Opt. Lett. 20, 1652–1654 (1995).
[CrossRef] [PubMed]

Launay, J. C.

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

L. Labrunie, G. Pauliat, G. Roosen, J. C. Launay, “Simultaneous acquisition of π/2 phase-stepped interferograms with a photorefractive Bi12GeO20 crystal: application to real-time double-pulse holography,” Opt. Lett. 20, 1652–1654 (1995).
[CrossRef] [PubMed]

Leidenbach, S.

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

Lemaire, Ph. C.

M. P. Georges, Ph. C. Lemaire, “Phase-shifting real-time holographic interferometry that uses bismuth oxide crystals,” Appl. Opt. 34, 7497–7506 (1995).
[CrossRef] [PubMed]

M. P. Georges, Ph. C. Lemaire, “Real-time interferometer with BSO crystal using phase-shifting for quantitative deformation measurement,” in Proceedings of Conference on Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 403–407.

Magnusson, R.

X. Wang, R. Magnusson, A. Haji-Sheikh, “Real-time interferometry with photorefractive reference holograms,” Appl. Opt. 32, 1983–1986 (1993).
[CrossRef] [PubMed]

R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
[CrossRef]

Malacara, D.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Malacara, Z.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Mann, M.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

M. Mann, E. Shamonina, K. H. Ringhofer, “Modelling of two wave mixing experiments in sillenite crystals,” Comp. Phys. Comm. 96, 61–86 (1996).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Marrakchi, A.

Matthes, F.

D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
[CrossRef]

Mitchell, J. H.

R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Pauliat, G.

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

L. Labrunie, G. Pauliat, G. Roosen, J. C. Launay, “Simultaneous acquisition of π/2 phase-stepped interferograms with a photorefractive Bi12GeO20 crystal: application to real-time double-pulse holography,” Opt. Lett. 20, 1652–1654 (1995).
[CrossRef] [PubMed]

Petrov, M. P.

A. A. Kamshilin, M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, (Springer-Verlag, Berlin, 1991).
[CrossRef]

Powell, A. K.

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, Holographic Interferometry: Principles and Methods, Vol. 68 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1994).
[CrossRef]

Rehn, H.

H. Rehn, M. Esselbach, R. M. Kowarschik, K. H. Ringhofer, “Photorefractive novelty filters for transient phase evaluation,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 730–737 (1996).
[CrossRef]

Rickermann, F.

G. von Bally, F. Rickermann, S. Riehemann, “Application of photorefractive crystals in stroboscopic double-exposure holographic interferometry,” in Proceedings of Conference Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 527–530.

Riehemann, S.

D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
[CrossRef]

G. von Bally, F. Rickermann, S. Riehemann, “Application of photorefractive crystals in stroboscopic double-exposure holographic interferometry,” in Proceedings of Conference Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 527–530.

Ringhofer, K. H.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

M. Mann, E. Shamonina, K. H. Ringhofer, “Modelling of two wave mixing experiments in sillenite crystals,” Comp. Phys. Comm. 96, 61–86 (1996).
[CrossRef]

H. Rehn, M. Esselbach, R. M. Kowarschik, K. H. Ringhofer, “Photorefractive novelty filters for transient phase evaluation,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 730–737 (1996).
[CrossRef]

Roosen, G.

L. Labrunie, G. Pauliat, J. C. Launay, S. Leidenbach, G. Roosen, “Real-time double exposure holographic phase shifting interferometer using a photorefractive crystal,” Opt. Commun. 140, 119–127 (1997).
[CrossRef]

L. Labrunie, G. Pauliat, G. Roosen, J. C. Launay, “Simultaneous acquisition of π/2 phase-stepped interferograms with a photorefractive Bi12GeO20 crystal: application to real-time double-pulse holography,” Opt. Lett. 20, 1652–1654 (1995).
[CrossRef] [PubMed]

Servin, M.

D. Malacara, M. Servin, Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).

Shamonina, E.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

M. Mann, E. Shamonina, K. H. Ringhofer, “Modelling of two wave mixing experiments in sillenite crystals,” Comp. Phys. Comm. 96, 61–86 (1996).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Stace, C.

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
[CrossRef]

Staebler, D. L.

D. L. Staebler, J. J. Amodei, “Coupled-wave analysis of holographic storage in LiNbO3,” J. Appl. Phys. 43, 1042–1049 (1972).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, “Adaptive interferometry: a new area of applications of photorefractive crystals,” in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), pp. 125–140.
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, (Springer-Verlag, Berlin, 1991).
[CrossRef]

Tamita, Y.

Tiziani, H. J.

H. J. Tiziani, “Real-time metrology with BSO crystals,” Opt. Act. 29, 463–470 (1982).
[CrossRef]

Valentin, T.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

von Bally, G.

D. Dirksen, F. Matthes, S. Riehemann, G. von Bally, “Phase shifting holographic double exposure interferometry with fast photorefractive crystals,” Opt. Commun. 134, 310–316 (1997).
[CrossRef]

D. Dirksen, G. von Bally, “Holographic double-exposure interferometry in near real time with photorefractive crystals,” J. Opt. Soc. Am. B 11, 1858–1863 (1994).
[CrossRef]

G. von Bally, F. Rickermann, S. Riehemann, “Application of photorefractive crystals in stroboscopic double-exposure holographic interferometry,” in Proceedings of Conference Topical Meeting on Photorefractive Materials, Effects, and Devices, (PR’ 97) (N.p., 1997), pp. 527–530.

Walsh, K.

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 3, 288–303 (1990).
[CrossRef]

Wang, X.

Webb, D. J.

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

Wilson, D. R.

R. Magnusson, J. H. Mitchell, T. D. Black, D. R. Wilson, “Holographic interferometry using iron-doped lithium niobate,” Appl. Phys. Lett. 51, 81–82 (1987).
[CrossRef]

Yariv, A.

Appl. Opt. (4)

Appl. Phys. B (1)

E. Shamonina, G. Cedilnik, M. Mann, A. Kiessling, D. J. Webb, R. Kowarschik, K. H. Ringhofer, “Investigation of two-wave mixing in arbitrary oriented sillenite crystals,” Appl. Phys. B 64, 49–56 (1997).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Two-wave mixing in a photorefractive crystal (PRC). The wave R that is diffracted from the pump wave P at the index grating IG acts as a reference wave that interferes with the signal wave S. The intensity is measured by a detector D (CCD camera or photodiode).

Fig. 2
Fig. 2

(a) Setup for double two-wave mixing with signal wave S and two pump waves P A and P B from different directions with coherent light source L (He–Ne laser, λ = 633 nm); beam splitters, BS; mirrors M; high voltage supply U0; detector D (CCD camera or pair of photodiodes); and a photorefractive crystal PRC (Bi12TiO20). (b) Pump waves P A and P B fall into the crystal at different locations A and B.

Fig. 3
Fig. 3

Experimental result (open circles and crosses) and calculated curves (lines) for the intensity change ΔG after phase shift Δφ S in the signal wave. No electric field was applied to the photorefractive crystal.

Fig. 4
Fig. 4

Experimental results and calculated curves for the intensity change ΔG after phase shift Δφ S in the signal wave. The applied electric fields were (a) E 0 = 2.0 kV/cm and (b) 6.7 kV/cm.

Fig. 5
Fig. 5

Experimental results (crosses and open dots) and calculated values (lines) for intensity change pairs (ΔG A , ΔG B ) behind the photorefractive crystal after phase change Δφ S and amplitude change K in the signal wave. No electric field was applied to the crystal.

Fig. 6
Fig. 6

Experimental and calculated values of intensity change pairs (ΔG A , ΔG B ) behind the photorefractive crystal after phase change Δφ S in the signal wave with applied electric fields (a) E 0 = 2.0 kV/cm and (b) 6.7 kV/cm.

Fig. 7
Fig. 7

Possible arrangements for two-dimensional measurement with locally separated regions A and B. (a) Signal wave is split into separate crystal regions A and B. (b) Two complementary grid masks in the paths of the pump waves result in alternating layers A and B in the crystal.

Fig. 8
Fig. 8

Camera images of the plane signal wave behind the crystal when complementary grids in the pump wave paths are used. No electric field was applied to the crystal. (a) Stationary state with attenuated regions (A) and enhanced regions (B). (b) Intensity immediately after insertion of a neutral density filter with a wedge aberration. (c) Stationary state several minutes after insertion of the filter.

Fig. 9
Fig. 9

Interactions A and B are temporally separated. The pump waves fall in a temporally alternating sequence into the same crystal region. Two modulators (Sh A and Sh B ) switch the pump waves in antiphase on and off. The lenses L are used for 4f imaging of an object. Detector D (video camera) and the modulators are synchronized.

Fig. 10
Fig. 10

Phase shifts in the signal wave (modulo 2π) measured by double two-wave mixing with temporal splitting. (a) Hot tip of a soldering iron (dark area) is introduced into the signal path. (b) Cylindrical lens in the signal path (D = 0.25) was rotated by 90°.

Equations (10)

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ddz ASz=12 mzΓApz-αASz.
dASzdz=ASzΓ-αASz.
ARstd=VASstd.
AIF=AS+VASstd.
AS=KASstdexpiΔφS
IIF,A/B=|ASstd|2K2+VA/B2+2KVA/B cosΔφS.
ΔGA/B=IIF, A/BIIF,A/Bstd -1.
ΔGA/B=K2-1+2VA/B(K cosΔφS-1)VA/B+12.
VA/B=|VA/B|expiφV,A/B.
ΔGA/B=2|VA/B| cosΔφS-φV,A/B-cosφV,A/B|VA/B|2+2|VA/B| cosφV,A/B+1.

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