Abstract

A transient phase-measuring technique that uses a self-pumped phase-conjugate mirror as an optical novelty filter is presented. A change in the reflectivity of the mirror as a function of a change in the incident wave front permits the transient measurement of a two-dimensional phase distribution. This method allows us to investigate fast processes using media with slow response. A simple theoretical model explains the experimental results with sufficient accuracy. The results can be used for the calibration of the measuring system. The described method is used for the measurement of a temporally varying wave front.

© 1997 Optical Society of America

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References

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  1. E. Kubota, T. Aoyama, and Y. Uesu, “Optimum velocity and frequency of a moving phase object in the BaTiO3 novelty filter using self-pumped phase conjugation,” in Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1995), pp. 412–415.
  2. M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
    [Crossref]
  3. J. E. Ford, Y. Fainman, and S. H. Lee, “Time-integrating interferometry using photorefractive fanout,” Opt. Lett. 13, 856–858 (1988).
    [Crossref] [PubMed]
  4. M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
    [Crossref]
  5. H. Rehn and R. Kowarschik, “Beam fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
    [Crossref] [PubMed]
  6. J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
    [Crossref]
  7. D. Z. Anderson and J. Feinberg, “Optical novelty filters,” IEEE J. Quantum Electron. 25, 635–647 (1989).
    [Crossref]
  8. H. Rehn and R. Kowarschik, “Experimental investigations of the external self-pumped phase conjugate mirror,” Opt. Commun. 109, 155–162 (1994).
    [Crossref]
  9. P. M. Petersen, “A simple analytic approach to degenerated four-wave mixing by comparison with real-time holography,” IEEE J. Quantum Electron. QE-23, 2095–2101 (1987).
    [Crossref]
  10. P. Yeh, Introduction to Photorefractive Nonlinear Optics, J. W. Goodman, ed. (Wiley, New York, 1993), Chap. 4.
  11. A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
    [Crossref] [PubMed]
  12. J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
    [Crossref]
  13. A. Chiou, “Anisotropic cross talk in optical interconnection using self-pumped phase conjugate mirror at the Fourier plane,” Opt. Lett. 17, 1018–1020 (1992).
    [Crossref] [PubMed]

1995 (3)

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

H. Rehn and R. Kowarschik, “Beam fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
[Crossref] [PubMed]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

1994 (1)

H. Rehn and R. Kowarschik, “Experimental investigations of the external self-pumped phase conjugate mirror,” Opt. Commun. 109, 155–162 (1994).
[Crossref]

1992 (1)

1991 (1)

J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
[Crossref]

1989 (2)

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

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

1988 (1)

1987 (1)

P. M. Petersen, “A simple analytic approach to degenerated four-wave mixing by comparison with real-time holography,” IEEE J. Quantum Electron. QE-23, 2095–2101 (1987).
[Crossref]

1986 (1)

Anderson, D. Z.

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

Aoyama, T.

E. Kubota, T. Aoyama, and Y. Uesu, “Optimum velocity and frequency of a moving phase object in the BaTiO3 novelty filter using self-pumped phase conjugation,” in Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1995), pp. 412–415.

Cescato, L.

Chiou, A.

Cronin-Golomb, M.

J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
[Crossref]

Denz, C.

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

Fainman, Y.

Feinberg, J.

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

Ford, J. E.

Frejlich, J.

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
[Crossref] [PubMed]

Kamshilin, A. A.

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

A. A. Kamshilin, J. Frejlich, and L. Cescato, “Photorefractive crystals for the stabilization of the holographic setup,” Appl. Opt. 25, 2375–2381 (1986).
[Crossref] [PubMed]

Khoury, J.

J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
[Crossref]

Kowarschik, R.

H. Rehn and R. Kowarschik, “Beam fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
[Crossref] [PubMed]

H. Rehn and R. Kowarschik, “Experimental investigations of the external self-pumped phase conjugate mirror,” Opt. Commun. 109, 155–162 (1994).
[Crossref]

Kubota, E.

E. Kubota, T. Aoyama, and Y. Uesu, “Optimum velocity and frequency of a moving phase object in the BaTiO3 novelty filter using self-pumped phase conjugation,” in Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1995), pp. 412–415.

Kulikov, V. V.

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

Lee, S. H.

Mokrushina, E. V.

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

Petersen, P. M.

P. M. Petersen, “A simple analytic approach to degenerated four-wave mixing by comparison with real-time holography,” IEEE J. Quantum Electron. QE-23, 2095–2101 (1987).
[Crossref]

Rauch, T.

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

Rehn, H.

H. Rehn and R. Kowarschik, “Beam fanning novelty filter with enhanced dynamic phase resolution,” Appl. Opt. 34, 4907–4911 (1995).
[Crossref] [PubMed]

H. Rehn and R. Kowarschik, “Experimental investigations of the external self-pumped phase conjugate mirror,” Opt. Commun. 109, 155–162 (1994).
[Crossref]

Sedlatschek, M.

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

Tschudi, T.

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

Uesu, Y.

E. Kubota, T. Aoyama, and Y. Uesu, “Optimum velocity and frequency of a moving phase object in the BaTiO3 novelty filter using self-pumped phase conjugation,” in Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1995), pp. 412–415.

Woods, C. L.

J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
[Crossref]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics, J. W. Goodman, ed. (Wiley, New York, 1993), Chap. 4.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

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

P. M. Petersen, “A simple analytic approach to degenerated four-wave mixing by comparison with real-time holography,” IEEE J. Quantum Electron. QE-23, 2095–2101 (1987).
[Crossref]

Opt. Commun. (4)

H. Rehn and R. Kowarschik, “Experimental investigations of the external self-pumped phase conjugate mirror,” Opt. Commun. 109, 155–162 (1994).
[Crossref]

J. Khoury, C. L. Woods, and M. Cronin-Golomb, “Photorefractive holographic interference novelty filter,” Opt. Commun. 82, 533–538 (1991).
[Crossref]

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Generalized theory of the resolution of object tracking novelty filters,” Opt. Commun. 116, 25–30 (1995).
[Crossref]

J. Frejlich, A. A. Kamshilin, V. V. Kulikov, and E. V. Mokrushina, “Adaptive holographic interferometry using photorefractive crystals,” Opt. Commun. 70, 82–86 (1989).
[Crossref]

Opt. Lett. (2)

Opt. Mater. (1)

M. Sedlatschek, T. Rauch, C. Denz, and T. Tschudi, “Demonstrator concepts and performance of a photorefractive optical novelty filter,” Opt. Mater. 4, 376–380 (1995).
[Crossref]

Other (2)

P. Yeh, Introduction to Photorefractive Nonlinear Optics, J. W. Goodman, ed. (Wiley, New York, 1993), Chap. 4.

E. Kubota, T. Aoyama, and Y. Uesu, “Optimum velocity and frequency of a moving phase object in the BaTiO3 novelty filter using self-pumped phase conjugation,” in Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1995), pp. 412–415.

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Figures (7)

Fig. 1
Fig. 1

Basic situation and interacting waves.

Fig. 2
Fig. 2

Theoretical dependence between the relative reflectivity decrease D and the introduced phase shift ϕn. The functions correspond to Eq. (8). q and η are parameters. (a) The value of q is varied (q=0.10.35 from top to bottom) for a given η=0.2. (b) The value of η is varied (η=0.10.45 from top to bottom) for a given q=0.2.

Fig. 3
Fig. 3

Experimental arrangement. The optical addressable liquid-crystal spatial light modulator is used to simulate a temporal-varying-phase object. The actual measuring instrument consists of the ESPPCM (or the cat PCM), the beam splitter, the lens, and the camera only.

Fig. 4
Fig. 4

Temporal behavior of the reflectivity of an ESPPCM after the introduction of a phase change into the signal wave. Data: barium titanate crystal 6 mm × 6 mm × 6 mm with 45° cut, signal intensity on the crystal surface 3mW/mm2, and phase change ϕn=π/2.

Fig. 5
Fig. 5

Geometry of the interaction region inside the crystal (simplified model). An example of a changed wave front that was a plane wave before is shown, and the different parts of it are marked.

Fig. 6
Fig. 6

Result of the measurement of the dependence between D and ϕn. Data: barium titanate crystal 6 mm × 6 mm × 6 mm with 45° cut and signal intensity on the crystal surface 1 mW/mm2. The symbols (squares for the ESPPCM and triangles for the cat PCM) represent the measured values, and the curve represents the fit with a function according to Eq. (8).

Fig. 7
Fig. 7

Measurement of a given wave front: (a) Given phase distribution to be measured. (b) Recorded intensity distribution of the pc signal before the introduction of the phase change and (c) after the phase change. (d) Calculated distribution of the relative reflectivity decrease D. (e) Calculated distribution of the ϕn that is the result of the measurement.

Equations (8)

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

R=IpcIs,
I3=I1(1-η)+I2η-2I1(1-η)I2η cos ϕ,
I4=I1η+I2(1-η)+2I1ηI2(1-η) cos ϕ,
Ipc=I3η+I4(1-η)+2I3ηI4(1-η)cos(ϕ),
I2=qI1,
ϕ=ϕss+ϕn,
D=1-RnRss,
D=1-R(q, η, ϕss+ϕn)R(q, η, ϕss).

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