Abstract

We demonstrate a technique by which components of an image moving with a given speed and direction may be selectively enhanced. By using the strong grating velocity sensitivity of the nonlinear photorefractive response, we show that a BSO crystal used in a schlieren imaging system may be used as a real-time velocity filter. The velocity selectivity, tunability and resolution constraints of this system are discussed in detail.

© 1988 Optical Society of America

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References

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  1. Y. H. Ja, “Real-Time Image Division in Four-Wave Mixing with Photorefractive BGO Crystals,” Opt. Commun. 44, 24 (1982).
    [CrossRef]
  2. J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5 (1980).
    [CrossRef]
  3. E. Ochoa, “Real-Time Intensity Inversion Using Four-Wave Mixing in Photorefractive Crystals,” Ph.D. Dissertation, Stanford U., Stanford, CA (1985).
  4. A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
    [CrossRef]
  5. D. Z. Anderson, D. M. Lininger, J. Feinberg, “Optical Tracking Novelty Filter,” Opt. Lett. 12, 123 (1987).
    [CrossRef] [PubMed]
  6. M. Cronin-Golomb, “Analytic Solution for Photorefractive Two Beam Coupling with Time Varying Signal,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, DC, 1987), paper ThC5.
  7. S. K. Kwong, “Optical Tracking Filter via Transient Energy Coupling Effect,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects and Devices (Optical Society of America, Washington, DC, 1987), paper ThC7.
  8. J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive BSO Crystals,” Opt. Commun. 38, 249 (1981).
    [CrossRef]
  9. G. C. Valley, “Two-Wave Mixing with an Applied Field and a Moving Grating,” J. Opt. Soc. Am. B 1, 868 (1984).
    [CrossRef]
  10. P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
    [CrossRef]
  11. G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704 (1983).
    [CrossRef]
  12. F. Vachss, L. Hesselink, “Selective Enhancement of Spatial Harmonics of a Photorefractive Grating,” J. Opt. Soc. Am. B (in press).
  13. A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
    [CrossRef]
  14. T. Y. Chang, P. Yeh, “Observation of Harmonic Phase Conjugation in a Photorefractive Medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).
  15. T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
    [CrossRef]
  16. F. Vachss, L. Hesselink, “Holographic Beam Coupling in Anisotropic Photorefractive Media,” J. Opt. Soc. Am. A 4, (1987).
    [CrossRef]
  17. R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  18. P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Ph.D. Dissertation, Swiss Federal Institute of Technology (ETH), Zurich (1981).
  19. F. Vachss, L. Hesselink, “Measurement of the Electro-Optic and Electrogyratory Effects in BSO and BGO,” Opt. Commun. 62, 159 (1987).
    [CrossRef]

1987 (3)

D. Z. Anderson, D. M. Lininger, J. Feinberg, “Optical Tracking Novelty Filter,” Opt. Lett. 12, 123 (1987).
[CrossRef] [PubMed]

F. Vachss, L. Hesselink, “Holographic Beam Coupling in Anisotropic Photorefractive Media,” J. Opt. Soc. Am. A 4, (1987).
[CrossRef]

F. Vachss, L. Hesselink, “Measurement of the Electro-Optic and Electrogyratory Effects in BSO and BGO,” Opt. Commun. 62, 159 (1987).
[CrossRef]

1986 (1)

T. Y. Chang, P. Yeh, “Observation of Harmonic Phase Conjugation in a Photorefractive Medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).

1985 (1)

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1984 (1)

1983 (1)

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704 (1983).
[CrossRef]

1982 (2)

T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
[CrossRef]

Y. H. Ja, “Real-Time Image Division in Four-Wave Mixing with Photorefractive BGO Crystals,” Opt. Commun. 44, 24 (1982).
[CrossRef]

1981 (2)

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive BSO Crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

1980 (2)

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
[CrossRef]

Anderson, D. Z.

Burkhardt, C. B.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Chang, T. Y.

T. Y. Chang, P. Yeh, “Observation of Harmonic Phase Conjugation in a Photorefractive Medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).

Collier, R. J.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Cronin-Golomb, M.

M. Cronin-Golomb, “Analytic Solution for Photorefractive Two Beam Coupling with Time Varying Signal,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, DC, 1987), paper ThC5.

Feinberg, J.

Gunter, P.

A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Ph.D. Dissertation, Swiss Federal Institute of Technology (ETH), Zurich (1981).

Herriau, J. P.

A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
[CrossRef]

Hesselink, L.

F. Vachss, L. Hesselink, “Holographic Beam Coupling in Anisotropic Photorefractive Media,” J. Opt. Soc. Am. A 4, (1987).
[CrossRef]

F. Vachss, L. Hesselink, “Measurement of the Electro-Optic and Electrogyratory Effects in BSO and BGO,” Opt. Commun. 62, 159 (1987).
[CrossRef]

F. Vachss, L. Hesselink, “Selective Enhancement of Spatial Harmonics of a Photorefractive Grating,” J. Opt. Soc. Am. B (in press).

Huignard, J. P.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive BSO Crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
[CrossRef]

Ja, Y. H.

Y. H. Ja, “Real-Time Image Division in Four-Wave Mixing with Photorefractive BGO Crystals,” Opt. Commun. 44, 24 (1982).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704 (1983).
[CrossRef]

Kwong, S. K.

S. K. Kwong, “Optical Tracking Filter via Transient Energy Coupling Effect,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects and Devices (Optical Society of America, Washington, DC, 1987), paper ThC7.

Lin, L. H.

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Lininger, D. M.

Marrakchi, A.

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive BSO Crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
[CrossRef]

Ochoa, E.

E. Ochoa, “Real-Time Intensity Inversion Using Four-Wave Mixing in Photorefractive Crystals,” Ph.D. Dissertation, Stanford U., Stanford, CA (1985).

Pencheva, T. G.

T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
[CrossRef]

Petrov, M. P.

T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
[CrossRef]

Rajbenbach, H.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Refregier, P.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Solymar, L.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Stepanov, S. I.

T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
[CrossRef]

Vachss, F.

F. Vachss, L. Hesselink, “Holographic Beam Coupling in Anisotropic Photorefractive Media,” J. Opt. Soc. Am. A 4, (1987).
[CrossRef]

F. Vachss, L. Hesselink, “Measurement of the Electro-Optic and Electrogyratory Effects in BSO and BGO,” Opt. Commun. 62, 159 (1987).
[CrossRef]

F. Vachss, L. Hesselink, “Selective Enhancement of Spatial Harmonics of a Photorefractive Grating,” J. Opt. Soc. Am. B (in press).

Valley, G. C.

G. C. Valley, “Two-Wave Mixing with an Applied Field and a Moving Grating,” J. Opt. Soc. Am. B 1, 868 (1984).
[CrossRef]

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704 (1983).
[CrossRef]

White, J. O.

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Yariv, A.

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Yeh, P.

T. Y. Chang, P. Yeh, “Observation of Harmonic Phase Conjugation in a Photorefractive Medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).

Appl. Phys. (1)

A. Marrakchi, J. P. Huignard, P. Gunter, “Diffraction Efficiency and Energy Transfer in Two-Wave Mixing Experiments with BSO Crystals,” Appl. Phys. 24, 131 (1981).
[CrossRef]

Appl. Phys. Lett. (1)

J. O. White, A. Yariv, “Real-Time Image Processing via Four-Wave Mixing in a Photorefractive Medium,” Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

J. Appl. Phys. (1)

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two-Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Grating: Theory and Experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

J. Opt. Soc. Am. A (2)

T. Y. Chang, P. Yeh, “Observation of Harmonic Phase Conjugation in a Photorefractive Medium,” J. Opt. Soc. Am. A 3(13), P33 (1986).

F. Vachss, L. Hesselink, “Holographic Beam Coupling in Anisotropic Photorefractive Media,” J. Opt. Soc. Am. A 4, (1987).
[CrossRef]

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

Opt. Commun. (5)

F. Vachss, L. Hesselink, “Measurement of the Electro-Optic and Electrogyratory Effects in BSO and BGO,” Opt. Commun. 62, 159 (1987).
[CrossRef]

T. G. Pencheva, M. P. Petrov, S. I. Stepanov, “Selective Properties of Volume Phase Holograms in Photorefractive Crystals,” Opt. Commun. 40, 175 (1982).
[CrossRef]

Y. H. Ja, “Real-Time Image Division in Four-Wave Mixing with Photorefractive BGO Crystals,” Opt. Commun. 44, 24 (1982).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive BSO Crystals,” Opt. Commun. 38, 249 (1981).
[CrossRef]

A. Marrakchi, J. P. Huignard, J. P. Herriau, “Application of Phase Conjugation in BSO Crystals to Mode Pattern Visualisation of Diffuse Vibrating Structures,” Opt. Commun. 34, 15 (1980).
[CrossRef]

Opt. Eng. (1)

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” Opt. Eng. 22, 704 (1983).
[CrossRef]

Opt. Lett. (1)

Other (6)

M. Cronin-Golomb, “Analytic Solution for Photorefractive Two Beam Coupling with Time Varying Signal,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, DC, 1987), paper ThC5.

S. K. Kwong, “Optical Tracking Filter via Transient Energy Coupling Effect,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects and Devices (Optical Society of America, Washington, DC, 1987), paper ThC7.

E. Ochoa, “Real-Time Intensity Inversion Using Four-Wave Mixing in Photorefractive Crystals,” Ph.D. Dissertation, Stanford U., Stanford, CA (1985).

F. Vachss, L. Hesselink, “Selective Enhancement of Spatial Harmonics of a Photorefractive Grating,” J. Opt. Soc. Am. B (in press).

R. J. Collier, C. B. Burkhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

P. Gunter, “Holography, Coherent Light Amplification and Optical Phase Conjugation with Photorefractive Materials,” Ph.D. Dissertation, Swiss Federal Institute of Technology (ETH), Zurich (1981).

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Figures (8)

Fig. 1
Fig. 1

One-to-one imaging system with the moving object. Here angular frequency components Δk give rise to frequency shifts of ω = ν · Δk. Interference with a reference beam kr results in moving grating components in the holographic medium.

Fig. 2
Fig. 2

Imaging system as in Fig. 1 with the inclusion of a knife-edge in the Fourier plane to reject negative velocity components.

Fig. 3
Fig. 3

Views of the Fourier plane with the knife-edge in place. Here the image velocity is assumed to point in the positive x direction. This results in a vertical enhancement band in the right half-plane and a corresponding band of deenhancement in the left. (a)–(c) Relative sizes of these two bands for differing orientations of the knife-edge.

Fig. 4
Fig. 4

Experimental setup showing the schlieren system in a photorefractive recording configuration. The He–Ne beam probes the resulting hologram in the second harmonic readout angle.

Fig. 5
Fig. 5

Reproductions of a holographic output for varying image speeds both vertically (parallel to knife-edge) and horizontally (perpendicular to edge). The zero image velocity case is shown in the center. The incident intensity on the crystal is 2.7 mW/cm2.

Fig. 6
Fig. 6

Holographic output for horizontal velocities with the incident intensity reduced to 0.9 mW/cm2.

Fig. 7
Fig. 7

Holographic image readout geometry showing the existence of multiple Bragg angles when the reading and writing wavelengths differ.

Fig. 8
Fig. 8

Angular sensitivity spectrum for an 8 × 8 × 8-mm BSO crystal with 6 kV applied in the 〈110〉 direction. The normalized diffraction efficiency is plotted vertically vs angular deviation of the readout beam from the Bragg angle in milliradians on the horizontal axis.

Equations (20)

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E ( r ) = E 1 t ( r ) exp [ i ( k 1 · r - ω t ) ] + E 2 exp [ i ( k 2 · r - ω t ) ] .
I ( r ) = E 1 2 t 2 ( r ) + E 2 2 + [ E 1 · E 2 * t ( r ) × exp [ i ( k 1 - k 2 ) · r ] + c . c . ]
= I 1 t 2 ( r ) + I 2 + 2 ( I 1 I 2 ) 1 / 2 × { d k A ( k ) exp [ i ( k + k G ) · r ] + c . c . } ,
I ( r , t ) = I 1 t 2 ( r - ν t ) + I 2 + 2 ( I 1 I 2 ) 1 / 2 × ( d k A ( k ) exp { i [ ( k + k G ) · r - k · ν t ] } + c . c . )
ν ( k ) k · ν k + k G .
ν = s I 0 R k G e 0 ν 1 ,
ν n ν 1 / n 2
ν ( k ) ν 2 .
k · n ^ > 0 ,
θ B = sin - 1 [ λ r λ w sin ( θ r + θ i 2 ) ] + θ r - θ i 2 ,
θ B 1 2 ( λ r λ w + 1 ) θ r + 1 2 ( λ r λ w - 1 ) θ i .
Δ θ B 1 = 1 2 ( λ r λ w - 1 ) Δ θ i
η ( δ ) = η ( 0 ) sinc 2 ( δ L Λ G )
δ 1 / 2 = 0.88 Λ G L             ( FWHM ) .
Δ θ i < 1.76 Λ G ( λ r λ w - 1 ) L .
2 λ w d < 4 Λ G ( λ r λ w - 1 )             or             d > ( λ r - λ w ) L 2 Λ G ,
Δ θ B 2 = 1 2 ( 2 λ r λ w - 1 ) Δ θ i .
Λ G r π < Λ G L .
δ 1 / 2 total = 2 Λ G ( 2 ) r π + 0.88 Λ G ( 2 ) L = 2.88 Λ G ( 2 ) L = 1.44 Λ G L ( FWHM ) ,
d > ( 2 λ r - λ w ) L 1.44 Λ G .

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