Abstract

A holographic interferometer that uses two-wave mixing in a photorefractive (Bi12SiO20) crystal under an applied ac field is described. The interferometer uses a repetitive sequence of separate record and readout times to obtain quasi real-time holographic interferograms of vibrating objects. It is shown that a good signal-to-noise ratio of the interferometer is obtained by turning off the object illumination and the applied ac field during readout of the hologram. The good signal-to-noise ratio of the resulting holographic interferograms enables phase measurement, which allows for quantitative deformation analysis.

© 1996 Optical Society of America

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References

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  1. J. P. Huignard, J. P. Herriau, T. Valentin, “Time average holographic interferometry with photoconductive electrooptic BSO crystals,” Appl. Opt. 16, 2796–2798 (1977).
    [Crossref] [PubMed]
  2. 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, 15–18 (1980).
    [Crossref]
  3. R. C. Troth, J. C. Dainty, “Holographic interferometry using anisotropic self-diffraction in BSO,” Opt. Lett. 16, 53–55 (1991).
    [Crossref] [PubMed]
  4. M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
    [Crossref]
  5. S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
    [Crossref]
  6. K. Walsh, A. K. Powell, C. Stace, T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
    [Crossref]
  7. A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
    [Crossref]
  8. A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (1981).
    [Crossref]
  9. S. I. Stepanov, M. P. Petrov, “Efficiency unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
    [Crossref]
  10. J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
    [Crossref]
  11. A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).
  12. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  13. C. Besson, J. M. C. Jonathan, A. Villing, G. Pauliat, G. Roosen, “Influence of alternating field frequency on enhanced photorefractive gain in two-beam coupling,” Opt. Lett. 14, 1359–1361 (1989).
    [Crossref] [PubMed]
  14. D. Dirksen, G. von Bally, “Holographic double-exposure interferometry in near real time with photorefractive crystal,” J. Opt. Soc. Am. B 11, 1858–1863 (1994).
    [Crossref]
  15. C. C. Aleksoff, “Temporally modulated holography,” Appl. Opt. 10, 1329–1341 (1971).
    [Crossref] [PubMed]
  16. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 351–393 (1988).
  17. L.-S. Wang, S. Krishnaswamy, “Additive-subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. (to be published).

1994 (2)

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
[Crossref]

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

1991 (1)

1990 (1)

1989 (2)

C. Besson, J. M. C. Jonathan, A. Villing, G. Pauliat, G. Roosen, “Influence of alternating field frequency on enhanced photorefractive gain in two-beam coupling,” Opt. Lett. 14, 1359–1361 (1989).
[Crossref] [PubMed]

A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).

1988 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 351–393 (1988).

1987 (1)

A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
[Crossref]

1985 (2)

S. I. Stepanov, M. P. Petrov, “Efficiency unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[Crossref]

1981 (1)

A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

1980 (1)

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, 15–18 (1980).
[Crossref]

1979 (1)

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[Crossref]

1977 (1)

1971 (1)

Aleksoff, C. C.

Apostolidis, A. G.

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[Crossref]

Barbosa, E.

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
[Crossref]

Besson, C.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 351–393 (1988).

Dainty, J. C.

Dirksen, D.

Günter, P.

A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Hall, T. J.

Herriau, J. P.

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[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, 15–18 (1980).
[Crossref]

J. P. Huignard, J. P. Herriau, T. Valentin, “Time average holographic interferometry with photoconductive electrooptic BSO crystals,” Appl. Opt. 16, 2796–2798 (1977).
[Crossref] [PubMed]

Huignard, J. P.

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[Crossref]

A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (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, 15–18 (1980).
[Crossref]

J. P. Huignard, J. P. Herriau, T. Valentin, “Time average holographic interferometry with photoconductive electrooptic BSO crystals,” Appl. Opt. 16, 2796–2798 (1977).
[Crossref] [PubMed]

Johnson, R. V.

A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
[Crossref]

Jonathan, J. M. C.

Kamshilin, A. A.

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
[Crossref]

A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).

Krishnaswamy, S.

L.-S. Wang, S. Krishnaswamy, “Additive-subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. (to be published).

Kulikov, V. V.

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[Crossref]

Mallick, S.

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[Crossref]

Marrakchi, A.

A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
[Crossref]

A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (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, 15–18 (1980).
[Crossref]

Miridonov, S. V.

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[Crossref]

Mokrushina, E. V.

A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).

Pauliat, G.

Petrov, M. P.

A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).

S. I. Stepanov, M. P. Petrov, “Efficiency unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[Crossref]

Powell, A. K.

Roosen, G.

Stace, C.

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, “Efficiency unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[Crossref]

Tanguay, A. R.

A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
[Crossref]

Troth, R. C.

Valentin, T.

Villing, A.

von Bally, G.

Walsh, K.

Wang, L.-S.

L.-S. Wang, S. Krishnaswamy, “Additive-subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. (to be published).

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Opt. (2)

Appl. Phys. (1)

A. Marrakchi, J. P. Huignard, P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiment with BSO crystals,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Marrakchi, R. V. Johnson, A. R. Tanguay, “Polarization properties of enhanced self-diffraction in sellenite crystals,” IEEE J. Quantum Electron. QE-23, 2142–2151 (1987).
[Crossref]

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

S. V. Miridonov, A. A. Kamshilin, E. Barbosa, “Recyclable holographic interferometer with a photorefractive crystal: optical scheme optimization,” J. Opt. Soc. Am. A. 11, 1780–1788 (1994).
[Crossref]

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

Opt. Commun. (4)

M. P. Petrov, S. V. Miridonov, S. I. Stepanov, V. V. Kulikov, “Light diffraction and nonlinear image processing in electro-optic BSO,” Opt. Commun. 31, 301–304 (1979).
[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, 15–18 (1980).
[Crossref]

S. I. Stepanov, M. P. Petrov, “Efficiency unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

J. P. Herriau, J. P. Huignard, A. G. Apostolidis, S. Mallick, “Polarization properties in two wave mixing with moving grating in photorefractive BSO crystals: application to dynamic interferometry,” Opt. Commun. 56, 141–144 (1985).
[Crossref]

Opt. Eng. (1)

A. A. Kamshilin, E. V. Mokrushina, M. P. Petrov, “Adaptive holographic interferometers operating through self-diffraction of recording beams in photorefractive crystals,” Opt. Eng. 28, 580–585 (1989).

Opt. Lett. (2)

Prog. Opt. (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt. 26, 351–393 (1988).

Other (2)

L.-S. Wang, S. Krishnaswamy, “Additive-subtractive speckle interferometry: extraction of phase data in noisy environments,” Opt. Eng. (to be published).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

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Figures (9)

Fig. 1
Fig. 1

Principle of the holographic interferometer with two-wave mixing in BSO crystal.

Fig. 2
Fig. 2

Diffraction efficiency η versus the writing-beam angle 2θ for various applied external sinusoidal ac electric fields: ●, E0 = 0 kV/cm; ◯, 1.9 kV/cm; ◆, 2.8 kV/cm; ×, 3.7 kV/cm; ▼, 4.6 kV/cm; △, 5.6 kV/cm; ■, 6.5 kV/cm.

Fig. 3
Fig. 3

Dynamic sensitivity S versus the writing-beam angle 2θ for E0 = 0kV/cm and E0 = 4kV/cm.

Fig. 4
Fig. 4

Dynamic holographic interferometer setup.

Fig. 5
Fig. 5

Dependence of the signal intensity (◆), the reference-beam noise (◯), and the object-beam noise (□) on the input polarization angle.

Fig. 6
Fig. 6

Timing diagram.

Fig. 7
Fig. 7

Piezoelectric membrane vibrating at 2.7kHz: (A) continuous readout and (B) separate readout.

Fig. 8
Fig. 8

Clamped circular plate vibrating at 15 kHz with separate readout: (A) diffusion (E0 = 0) and (B) with an external sinusoidal electric field (E0 = 5.6 kV/cm).

Fig. 9
Fig. 9

Clamped circular plate vibrating at 15 kHz. Holographic interferograms with (A) no phase shift, (B) π phase shift, and (C) π /2 phase shift. (D) Three-dimensional view of the unwrapped phase map.

Equations (6)

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

E ( t ) = E sat [ 1 exp ( t ) ] ,
η ( t ) = η sat [ 1 exp ( t ) ] 2 ,
I 1 = A ( 1 + B    cos    2 M ) ,
I 2 = A ( 1 B    cos    2 M ) .
I 3 = A ( 1 + B    sin    2 M ) .
tan    2 M = 2 I 3 ( I 1 + I 2 ) I 2 I 1 .

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