Abstract

The measurement of optical contrasts within thick biological tissues can be performed with the hybrid technique of acousto-optic imaging, but it has been shown that an acquisition rate in the 1 - 10kHz range is required for a good efficiency. This comes from the interferometric nature of the signal, blurred by speckle decorrelation in a time τc, due to a decrease of the speckle pattern contrast at the exit of the sample. An holographic setup that associates a fast and large area single photodetector and a photorefractive crystal, can measure in real-time the acousto-optic signal: this is the so-called self-adaptive wavefront holography technique. Nevertheless, it is essential to size the photorefractive response time (τPR) of the crystal with τc in order to optimize the signal-to-noise ratio of the measurement. This time mainly depends on the overall light intensity within the crystal. We have developed an original in situ method to determine τPR with the combination of acoustic pulses and a frequency de-tuning of the reference beam. We can measure precisely this time but also monitor it according to a theoretical model that we have previously described. We are able to adapt the response time of the setup to the decorrelation time of the medium under study.

© 2007 Optical Society of America

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References

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  1. A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
    [CrossRef]
  2. L. H. Wang, S. L. Jacques and X. Zhao, "Continuous wave ultrasonic modulation of scattered light to image objcets in turbid media," Opt. Lett. 20, 629 (1995).
    [CrossRef] [PubMed]
  3. W. Leutz and G. Maret, "Ultrasonic modulation of multiply scattered light," Physica B 204, 14 (1995).
    [CrossRef]
  4. L. Wang, "Mechanisms of ultrasonic modulation of multiply scattered coherent light: a analytic model," Phys. Rev. Lett. 87, 1 (2001).
    [CrossRef]
  5. M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
    [CrossRef]
  6. A. Lev and B. Sfez, "In vivo demonstration of ultrasound-modulated light technique," J. Opt. Soc. Am. A 20, 2347-2354 (2003).
    [CrossRef]
  7. M. Gross, P. Goy, B. C. Forget, M. Atlan, F. Ramaz, A. C. Boccara, and A. K. Dunn, "Heterodyne detection of multiply scattered monochromatic light with a multipixel detector," Opt. Lett. 30, 1357 (2005).
    [CrossRef] [PubMed]
  8. C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
    [CrossRef] [PubMed]
  9. M. Atlan, M. Gross, T. Vitalis, A. Rancillac, B. C. Forget, and A. K. Dunn, "Frequency-domain, wide-field laser doppler in vivo imaging," Opt. Lett. submitted 3/21/2006, accepted for publication (2006).
  10. A. Lev, Z. Kotler, and B. Sfez, "Ultrasound tagged light imaging in turbid media in a reflectance geometry," Opt. Lett. 25, 378 (2000).
    [CrossRef]
  11. A. L. and B. G. Sfez, "Direct, noninvasive detection of photon density in turbid media," Opt. Lett. 27, 473 (2002).
    [CrossRef]
  12. M. Gross, P. Goy, and M. Al-Koussa, "Shot-noise detection of ultrasound-tagged photons in ultrasoundmodulated optical imaging," Opt. Lett. 28, 2482-2484 (2003).
    [CrossRef] [PubMed]
  13. M. Atlan, B. C. Forget, F. Ramaz, A. C. Boccara, and M. Gross, "Pulsed acousto-optic imaging in dynamic scattering media with heterodyne parallel speckle detection," Opt. Lett. 30, 1360-1362 (2005).
    [CrossRef] [PubMed]
  14. G. Yao and L. V. Wang, "theoretical and experimental studies of ultrasound modulated optical tomography in biological tissues," Appl. Opt. 39, 659 (2000).
    [CrossRef]
  15. S. Leveque, A. C. Boccara, M. Lebec, and H. Saint-Jalmes, "Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing," Opt. Lett. 24, 181 (1999).Q1
    [CrossRef]
  16. F. Ramaz, B. C. Forget,M. Atlan, A. C. Boccara,M. Gross, P. Delaye, and G. Roosen, "Photorefractive detection of tagged photons in ultrasound modulated optical tomography of thick biological tissues," Opt. Express 12, 5469-5474 (2004).
    [CrossRef] [PubMed]
  17. T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, and C. A. DiMarzio, "Detection of ultrasound-modulated photons in diffuse media using the photorefractive effect," Opt. Lett. 29, 2509 (2004).
    [CrossRef] [PubMed]
  18. E. Bossy, L. Sui, T. W. Murray, and R. A. Roy, "Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner," Opt. Lett. 30, 744 (2005).
    [CrossRef] [PubMed]
  19. F. J. Blonigen, A. Nieva, C. DiMarzio, S. Manneville, L. Sui, G. Maguluri, T.W. Murray, and R. A. Roy, "Computations of the acoustically induced phase shifts of optical paths in acoustophotonic imaging with photorefractivebased detection," Appl. Opt. 44, 3735 (2005).
    [CrossRef] [PubMed]
  20. L. Sui, R. A. Roy, C. DiMarzio, and T. W. Murray, "Imaging in diffuse media with pulsed-ultrasound-modulated light and the photorefractive effect," Appl. Opt. 44, 4041 (2005).
    [CrossRef] [PubMed]
  21. M. Gross, F. Ramaz, B. C. Forget, M. Atlan, A. C. Boccara, P. Delaye, and G. Roosen, "Theoretical description of the photorefractive detection of the ultrasound modulated photons in scattering media," Opt. Express 13, 7097-7112 (2005).
    [CrossRef] [PubMed]
  22. S. Bian and J. Frejlich, "Photorefractive response time measurement in GaAs crystals by phase modulation in two wave mixing," Opt. Lett. 19, 1702-1704 (1994)
    [CrossRef] [PubMed]
  23. B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
    [CrossRef]
  24. G. Brost, J. Norman, S. Odoulov, K. Shcherbin, A. Shumelyuk, and V. Tarano, "Gain Spectra of beam coupling in photorefractive semiconductors," J. Opt. Soc. Am. B,  15, 2083-2091 (1998).
    [CrossRef]
  25. P. Delaye, S. de Rossi, and G. Roosen, "High amplitude vibrations detection on rough surfaces using a photorefractive velocimeter," Opt. and Las. in Eng. 33, 335-347 (2000).
    [CrossRef]
  26. B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
    [CrossRef]
  27. P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154 (1995).
    [CrossRef]
  28. P. Yeh, "Introduction to Photorefractive Nonlinear Optics" Wiley eds, ISBN: 0-471-58692-7.

2005

A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
[CrossRef]

M. Gross, P. Goy, B. C. Forget, M. Atlan, F. Ramaz, A. C. Boccara, and A. K. Dunn, "Heterodyne detection of multiply scattered monochromatic light with a multipixel detector," Opt. Lett. 30, 1357 (2005).
[CrossRef] [PubMed]

M. Atlan, B. C. Forget, F. Ramaz, A. C. Boccara, and M. Gross, "Pulsed acousto-optic imaging in dynamic scattering media with heterodyne parallel speckle detection," Opt. Lett. 30, 1360-1362 (2005).
[CrossRef] [PubMed]

E. Bossy, L. Sui, T. W. Murray, and R. A. Roy, "Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner," Opt. Lett. 30, 744 (2005).
[CrossRef] [PubMed]

F. J. Blonigen, A. Nieva, C. DiMarzio, S. Manneville, L. Sui, G. Maguluri, T.W. Murray, and R. A. Roy, "Computations of the acoustically induced phase shifts of optical paths in acoustophotonic imaging with photorefractivebased detection," Appl. Opt. 44, 3735 (2005).
[CrossRef] [PubMed]

L. Sui, R. A. Roy, C. DiMarzio, and T. W. Murray, "Imaging in diffuse media with pulsed-ultrasound-modulated light and the photorefractive effect," Appl. Opt. 44, 4041 (2005).
[CrossRef] [PubMed]

M. Gross, F. Ramaz, B. C. Forget, M. Atlan, A. C. Boccara, P. Delaye, and G. Roosen, "Theoretical description of the photorefractive detection of the ultrasound modulated photons in scattering media," Opt. Express 13, 7097-7112 (2005).
[CrossRef] [PubMed]

2004

2003

2002

2001

L. Wang, "Mechanisms of ultrasonic modulation of multiply scattered coherent light: a analytic model," Phys. Rev. Lett. 87, 1 (2001).
[CrossRef]

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

2000

1999

1998

1997

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

1995

L. H. Wang, S. L. Jacques and X. Zhao, "Continuous wave ultrasonic modulation of scattered light to image objcets in turbid media," Opt. Lett. 20, 629 (1995).
[CrossRef] [PubMed]

W. Leutz and G. Maret, "Ultrasonic modulation of multiply scattered light," Physica B 204, 14 (1995).
[CrossRef]

P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154 (1995).
[CrossRef]

B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
[CrossRef]

1994

Al-Koussa, M.

Arridge, S. R.

A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
[CrossRef]

Atlan, M.

Ayata, C.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Bian, S.

Blonigen, F.

Blonigen, F. J.

Blouin, A.

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

Boas, D. A.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Boccara, A. C.

Bossy, E.

Brost, G.

Campagne, B.

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

de Montmorillon, L. A.

P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154 (1995).
[CrossRef]

Delaye, P.

DiMarzio, C.

DiMarzio, C. A.

Dunn, A. K.

M. Gross, P. Goy, B. C. Forget, M. Atlan, F. Ramaz, A. C. Boccara, and A. K. Dunn, "Heterodyne detection of multiply scattered monochromatic light with a multipixel detector," Opt. Lett. 30, 1357 (2005).
[CrossRef] [PubMed]

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Forget, B. C.

Frejlich, J.

B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
[CrossRef]

S. Bian and J. Frejlich, "Photorefractive response time measurement in GaAs crystals by phase modulation in two wave mixing," Opt. Lett. 19, 1702-1704 (1994)
[CrossRef] [PubMed]

Genack, A. Z.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
[CrossRef]

Goy, P.

Gross, M.

Gursoy-Ozdemir, Y.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
[CrossRef]

Huang, Z.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Jacques, S. L.

Kempe, M.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

Kotler, Z.

Larionov, M.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

Leutz, W.

W. Leutz and G. Maret, "Ultrasonic modulation of multiply scattered light," Physica B 204, 14 (1995).
[CrossRef]

Lev, A.

Maguluri, G.

Manneville, S.

Maret, G.

W. Leutz and G. Maret, "Ultrasonic modulation of multiply scattered light," Physica B 204, 14 (1995).
[CrossRef]

Monchalin, J. P.

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

Moskowitz, M. A.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

Murray, T. W.

Murray, T.W.

Nieva, A.

Norman, J.

Odoulov, S.

Pujol, L.

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

Ramaz, F.

Roosen, G.

Roy, R. A.

Sfez, B.

Shcherbin, K.

Shcherbin, K. V.

B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
[CrossRef]

Shumelyuk, A.

Sugg, B.

B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
[CrossRef]

Sui, L.

Tarano, V.

Wang, L.

L. Wang, "Mechanisms of ultrasonic modulation of multiply scattered coherent light: a analytic model," Phys. Rev. Lett. 87, 1 (2001).
[CrossRef]

Wang, L. H.

Wang, L. V.

Yao, G.

Zaslavsky, D.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

Zhao, X.

Appl. Opt.

Appl. Phys. Lett.

B. Sugg, K. V. Shcherbin, and J. Frejlich, enquoteDetermination of the time constant of fast photorefarctive materials using the phase modulation technique, Appl. Phys. Lett. 66, 3257-3259 (1995).
[CrossRef]

J. Cereb. Blood Flow Metab.

C. Ayata, A. K. Dunn,Y. Gursoy-Ozdemir,Z. Huang,D. A. Boas and M. A. Moskowitz, "Laser Speckle Flowmetry for the Study of Cerebrovascular Physiology in Normal and Ischemic Mouse Cortex," J. Cereb. Blood Flow Metab. 24, 744-755 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

G. Brost, J. Norman, S. Odoulov, K. Shcherbin, A. Shumelyuk, and V. Tarano, "Gain Spectra of beam coupling in photorefractive semiconductors," J. Opt. Soc. Am. B,  15, 2083-2091 (1998).
[CrossRef]

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, "Acousto-optic tomography with multiple scattered light," J. Opt. Soc. Am. B 14, 1151-1158 (1997).
[CrossRef]

Opt. Commun.

P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

T. W. Murray, L. Sui, G. Maguluri, R. A. Roy, A. Nieva, F. Blonigen, and C. A. DiMarzio, "Detection of ultrasound-modulated photons in diffuse media using the photorefractive effect," Opt. Lett. 29, 2509 (2004).
[CrossRef] [PubMed]

E. Bossy, L. Sui, T. W. Murray, and R. A. Roy, "Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner," Opt. Lett. 30, 744 (2005).
[CrossRef] [PubMed]

S. Leveque, A. C. Boccara, M. Lebec, and H. Saint-Jalmes, "Ultrasonic tagging of photon paths in scattering media: parallel speckle modulation processing," Opt. Lett. 24, 181 (1999).Q1
[CrossRef]

A. Lev, Z. Kotler, and B. Sfez, "Ultrasound tagged light imaging in turbid media in a reflectance geometry," Opt. Lett. 25, 378 (2000).
[CrossRef]

A. L. and B. G. Sfez, "Direct, noninvasive detection of photon density in turbid media," Opt. Lett. 27, 473 (2002).
[CrossRef]

M. Gross, P. Goy, and M. Al-Koussa, "Shot-noise detection of ultrasound-tagged photons in ultrasoundmodulated optical imaging," Opt. Lett. 28, 2482-2484 (2003).
[CrossRef] [PubMed]

M. Atlan, B. C. Forget, F. Ramaz, A. C. Boccara, and M. Gross, "Pulsed acousto-optic imaging in dynamic scattering media with heterodyne parallel speckle detection," Opt. Lett. 30, 1360-1362 (2005).
[CrossRef] [PubMed]

M. Gross, P. Goy, B. C. Forget, M. Atlan, F. Ramaz, A. C. Boccara, and A. K. Dunn, "Heterodyne detection of multiply scattered monochromatic light with a multipixel detector," Opt. Lett. 30, 1357 (2005).
[CrossRef] [PubMed]

L. H. Wang, S. L. Jacques and X. Zhao, "Continuous wave ultrasonic modulation of scattered light to image objcets in turbid media," Opt. Lett. 20, 629 (1995).
[CrossRef] [PubMed]

S. Bian and J. Frejlich, "Photorefractive response time measurement in GaAs crystals by phase modulation in two wave mixing," Opt. Lett. 19, 1702-1704 (1994)
[CrossRef] [PubMed]

Phys. Med. Biol

A. P. Gibson, J. C. Hebden, S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol 50, 1-43 (2005).
[CrossRef]

Phys. Rev. Lett.

L. Wang, "Mechanisms of ultrasonic modulation of multiply scattered coherent light: a analytic model," Phys. Rev. Lett. 87, 1 (2001).
[CrossRef]

Physica B

W. Leutz and G. Maret, "Ultrasonic modulation of multiply scattered light," Physica B 204, 14 (1995).
[CrossRef]

Rev. Sc. Inst.

B. Campagne, A. Blouin, L. Pujol, and J. P. Monchalin, "Compact and fast response ultrasonic detection device based on two-wave mixing in a gallium arsenide photorefractive crystal," Rev. Sc. Inst. 725, 2478-2482 (2001).Q2
[CrossRef]

Other

P. Delaye, S. de Rossi, and G. Roosen, "High amplitude vibrations detection on rough surfaces using a photorefractive velocimeter," Opt. and Las. in Eng. 33, 335-347 (2000).
[CrossRef]

P. Yeh, "Introduction to Photorefractive Nonlinear Optics" Wiley eds, ISBN: 0-471-58692-7.

M. Atlan, M. Gross, T. Vitalis, A. Rancillac, B. C. Forget, and A. K. Dunn, "Frequency-domain, wide-field laser doppler in vivo imaging," Opt. Lett. submitted 3/21/2006, accepted for publication (2006).

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Figures (5)

Fig. 1.
Fig. 1.

Spatio-temporal principle for a self-adaptive wavefront holography using a photore-fractive crystal with time constant τPR . As mentionned in section 3, the interference pattern between the signal ES (r,t) and the reference ER (r,t) beam is recorded within the crystal via its refractive index Δn(r,t): the reference beam diffracts a spatial replica of the signal ED (r,t), smoothed in time by the finite photorefractive time establishment.

Fig. 2.
Fig. 2.

Simulation of the response S Δω ωmod for different τPR , with a rectangular [0,π] phase modulation of the US excitation and a cyclic ratio of 25%

Fig. 3.
Fig. 3.

Experimental setup : (L) 1W Nd:YAG laser, (OA) 5W Yb-doped optical amplifier, (OI) optical Faraday isolator, (HW) half-wave plate, (AMO1,2) acousto-optic modualtor, (W) water tank, (PBS) polarizing beam-splitter, (T) acoustic-transducer, (PR) photorefractive GaAs crystal, (LP) linear polarizer, (L1,2) wide aperture collection lenses, (D) ϕ= 5mm InGaAs photodiode.

Fig. 4.
Fig. 4.

Example of a lock-in measurement at 2.5kHz of the acousto-optic normalized response for a diluted scattering liquid as a function of a frequency shift Δω/2π of the reference beam. The left column represents spectra (a,c,e,g) that have been obtained for an orthogonal pumping configuration with an incident flux of 240mW/cm 2, while the right column (b,d, f ,h) corresponds to a co-directional pumping with an incident flux of 300mW/cm 2. From top to bottom, each line corresponds respectively to Rω), φ(Δω), Pω), Qω) quantities, as defined in section 4. The width of the resonance peaks is connected to 1/τPR . Experimental data are black and theoretical fit prediction with a single parameter τPR is red (see text for details).

Fig. 5.
Fig. 5.

Plot of the photorefractive response time τPR as a function of the incident intensity for a co-directional (type I crystal) or an orthogonal pumping configuration (type II crystal).

Equations (28)

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

ω n = ω 0 ± US
ω n , p = ω 0 ± US ± mod
G ( z , t ) = γz e t τ PR τ PR
E S , i ( r , t ) = n E S , i ω n ( r , t )
E S , i ω n ( r , t ) = a i ( r ) e i ( r ) J n ( β i ( t ) ) e 0 t e jnω US t e jn ( ϕ i ( t ) + π 2 )
E R ( r , t ) = E 0 e j ( ω 0 + US ) t e j Δ ωt
Δ n ( r , t ) = ( E S , i ω n ( r , t ) E R * ( r , t ) E S , i ω n ( r , t ) E S , i * ω n ( r , t ) + E R ( r , t ) E R * ( r , t ) ) * G ( z , t )
Δ n ( r , t ) η a i ( r ) e j θ i ( r ) E 0 ( J n ( β i ( t ) ) e jn ( ϕ i ( t ) + π 2 ) e j Δ ωt ) * ( e t τ PR τ PR )
E D , i , Δ ω ω n ( r , t ) = η a i ( r ) e i ( r ) [ ( J n ( β i ( t ) ) e jn ( ϕ i ( t ) + π 2 ) e j Δ ωt ) * ( e t τ PR τ PR ) ] e j ( ω 0 + US ) t e j Δ ωt
β i ( t ) = H AM ( t ) β i
ϕ i ( t ) = ϕ i + H PM ( t )
e jnϕ i ( t ) J n ( β i ( t ) ) = p c i , n , p e jpω mod t
E S , i ω n , p ( r , t ) = a i ( r ) e i ( r ) e jn ( ϕ i + π 2 ) e 0 t e jnω US t p c i , n , p e jnω mod t
E D , i , Δ ω ω n , p ( r , t ) = η a i ( r ) e j θ i ( r ) e jn ( θ i + π 2 ) e 0 t e jnω US t p c i , n , p ( r ) 1 + j ( p ω mod Δ ω ) τ PR e jpω mod t
S i , n Δ ω ( t ) = Re [ 2 E S , i * ω n ( r , t ) E D , i , Δ ω ω n ( r , t ) ] = 2 ηa i 2 ( r ) Re [ k , p c i , n , k * c i , n , p e j ( p k ) ω mod t 1 + j ( mod Δ ω ) τ PR ]
H AM ( t ) = Rect ( t xT ) * m δ ( t mT )
J 0 ( β i H AM ( t ) ) p c i , 0 , p e jpω mod t = 1 + ( J 0 ( β i ) 1 ) p x sin c ( pπx ) e jpπx e jpω mod t
c i , 0,0 = ( 1 x ) + x J 0 ( β i )
c i , 0 , p 0 = x ( J 0 ( β i ) 1 ) sin c ( pπx ) e jpπx
P ( Δ ω ) = s i , 0 Δ ω ( t ) cos ( ω mod t π 2 ) dt
Q ( Δ ω ) = S i , 0 Δ ω ( t ) sin ( ω mod t π 2 ) dt
P 0 ( Δ ω ) = 2 A i , 0 ( 1 + Δ ω τ PR ) 2
P ± ( Δ ω ) = A i , 0 1 + ( ω mod Δ ω ) 2 τ PR 2
Q ± ( Δ ω ) = A i , 0 1 + ( ω mod Δ ω ) 2 τ PR 2 ( ω mod Δ ω ) τ PR
A i , 0 = 1 π η a i 2 ( r ) [ 1 + 1 2 ( J 0 ( β i ) 1 ) ] [ J 0 ( β i ) 1 ]
R ( Δ ω ) = P 2 ( Δ ω ) + Q 2 ( Δ ω )
tan φ ( Δ ω ) = P ( Δ ω ) Q ( Δ ω )
tan φ ± ( Δ ω ± ω mod ) P ± ( Δ ω ) Q ± ( Δ ω ) ( ω mod Δ ω ) τ PR

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