Abstract

A photorefractive BSO single crystal can be used for axially resolved acousto-optic imaging of thick scattering media in absence of a reference beam. This configuration renders the experimental setup easier to realize for imaging through thick scattering media with an improved optical etendue. We present here a model and simulations that explains these results. It is based on the spatial heterogeneity of the speckle pattern incident on the crystal. Optimization of the detector position and of the speckle grain size is confirmed by the model.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
    [CrossRef]
  16. J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
    [CrossRef]
  17. J. W. Goodman, Laser Speckle and Related Phenomena (Springer, 1975).

2013 (1)

2012 (2)

2011 (2)

A. Bratchenia, R. Molenaar, T. G. van Leeuwen, R. P. H. Kooyman, “Acousto-optic-assisted diffuse optical tomography,” Opt. Lett. 36, 1539–1541 (2011).
[CrossRef] [PubMed]

J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
[CrossRef]

2010 (1)

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

2009 (1)

2007 (1)

2003 (2)

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

1998 (1)

A. A. Kamshilin, T. Jaaskelainen, Y. N. Kulchin, “Adaptive correlation filter for stabilization of interference fiber optic sensors,” Appl. Phys. Lett. 73, 705–707 (1998).
[CrossRef]

1995 (3)

O. Daniel, J.-M. C. Jonathan, G. Roosen, “Photorefractrive effect in the Fourier plane,” Opt. Mater. 4, 294–298 (1995).
[CrossRef]

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

L. Wang, S. L. Jacques, X. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
[CrossRef] [PubMed]

Al-Koussa, M.

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

Benoit à la Guillaume, E.

Blouin, A.

Boccara, A. C.

Bortolozzo, U.

Bossy, E.

Bratchenia, A.

Daniel, O.

O. Daniel, J.-M. C. Jonathan, G. Roosen, “Photorefractrive effect in the Fourier plane,” Opt. Mater. 4, 294–298 (1995).
[CrossRef]

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

Delaye, P.

Farahi, S.

Gómez, J. A.

J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Laser Speckle and Related Phenomena (Springer, 1975).

Goy, P.

Grabar, A. A.

Gross, M.

Huignard, J. P.

Huignard, J.-P.

Jaaskelainen, T.

A. A. Kamshilin, T. Jaaskelainen, Y. N. Kulchin, “Adaptive correlation filter for stabilization of interference fiber optic sensors,” Appl. Phys. Lett. 73, 705–707 (1998).
[CrossRef]

Jacques, S. L.

Jean, F.

Jonathan, J.-M. C.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

O. Daniel, J.-M. C. Jonathan, G. Roosen, “Photorefractrive effect in the Fourier plane,” Opt. Mater. 4, 294–298 (1995).
[CrossRef]

Kamshilin, A. A.

A. A. Kamshilin, T. Jaaskelainen, Y. N. Kulchin, “Adaptive correlation filter for stabilization of interference fiber optic sensors,” Appl. Phys. Lett. 73, 705–707 (1998).
[CrossRef]

Kooyman, R. P. H.

Kothapalli, S.-R.

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

Kulchin, Y. N.

A. A. Kamshilin, T. Jaaskelainen, Y. N. Kulchin, “Adaptive correlation filter for stabilization of interference fiber optic sensors,” Appl. Phys. Lett. 73, 705–707 (1998).
[CrossRef]

Lesaffre, M.

Lev, A.

Liu, H.

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

Lorduy Gómez, H.

J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
[CrossRef]

Molenaar, R.

Monchalin, J.-P.

Ramaz, F.

Residori, S.

Roosen, G.

M. Lesaffre, F. Jean, F. Ramaz, A. C. Boccara, P. Delaye, G. Roosen, “In situ monitoring of the photorefractive response time in a self-adaptive holography setup developed for acousto-optic imaging,” Opt. Express 15, 1030–1042 (2007).
[CrossRef] [PubMed]

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

O. Daniel, J.-M. C. Jonathan, G. Roosen, “Photorefractrive effect in the Fourier plane,” Opt. Mater. 4, 294–298 (1995).
[CrossRef]

Rousseau, G.

Salazar, Á.

J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
[CrossRef]

Sfez, B.

Stelmach, A.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

van Leeuwen, T. G.

Wang, L.

Wang, L. V.

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

Xu, X.

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

Yeh, P.

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

Zhao, X.

Appl. Phys. Lett. (1)

A. A. Kamshilin, T. Jaaskelainen, Y. N. Kulchin, “Adaptive correlation filter for stabilization of interference fiber optic sensors,” Appl. Phys. Lett. 73, 705–707 (1998).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

J. Biomed. Opt. (1)

X. Xu, S.-R. Kothapalli, H. Liu, L. V. Wang, “Spectral hole burning for ultrasound-modulated optical tomography of thick tissue,” J. Biomed. Opt. 15, 066018 (2010).
[CrossRef]

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

Opt. Commun. (2)

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, “Whole-beam method analysis of photorefractive effect in correlators,” Opt. Commun. 113, 559–567 (1995).
[CrossRef]

J. A. Gómez, H. Lorduy Gómez, Á. Salazar, “Novel procedure for the simultaneous determination of the Debye length and electro-optic coefficient for an optically active photorefractive Bi12SiO20 crystal,” Opt. Commun. 284, 460–466 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Opt. Mater. (1)

O. Daniel, J.-M. C. Jonathan, G. Roosen, “Photorefractrive effect in the Fourier plane,” Opt. Mater. 4, 294–298 (1995).
[CrossRef]

Other (2)

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

J. W. Goodman, Laser Speckle and Related Phenomena (Springer, 1975).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

(a) Intensity of a typical speckle pattern in the (x, y) spatial domain where the 1 e 2 half width of the speckle grains is σs = 0.21μm. (b) Intensity of the spatial frequency spectrum of the speckle field. (c) Modulus of the Fourier transform of the speckle intensity. In the spatial frequency domain, the axes are normalized by k0, the Debye screening wave number.

Fig. 3
Fig. 3

(a) and (c) Modulus of the transverse components of the space charge electric field in the (kx, ky) spatial frequency domain. (b) and (d) Modulus the transverse components of the space charge electric field in the (x, y) spatial domain.

Fig. 4
Fig. 4

Variation of the modulus of the x component of the space charge field (a) and of the PR signal (b) as a function of the normalized spatial frequency k x k 0 (ky = 0) and of the mean size σs of the speckle grains. (c) Normalized PR signal as a function of the normalized spatial frequency k x k 0 and the normalized half width of the gaussian envelop of the speckle spectrum σ k k 0. The black dotted curve depicts the optimized position of the detector that gives the higher PR signal as a fonction of σk.

Fig. 5
Fig. 5

(a) and (b) intensities in the (x, y) domain of the reference speckle and the fully decorrelated noise speckle. (c) Real part of the interference term between the reference and the noise speckles.

Fig. 6
Fig. 6

(a) Intensity of the spatial frequency spectrum of a tagged speckle. The two yellow squares represent the detector area in the (kx, ky) domain when it is centered respectively on the spatial frequencies k x = ± k 0 2. (b) Amplitude of the AO signals as a function of the level γ of noise in the tagged speckle for the two positions of the detector.

Equations (12)

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E sc ( r ) 1 k 0 2 ( E sc ( r ) ) = k B T e ln [ I r ( r ) + I d ] ,
𝒯 { E sc ( r ) } = k B T e i k 1 + | k | 2 k 0 2 𝒯 { ln [ I r ( r + I d ) ] } ,
{ E ˜ sc x ( k t ) = i α k x 1 + | k t | 2 k 0 2 I ˜ r ( k t ) E ˜ sc y ( k t ) = i α k y 1 + | k t | 2 k 0 2 I ˜ r ( k t )
{ Δ n x ( k x ) = 0 Δ n y ( k x ) = 1 2 r 41 n 0 3 E ˜ sc x ( k x ) .
H y ( x , y ) = exp ( i 2 π Δ n y L λ ) 1 i 2 π Δ n y L λ
S r y out ( x , y ) = S r y in ( x , y ) H y ( x , y ) .
S ˜ r y out ( k x ) = S ˜ r y in ( k x ) ( δ ( k x ) + β k x 1 + k x 2 k 0 2 I ˜ r ( k x ) ) = S ˜ r y in ( k x ) + S ˜ r y in ( k x ) β k x 1 + k x 2 k 0 2 I ˜ r ( k x ) ,
I PR ( k x ) = | S ˜ r y out ( k x ) | 2 | S ˜ r y in ( k x ) | 2 .
S t in = γ S n + 1 γ S r ,
I t in = γ I n + ( 1 γ ) I r + 2 γ ( 1 γ ) 𝔢 { S n S r * } .
| S ˜ t out | 2 γ | S ˜ n out | 2 + ( 1 γ ) | S ˜ r out | 2 .
R AO = Δ k D | S ˜ t out | 2 d 2 k Δ k D | S ˜ r out | 2 d 2 k Δ k D | S ˜ r out | 2 d 2 k

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