Abstract

This work extends modulated imaging, a recently developed technique based on the projection of structured light on a turbid medium that is able to measure optical properties of the high-scattering medium and perform tomography. We observe that structured light obliquely projected on a turbid medium undergoes a spatial shift during propagation. We propose a method to measure the spatial phase shift of a sinusoidal fringe pattern projected in a turbid medium, and we present a model derived from the diffusion approximation to describe the light propagation. Experimental validation by measurements performed on liquid phantoms is presented.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]

2006

2005

2004

Q. Liu and N. Ramanujam, “Experimental proof of the feasibility of using an angled fiber-optic probe for depth-sensitive fluorescence spectroscopy of turbid media,” Opt. Lett. 29, 2034-2036 (2004).
[CrossRef] [PubMed]

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9, 632-647 (2004).
[CrossRef] [PubMed]

1999

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

1998

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963-982 (1998).
[CrossRef]

1997

1994

1993

1991

1984

1971

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319-329 (1971).
[CrossRef]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Batlle, J.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963-982 (1998).
[CrossRef]

Berns, M. W.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

Bevilacqua, F.

Carp, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9, 632-647 (2004).
[CrossRef] [PubMed]

Cuccia, D. J.

Donner, C.

Durkin, A. J.

Feng, T. C.

Fishkin, J. B.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Halioua, M.

Haskell, R. C.

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jacques, S. L.

Jensen, H. W.

Joshi, N.

Lin, S. P.

Liu, H.

Liu, Q.

McAdams, M. S.

Moes, C. J. M.

Mouaddib, E.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963-982 (1998).
[CrossRef]

Pennington, K. S.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319-329 (1971).
[CrossRef]

Pham, T.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

Prahl, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9, 632-647 (2004).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400-1100 nm,” Appl. Opt. 30, 4507-4514 (1991).
[CrossRef] [PubMed]

Ramanujam, N.

Salvi, J.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963-982 (1998).
[CrossRef]

Spott, T.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

Srinivasan, V.

Svaasand, L. O.

Tittel, F. K.

Tromberg, B. J.

Tsay, T. T.

Tsay, T.-T.

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Venugopalan, V.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9, 632-647 (2004).
[CrossRef] [PubMed]

Wang, L.

Will, P. M.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319-329 (1971).
[CrossRef]

Appl. Opt.

Artif. Intell.

P. M. Will and K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319-329 (1971).
[CrossRef]

J. Biomed. Opt.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9, 632-647 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Lett.

Pattern Recogn.

J. Batlle, E. Mouaddib, and J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963-982 (1998).
[CrossRef]

Phys. Med. Biol.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801-813 (1999).
[CrossRef] [PubMed]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

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Figures (6)

Fig. 1
Fig. 1

Scheme of structured light propagation in a turbid medium. The light source (a sinusoidal fringe pattern) propagates obliquely. During propagation it is attenuated and undergoes a phase shift.

Fig. 2
Fig. 2

Experimental setup: a sinusoidal fringe pattern is projected on the liquid phantom. The scattered light is filtered at 660 nm and acquired by a CCD.

Fig. 3
Fig. 3

Effect of the transport coefficient (a) and of the reduced albedo (b) on the phase. The values of μ t r and μ s μ a are indicated in the legend.

Fig. 4
Fig. 4

Calculated amplitude (a) and phase (b) of the reflectance at different scattering. The values of the reduced scattering coefficient μ s are indicated in the legend. The expected values for the amplitude and the phase are indicated by the solid curves.

Fig. 5
Fig. 5

Calculated amplitude (a) and phase (b) of the reflectance at different absorption. The values of the absorption coefficient μ a are indicated in the legend. The expected values for the amplitude and the phase are indicated by the solid curves.

Fig. 6
Fig. 6

Calculated amplitude (a) and phase (b) of the reflectance at different projection angles (indicated in the legend). The expected values for the amplitude and the phase are indicated by the solid curves.

Equations (18)

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2 φ μ eff 2 φ = 3 μ tr q ,
2 φ ̃ 0 2 z μ eff 2 φ ̃ 0 = 3 μ tr q ̃ 0 ,
μ eff = μ eff 2 + ( 2 π f x ) 2 .
q ̃ 0 = P 0 μ tr cos θ exp ( μ tr z cos θ ) exp ( i ϕ q ) .
2 φ ̃ 0 2 z μ eff 2 φ ̃ 0 = P 0 μ tr cos θ exp ( μ tr z cos θ ) exp ( i 2 π f x z tan θ ) .
φ ̃ 0 = α exp [ ( μ tr cos θ i 2 π f x tan θ ) z ] + C exp ( μ eff z ) ,
α = 3 P 0 μ tr μ tr cos θ [ ( μ eff ) 2 ( μ tr cos θ i 2 π f x tan θ ) 2 ] ,
C = α [ ( μ tr cos θ i 2 π f x tan θ ) + 3 η μ tr ] 3 η μ tr + μ eff .
φ ̃ 0 ( 0 ) = α + C = 3 P 0 μ tr ( 3 η μ tr + μ eff ) μ tr cos θ μ eff + μ tr cos ( ϑ ) + i 2 π f x tan θ [ ( μ eff + μ tr cos θ ) 2 + ( 2 π f x tan θ ) 2 ] .
R = η φ ̃ 0 ( 0 ) = 3 P 0 η μ tr ( 3 η μ tr + μ eff ) μ tr cos θ [ ( μ eff + μ tr cos θ ) 2 + ( 2 π f x tan θ ) 2 ] 1 2 .
ϕ = arctan ( 2 π f x tan θ μ eff + μ tr cos θ ) .
I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ 2 π f x x + ϕ ( x , y ) 2 π 3 ] ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ 2 π f x x + ϕ ( x , y ) ] ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ 2 π f x x + ϕ ( x , y ) + 2 π 3 ] .
A ( x , y ) = 2 1 2 3 { [ I 1 ( x , y ) I 2 ( x , y ) ] 2 + [ I 2 ( x , y ) I 3 ( x , y ) ] 2 + [ I 3 ( x , y ) I 1 ( x , y ) ] 2 } 1 2 .
ϕ ( x , y ) = arctan ( 3 I 1 ( x , y ) I 3 ( x , y ) 2 I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y ) ) .
A SAMPLE = A SAMPLE MEASURED A PHANTOM MEASURED A PHANTOM PREDICTED .
ϕ SAMPLE = ϕ SAMPLE MEASURED ϕ PHANTOM MEASURED + ϕ PHANTOM PREDICTED .

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