Abstract

We employ a Monte Carlo (MC) algorithm to investigate the decoherence of diffuse photons in turbid media. For the MC simulation of coherent photons, the degree of coherence, defined as a random variable for a photon packet, is associated with a decoherence function that depends on the scattering angle and is updated as a photon interacts with a medium via scattering. Using a slab model, the effects of medium scattering properties were studied, which reveals that a linear random variable model for the degree of coherence is in better agreement with experimental results than a sinusoidal model and that decoherence is quick for the initial few scattering events followed by a slow and gradual decrease of coherence.

© 2008 Optical Society of America

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2006 (2)

2005 (3)

2004 (4)

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, "Advanced modeling of optical coherence tomography systems," Phys. Med. Biol. 49, 1307-1327 (2004).
[CrossRef] [PubMed]

C. Mujat and A. Dogariu, "Statistics of partially coherent beams: a numerical analysis," J. Opt. Soc. Am. A 21, 1000-1003 (2004).
[CrossRef]

J. M. Dela Cruz, I. Pastirk, M. Comstock, V. V. Lozovoy, and M. Dantus, "Use of coherent control methods through scattering biological tissue to achieve functional imaging," Proc. Natl. Acad. Sci. USA 101, 16996-17001 (2004).
[CrossRef] [PubMed]

B. Parys, J.-F. Allard, F. Desmullier, D. Houde, and A. Cornet, "Coherence analysis of diffused femtosecond laser pulses," J. Opt. A 6, L23-L27 (2004).
[CrossRef]

2003 (2)

2002 (4)

2001 (2)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

L. V. Wang, "Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model," Opt. Lett. 26, 1191-1193 (2001).
[CrossRef]

2000 (1)

1999 (2)

1997 (3)

1996 (1)

1995 (2)

M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, "Multiple scattering in optical coherence microscopy," Appl. Opt. 34, 5699-5707 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1993 (1)

1987 (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

1969 (1)

A. Y. Khairullina, "Coherent properties of radiation scattered by a turbid medium," J. Appl. Spectrosc. 11, 778-781 (1969).
[CrossRef]

1963 (1)

R. J. Glauber, "The quantum theory of optical coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

1941 (1)

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the Galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

1938 (1)

F. Zernike, "The concept of degree of coherence and its application to optical problems," Physica 5, 785-795 (1938).
[CrossRef]

Appl. Opt. (8)

T. O. McBride, B. W. Pogue, E. D. Gerety, S. B. Poplack, U. L. Osterberg, and K. D. Paulsen, "Spectroscopic diffuse optical tomography for the quantitative assessment of hemoglobin concentration and oxygen saturation in breast tissue," Appl. Opt. 38, 5480-5490 (1999).
[CrossRef]

J. S. Reynolds, S. Yeung, A. Przadka, and K. Webb, "Optical diffusion imaging: a comparative numerical and experimental study," Appl. Opt. 35, 3671-3679 (1996).
[CrossRef] [PubMed]

M. L. Shendeleva and J. A. Molloy, "Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry," Appl. Opt. 45, 7018-7025 (2006).
[CrossRef] [PubMed]

G. Pal, S. Basu, K. Mitra, and T. Vo-Dihn, "Time-resolved optical tomography using short-pulse laser for tumor detection," Appl. Opt. 45, 6270-6282 (2006).
[PubMed]

M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, "Multiple scattering in optical coherence microscopy," Appl. Opt. 34, 5699-5707 (1995).
[CrossRef] [PubMed]

V. R. Daria, C. Saloma, and S. Kawata, "Excitation with a focused, pulsed optical beam in scattering media: diffraction effects," Appl. Opt. 39, 5244-5255 (2000).
[CrossRef]

A. Tycho and T. M. Jørgensen, Comment on "Excitation with a focused, pulsed optical beam in scattering media: diffraction effects," Appl. Opt. 41, 4709-4711 (2002).
[CrossRef] [PubMed]

A. Tycho, T. M. Jørgensen, H. T. Yura, and P. E. Andersen, "Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems," Appl. Opt. 41, 6676-6691 (2002).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the Galaxy," Astrophys. J. 93, 70-83 (1941).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

IEEE Signal Process. Mag. (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. Dimarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

J. Appl. Spectrosc. (1)

A. Y. Khairullina, "Coherent properties of radiation scattered by a turbid medium," J. Appl. Spectrosc. 11, 778-781 (1969).
[CrossRef]

J. Opt. A (1)

B. Parys, J.-F. Allard, F. Desmullier, D. Houde, and A. Cornet, "Coherence analysis of diffused femtosecond laser pulses," J. Opt. A 6, L23-L27 (2004).
[CrossRef]

J. Opt. Soc. Am. A (7)

Lasers Life Sci. (1)

S. L. Jacques, C. A. Alter, and S. A. Prahl, "Angular dependence of HeNe laser light scattering by human dermis," Lasers Life Sci. 1, 309-333 (1987).

Nat. Biotechnol. (1)

J. G. Fujimoto, "Optical coherence tomography for ultrahigh resolution in vivo imaging," Nat. Biotechnol. 21, 1361-1367 (2003).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Med. Biol. (3)

G. Yao and L. V. Wang, "Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media," Phys. Med. Biol. 44, 2307-2320 (1999).
[CrossRef] [PubMed]

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, "Advanced modeling of optical coherence tomography systems," Phys. Med. Biol. 49, 1307-1327 (2004).
[CrossRef] [PubMed]

J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine 1: experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).
[CrossRef] [PubMed]

Phys. Rev. (1)

R. J. Glauber, "The quantum theory of optical coherence," Phys. Rev. 130, 2529-2539 (1963).
[CrossRef]

Physica (1)

F. Zernike, "The concept of degree of coherence and its application to optical problems," Physica 5, 785-795 (1938).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

J. M. Dela Cruz, I. Pastirk, M. Comstock, V. V. Lozovoy, and M. Dantus, "Use of coherent control methods through scattering biological tissue to achieve functional imaging," Proc. Natl. Acad. Sci. USA 101, 16996-17001 (2004).
[CrossRef] [PubMed]

Other (4)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), Chap. 3.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, 1996).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

S. L. Jacques and J. C. Ramella-Roman, "Polarized light imaging of tissues," in Lasers and Current Optical Techniques in Biology, G. Palumbo and R. Pratesi, eds. (Royal Society of Chemistry, 2004).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(Color online) Model geometry: (a) transmission-based slab and (b) reflection-based semi-infinite medium. Source and detector locations are also shown at the medium-ambient boundary. The thickness of transmission-based slab media is fixed at 5   mm throughout the paper.

Fig. 2
Fig. 2

MC validation in comparison with the solution of the diffusion approximation in the semi-infinite reflectance geometry of Fig. 1(b). Parameters are listed in Table 1. Diffuse reflectance data for a short source-to-detector distance ( < 5   mm ) is shown in the inset.

Fig. 3
Fig. 3

MC validation to empirical data conducted on slab geometry in Fig. 1(a). The decoherence function ζ ( θ ) is assumed to have linear and sinusoidal dependence on scattering angle for (a) and (b), respectively.

Fig. 4
Fig. 4

(a) Effect of scattering coefficients ( μ s = 0.2 , 0.4 , and 0.6 mm 1 ) on the DOC as a function of the source-to-detector separation using a linear ζ ( θ ) given in Eq. (5). (b) Same as (a) with a sinusoidal ζ ( θ ) given in Eq. (6). Medium anisotropy factor and absorption coefficient are fixed at g = 0.9 and μ a = 0.01 mm 1 , respectively.

Fig. 5
Fig. 5

(a) Effect of medium anisotropy factor on the DOC as a function of the source-to-detector separation and (b) dependence of the number of scattering events on the source-to-detector separation using a linear ζ ( θ ) . (c) and (d) The same as (a) and (b), respectively, except for using a sinusoidal model for ζ ( θ ) . Scattering and absorption coefficients are, respectively, fixed at μ s = 0.2 mm 1 and μ a = 0.01 mm 1 .

Fig. 6
Fig. 6

(a) Relation between the DOC and the number of scattering events plotted for different scattering coefficients ( μ s = 0.2 , 0.4, and 0.6 mm 1 ), and (b) the number of scattering events with respect to the source-to-detector separation, using a linear ζ ( θ ) ; (c) and (d) are, respectively, the same as (a) and (b), except for using a sinusoidal model for ζ ( θ ) .

Fig. 7
Fig. 7

Two-dimensinal transmittance images when (a) μ s = 0.2 mm 1 and (b) μ s = 0.6 mm 1 . DOC images are also shown in the case of (c) μ s = 0.2 mm 1 and (d) μ s = 0.6 mm 1 ; x and y axes are in millimeters.

Tables (1)

Tables Icon

Table 1 Medium Parameters and Model Geometry Used in this Study a

Equations (6)

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

1 c φ ( r ) t = D ( r ) φ ( r ) μ a ( r ) φ ( r ) + S ( r ) ,
D ( r ) = 1 / { 3 [ μ a ( r ) + μ s ( r ) ( 1 g ) ] } .
DOC ( n + 1 ) = DOC ( n )   exp [ k ζ ( θ n ) ] ,
ζ ( θ n ) = 1 | | θ n | π / 2 | π / 2 ,
ζ ( θ n ) = | sin   θ n |
p ( cos   θ n ) = 1 g 2 2 ( 1 + g 2 2 g   cos   θ n ) 3 / 2 ,

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