Abstract

We present an approach to solving the radiative transport equation (RTE) for layered media in the spatial frequency domain (SFD) using Monte Carlo (MC) simulations. This is done by obtaining a complex photon weight from analysis of the Fourier transform of the RTE. We also develop a modified shortcut method that enables a single MC simulation to efficiently provide RTE solutions in the SFD for any number of spatial frequencies. We provide comparisons between the modified shortcut method and conventional discrete transform methods for SFD reflectance. Further results for oblique illumination illustrate the potential diagnostic utility of the SFD phase-shifts for analysis of layered media.

© 2011 Optical Society of America

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    [CrossRef]

2010

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

R. B. Saager, D. J. Cuccia, and A. J. Durkin, J. Biomed. Opt. 15, 017012 (2010).
[CrossRef] [PubMed]

2009

V. Lukic, V. A. Markel, and J. C. Schotland, Opt. Lett. 34, 983 (2009).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

2008

2004

A. D. Kim, J. Opt. Soc. Am. A 21, 820 (2004).
[CrossRef]

S. A. Carp, S. A. Prahl, and V. Venugopalan, J. Biomed. Opt. 9, 632 (2004).
[CrossRef] [PubMed]

2001

1999

Ayers, F. R.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

Bassi, A.

Bevilacqua, F.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

C. K. Hayakawa, J. Spanier, F. Bevilacqua, A. K. Dunn, J. S. You, B. J. Tromberg, and V. Venugopalan, Opt. Lett. 26, 1335 (2001).
[CrossRef]

Carp, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, J. Biomed. Opt. 9, 632 (2004).
[CrossRef] [PubMed]

Cuccia, D. J.

R. B. Saager, D. J. Cuccia, and A. J. Durkin, J. Biomed. Opt. 15, 017012 (2010).
[CrossRef] [PubMed]

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

A. Bassi, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, J. Opt. Soc. Am. A 25, 2833 (2008).
[CrossRef]

Dunn, A. K.

Durkin, A. J.

R. B. Saager, D. J. Cuccia, and A. J. Durkin, J. Biomed. Opt. 15, 017012 (2010).
[CrossRef] [PubMed]

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

A. Bassi, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, J. Opt. Soc. Am. A 25, 2833 (2008).
[CrossRef]

Erickson, T. A.

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

Hayakawa, C. K.

Kim, A. D.

Lukic, V.

Markel, V. A.

Mazhar, A.

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

Österberg, U.

Paulsen, K.

Pogue, B.

Prahl, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, J. Biomed. Opt. 9, 632 (2004).
[CrossRef] [PubMed]

Saager, R. B.

R. B. Saager, D. J. Cuccia, and A. J. Durkin, J. Biomed. Opt. 15, 017012 (2010).
[CrossRef] [PubMed]

Schotland, J. C.

Spanier, J.

Testorf, M.

Tromberg, B. J.

Tunnell, J. W.

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

Venugopalan, V.

You, J. S.

Appl. Opt.

J. Biomed. Opt.

S. A. Carp, S. A. Prahl, and V. Venugopalan, J. Biomed. Opt. 9, 632 (2004).
[CrossRef] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, J. Biomed. Opt. 14, 024012 (2009).
[CrossRef] [PubMed]

T. A. Erickson, A. Mazhar, D. J. Cuccia, A. J. Durkin, and J. W. Tunnell, J. Biomed. Opt. 15, 036013 (2010).
[CrossRef] [PubMed]

R. B. Saager, D. J. Cuccia, and A. J. Durkin, J. Biomed. Opt. 15, 017012 (2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Reflectance versus spatial frequency computed using f x , f y , and f ρ kernels in the 1D MSM. Relative differences between the f x and f y kernel results relative to the f ρ kernel are also shown.

Fig. 2
Fig. 2

SFD reflectance computed by 1D discrete transform using f x , f y , and f ρ kernels versus the MSM using the Hankel kernel. Colors denote the spatial widths Δ used in the discrete transforms.

Fig. 3
Fig. 3

Reflectance amplitude and phase versus spatial frequency for a two-layered “epithelial” tissue illuminated with an obliquely oriented 1D modulated source. Arrow indicates the effect of increasing top-layer scattering on the reflectance and phase-shift.

Equations (6)

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Ω · L ( r , Ω ) = - μ a L ( r , Ω ) μ s L ( r , Ω ) + μ s S 2 L ( r , Ω ) p ( Ω , Ω ) d Ω ,
Ω z d L ^ ( z , f , Ω ) d z = [ μ a + 2 π i ( Ω x f x + Ω y f y ) ] L ^ ( z , f , Ω ) μ s L ^ ( z , f , Ω ) + μ s S 2 L ^ ( z , f , Ω ) p ( Ω , Ω ) d Ω .
W j = W j 1 exp { [ μ a + 2 π i ( Ω x , j f x + Ω y , j f y ) ] j } = W j ( a ) W j ( f x ) W j ( f y ) ,
W j ( f x ) = exp [ - 2 π i f x m = 1 j ( x m x m 1 ) ] = exp [ 2 π i f x ( x j x 0 ) ] .
W j = exp ( μ a d ) exp ( 2 π i f x x j ) exp ( 2 π i f y y j ) .
R ( f ρ ) = 1 N n W n = 1 N n exp ( μ a d n ) J 0 ( 2 π f ρ ρ n ) .

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