Diffusion equation boundary conditions for the interface between turbid media: a comment
JOSA A, Vol. 19, Issue 3, pp. 519-520 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000519
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Abstract
This discussion reconciles differences in literature expressions for the diffusion approximation boundary conditions for the interface between two turbid media with different refractive indices.
© 2002 Optical Society of America
OCIS Codes
(170.5270) Medical optics and biotechnology : Photon density waves
(170.5280) Medical optics and biotechnology : Photon migration
(290.1990) Scattering : Diffusion
(290.4210) Scattering : Multiple scattering
(290.7050) Scattering : Turbid media
Citation
Gregory W. Faris, "Diffusion equation boundary conditions for the interface between turbid media: a comment," J. Opt. Soc. Am. A 19, 519-520 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-3-519
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References
- S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998) [see Eqs. (9)–(15)].
- J. Ripoll and M. Nieto-Vesperinas, “Index mismatch for diffuse photon density waves at both flat and rough diffuse–diffuse interfaces,” J. Opt. Soc. Am. A 16, 1947–1957 (1999) [see Eqs. (14) and (15)]. This paper adds consideration of transverse flux to the derivation of Aronson.3 The parameters R_{U(i)} and R_{J(i)} of this reference are equivalent to [1−R_{φ(i)} ]/2 and 1−R_{J(i)} when expressed in the parameters used here.
- R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995) [see Eqs. (34)–(36)].
- M. Gerken and G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1999).
- R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994). See the paragraph beginning, “We mention in passing ...” (p. 2731). This expression is based incorrectly on the effective reflectance coefficient for the interface between a turbid medium and a transparent medium and has a sign error.
- S. A. Walker, S. Fantini, and E. Gratton, “Effect of index of refraction mismatch on the recovery of optical properties of cylindrical inhomogeneities in an infinite turbid medium,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance and R. R. Alfano, eds., Proc. SPIE 2979, 219–225 (1997) [see Eq. (6)].
- The total flux and surface irradiance approaches are equivalent in the diffusion approximation. For higher-order approximations, the surface irradiance approach must be used. For example, the total flux balance expression in Eq. (7–4) of Ref. 8 is valid only in the diffusion approximation.
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
- M. Keijzer, W. M. Star, and P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988) [see Eq. (19)]. Note that Aronson’s subsequent approximations [Ref. 3, Eqs. (38)] are more accurate than this result.
- J. Ripoll and M. Nieto-Vesperinas, “Reflection and transmission coefficients for diffuse photon density waves,” Opt. Lett. 24, 796–798 (1999).
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