## 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

**History**

Original Manuscript: April 5, 2001

Revised Manuscript: July 20, 2001

Manuscript Accepted: August 27, 2001

Published: March 1, 2002

**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, E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998) [see Eqs. (9)–(15)]. [CrossRef]
- J. Ripoll, 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 RU(i) and RJ(i) of this reference are equivalent to [1-Rϕ(i)]/2 and 1-RJ(i) when expressed in the parameters used here. [CrossRef]
- R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995) [see Eqs. (34)–(36)]. [CrossRef]
- M. Gerken, G. W. Faris, “Frequency-domain immersion technique for accurate optical property measurements of turbid media,” Opt. Lett. 24, 1726–1728 (1999). [CrossRef]
- R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, 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. [CrossRef]
- S. A. Walker, S. Fantini, 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, R. R. Alfano, eds., Proc. SPIE2979, 219–225 (1997) [see Eq. (6)]. [CrossRef]
- 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, 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. [CrossRef] [PubMed]
- J. Ripoll, M. Nieto-Vesperinas, “Reflection and transmission coefficients for diffuse photon density waves,” Opt. Lett. 24, 796–798 (1999). [CrossRef]

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