V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

J. J. DePalma and J. Gasper, "Determining the optical properties of photographic emulsions by the Monte Carlo method," Photograph. Sci. Eng. 16, 181-191 (1972).

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

[CrossRef]

P. Kubelka and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

J. J. DePalma and J. Gasper, "Determining the optical properties of photographic emulsions by the Monte Carlo method," Photograph. Sci. Eng. 16, 181-191 (1972).

J. J. DePalma and J. Gasper, "Determining the optical properties of photographic emulsions by the Monte Carlo method," Photograph. Sci. Eng. 16, 181-191 (1972).

V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

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

[CrossRef]

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, "A practical model for subsurface light transport," in Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001), pp. 511-518.

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

[CrossRef]

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, "A practical model for subsurface light transport," in Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001), pp. 511-518.

S. H. Kong and J. D. Shore, "Modeling the impact of silver particle size and morphology on the covering power of photothermographic media," in Proceedings of the 30th International Congress of Imaging Science (The Society of Imaging Science and Technology, 2006) pp. 205-207.

P. Kubelka and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, "A practical model for subsurface light transport," in Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001), pp. 511-518.

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, "A practical model for subsurface light transport," in Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001), pp. 511-518.

L. Yang and S. J. Miklavcic, "Theory of light propagation incorporating scattering and absorption in turbid media," Opt. Lett. 30, 792-794 (2005).

[CrossRef]

L. Yang and S. J. Miklavcic, "Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media," J. Opt. Soc. Am. A 22, 1866-1873 (2005).

[CrossRef]

L. Yang, B. Kruse, and S. J. Miklavcic, "Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media," J. Opt. Soc. Am. A 21, 1942-1952 (2004).

P. Kubelka and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

K. R. Naqvi, "On the diffusion coefficient of a photon migrating through a turbid medium: Fresh look from a broader perspective," arXiv.org e-print archive, cond-mat/0504429, June 9, 2005, http://arxiv.org/abs/cond-mat/0504429.

V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

S. H. Kong and J. D. Shore, "Modeling the impact of silver particle size and morphology on the covering power of photothermographic media," in Proceedings of the 30th International Congress of Imaging Science (The Society of Imaging Science and Technology, 2006) pp. 205-207.

V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

H. G. Völz, Industrial Color Testing (VCH, 1995).

L. Yang and S. J. Miklavcic, "Theory of light propagation incorporating scattering and absorption in turbid media," Opt. Lett. 30, 792-794 (2005).

[CrossRef]

L. Yang and S. J. Miklavcic, "Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media," J. Opt. Soc. Am. A 22, 1866-1873 (2005).

[CrossRef]

L. Yang, B. Kruse, and S. J. Miklavcic, "Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media," J. Opt. Soc. Am. A 21, 1942-1952 (2004).

L. Yang and B. Kruse, "Revised Kubelka-Munk theory. I. Theory and application," J. Opt. Soc. Am. A 21, 1933-1941 (2004).

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

[CrossRef]

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. MacAdams, and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).

R. Aronson and N. Corngold, "Photon diffusion coefficient in an absorbing medium," J. Opt. Soc. Am. A 16, 1066-1071 (1999).

D. J. Durian and J. Rudnick, "Photon migration at short times and distances and in cases of strong absorption," J. Opt. Soc. Am. A 14, 235-245 (1997).

L. Yang and B. Kruse, "Revised Kubelka-Munk theory. I. Theory and application," J. Opt. Soc. Am. A 21, 1933-1941 (2004).

L. Yang, B. Kruse, and S. J. Miklavcic, "Revised Kubelka-Munk theory. II. Unified framework for homogeneous and inhomogeneous optical media," J. Opt. Soc. Am. A 21, 1942-1952 (2004).

L. Yang and S. J. Miklavcic, "Revised Kubelka-Munk theory. III. A general theory of light propagation in scattering and absorptive media," J. Opt. Soc. Am. A 22, 1866-1873 (2005).

[CrossRef]

R. Pierrat, J.-J. Greffet, and R. Carminati, "Photon diffusion coefficient in scattering and absorbing media," J. Opt. Soc. Am. A 23, 1106-1110 (2006).

[CrossRef]

L. Yang and S. J. Miklavcic, "Theory of light propagation incorporating scattering and absorption in turbid media," Opt. Lett. 30, 792-794 (2005).

[CrossRef]

D. J. Durian, "The diffusion coefficient depends on absorption," Opt. Lett. 23, 1502-1504 (1998).

W. Cai, M. Xu, M. Lax, and R. R. Alfano, "Diffusion coefficient depends on time, not on absorption," Opt. Lett. 27, 731-733 (2002).

J. J. DePalma and J. Gasper, "Determining the optical properties of photographic emulsions by the Monte Carlo method," Photograph. Sci. Eng. 16, 181-191 (1972).

V. Gopal, S. A. Ramakrishna, A. K. Sood, and N. Kumar, "Photon transport in thin disordered slabs," Pramana, J. Phys. 56, 767-778 (2001).

P. Kubelka and F. Munk, "Ein beitrag zur optik der farbanstriche," Z. Tech. Phys. (Leipzig) 12, 593-601 (1931).

H. G. Völz, Industrial Color Testing (VCH, 1995).

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan, "A practical model for subsurface light transport," in Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 2001), pp. 511-518.

S. H. Kong and J. D. Shore, "Modeling the impact of silver particle size and morphology on the covering power of photothermographic media," in Proceedings of the 30th International Congress of Imaging Science (The Society of Imaging Science and Technology, 2006) pp. 205-207.

K. R. Naqvi, "On the diffusion coefficient of a photon migrating through a turbid medium: Fresh look from a broader perspective," arXiv.org e-print archive, cond-mat/0504429, June 9, 2005, http://arxiv.org/abs/cond-mat/0504429.

In the earliest two papers of Yang et al. [Refs. ], the authors make it clear that μ should be greater than or equal to 1, as we assume here, since μ physically corresponds to the factor of increase in the path length due to the scattering. In their later two papers [Refs. ], however, they are unclear on this point and, in fact, seem to implicitly assume that limits in which μ<1 are sensible to discuss. If we do not assume μ must be greater or equal to 1 but instead use the expression shown for s^{2}>/=a^{2}+as over the entire range of ad, it does significantly affect the quantitative results that we obtain for the transmission density for the RKM theory in Section . However, it does not change our basic conclusions concerning the quality of the agreement between the RKM theory and the Monte Carlo results.

To verify the correctness of the Monte Carlo results, we have made comparisons between two different codes written independently by the two authors in different programming languages using different random number generators. Furthermore, the Monte Carlo results for no scattering (i.e., the rightmost data point in each figure) are found to be in excellent agreement with the exact results that can readily be calculated for that simpler case.

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