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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).

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

[Crossref]

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[Crossref]

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[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).

[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.

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

[Crossref]

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[Crossref]

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[Crossref]

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

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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).

[Crossref]

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).

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.

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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.