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The Kubelka-Munk Diffuse Reflectance Formula Revisited

2011; Taylor & Francis; Volume: 46; Issue: 2 Linguagem: Inglês

10.1080/05704928.2010.537004

1520-569X

Michael L. Myrick, Michael N. Simcock, Megan Baranowski, Heather Brooke, Stephen L. Morgan, Jessica N. McCutcheon,

Atmospheric Ozone and Climate

Abstract Abstract We use an integral equation approach to finding the Kubelka-Munk (KM) diffuse reflectance formula and extend the result by finding the apparent path length and total intensity distribution inside an infinite, homogeneous, diffusely reflecting medium with isotropic scattering. We then expand the approach to three dimensions to show that the KM formula is correct for total diffuse reflectance when scattering, excitation, and detection are all isotropic. We obtain simple and exact results for the angular distribution of diffuse reflection and for the total diffuse reflectance when the incident light has an isotropic angular distribution, when it strikes at a single angle of elevation, and when it has the steady-state angular distribution. This work includes some results that employ Chandrasekhar's H function, so we also provide a program for the rapid evaluation of H. “[Supplementary material is available for this article. Go to the publisher's online edition of Applied Spectroscopy Reviews for the following free supplemental resource: Program to compute the value of Chandrasekhar's H function] Keywords: Diffuse reflectanceKubelka-Munkscattering Acknowledgments The authors thank Professor Dan Dix of the University of South Carolina's Department of Mathematics for helpful discussions. This project was supported by Award No. 2007-DN-BX-K199 awarded by the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication/program/exhibition are those of the author(s) and do not necessarily reflect those of the Department of Justice.