Perturbation Theoretical Approach to the Generalized Kubelka-Munk Problem in Nonhomogeneous Optical Media

Abstract

The generalized Kubelka-Munk problem is considered in nonhomogeneous optical media with arbitrary depth-dependent absorption and scattering coefficients. Regular perturbation theory is applied to the resulting Riccati equation, and explicit expressions are derived for the diffuse reflectance and transmittance of a finite thickness layer. The first-order perturbation solution to the problem with exponentially distributed absorption and scattering coefficients is presented, and the implications for the quantitative study of nonhomogeneous optical media, such as powdered layers, are discussed.