Abstract

The generalized Kubelka–Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one ($D{P}_1$) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an $8\times 8$ system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

© 2015 Optical Society of America

Generalized Kubelka–Munk approximation for multiple scattering of polarized light

Christopher Sandoval and Arnold D. Kim
J. Opt. Soc. Am. A 34(2) 153-160 (2017)

Deriving Kubelka–Munk theory from radiative transport

Christopher Sandoval and Arnold D. Kim
J. Opt. Soc. Am. A 31(3) 628-636 (2014)

Relationship between the Kubelka-Munk scattering and radiative transfer coefficients

Suresh N. Thennadil
J. Opt. Soc. Am. A 25(7) 1480-1485 (2008)

Decoupling scattering and absorption of turbid samples using a simple empirical relation between coefficients of the Kubelka–Munk and radiative transfer theories

Harshavardhan Ashok Gaonkar, Dinesh Kumar, Rajagopal Ramasubramaniam, and Arindam Roy
Appl. Opt. 53(13) 2892-2898 (2014)

Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media

Zhixiong Guo and Sunil Kumar
Appl. Opt. 39(24) 4411-4417 (2000)