Abstract

An instantaneous point source generating a light field in an infinite turbid medium with anisotropic individual scatterers is considered. Single-scattering solutions are sought as the first term of a series expansion of the solution of the radiative transfer equation in successive scattering orders. A simple formula for a single-scattering solution in media with an arbitrary axially symmetric phase function is derived. Applications of this formula are shown for the Henyey–Greenstein phase function, an ellipsoidal phase function, and a linear phase function. In addition, the single-scattering term of the RTE solution derived by Kholin [Zh. Vych. Mat. i Mat. Fys. 4, 1126 (1964)] for media with a phase function represented by a finite series in Legendre polynomials is considered in more detail.

© 2013 Optical Society of America

Time-domain solution to the radiative transfer equation in an infinite turbid medium with linearly anisotropic scattering

Margarita L. Shendeleva
J. Opt. Soc. Am. A 32(3) 471-477 (2015)

Analytical solution of the radiative transfer theory for the coherent backscattering from two-dimensional semi-infinite media

Philipp Hank, André Liemert, and Alwin Kienle
J. Opt. Soc. Am. A 39(4) 634-642 (2022)

Analytical solution of the vector radiative transfer equation for single scattered radiance

Philipp Hank, André Liemert, and Alwin Kienle
J. Opt. Soc. Am. A 39(11) 2045-2053 (2022)

Single-scattering solution for radiative transfer through a turbid atmosphere

J. Otterman
Appl. Opt. 17(21) 3431-3438 (1978)

Analytical solution for first-order scattering in bistatic radiative transfer interaction problems of layered media

Raphael Quast and Wolfgang Wagner
Appl. Opt. 55(20) 5379-5386 (2016)