Abstract

The objective of these inverse methods is to estimate the coefficients of a Legendre expansion of the angular single-scattering function from angular moments of external measurements of the ingoing and outgoing angular radiance. Two distinct methods based on the radiative transfer equation have been developed for non-normally illuminated slab geometry targets: a formally exact method that requires the solution of an upper triangular system of equations linear in the unknown coefficients, and an approximate method that requires the solution of a set of uncoupled equations. The first method requires angular moments over both the azimuthal and polar angles of both slab surfaces and is ill-conditioned with respect to simulated measurement errors. One way of circumventing the ill-conditioning is to reduce the number of unknowns by seeking only the coefficients for a model scattering law; example calculations illustrate the estimation of the two coefficients for the Henyey-Greenstein model. The second method, which requires only backscattered azimuthal moments following a pulsed irradiation, is surprisingly accurate, even to simulated measurement errors, but only the single scattering albedo, the asymmetry factor, and perhaps the second-order Legendre moment can be determined.The objective of these inverse methods is to estimate the coefficients of a Legendre expansion of the angular single-scattering function from angular moments of external measurements of the ingoing and outgoing angular radiance. Two distinct methods based on the radiative transfer equation have been developed for non-normally illuminated slab geometry targets: a formally exact method that requires the solution of an upper triangular system of equations linear in the unknown coefficients, and an approximate method that requires the solution of a set of uncoupled equations. The first method requires angular moments over both the azimuthal and polar angles of both slab surfaces and is ill-conditioned with respect to simulated measurement errors. One way of circumventing the ill-conditioning is to reduce the number of unknowns by seeking only the coefficients for a model scattering law; example calculations illustrate the estimation of the two coefficients for the Henyey-Greenstein model. The second method, which requires only backscattered azimuthal moments following a pulsed irradiation, is surprisingly accurate, even to simulated measurement errors, but only the single scattering albedo, the asymmetry factor, and perhaps the second-order Legendre moment can be determined.

© 1985 Optical Society of America