Solution of time-independent inverse problems for linear transport theory.

摘要

In this study three inverse radiative transfer problems are investigated: two inverse remote sensing boundary problems for a homogeneous plane-parallel cloud, and an inverse in situ sensing source problem for a multilayered plane-parallel ocean. All problems involve highly anisotropic scattering. One inverse cloud problem is the one-parameter estimation of the cloud thickness assuming known optical properties and underlying surface albedo, and the second cloud problem is the two-parameter estimation of the cloud thickness and the underlying surface albedo. The inverse ocean problem involves the estimation of the spatial variation of the bioluminescent source magnitude.; The algorithms developed to estimate the optical thickness of clouds are for an irradiance detector located above, deep within, or beneath the cloud. Radiative transfer calculations with a computer program developed on the basis of the F{dollar}sb{lcub}rm N{rcub}{dollar} method are used to numerically test the above-cloud detector algorithms for monodirectional illumination for results of Haze-L and Fair Weather Cumulus clouds. An error analysis for the above-cloud detector algorithms confirms the difficulty of estimating the optical thickness under certain conditions that are defined.; An iterative algorithm for simultaneously estimating the optical thickness of a homogeneous, plane-parallel cloud and the albedo of an obscured underlying surface are developed and numerically tested. Only two or more remote measurements of radiances or irradiances are required. The method incorporates analytically-computed first derivatives of the unknowns that are obtained very directly from the F{dollar}sb{lcub}rm N{rcub}{dollar} method of transport theory. The ill-posed nature of the problem is quantified in terms of sensitivity coefficients. Sensitivity coefficients obtained for the converged results are useful for assessing the effects of errors in the measurements.; The algorithm for estimating the spatial location and magnitude of a bioluminescent radiation source from measurements of the in situ irradiance and scalar irradiance at two depths is based on the principle of photon conservation. The most direct application of the algorithm requires that the absorption coefficient be known, but the algorithm is useful even if that coefficient in unknown. If that coefficient is known, the source magnitude can be accurately estimated as a function of depth except near the seasurface for cases with strong external illumination, such as from moonlight.