Retrieval of the albedo and phase function from exiting radiances with radiative perturbation theory.

We use radiative perturbation theory to develop a retrieval technique for determining the radiative properties of a scattering medium, such as the Earth's atmosphere, based on measurements of the radiation emerging at either the top or bottom of the medium. In a previous paper [J. Quant. Spectrosc. Radiat. Transfer 54, 695 (1995)] we have shown the capacity of radiative perturbation theory to describe variations in exiting intensity as a linear combination of the parameters that characterize the scattering medium. Here we show that it is possible to set up a matrix relation such that the matrix inversion solves the inverse scattering problem. Using simulated data, we observe that the quality of the solution can be controlled by studying the singular values associated with the kernel matrix, obtaining in this way a stable solution, even in the presence of noise.

Information content of the kernel matrix for the phase function retrieval problem.

We investigate the information content of the radiation measurements to be used in the retrieval of the scattering properties of the atmosphere with the perturbation technique that we previously introduced. Applying this technique to different sets of data, we obtained solutions with varying accuracy. An analysis of these solutions shows that selecting linearly independent data in directions corresponding to small values of the scattering angle increases the number of pieces of information. (This result is in accord with conclusions reached by other researchers, based on a variety of criteria.) This information content should be largely independent of the method or methods employed to perform the inversion procedure.