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.