Stable analytical inversion solution for processing lidar returns

A simple analytical method is presented that shows some potential for application to the problem of extracting attenuation and backscatter coefficients in an inhomogeneous atmosphere from the return signal of a monostatic single-wavelength lidar system. The method assumes the validity of the single-scattering lidar equation and a power law relationship between backscatter and attenuation. For optical depths greater than unity the inversion method can be applied in principle using only information contained in the signal itself. In contrast to a well-known related analytical inversion solution, the new solution form is shown to be stable with respect to perturbations in the signal, the postulated relationship between backscatter and attenuation, and the assumed or estimated boundary value of attenuation.