Mathematical inversion of angular single and double scattering of laser light from aerosol particles

A method to obtain the size distribution function of aerosols in the single-scattering and the intermediate optical-depth regimes is presented. It is shown that the double-scattering inversion problem can be reduced to a perturbation expansion in powers of the optical depth T about the single-scattering solution. The perturbation expansion is summed for all the relevant values of the optical depth by using the Levin convergence acceleration method [J. Comp. Math. 3, 371 (1973)].