Two-wavelength lidar inversion algorithm

Potter [Appl. Opt. 26, 1250 (1987)] has presented a method to determine profiles of the atmospheric aerosol extinction coefficients by use of a two-wavelength lidar with the assumptions of a constant value for the extinction-to-backscatter ratio for each wavelength and a constant value for the ratio between the two extinction coefficients at the two wavelengths. Triggered by this idea, Ackermann [Appl. Opt. 36, 5134 (1997)] expanded this method to consider lidar returns that are a composition of scattering by atmospheric aerosols and molecules, assuming that the molecular scattering is known. In both papers the method is based on the well-known solutions of Bernoulli's differential equation in an iterative scheme with an unknown boundary transmission condition. This boundary condition is less sensitive to noise than boundary extinction conditions. My main purpose is to critically consider the principle behind Potter's method, because it seems that there are several reasons why the number of solutions is not limited to one, as suggested by his original work.