On the inversion of the lidar equation

A modified form of the Klett inversion method of the lidar equation is developed. The accuracy of this inversion method is explored and validated. Unlike previous inversions, this one does not require making a guess for each lidar return to initiate the calculation. Included are discussions of the other inversion methods. The assumptions contained in the single-scatter lidar equation and in the inversion method are outlined as is their relative importance. Special attention is given to the backscatter versus total extinction relation, multi-scattering and non-ideal detector response. The lidar equation is the governing relation which permits the calculation of extinction and estimates of concentration under conditions of single scattering from a given lidar return. However, to obtain the solution, an inversion of the equation must be performed.