Recursive technique for inverting the lidar equation

A method for extracting the extinction coefficient from lidar signals is presented. The method assumes the backscatter and extinction coefficient to be related by a power law and consists of approximating the integral in the lidar equation by a Riemann sum of the extinction coefficients. This approximation allows us to develop two recursion formulas for extracting the extinction coefficient as a function of range. One formula is a forward recursion, and the other is a backward recursion in the sense that solutions are generated for r >/= r(0) and for r </= r(m), respectively, where r(0) is a near-end range and r(m) is a far-end reference range.