Statistics of the slope-method estimator

The slope method has customarily been used and is still used for inversion of atmospheric optical parameters, extinction, and backscatter in homogeneo us atmospheres from lidar returns. Our aim is to study the underlying stati stics of the old slope method and ultimately to compare its inversion perfo rmance with that of the present-day nonlinear least-squares solution (the s o-called exponential-curve fitting). The contents are twofold: First, an an alytical study is conducted to characterize the bias and the mean-square-es timation error of the regression operator, which permits estimation of the optical parameters from the logarithm of the range-compensated lidar return . Second, universal plots for most short- and far-range tropospheric backsc atter lidars are presented as a rule of thumb for obtaining the optimum reg ression interval length that yields unbiased estimates. As a result, the si mple graphic basis of the slope method is still maintained, and its inversi on performance improves up to that of the present-day computer-oriented exp onential-curve fitting, which ends the controversy between these two algori thms. (C) 2000 Optical Society of America. OCIS codes: 010.0010, 010.1290, 010.3640..