Error analysis for the lidar backward inversion algorithm

Here we depart from the inhomogeneous solution of a lidar equation using th e backward inversion algorithm that is nowadays generally referred to as th e Klett method. In particular, we develop an error sensitivity study that r elates errors in the user-input parameters boundary extinction and exponent ial term in the extinction-to-backscatter relationship to errors in the inv erted extinction profile. The validity of the analysis presented is limited only by the validity of application of the inversion algorithm itself, its numerical performance having been tested for optical depths in the 0.01-10 range. Toward this end, we focus on an introductory background about how u ncertainties in these two parameters can apply to a family of inverted exti nction profiles rather than a single profile and on its range-dependent beh avior as a function of the optical thickness of the lidar inversion range. Next, we performed a mathematical study to derive the error span of the inv erted extinction profile that is due to uncertainties in the above-mentione d user calibration parameters. This takes the form of upper and lower range -dependent error bounds. Finally, appropriate inversion plots are presented as application examples of this study to a parameterized set of atmospheri c scenes inverted from both synthesized elastic-backscatter lidar signals a nd a live signal. (C) 1999 Optical Society of America. OCIS codes: 010.0010 , 010.1290, 010.3640.