Rocadenbosch F, Comerón A
Department of Signal Theory and Communications, Antennas, Microwaves, Radar, and Optics Group, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain.
Appl Opt. 1999 Jul 20;38(21):4461-74. doi: 10.1364/ao.38.004461.
Here we depart from the inhomogeneous solution of a lidar equation using the backward inversion algorithm that is nowadays generally referred to as the Klett method. In particular, we develop an error sensitivity study that relates errors in the user-input parameters boundary extinction and exponential term in the extinction-to-backscatter relationship to errors in the inverted 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 uncertainties in these two parameters can apply to a family of inverted extinction profiles rather than a single profile and on its range-dependent behavior 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 inverted extinction profile that is due to uncertainties in the above-mentioned 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 atmospheric scenes inverted from both synthesized elastic-backscatter lidar signals and a live signal.
在此，我们背离了使用如今通常称为克莱特方法的反向反演算法得到的激光雷达方程的非均匀解。具体而言，我们开展了一项误差敏感性研究，该研究将用户输入参数（边界消光以及消光与后向散射关系中的指数项）的误差与反演得到的消光剖面中的误差联系起来。所呈现分析的有效性仅受反演算法本身应用有效性的限制，其数值性能已针对0.01 - 10范围内的光学深度进行了测试。为此，我们重点关注关于这两个参数的不确定性如何应用于一族反演得到的消光剖面而非单个剖面的介绍性背景，以及其作为激光雷达反演范围光学厚度函数的与范围相关的行为。接下来，我们进行了一项数学研究，以推导由于上述用户校准参数的不确定性导致的反演消光剖面的误差范围。这采取与范围相关的上下误差界限的形式。最后，给出了合适的反演图，作为本研究对从合成弹性后向散射激光雷达信号和实时信号反演得到的一组参数化大气场景的应用示例。
