Due to three-dimensionality of the surrounding space, power of the optical echo in laser rangefinders, scanners and variety of lidar systems shows a well-known range⁻² dependence. It creates demanding requirements for the receiving electronics in terms of extremely high dynamics of the detected signal. In order to meet these requirements, specific solutions have to be implemented, the side effect of which may be a signal distortion and corresponding precision degradation. In this paper, it is shown, that it is possible to design freeform optical component, which can compensate 1/range² effect. The aim of this study was to design such a freeform lens which makes laser tele-detection system receiving the same level of optical echo power, no matter of the distance to the target. From simple energy-conservation rules, the required ray mapping for collecting optics can be deduced, which appears however to be non-integrable. To overcome this problem, the modified fully integrable ray mappings were calculated, based on functional minimization method and Monge-Ampere equation, which enabled to obtain smooth freeform refractive surface.

由于周围空间的三维性，激光测距仪，扫描仪和各种激光雷达系统中的光回波功率表现出众所周知的范围^-2依赖性。就所检测信号的极高动态而言，它对接收电子器件提出了苛刻的要求。为了满足这些要求，必须实施特定的解决方案，其副作用可能是信号失真和相应的精度下降。在本文中显示，可以设计自由光学组件，该组件可以补偿1 /范围²影响。这项研究的目的是设计一种自由形式的透镜，该透镜可以使激光遥测系统接收到相同水平的光回波功率，而与目标之间的距离无关。从简单的节能规则，可以得出收集光学器件所需的光线映射，但是这似乎是不可整合的。为了克服这个问题，基于功能最小化方法和Monge-Ampere方程，计算了修正的完全可积分射线映射，从而能够获得光滑的自由形折射面。