Abstract
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.
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