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Construction of freeforms in illumination systems via generalized Cartesian oval representation

机译：通过广义笛卡尔椭圆表示法构造照明系统中的自由形式

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摘要

Freeforms in illumination systems are directly constructed by adapting some ideas of Oliker and co-workers [1]. The freeform is created by a set of primitive surface elements which are generalized Cartesian ovals including the optical response of the residual system. Hamiltonian theory of ray optics can be used to determine the family of primitives which is in particular a simple task if the freeform is the exit surface of the illumination system. For simple optical systems an analytical description of the primitives is possible. Contrarily, for more complex optics a conventional ray-tracer is additionally utilized to determine the required system's information, like the optical path lengths or mixed characteristics. To this end a discrete set of rays is traced through the residual systems and the required relations are interpolated to obtain a quasi-analytic representation of the primitives. The potential of this approach is demonstrated by some examples, e.g. freeform optics including collimating or deflection elements.
机译：照明系统中的自由形式是通过改编Oliker及其同事的一些想法直接构建的[1]。自由形式由一组原始表面元素创建，这些元素是广义的笛卡尔椭圆形，包括残留系统的光学响应。哈密​​顿射线光学理论可以用于确定基元族，如果自由形式是照明系统的出射面，那么这尤其是一项简单的任务。对于简单的光学系统，可以对图元进行分析描述。相反，对于更复杂的光学器件，还需要使用常规的光线跟踪器来确定所需的系统信息，例如光程长度或混合特性。为此，通过残差系统追踪了一组离散的射线，并对所需的关系进行了插值，以获得了基元的准解析表示。一些例子证明了这种方法的潜力，例如。自由光学器件，包括准直或偏转元件。

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