We propose a multiscale approach for designing mirrors generating prescribed irradiance distributions in the far field. Our design method is based on calculating a ray mapping from a Monge–Kantorovich mass transportation problem and on reducing this problem to a linear assignment problem (LAP). The proposed multiscale formulation of the LAP allows one to efficiently calculate freeform mirror surfaces defined on meshes with a size of up to at least $1000 \times 1000$. As an example requiring a mesh of this size, we design a mirror generating a grayscale image of A. Einstein on a zero background. The proposed multiscale approach is general and can be applied to a wide range of inverse problems of nonimaging optics.

中文翻译：

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设计产生远场辐照度分布的反射镜时的多尺度方法和线性分配问题。

我们提出了一种用于设计在远场中生成规定的辐照度分布的反射镜的多尺度方法。我们的设计方法是基于计算蒙格–坎托罗维奇大规模运输问题的射线映射并将此问题简化为线性分配问题（LAP）。提出的LAP多尺度公式使人们可以有效地计算在网格上定义的自由曲面镜表面，尺寸至少为$ 1000 \ x 1000 $。作为一个需要这种大小的网格的示例，我们设计了一个在零背景上生成A.爱因斯坦灰度图像的镜子。所提出的多尺度方法是通用的，并且可以应用于广泛的非成像光学反问题。