Ray mapping approach for the efficient design of continuous freeform surfaces.
Ray mapping approach for the efficient design of continuous freeform surfaces.
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DOI：
10.1364/oe.24.014271
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发表时间：
2015-10
期刊：
影响因子：
3.8
通讯作者：
C. Bösel;H. Gross
中科院分区：
文献类型：
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作者：
C. Bösel;H. Gross
连续自由曲面的有效设计，它映射一个给定的光源到一个任意的目标照明图案，仍然是一个具有挑战性的问题，这里被认为是准直输入光束。一种常见的方法是射线映射方法，其中首先计算源和目标平面上的辐照度分布之间的射线映射，并且在后续步骤中构建表面。这种方法的挑战性方面是找到一个可积映射，确保连续的表面。基于反射/折射定律和可积性条件，我们推导出了准直入射光束的表面和光线映射的一般条件。它表明，在一个小角度近似的适当的映射，可以通过计算最佳的质量传输-一个数学框架计算两个正密度函数之间的映射。我们表明，表面可以通过求解线性平流方程。适当的边界条件。结果表明，最佳的质量输运映射是近似可积的自由形式和目标平面之间的距离在很宽的范围内，并提供了一种有效的方法来构建的表面通过解决标准积分。通过将其应用于两个具有挑战性的设计实例来证明该方法的效率，该实例显示了所提出的方法处理具有陡峭辐照度梯度和众多灰度级的目标照明图案的能力。
The efficient design of continuous freeform surfaces, which maps a given light source to an arbitrary target illumination pattern, remains a challenging problem and is considered here for collimated input beams. A common approach are ray-mapping methods, where first a ray mapping between the source and the irradiance distribution on the target plane is calculated and in a subsequent step the surface is constructed. The challenging aspect of this approach is to find an integrable mapping ensuring a continuous surface. Based on the law of reflection/refraction and an integrability condition, we derive a general condition for the surface and ray mapping for a collimated input beam. It is shown that in a small-angle approximation a proper mapping can be calculated via optimal mass transport - a mathematical framework for the calculation of a mapping between two positive density functions. We show that the surface can be constructed by solving a linear advection Eq. with appropriate boundary conditions. The results imply that the optimal mass transport mapping is approximately integrable over a wide range of distances between the freeform and the target plane and offer an efficient way to construct the surface by solving standard integrals. The efficiency is demonstrated by applying it to two challenging design examples, which shows the ability of the presented approach to handle target illumination patterns with steep irradiance gradients and numerous gray levels.