Takaki Nick, Bauer Aaron, Rolland Jannick P
Opt Express. 2019 Mar 4;27(5):6129-6146. doi: 10.1364/OE.27.006129.
When leveraging orthogonal polynomials for describing freeform optics, designers typically focus on the computational efficiency of convergence and the optical performance of the resulting designs. However, to physically realize these designs, the freeform surfaces need to be fabricated and tested. An optimization constraint is described that allows on-the-fly calculation and constraint of manufacturability estimates for freeform surfaces, namely peak-to-valley sag departure and maximum gradient normal departure. This constraint's construction is demonstrated in general for orthogonal polynomials, and in particular for both Zernike polynomials and Forbes 2D-Q polynomials. Lastly, this optimization constraint's impact during design is shown via two design studies: a redesign of a published unobscured three-mirror telescope in the ball geometry for use in LWIR imaging and a freeform prism combiner for use in AR/VR applications. It is shown that using the optimization penalty with a fixed number of coefficients enables an improvement in manufacturability in exchange for a tradeoff in optical performance. It is further shown that, when the number of coefficients is increased in conjunction with the optimization penalty, manufacturability estimates can be improved without sacrificing optical performance.
在利用正交多项式描述自由曲面光学元件时，设计人员通常关注收敛的计算效率以及最终设计的光学性能。然而，为了实际实现这些设计，需要制造和测试自由曲面。本文描述了一种优化约束，它允许对自由曲面的可制造性估计进行实时计算和约束，即峰谷矢高偏差和最大梯度法向偏差。一般来说，该约束的构建适用于正交多项式，特别是对于泽尼克多项式和福布斯二维Q多项式。最后，通过两项设计研究展示了这种优化约束在设计过程中的影响：一是对已发表的用于长波红外成像的球形无遮拦三镜望远镜进行重新设计，二是设计用于增强现实/虚拟现实应用的自由曲面棱镜组合器。结果表明，使用固定系数数量的优化惩罚能够在光学性能有所折衷的情况下提高可制造性。进一步表明，当系数数量与优化惩罚一起增加时，可以在不牺牲光学性能的情况下提高可制造性估计。
