Tong Kainian, Zheng Yi, Zhang Zan, Zhao Xing, Zhang Bo, Song Lipei, Wang Lingjie, Wang Chao, Wu Pengfei
Opt Express. 2018 May 28;26(11):14010-14023. doi: 10.1364/OE.26.014010.
The model fitting degree of optical freeform surfaces is of utmost design importance. We develop a model with radial basis functions based on the surface slope (RBF-slope) for optical freeform surfaces with asymmetric structures. The RBF-slope model improves the basis-function distribution for circular apertures and establishes a relationship between shape factor and local surface slope, which provides the model with better fitting ability than the conventional RBF model (RBF-direct); fitting experiments for off-axis conic surfaces, "bumpy" paraboloids, and the design of a single mirror magnifier demonstrate the efficacy of our approach. Our method can effectively improve aberration balancing of optical freeform surfaces, resulting in high-quality imaging.
光学自由曲面的模型拟合度在设计中至关重要。我们基于表面斜率开发了一种具有径向基函数的模型（RBF-斜率），用于具有非对称结构的光学自由曲面。RBF-斜率模型改善了圆形孔径的基函数分布，并建立了形状因子与局部表面斜率之间的关系，这使得该模型比传统的RBF模型（RBF-直接）具有更好的拟合能力；对离轴圆锥曲面、“凹凸不平”抛物面的拟合实验以及单镜放大镜的设计证明了我们方法的有效性。我们的方法可以有效地改善光学自由曲面的像差平衡，从而实现高质量成像。
