Fuerschbach Kyle, Rolland Jannick P, Thompson Kevin P
Opt Express. 2014 Nov 3;22(22):26585-606. doi: 10.1364/OE.22.026585.
This paper utilizes the framework of nodal aberration theory to describe the aberration field behavior that emerges in optical systems with freeform optical surfaces, particularly φ-polynomial surfaces, including Zernike polynomial surfaces, that lie anywhere in the optical system. If the freeform surface is located at the stop or pupil, the net aberration contribution of the freeform surface is field constant. As the freeform optical surface is displaced longitudinally away from the stop or pupil of the optical system, the net aberration contribution becomes field dependent. It is demonstrated that there are no new aberration types when describing the aberration fields that arise with the introduction of freeform optical surfaces. Significantly it is shown that the aberration fields that emerge with the inclusion of freeform surfaces in an optical system are exactly those that have been described by nodal aberration theory for tilted and decentered optical systems. The key contribution here lies in establishing the field dependence and nodal behavior of each freeform term that is essential knowledge for effective application to optical system design. With this development, the nodes that are distributed throughout the field of view for each aberration type can be anticipated and targeted during optimization for the correction or control of the aberrations in an optical system with freeform surfaces. This work does not place any symmetry constraints on the optical system, which could be packaged in a fully three dimensional geometry, without fold mirrors.
本文利用节点像差理论框架来描述在具有自由曲面光学表面的光学系统中出现的像差场行为，特别是位于光学系统中任何位置的φ多项式表面，包括泽尼克多项式表面。如果自由曲面位于孔径光阑或光瞳处，自由曲面的净像差贡献与视场无关。随着自由曲面光学表面沿纵向远离光学系统的孔径光阑或光瞳，净像差贡献变得与视场有关。结果表明，在描述引入自由曲面光学表面时产生的像差场时，不存在新的像差类型。重要的是，结果表明在光学系统中包含自由曲面时出现的像差场恰好是节点像差理论针对倾斜和偏心光学系统所描述的那些像差场。这里的关键贡献在于确定每个自由曲面项的视场相关性和节点行为，这是有效应用于光学系统设计的必备知识。通过这一进展，在优化具有自由曲面的光学系统中的像差校正或控制时，可以预测并针对每种像差类型在整个视场中分布的节点。这项工作对光学系统不施加任何对称约束，该光学系统可以封装在没有折叠镜的完全三维几何结构中。
