Lin Psang Dain
Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
Heliyon. 2022 Sep 6;8(9):e10531. doi: 10.1016/j.heliyon.2022.e10531. eCollection 2022 Sep.
The ray-aberrations in axis-symmetrical systems are conventionally derived from wavefront functions or characteristic functions using classical approximate partial derivatives. However, the resulting aberrations typically have fifth-order errors, as described by Restrepo et al. (2017) [1]. Accordingly, in the present study, the secondary ray-aberration coefficients for object placed at finite distance are determined using the fifth-order Taylor series expansion of a skew ray. Notably, the derived expressions are exact since they are determined without any approximations. It is found that some of the aberration coefficients are not constants, but are functions of the polar angle of the entrance pupil. It is additionally found that, once the required derivative matrices have been generated, determination of the secondary aberration coefficients is straightforward without iteration, and incurs only a low computational cost.
轴对称系统中的光线像差通常是使用经典的近似偏导数从波前函数或特征函数中推导出来的。然而，如Restrepo等人（2017年）[1]所述，由此产生的像差通常具有五阶误差。因此，在本研究中，使用倾斜光线的五阶泰勒级数展开来确定放置在有限距离处物体的二级光线像差系数。值得注意的是，导出的表达式是精确的，因为它们是在没有任何近似的情况下确定的。研究发现，一些像差系数不是常数，而是入瞳极角的函数。此外还发现，一旦生成了所需的导数矩阵，二级像差系数的确定就很简单，无需迭代，并且计算成本很低。
