Lin Psang Dain, Liu Chien-Sheng
Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan.
J Opt Soc Am A Opt Image Sci Vis. 2012 Nov 1;29(11):2272-80. doi: 10.1364/JOSAA.29.002272.
The first- and second-order derivative matrices of the ray (i.e., ∂R¯(i)/∂X¯(0) and ∂(2)R¯(i)/∂X¯02) and optical path length (i.e., ∂OPL(i)/∂X¯(0) and (2)OPL(i)/∂X¯02) were derived with respect to the variable vector X¯(0) of the source ray in an optical system by our previous papers. Using the first and second fundamental forms of the wavefront, these four matrices are used to investigate the local principal curvatures of the wavefront at each boundary surface encountered by a ray traveling through the optical system. The proposed method not only yields the data needed to compute the irradiance of the wavefront but also provides the information required to determine the caustics. Importantly, the proposed methodology is applicable to both axisymmetric and nonaxisymmetric optical systems.
通过我们之前的论文，推导了光线的一阶和二阶导数矩阵（即∂R¯(i)/∂X¯(0) 和 ∂(2)R¯(i)/∂X¯02）以及光程长度（即∂OPL(i)/∂X¯(0) 和 (2)OPL(i)/∂X¯02），它们是关于光学系统中源光线的变量向量X¯(0) 的。利用波前的第一和第二基本形式，这四个矩阵用于研究光线穿过光学系统时在每个边界表面处波前的局部主曲率。所提出的方法不仅产生计算波前辐照度所需的数据，还提供确定焦散所需的信息。重要的是，所提出的方法适用于轴对称和非轴对称光学系统。
