确定高阶光学系统模型矩阵系数的一般方法
A General Method for the Determination of Matrix Coefficients for High Order Optical System Modelling
摘要：
由光学系统中的光线引起的非线性变换可以通过矩阵适当地描述为任何期望的近似阶数。在由均匀折射率元件组成的系统中，每个单独的光线折射或平移具有相关联的矩阵，并且一系列变换对应于相应矩阵的乘积。本文介绍了一种通用的方法来寻找矩阵系数的平移和表面折射的表面形状或近似的顺序无关。坐标的选择是不寻常的射线的方向的特点是由方向余弦，而不是斜率，这是大大简化和概括系数计算。两个例子，以证明该方法的力量：第一个是球面的第七阶系数的测定，第二个是三阶系数的测定为环面。
英文摘要：
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction or translation has an associated matrix and a succession of transformations correspond to the product of the respective matrices. This paper describes a general method to find the matrix coefficients for translation and surface refraction irrespective of the surface shape or the order of approximation. The choice of coordinates is unusual as the orientation of the ray is characterised by the direction cosines, rather than slopes; this is shown to greatly simplify and generalise coefficient calculation. Two examples are shown in order to demonstrate the power of the method: The first is the determination of seventh order coefficients for spherical surfaces and the second is the determination of third order coefficients for a toroidal surface.
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