非球面光学系统的光路计算方法与编程实现

A Method and Its Programming for Calculating the Light Path of Aspheric Optical System

针对非球面光学系统的复杂性,给出了一种有效的光路计算方法,并导出了光路计算的通用公式和符号规则。该方法首先以光线与过折射面顶点的切平面的交点为起点,采取步进逼近的方法确定入射点在光线上的位置区间;然后利用二分法在该区间内高精度求解入射点的坐标。可高精度求得入射点法线和折射光线方位,并计算出累积光程和系统透过率。基于该方法编制的光路计算程序已应用于OCT(光学层析成像)系统的仿真研究,其计算精度和效率得到了验证。

Being aimed at the complexity of aspheric optical system, this paper presents an efficient method for light path calculation. And the general formulas and the sign rules are analyzed and derived in the paper. The principle of the method is as follows： the position range of incident point on the ray is firstly determined by use of the stepping approximation which starts from the cross point of the ray and the tangent plane of refraeting surface at its vertex, and then the coordinates of the incident point are calculated at high degree of accuracy by use of dichotomy within this range. Consequently, the surface＇s normal line at incident point and the refractive ray can be determined at high degree of accuracy, and meanwhile, the accumulative optical path length and system transmittance can be calculated. The program based on the method has been applied in the simulation research on OCT （optical coherence tomography） system, which testifies its accuracy and efficiency.