摘要
针对研究光线传输问题,光线在任意梯度折射率介质中的传输路径难以用解析式给出精确解,通常采用数值方法求解,而欧拉法、龙格库塔法和泰勒级数展开法,正是针对介质中光线传输进行追迹的数值方法。在对折射率离散分布介质中的光线追迹过程中,所需空间点的折射率及其梯度采用距离加权插值和Barron梯度算子进行求解。通过对任意梯度折射率介质中的光线传输进行仿真,并将仿真结果与解析解进行比较和分析,结果表明龙格库塔法的追迹精度最高,泰勒级数展开法次之,而欧拉法的相对最低;此外,光线追迹精度还受到追迹步长和插值方法精度的影响。
Generally, the ray transmission track of discretionary gradient refraction index medium can not be exactly expressed by analytic representation. Numerical methods are usually used to solve this problem, and Euler, Runge - Kutta, and Taylor series expansion are three kinds of these numerical methods. During the ray tracing process in discrete medium, the distance -weighed interpolation method and Barton arithmetic operator are used to calculate refraction index and gradient. At last, the three ray tracing methods are applied to simulate the ray transport in discretionary gradient refraction index medium. By comparing the simulative results and actual ones, some results are obtained. The results show that Runge - Kutta method has the highest precision, and the following is Taylor series expansion method, and the last is Euler method. Tracing step and gradient interpolation can also influence the tracing precision.
出处
《计算机仿真》
CSCD
北大核心
2010年第2期135-139,共5页
Computer Simulation
基金
国防科技大学优秀研究生创新资助项目(B080103)
关键词
光线追迹
梯度折射率
欧拉法
龙格库塔法
泰勒级数展开法
Ray tracing
Gradient refraction index
Euler method
Runge - Kutta method
Taylor series expansion method
