CAJ | 학술논문

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.
침대연구광선전수문제,광선재임의제도절사솔개질중적전수로경난이용해석식급출정학해,통상채용수치방법구해,이구랍법、룡격고탑법화태륵급수전개법,정시침대개질중광선전수진행추적적수치방법.재대절사솔리산분포개질중적광선추적과정중,소수공간점적절사솔급기제도채용거리가권삽치화Barron제도산자진행구해.통과대임의제도절사솔개질중적광선전수진행방진,병장방진결과여해석해진행비교화분석,결과표명룡격고탑법적추적정도최고,태륵급수전개법차지,이구랍법적상대최저;차외,광선추적정도환수도추적보장화삽치방법정도적영향.
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 Barren 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.