变折射率介质中光线追迹通用算法的研究

基于几何光学的光线折射和反射原理提出了变折射率介质中的光线追迹算法，给出了在光线追迹过程中进行递推的反射光线和折射光线的方向余弦方程；解决了空间中法线的确定和光线回转等问题。最后通过对多种不同的存在解析解的特殊折射率分布的数值解值和解析解值的比较，验证了算法的正确性，并且讨论了应用算法时应该注意的问题和算法中还有待解决的问题。该算法不但具有广泛的适用性，基本不受折射率分布的制约，而且其数值解精度达10^-5。该算法在变折射率介质的光学设计和空间成像补偿等方面有着广阔的应用前景。

A Study on Universal Ray Tracing Algorithm in the Medium of Variable Refractive Index

An algorithm of ray tracing based on light ray refraction and reflection in geometrical optics in the medium of variable refractive index is proposed and a recursive direction-cosine equation of reflected light and refractive light for ray tracing in the medium of variable refractive index is carried out, In the algorithm, some problems, confirmation of normal line, light turning etc., are resolved. At last its correctness is validated by comparing numerical value and analytic value of several different special distribution of refractive index of analytic solution, furthermore some problems in the during of applying the algorithm and under solution in the algorithm are discussed. Not only the algorithm has extensive feasibility and is independent of distribution of refractive index, but also its numeric precision is about 10-5. The application of the algorithm is prospective in the many cases, such as optical designing and spatial imaging compensation of variable refractive index.