28 November 2007 Comparison of ray-tracing methods in self-adaptive grid for inhomogeneous medium
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The difficulty of tracing rays through the random index medium, like atmosphere, or flowing liquid, lies on how to fast obtain the refractive index and gradient values of each location along the ray trajectory in space. Recently, the method of "self-adapting grid" has been developed to efficiently describe such a medium. There are several available numerical techniques for tracing rays through inhomogeneous medium, such as Taylor method and 3rd order Runge-Kutta method, the combinations of the self-adapting grid with different ray tracing techniques result in different accuracy and require different computational effort. In this paper, according to the fundamentals of numerical computation, the derivation of 4th order Runge-Kutta method is presented. For the convenience of comparison, the ray trace through a regular gradient medium (GRIN) has also been made by these methods, and the results are compared with that from other commercial lens design codes. The results show that the 4th order Runge-Kutta method has the highest accuracy for the same step size, but it consumes the longest time. When the ray trace step is relatively large, i. e., one fifth of the GRIN rod size, the 4th Runge-Kutta method is much more accurate than the 3rd method, however, there's few difference of the accuracy when ray trace with a small step size. Therefore, the 3rd order Runge-Kutta method is the optimum choice for ray tracing in self-adapting grid when comprehensively considering the accuracy and computational efforts.
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S. T. Deng, S. T. Deng, X. T. Li, X. T. Li, Z. F. Cen, Z. F. Cen, Q. S. Liu, Q. S. Liu, } "Comparison of ray-tracing methods in self-adaptive grid for inhomogeneous medium", Proc. SPIE 6834, Optical Design and Testing III, 68341D (28 November 2007); doi: 10.1117/12.754656; https://doi.org/10.1117/12.754656

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