三维无规则不均匀折射率场光线追迹新方法

Xiong Haoxi; Yi Shihe; Ding Haolin; Xu Xiwang; Ouyang Tianci

doi:doi:10.3788/irla201948.0503005

红外与激光工程, 2019, 48 (5): 0503005, 网络出版: 2019-06-22

三维无规则不均匀折射率场光线追迹新方法

New ray tracing method for 3D irregular non-uniform refractive index field

论文大纲

Xiong Haoxi ^*Yi Shihe Ding Haolin Xu Xiwang Ouyang Tianci

作者单位

国防科技大学空天科学学院, 湖南长沙 410073

非均匀介质折射率高精度光线追迹 inhomogeneous medium refractive index high precision ray tracing

摘要

飞行器在大气层中高速飞行时, 气动加热, 光学窗口与外部气流相互作用形成了复杂的流场结构。其折射率分布无规则、不均匀, 很难准确得到光线的传播路径。为此, 提出三种四阶精度方法的光线追迹方案, 通过与螺旋光线解析解结果进行对比, 发现四阶Runge-Kutta方法光线追迹过程中最大相对误差为1.6×10-8, Richardson外推法为1.2×10-8, Adams线性多步法为1.2×10-11, 确定Adams线性多步法是可用于光线追迹的高精度、高速的方法。基于多项式拟合的任意点插值方法可以获得比距离反比法更高的折射率场插值精度。并将该方法运用在导弹的光学窗口附近流场引起的波前畸变的计算, 对计算结果进行了对比, 结果表明Adams线性多步法以Runge-Kutta方法起步, 但Admas方法没有忽略前一步的计算结果, 不会带来误差的累积, 所以结果更接近真实解, 而Richardson外推方法算出的光程差大小与其他两种方法明显不同。

Abstract

When a flight flies at high speed in the atmospheric, aerodynamic heating, the optical window interacts with the external airflow to form a complex flow field structure. Its refractive index distribution was irregular and non-uniform, so it was difficult to accurately obtain the ray trajectory. In order to obtain accurate ray trajectory, three ray tracing methods with fourth-order accuracy were proposed. Via comparing the results with the analytical solutions of helical rays, it is found that the maximum relative error of the fourth-order Runge-Kutta method is 1.6×10-8, Richardson extrapolation method is 1.2×10-8, and Adams method is 1.2×10-11. The Adams method is a high-precision and high-speed method for ray tracing. An arbitrary point interpolation method based on the polynomial fitting can obtain higher accuracy refractive index field than that computed by distance inverse ratio method. The method was applied to compute the distorted wavefront caused by the flow field around the optical window of a missile, and the calculation results were compared. It is found that Adams linear multi-step method starts with Runge-Kutta method, but Admas method does not neglect the calculation results of the previous step and will not lead to the accumulation of errors, so the results are closer to the real solution, while Richardson extrapolation method calculates the optical path difference significantly different from the other two algorithms.

参考文献

[1] Yin Xingliang. A new subdiscipline of contemporaryoptics-aero-optics[J]. China Engineering Science, 2005, 7(12): 1-6. (in Chinese)

[2] Yin Xingliang. Principle of Aero-optics[M]. Beijing: China Aerospace Publishing House, 2003. (in Chinese)

[3] Rimmer M P. Ray tracing in inhomogeneous media[J]. Journal of the Optical Society of America, 1968, 58(12): 1667-1668.

[4] Liu Chunsheng, Zhang Tianxu, Li Xiaotong, et al. Description of irregular inhomogeneous refractive index field[J]. Infrared and Laser Engineering, 2007, 36(1): 127-130. (in Chinese)

[5] Feng Dinghua. Fine numerical simulation/experimental study on high speed flow and aero-optics application[D]. Changsha: National University of Defense Technology, 2010. (in Chinese)

[6] Kalish S, Lin Z, Kottos T. Light transport in random media with PT-symmetry[J]. Physics Optics, 2012, 85(5): 1-5.

[7] Lin Dainpsang, Tsai Chungyu. Paraxial ray-tracing equations for optical systems containing triangular prisms[J]. Journal of the Optical Society of America A, 2017, 34(3): 361-368.

[8] Lv Meibo, Wang Pei. Ray tracing in Rochon prisms with absorption[J]. Optics Express, 2017, 25(13): 14676-14690.

[9] Wang Yejun, Waruna D Kulatilaka. Optical ray tracing method for simulating beam-steering effects during laser diagnostics in turbulent media[J]. Applied Optics, 2017, 56(11): 106-115.

[10] Paces Pavel, Yu Wenkai, Klesa Jan. Optical measurement methods for attitude determination of unmanned aerial systems[C]//2018 IEEE/AIAA Digital Avionics Systems Conference, 2018: 23-27.

[11] Si Tongling, Piao Yan, Li Min. Research on collimation of LED naked eye 3D display technology based on ray tracing[J]. Infrared and Laser Engineering, 2018, 47(6): 0603002. (in Chinese)

[12] Liu Wanguo, Hu Hai, Liu Fenghua, et al. Manipulating light trace in a gradientrefractive-index medium: a Lagrangian optics method[J]. Optics Express, 2019, 27(4): 004714.

[13] Zhang Wensheng. Numerical Solution of Differentiale Quations[M]. Beijing: Science Press, 2015. (in Chinese)

[14] Nie Cunyun. Richardson extrapolation method and its generalization[J]. Mathematical Theory and Applications, 2006, 26(2): 15-17. (in Chinese)

, , , , . 三维无规则不均匀折射率场光线追迹新方法[J]. 红外与激光工程, 2019, 48(5): 0503005. Xiong Haoxi, Yi Shihe, Ding Haolin, Xu Xiwang, Ouyang Tianci. New ray tracing method for 3D irregular non-uniform refractive index field[J]. Infrared and Laser Engineering, 2019, 48(5): 0503005.

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