New ray tracing method for 3D irregular non-uniform refractive index field
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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1.610-8，Richardson外推法为1.210-8，Adams线性多步法为1.210-11，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 1.610-8, Richardson extrapolation method is 1.210-8, and Adams method is 1.210-11. 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.
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Key words:
- inhomogeneous medium /
- refractive index /
- high precision /
- ray tracing
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