Zernike圆域多项式镜面拟合仿真与精度研究

Fitting Simulation and Precision of Mirror Surface With Zernike Circular Polynomial

引入光机热集成分析利于综合考虑红外光学系统在多种物理场综合作用下的性能变化,Zernike圆域多项式作为光机热集成分析中的数据转换接口,是实现光、机、热各分析软件间数据有效传递的重要手段。采用不完全归纳法,针对常见的三种镜面面形(二次曲面、球面、自由曲面)研究了采样点数目和Zernike圆域多项式项数对拟合曲面的精度影响。仿真结果表明:不同曲面类型所需要的多项式项数不同,多项式项数对曲面拟合精度的影响权重要大于采样点数目,过多的多项式项数会导致拟合精度下降甚至出现病态矩阵。最后通过设计实例对Zernike圆域多项式拟合算法和精度进行了验证。

The thermal/structural/optical(TSO)integrated analysis will be propitious to evaluate the performance change of infrared optical system under the multi-physical field influence.Zernike circular polynomial is an important means which can implement data effective transmission among thermal,structural and optical analysis program.The method of inadequate induction is used to obtain the relation between sampling point number,Zernike circular polynomial term number and fitting precision,according to three common surfaces(quadric,sphere,free-form surface).The simulated results show that different polynomial terms are required for different surface types.The influence of polynomial terms on surface fitting precision is greater than the number of sampling points.Too many polynomial terms will lead to the decrease of fitting precision and even the appearance of ill-conditioned matrix.Finally,the algorithm and accuracy of Zernike circular polynomial fitting are verified by a design example.