一种偏振定标单元方位角误差的约束非线性最小化优化定标方法

An Optimization Approach Based on the Constrained Nonlinear Minimization for Calibrating Azimuth Errors in Polarization Calibration Units

偏振定标单元(Polarization Calibration Unit,PCU)对于定标由偏振系统和天文望远镜产生的仪器偏振至关重要,然而偏振定标单元中偏振元件光轴的方位角误差是限制定标精度的主要因素之一.为解决该问题,提出了一种基于约束非线性最小化优化的方位角误差定标方法,该方法具有定标精度高、定标速度快的优点.首先将偏振定标单元中的线性偏振片和四分之一波片的光轴方位角误差设置为两个待优化的自由变量,然后利用产生和测量的Stokes参数以及偏振定标获得的响应矩阵定义优化目标函数,最终使用约束非线性最小化优化方法来确定两个偏振元件的方位角误差.分别从理论模拟和实际测量两个方面对优化方法进行了验证,实验结果表明,该优化方法能够成功获得上述两个方位角误差,精度分别优于2.79′和2.72′.此外,从理论上计算分析了不同方位角误差对各Stokes分量的影响情况.该优化方法有望应用到我国太阳望远镜中偏振定标装置的误差定标及研制之中.

Polarization calibration units(PCU)are critical in calibrating the instrumental polarization induced by the polarimetry system itself and the astronomical telescope.However,azimuth errors of optical axes of polarization components in the PCU are one of the main limitations to the calibration accuracy.To address this issue,an optimization approach based on constrained nonlinear minimization to derive azimuth errors in the PCU is proposed in this paper,this method has the advantages of high calibration accuracy and fast calibration speed.Specifically,azimuth errors of the polarizer and the quarter-wave plate are set as two free parameters to be optimized,and then an objective function for the optimization is defined by using generated and measured Stokes parameters and response matrices obtained from the polarization calibration procedure.Finally,values of the two azimuth errors obtained by the optimization are compared with their preset ones,and the optimization method is validated in the aspects of simulation and experiment respectively.Experimental results reveal that the two azimuth errors can be successfully determined by the optimization,with an accuracy better than 2.79′and 2.72′,respectively.Furthermore,the influence of azimuth errors on the Stokes parameters is theoretically analyzed.The optimization method presented in this paper is expected to be applied to the error calibration and development of polarization calibration devices in solar telescopes in our country.