基于龙贝格解算旋转波片型偏振仪Stokes参量的误差分析

Error analysis of the Stokes coefficients of a rotating wave-plate-type polarimeter based on the Romberg solution

摘要:

旋转波片型偏振仪是最常用的测量光束偏振态的仪器。基于旋转波片型偏振仪可以通过傅里叶变换解调将Stokes参量的计算问题转化为定积分的求解问题。在该系统中，波片快轴方位角误差是影响旋转波片型偏振仪的主要误差源之一。同时求解定积分所采用的解算算法也会影响Stokes参量最终获取精度。为了探究波片方位角误差和Stokes参量解算算法对获取被测目标Stokes参量的影响，本文首先对旋转波片型偏振仪中的波片方位角误差在复化梯形、复化辛普森、龙贝格数值积分三种解算算法下进行仿真分析，然后在波片方位角误差一定时，对不同偏振态下的目标进行了Stokes参量的误差分析。仿真结果表明，三种算法的全Stokes参量的解算误差都随着波片方位角误差的增大而增大，同时随着采样点的增加，全Stokes参量的解算误差也会越来越小。使用龙贝格数值积分算法的解算误差最小，S0、S1、S2、S3的解算误差分别为0.0092%、0.0184%、0.3133%、0.0785%（波片方位角误差在[-2?,2?]，采样点数n=128时）。不同偏振态对各Stokes分量测量误差影响不一致，经计算各Stokes参量的最大误差均出现在目标反射光Sin=[1 1 0 0]附近。该研究方法和结果可以为基于旋转波片型偏振成像仪的误差分析研究提供一定的研究思路和理论参考。

Abstract:

A rotating wave-plate-type polarimeter is the most commonly used instrument for measuring the polarization state of an optical beam. Based on the rotating-wavelength polarimeter, the problem of calculating the Stokes coefficients is transformed into the problem of solving the definite integrals by Fourier transform demodulation. In this system, the azimuthal error of the fast axis of the wave-plate is one of the main error sources affecting the rotating wave-plate-type polarimeter. Meanwhile, the solution algorithm used to solve the definite integral will also affect the final accuracy of the Stokes parameter. In order to investigate the effects of the wave-plate azimuth error and the Stokes parameter solving algorithm on the acquisition of the Stokes parameter of the measured target, this paper firstly simulates and analyzes the wave-plate azimuth error in the rotating wave-plate polarimeter under three solving algorithms, namely, complex trapezoidal, complex Simpson, and numerical integration of Romberg, and then performs the Stokes parameter error analysis on the target in different polarization states when the wave-plate azimuth error is certain. Stokes parametric error analysis. The simulation results show that the solution error of the full Stokes parameter of all three algorithms increases with the increase of the wave-guide azimuth error, and at the same time, the solution error of the full Stokes parameter becomes smaller and smaller with the increase of the sampling points. The solution errors using the Romberg numerical integration algorithm are the smallest, with 0.0092%, 0.0184%, 0.3133%, and 0.0785% for S0, S1, S2, and S3, respectively (for wave-plate azimuth errors at [-2?,2?] and n=128 sampling points). The effects of different polarization states on the measurement errors of each Stokes component are inconsistent, and the maximum errors of each Stokes parameter are calculated to occur near the target reflected light Sin=[1 1 0 0]. The research method and results can provide certain research ideas and theoretical references for the error analysis research based on the rotating wave-plate type polarization imager.