光纤阵列太阳光学望远镜研究组知识库

给出了在连续式旋转波片调制模式下傅里叶分析的推导过程和解调公式，并利用理论偏振轮廓对公式的准确性进行了验证。分别采用傅里叶分析和解调矩阵两种解调方法定量模拟了在连续式调制模式下波片的初始方位角误差、旋转定位误差以及探测器曝光过程中时间差占比3个因素对测量精度的影响。主要结论有（1）简单的傅里叶分析不再适用于连续式调制的结果解调，文中给出的新傅里叶分析方法与解调矩阵方法在进行误差分析时，可以得到基本一致的结果。（2）考虑初始方位角误差引起的影响，我们发现对于线偏振信号来说，采用傅里叶分析和解调矩阵可以得到非常一致的结果，而对于圆偏振来说，基于解调矩阵的方法得到的结果误差相对较小。但是两种解调方法都反映了初始方位角误差对圆偏振和线偏振产生的影响一致，且相对误差的大小与偏振信号本身的强弱有关。初始方位角的误差要求在十几角秒量级才能满足结果的相对误差在10-3以下。（3）考虑旋转定位误差引起的影响时发现，采用傅里叶分析和解调矩阵得到的结果非常接近。两者同时显示出旋转定位误差对线偏振信号造成的影响更为明显，且相对误差的大小与信号的强弱有关。当波片的重复定位精度在10″左右时，对10-2量级的弱偏振信号来说，测量误差也能在10-3量级左右。从这一点上，我们发现连续式调制模式对波片旋转的定位精度要求要明显高于步进式调制模式。（4）两种解调方法的结果均显示，在连续式调制模式下，波片的调制周期与探测器曝光时长的时间差（Δ）会造成线偏振信号之间的串扰，即时间差占比（Δ/T）对线偏振信号造成的影响比对圆偏振信号的影响更为明显。当Δ/T小于1%时，线偏振信号相对误差达到10-3量级。 

Continuously rotating waveplates as the polarization modulator is an important configuration which is widely adopted in many ground⁃based or space⁃based solar telescopes for the solar magnetic field measurement. In this paper, we present the derivation and formula of the Fourier demodulation in the context of continuously rotating waveplates. We testify the formula correctness by using the synthetic FeI Stokes profiles, which are produced by the RH radiative transfer code with a given atmosphere model. In addition, we calculate the effect of the home⁃position errors, the positioning errors of the waveplate rotation and the time difference between the waveplate slot time and the detector frame time on the demodulated results by using the demodulation matrix and the Fourier analysis. The main findings are： (1) The new Fourier analysis can provide more accurate results than the simple one adopted by the step⁃wise modulation. Similar results are obtained when we do the relative error estimation using these two demodulation methods. (2) Considering the relative errors due to the home⁃position angle error, we find the demodulated linear polarization are almost the same using these two methods. However, in the case of circular polarization, the demodulation based on the demodulation matrix is more reliable. No matter which method is applied, it is shown that the home⁃position angle error has the same effect on both circular and linear polarization. The relative error of 10-3 requires the home⁃position angle accuracy within ten arc seconds. (3) Calculating the relative error caused by the position error of the waveplate rotation, we find the demodulation results are almost equal using these two methods. Both show that the position error has more influence on the linear polarization. Furthermore, the requirements of the position accuracy are much higher (ten of arc seconds) than that in the case of step⁃wise modulation (0. 1 degree) in order to achieve the relative error of 10-3. (4) It is crucial to precisely match the detector frame time and the waveplate rotation slot time. We investigate the relative error due to the difference between them and find that the time difference (Δ) can cause cross⁃talk between the linear polarization signals. It has more prominent effect on the linear polarization than on the circular polarization. The time difference as a percent of the waveplate slot time (Δ/ T) is required to be smaller than 1％ if the relative error is smaller than 10-3 for the linear polarization.