Research on Fourier Demodulation Method Based on Continuous Rotating Waveplate Modulation

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.