Dong Hui, Tang Ming, Gong Yandong
RF Antenna and Optical Department, Institute for Infocomm Research, 1 Fusionopolis Way, # 21-01 Connexis South, Singapore 138632, Singapore.
Opt Express. 2013 Apr 22;21(8):9674-90. doi: 10.1364/OE.21.009674.
Rotatable retarder fixed polarizer (RRFP) Stokes polarimeters are most commonly used to measure the state of polarization (SOP) of an electromagnetic (EM) wave. Most of commercialized RRFP Stokes polarimeters realize the SOP measurements by rotating a 90° retarder to N(N≥5)uniformly spaced angles over 360° and performing a discrete Fourier transform of data. In this paper, we address the noise properties of such uniformly-rotating RRFP Stokes polarimeters employing a retarder with an arbitrary retardance. The covariance matrices on the measurement noises of four Stokes parameters are derived for Gaussian noise and Poisson noise, respectively. Based on these covariance matrices, it can be concluded that 1) the measurement noises of Stokes parameters seriously depend on the retardance of the retarder in use. 2) for Gaussian noise dominated RRFP Stokes polarimeters, the retardance 130.48° leads to the minimum overall measurement noises when the sum of the measurement noises of four Stokes parameters (viz., the trace of the covariance matrix) is used as the criterion. The retardance in the range from 126.06° to 134.72° can have a nearly-minimum measurement noise which is only 1% larger than the minimum. On the other hand, the retardance 126.87° results in the equalized noises of the last three Stokes parameters. 3) for Poisson noise dominated RRFP Stokes polarimeters, the covariance matrix is also a fuction of the SOP of the incident EM wave. Even so, the retardance in the range from 126.06° to 134.72° can also result in nearly-minimum measurement noise for Poisson noise. 4) in the case of Poisson noise, N=5, 10, 12uniformly spaced angles over 360° have special covariance matrices that depend on the initial angle (the first angle in use). Finally, simulations are performed to verify these theoretical findings.
旋转延迟器固定偏振器（RRFP）斯托克斯偏振计最常用于测量电磁波（EM）的偏振态（SOP）。大多数商业化的RRFP斯托克斯偏振计通过将90°延迟器在360°范围内旋转到N（N≥5）个均匀间隔的角度并对数据进行离散傅里叶变换来实现SOP测量。在本文中，我们研究了这种采用具有任意延迟的延迟器的均匀旋转RRFP斯托克斯偏振计的噪声特性。分别针对高斯噪声和泊松噪声推导了四个斯托克斯参数测量噪声的协方差矩阵。基于这些协方差矩阵，可以得出以下结论：1）斯托克斯参数的测量噪声严重依赖于所使用延迟器的延迟。2）对于以高斯噪声为主的RRFP斯托克斯偏振计，当以四个斯托克斯参数测量噪声之和（即协方差矩阵的迹）为标准时，延迟130.48°会导致总体测量噪声最小。在126.06°至134.72°范围内的延迟可以具有几乎最小的测量噪声，该噪声仅比最小值大1%。另一方面，延迟126.87°会使后三个斯托克斯参数的噪声均衡。3）对于以泊松噪声为主的RRFP斯托克斯偏振计，协方差矩阵也是入射EM波SOP的函数。即便如此，在126.06°至134.72°范围内的延迟对于泊松噪声也可导致几乎最小的测量噪声。4）在泊松噪声情况下，在360°范围内的N = 5、10、12个均匀间隔角度具有依赖于初始角度（所使用的第一个角度）的特殊协方差矩阵。最后，进行了仿真以验证这些理论结果。
