偏振测量分析I.全协方差矩阵对极化分量和角度测量的影响
Polarization measurements analysis I. Impact of the full covariance matrix on polarization fraction and angle measurements
摘要：
随着即将发布的高精度偏振测量，如从普朗克卫星，偏振的计量需要改进。特别是，它是至关重要的是要考虑到充分的知识的噪声属性时，估计偏振分数和角度，这遭受众所周知的偏见。虽然强大的简化假设通常已在偏振分析，我们提出了一种方法，包括完整的协方差矩阵的斯托克斯参数估计的偏振分数和角度的分布。因此，我们量化的噪声属性的影响，在观测量的偏差。我们推导出这些量的PDF的解析表达式，考虑到完整的复杂性的协方差矩阵，包括斯托克斯我的强度分量。我们进行模拟，以探讨的统计方差和偏置的偏振分数和角度的噪声属性的影响。我们表明，对于低的变化的Q和U组件之间的有效椭圆率对称的情况下，协方差矩阵可以被简化，通常是这样做的，可以忽略不计的影响的偏差。当强度的信噪比小于10时，总强度的不确定性会大大增加偏振分量的不确定性，但不会增加相对偏差，而强度和偏振分量之间的相关性为10%时，偏振分量的偏差不会受到显著影响。我们比较估计的不确定性影响极化测量，解决的S/N估计的局限性，我们展示了如何建立保守的置信区间极化分数和角度同时。这项研究是第一组文件，致力于分析偏振测量。
英文摘要：
With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, the metrology of polarization needs to improve. In particular, it is crucial to take into account full knowledge of the noise properties when estimating polarization fraction and angle, which suffer from well-known biases. While strong simplifying assumptions have usually been made in polarization analysis, we present a method for including the full covariance matrix of the Stokes parameters in estimates for the distributions of the polarization fraction and angle. We thereby quantify the impact of the noise properties on the biases in the observational quantities. We derive analytical expressions for the pdf of these quantities, taking into account the full complexity of the covariance matrix, including the Stokes I intensity components. We perform simulations to explore the impact of the noise properties on the statistical variance and bias of the polarization fraction and angle. We show that for low variations of the effective ellipticity between the Q and U components around the symmetrical case the covariance matrix may be simplified as is usually done, with negligible impact on the bias. For S/N on intensity lower than 10 the uncertainty on the total intensity is shown to drastically increase the uncertainty of the polarization fraction but not the relative bias, while a 10\% correlation between the intensity and the polarized components does not significantly affect the bias of the polarization fraction. We compare estimates of the uncertainties affecting polarization measurements, addressing limitations of estimates of the S/N, and we show how to build conservative confidence intervals for polarization fraction and angle simultaneously. This study is the first of a set of papers dedicated to the analysis of polarization measurements.
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