We attempt to quantitatively study the uncertainties of the polarized brightness and for the polarization angle which are to be expected for measurements from noisy image detectors in classical coronagraphs. We derive the probability density functions (PDF) which apply to polarization observations with polarization filters at 0^∘, 60^∘ and 120^∘. The noise in the directly observed image intensities is assumed to be normally distributed. We find that for low and medium signal-to-noise ratios the polarized brightness obeys a distribution with a strongly biased mean which, if not taken account of, leads to an overestimation of the polarized brightness and degree of polarization. The PDFs are compared with data from the SECCHI-COR1 coronagraph onboard STEREO-A in order to detect systematic or random perturbations of the polarized brightness and the polarization angle beyond the unavoidable photon and detector hardware noise. This noise is estimated from two successive filter sequences taken in-flight during calm coronal conditions on 18 May 2008 and is expressed in the form of an intensity–variance relation. Two small deviations between the measured distributions and the predicted PDF for the polarization angle were found. The standard deviation of the polarization angle error decreases with increasing signal-to-noise ratio of the polarized brightness. For ratios larger than about 8 this decrease was found not as steep anymore as predicted which could hint to a small additional noise source. Next, we found a systematic constant deviation of the polarization angle by \(-1^{\circ }\) for all signal-to-noise ratios of the polarized brightness. Besides these small discrepancies, our theoretically derived PDFs agree quite well with the distributions of measured brightnesses in test regions of the images. The PDFs we present here can equally be applied to similarly measured data from other coronagraphs and may help to quantify uncertainty limits of the derived polarization. They can be used for in-flight health checks of an instrument, are useful when separating unpolarized stray light from the polarized K-corona and when comparing the observed polarization data with results from model simulations.

我们试图定量研究偏振亮度和偏振角的不确定性，这些不确定性是在经典日冕仪中使用噪声图像检测器进行测量所期望的。我们推导出在0应用于偏振观测与偏振滤光器的概率密度函数（PDF）^∘，60 ^∘和120 ^∘。假定直接观察到的图像强度中的噪声是正态分布的。我们发现，对于中低信噪比，偏振亮度服从具有强烈偏差均值的分布，如果不考虑这一点，则会导致对偏振亮度和偏振度的高估。将PDF与STEREO-A机载SECCHI-COR1日冕仪上的数据进行比较，以检测超出不可避免的光子和检测器硬件噪声的偏振亮度和偏振角的系统或随机扰动。该噪声是根据2008年5月18日在平静的日冕条件下在飞行中获取的两个连续的滤波器序列估算出的，并以强度-方差关系的形式表示。发现在测量分布和偏振角的预测PDF之间存在两个小偏差。偏振角误差的标准偏差随着偏振亮度的信噪比的增加而减小。对于大于约8的比率，发现该下降不再像预期的那样陡峭，这可能暗示了一个小的附加噪声源。接下来，我们发现偏振角的系统常数偏差为\（-1 ^ {\ circ} \）表示偏振亮度的所有信噪比。除了这些小的差异外，我们从理论上得出的PDF与图像测试区域中测得的亮度分布非常吻合。我们在此提供的PDF可以等效地应用于其他日冕仪的类似测量数据，并且可以帮助量化所导出极化的不确定性限制。它们可用于仪器的飞行中健康检查，在将非偏振杂散光与偏振K电晕隔离以及将观察到的偏振数据与模型仿真结果进行比较时非常有用。