Error Estimation of Linear Polarization Data from Coronagraphs \u2013 Application to STEREO-A/SECCHI-COR1 Observations

Abstract

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.