Error Analysis for Dual-Beam Optical Linear Polarimetry

In this paper we present an error analysis for polarimetric data obtained with dual-beam instruments. After recalling the basic concepts, we introduce the analytical expressions for the uncertainties of polarization degree and angle. These are then compared with the results of Monte-Carlo simulations, which are also used to briefly discuss the statistical bias. Then we approach the problem of background subtraction and the errors introduced by a non-perfect Wollaston prism, flat-fielding and retarder plate defects. We finally investigate the effects of instrumental polarization and we propose a simple test to detect and characterize it. The application of this method to real VLT-FORS1 data has shown the presence of a spurious polarization, which is of the order of 1.5% at the edges of the field of view. The cause of this effect has been identified with the presence of rather curved lenses in the collimator, combined with the non complete removal of reflections by the coatings. This problem is probably common to all focal-reducer instruments equipped with a polarimetric mode. An additional spurious and asymmetric polarization field, whose cause is still unclear, is visible in the B band.