Biases induced by retardance and diattenuation in the measurements of long-baseline interferometers

Context. The coherence of long-baseline interferometers is affected by the polarization properties of the instrument. This is a possible source of biases, which would need to be calibrated. Aims. The goal of this paper is to study the biases due to retardance and diattenuation in long-baseline interferometers. In principle, the results can be applied to both optical and radio interferometers. Methods. We derived theoretical expressions for biases on fringe contrast and fringe visibility phase for interferometers whose polarizing properties can be described by beam rotation, retardance, and diattenuation. The nature of these biases are discussed for natural light, circular and linear polarization, and partially polarized light. Expansions were obtained for small degrees of polarization, small differential retardance, and small diattenuation. Results. The biases on fringe contrasts were already known. It is shown in this paper that retardance and diattenuation are also sources of bias on the visibility phases and derived quantities. In some cases, the bias is zero (for non-polarizing interferometers with natural or partially circulary polarized light.) If the retardance is achromatic, differential phases are not affected. Closure phases are not affected to the second order for an interferometer with weak diattenuation and weak differential retardance and for moderately polarized sources whatever the type of light. Otherwise, a calibration procedure is required. It has been shown that astrometric measurements are biased in the general case. The bias depends on both the polarization properties of the interferometer and on the (u, v) sampling. In the extreme case where the samples are aligned on a line crossing the origin of the spatial frequency plane, the bias is undetermined and can be arbitrarily large. In all other cases, it can be calibrated if the polarizing characteristics of the interferometer are known. In the case of a low differential retardance and low degree of polarization, the bias lies on a straight line, crossing the astrometric reference point. If the degree of linear polarization varies during the observations, then the astrometric bias has a remarkable signature, which describes a section of the line. For slightly polarizing interferometers, a fixed offset is added without changing the shape of the bias. Conclusions. A polarizing interferometer does generate bias on visibility contrast and visibility phase. The bias depends on the polarization characteristics of the source. In any case, the bias can be computed if the polarization characteristics of the interferometer are known. Astrometric biases can also be corrected and depend on the (u, v) sampling achieved for the measurements.