Aims: To propose a method for the polarimetric calibration of large astronomical mirrors that does not require use of special optical devices nor knowledge of the exact polarization properties of the calibration target. Methods: We study the symmetries of the Mueller matrix of mirrors to exploit them for polarimetric calibration under the assumptions that only the orientation of the linear polarization plane of the calibration target is known with certainty. Results: A method is proposed to calibrate the polarization effects of single astronomical mirrors by the observation of calibration targets with known orientation of the linear polarization. We study the uncertainties of the method and the signal-to-noise ratios required for an acceptable calibration. We list astronomical targets ready for the method. We finally extend the method to the calibration of two or more mirrors, in particular to the case when they share the same incidence plane.
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