The first three columns of the instrument matrix A of the four-detector photopolarimeter (FDP) are determined by Fourier analysis of the output current vector I(P) as a function of the azimuth angle P of the incident linearly polarized light. Therefore 12 of the 16 elements of A are measured free of the imperfections of the (absent) quarter-wave retarder (QWR). The effect of angular beam deviation by the polarizer is compensated for by taking the average, (1/2) [I(P) + I(P + 180°)], of the FDP output at 180°-apart, optically equivalent, angular positions of the polarizer. The remaining fourth column of A is determined by the FDP’s response to the right- and left-handed circular polarization states. Because these states are impossible to generate with an imperfect QWR, a novel procedure is developed. In particular, the response of the FDP to the unattainable right- or left-handed circular polarization state is found by taking the average of the responses of the FDP to an elliptical near-circular state and that state rotated in azimuth by 90°. This calibration scheme is applied to measure A of our prototype FDP of four Si detectors at λ = 632.8 nm. A is determined, in external and internal reference frames, free of imperfections in the polarizing optical elements. The FDP, with its uncontaminated A matrix, is used subsequently to evaluate the imperfections of the QWR with the help of an appropriate model.
Journal of the Optical Society of America A
R. M. A. Azzam and Ali G. Lopez, "Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements," J. Opt. Soc. Am. A 6, 1513-1521 (1989)