The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (<i>r<sub>i</sub></i>, ψ<i><sub>i</sub></i>, Δ<i><sub>i</sub></i>) of the first three detectors. The instrument matrix <b>A</b>, which relates the output signal vector <b>I</b> to the input Stokes vector <b>S</b> by <b>I</b> = <b>AS</b>, and its determinant are derived explicitly. The essential condition that <b>A</b> be nonsingular (det <b>A</b> ≠ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on the detectors are required, and a thin dielectric (e.g., thermal oxide) layer would suffice. The differential reflection phase shift Δ is unrestricted for the first and 0third detectors and has optimum values of ±90° for the second. The optimum rotation angles of the POI are ±45° and ±135°. The optimum values of the surface parameter ψ are 27.37°, 22.5° or 67.5°, and 0 or 90° for the first, second, and third reflections, respectively. The following topics are also considered: (1) the partition of energy among detectors, (2) the effect of tilting the last detector, (3) operation of the FDP over a broadband spectral range, (4) choice of the light-beam path, and (5) calibration.
© 1988 Optical Society of America
R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, "General analysis and optimization of the four-detector photopolarimeter," J. Opt. Soc. Am. A 5, 681-689 (1988)