General analysis and optimization of the four-detector photopolarimeter

Abstract

The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, /i, Ai) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A $ 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 A is unrestricted for the first and third detectors and has optimum values of ±90' for the second. The optimum rotation angles of the POI are +45 0 and +135'. The optimum values of the surface parameter ip are 27.37°, 22.50 or 67.50, 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.

Experimental polarization state tomography using optimal polarimeters

“…A general calibration technique for four detector polarimeters ("equator-poles method") was described by Azzam et al [18]. Incidentally, the phase dependency measurement shown in Figure 4 was an essential part of this calibration.…”

“…It is the technique that provides the best improvement to our estimated state for each additonal copy taken from the ensemble. Recently Rehácek et al proposed such a method for state estimation of polarization based single qubits [7], which can be viewed as an extension of classical techniques [10,11,18] to quantum systems.…”

Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements

“…The four-detector photopolarimeterl- 3 (FDP) is perhaps the simplest instrument for measuring the state of polarization of a monochromatic or quasi-monochromatic light beam as specified by the four Stokes parameters. 4 It consists of a stationary arrangement of four photodetectors as that produces an output current vector I = [ i i 2 it, which is linearly related by I =AS (1) to the input Stokes vector S = [So Si S 2 S 3 ]t, where the superscript t indicates the transpose.…”

GDx-MM: An Imaging Mueller Matrix Retinal Polarimeter

“…A geometrical interpretation relating the stability of W to the trajectory on the Poincaré sphere was first proposed by Azzam et al [133] and later extended by Ambirajan and Look [134,135], Sabatke et al [136], and Tyo [139]. retardance [136].…”