Optimal configurations for imaging polarimeters: impact of image noise and systematic errors

Abstract

The design of an optimal Mueller imaging polarimeter is not obvious: it necessitates the use of a well-conditioned polarization state generator as well as a well-conditioned polarization state analyser that permits proper inversion of intensity images to produce the Mueller matrix images. Even though a rigorous calibration procedure is applied, there remain uncertainties on measurements due to the non-ideal optical elements, misalignment, and photon noise in CCD cameras. The relationship between system conditioning and signal-to-noise ratio in an imaging polarimeter has been largely addressed in the recent literature. Herein, a different approach is used to study the error propagation and the impact of noise on the measurements in such a calibrated system quantitatively. The main contributions of this paper are: an extended theory of noise and errors, a development of the effect of noise resulting in a different merit function, a novel polarimeter solution using two retarders, and a practical demonstration of the sensitivity to noise, which are of interest for polarimetric imaging system designers.

Optimization and performance criteria of a Stokes polarimeter based on two variable retarders

“…In order to optimize the design of polarimeters it is very important to determine the sensitivity of the linear solution to experimental errors in the measurements. With the aim of minimizing the noise transmitted through the matrix inversion from the vector I to the solution S, in this work we compare three different indicators: the condition number (CN) [18], the Equally Weighted Variance (EWV) [7] and the error associated at every component of the Stokes vector [14]. Whereas the CN quantifies if the matrix A −1 is well-conditioned (i.e.…”

“…In order to diminish the effect of noise in the final measurements, some studies have been carried out [7,[13][14][15][16][17]. For instance, different indicators as the condition number (CN) [18] or the equally weighted variance (EWV) [7] have been used in optimization procedures.…”

Mueller Matrix Polarimetry by Means of Azimuthally Polarized Beams and Adapted Commercial Polarimeter

“…It must be noted that the polarimetric measurement matrix W is the same for obtaining the four rows of the Mueller submatrix formed by the first three columns. Minimization of the condition number of the polarimetric measurement matrix gives the optimum positions for measuring the output beam Stokes parameters (Peinado et al, 2015;Oberemok and Savenkov, 2002;Zallat et al, 2006). The optimum positions when using input linear polarization correspond to points where the input polarization linear states have azimuths equally spaced by π/3 (Oberemok and Savenkov, 2002) and where the intensity of the input beam is close to its maximum.…”

GDx-MM: An Imaging Mueller Matrix Retinal Polarimeter

“…Tyo [146] introduced Stokes cones and tight frames to discuss the effect of systematic polarimeter errors. Zallat et al [147] further developed the theory for random intensity measurement errors. and describe the set of vectors which can and cannot be reached via A.…”