Geometric optimization method for a polarization state generator of a Mueller matrix microscope

Abstract

We propose a geometric optimization method combined with the Coulombic energy indicator that can uniformly distribute N polarization states on the Poincaré sphere. Based on this method, we investigate the optimal frames of a rotating polarizer and rotating quarter-wave plate (RPRQ)-based polarization state generator (PSG) at different numbers of modulations. We use the PSG on a dual DoFP polarimeter-based Mueller matrix microscope to measure standard samples and pathological sections for testing the performance of an optimized RPRQ. The experimental results show that this method can effectively restrain noise and improve measurement accuracy.

Calibration of a collinear backscattering Mueller matrix imaging system

“…Relevant studies have shown that the optimization of analysis states over the Poincaré sphere can be described by the spherical-2 designs [26]. Considering each row of the N × 4 (N ≥ 4) matrix A as a point on the surface of Poincaré sphere, the regular tetrahedron (N = 4), the octahedron (N = 6), the cube (N = 8) are well-known examples of spherical-2 designs [27]. Nevertheless, the polarization modulation module of a CBMM system based on dual-rotating retarders is usually composed of a fixed polarizer and a rotating quarter-wave plate, which results that the modulated polarization states cannot cover the entire sphere but only form an 8-shaped curve on the surface of Poincaré sphere.…”

Optimal Configurations of Mueller Polarimeter for Gaussian–Poisson Mixed Noise

“…The equivalence condition of Equation ( 3) is: the sum of each row of W and A is zero [19]. When this condition is satisfied and the EWV of the instrument matrix of PSG and PSA is optimal, the estimation variance caused by Poisson noise is independent of the sample, and the estimation variance reaches the minimum value.…”

“…It is obvious that the sum of the last three rows in the measurement matrix is naturally zero when we divide the polarization states corresponding to the instrument matrix with N polarization illumination/analysis states into N/2 pairs of orthogonal polarization states [19]. The two polarization states symmetric about the center of the sphere are a pair of orthogonal polarization states on the Poincaré sphere.…”

“…It is worth noting that the above method can be used to optimize the optimal frame for N-dimensional instrument matrices (N is even), except for N = 4. For these optimal frames, both the sum of the estimation variance is optimal and the estimation variance of each Mueller matrix element is optimal, and independent of the sample [19]. For the case of N = 4, only two tetrahedrons with specific orientations have this property [9], the projections of these two tetrahedra at S 1 S 2 , S 1 S 3 , and S 2 S 3 planes are all squares.…”

“…In our previous study, we used a geometric optimization method based on Coulombic energy to optimize a rotating polarizer and rotating quarter-wave plate (RPRQ)-based PSG with a different number of illumination polarization states. This is combined with the dual division of a focal plane (DoFP) polarimeter [17,18] to build a Mueller matrix microscope capable of suppressing Gaussian-Poisson mixed noise [19]. Considering that DoFP cameras are not yet widely used, in this paper, we make the PSA have the same set of polarization analysis states as the set of PSG illumination states, which means the PSA also uses common devices such as waveplates or variable retarders followed by a standard camera; thus, we will not discuss these two parts separately.…”