Introduction of a 3 × 4 Mueller matrix decomposition method

Abstract

A Mueller matrix can completely characterize the polarimetric properties of a medium, where the parameters of depolarization, retardance and diattenuation can be obtained by decomposing a Mueller matrix with existing decomposition methods. The introduction of polarization sensitive cameras with integrated wire-grid polarizers has allowed for the fast acquisition and analysis of four linear states within a single snapshot. Moreover, these cameras provide the opportunity to capture a reduced 3 × 4 Mueller matrix with the acquisition of generated states polarization in the illumination arm. In order to measure and characterize samples using a reduced 3 × 4 Mueller matrix, a 3 × 4 decomposition algorithm is introduced. This new algorithm is compared and validated against established 4 × 4 decompositions. The validation of this algorithm is shown using a previously reported Mueller matrix of polyacrylamide phantom, and experimental Mueller matrices of quarter-wave plates, silicone phantoms and a skin model sample. The 3 × 4 decomposition compares well to established decompositions and is capable of characterizing the samples based on the calculation of depolarization, retardance and orientation.

Partial Mueller polarimetry for the complete optical diagnosis of biological tissue

“…At normal incidence the MM of a diattenuator can be replaced by a unity matrix in the Lu-Chipman polar decomposition. 4 In the absence of the polarizance the MM of a depolarizer can be diagonalized…”

“…Several studies have reported the results on using the reduced number of MM elements for the analysis and diagnosis of tissue. 3,4 The obvious advantage of extracting the same diagnostic information while doing less measurements consists in reducing the measurement time, hence, paving the way for in vivo medical applications of the partial Mueller polarimetry. In this paper we present theoretical and experimental studies focused on the extraction of the above mentioned polarimetric parameters of the optical phantoms and biological tissue samples using only the first three rows of measured MMs and validate the results against the parameters obtained with Lu-Chipman decomposition 5 of the corresponding complete MMs.…”

Polarization-Based Histopathology Classification of Ex Vivo Colon Samples Supported by Machine Learning

“…Ample diagnostic information related to the morphology of the tissue specimens under study is encoded in their Mueller matrices [26,[29][30][31][32]. Nevertheless, the intertwined relation between the samples' polarization and depolarization properties and their matrix elements is accessible only after the application of pertinent decomposition algorithms [33][34][35][36][37][38]. For instance, Cloude's physical realizability is able to filter out experimental errors and/or data noise [39,40], while logarithmic [37,41,42], Lu-Chipman [35,[43][44][45], or symmetric [36,46] decompositions were found capable of extracting the embedded diagnostic information for the samples under study.…”

Underdetermined polarimetric measurements for Mueller extrapolations

“…Partial polarimetric systems take fewer than 16 linearly independent measurements, making them underdetermined and incapable of reconstructing the full MM. Recent work by Gonzalez et al 29 . demonstrated analysis and decomposition of 3×4 partial MMs measured using four polarized illumination states and a snapshot linear Stokes camera.…”

“…For polarimetric imaging of biological tissue near normal incidence, Novikova et al showed the analysis of partial MM data can yield comparable results to complete MM data [41]. Gonzalez et al introduced a decomposition technique for MMs lacking the fourth row [42]. Kupinski et al optimized the polarization state generator (PSG) and polarization state analyzer (PSA) states to perform a binary classification task [43].…”