Isolating individual polarization effects from the Mueller matrix: comparison of two non-decomposition techniques

Abstract

The prevailing formalisms for isolating individual polarization effects from the experimental Mueller matrix M can be broadly divided into two categories; decomposition of M to derive the individual optical effects and directly associating the individual optical effects to specific elements of M (i.e., non-decomposition techniques). Mueller matrix transformation (MMT) and direct interpretation of Mueller matrix (DIMM) are two popular techniques of the latter category. In this study, these two non-decomposition techniques (i.e., MMT and DIMM) are compared in a detailed quantitative analysis comprising of tissues (n = 53) and phantom (n = 45) samples. In particular, two commonly investigated polarimetric variables (i.e., depolarization and retardance) were calculated from the experimentally measured M using both the non-decomposition (i.e., MMT and DIMM) techniques. The comparison carried out with scatter plots (integrated with the correlation coefficients), violin plots and Bland and Altman plots revealed better agreement of depolarization-related variables (as compared to the retardance) between the two non-decomposition techniques. The comparative analyses presented here would be beneficial for the interpretation of polarimetric variables and optical characterization of turbid media.

Fig. 1.

Comparison of depolarization variable for the two non-decomposition (MMT and DIMM) methods; Scatter plots coupled with the linear fitting of the depolarization variable as computed by Eq. (1) (MMT method) and Eq. (6) and 7 (DIMM method) for (A) tissue (n_tissue = 53), and (B) phantom (n_phantom=45) samples.

Fig. 2.

Comparison of the retardance variables for the two non-decomposition (MMT and DIMM) methods; Scatter plots integrated with the linear fitting of the retardance variables as computed by Eq. (2–4 (MMT method) and Eq. (9) (DIMM method) for (A) tissue, and (B) phantom samples. Values of correlation coefficients for Eq. (9) of the DIMM method and Eq. (4) of the MMT method were R² = 0.80 for tissue and R² = 0.98 for phantoms.

Fig. 3.

Violin plots of depolarization variable for (A, B) tissue (n_tissue = 53), and (C, D) phantom (n_phantom = 45) samples. The depolarization variables were computed from Eq. (1) (MMT method: black color) and Eq. (6,7) (DIMM method: red color), as mentioned on the x-axis.

Fig. 4.

Retardance variable based violin plots for (A) tissue (n_tissue = 53), and (B) phantom (n_phantom = 45) samples. The presented data of retardance variables were computed from Eqs. (2–4) (MMT method) and Eq. (9) (DIMM method), as mentioned on the x-axis.

Fig. 5.

Bland and Altman plots showing the paired differences for the paired depolarization variables as computed with the two non-decomposition techniques for (A) tissue (n_tissue = 55), and (B) phantom (n_phantom = 45) samples. The solid and dashed horizontal lines represent the mean bias and limits of agreement, respectively; the numbers in front of these lines represent the corresponding values.

Fig. 6.

The Bland and Altman plots showing the paired differences for the retardance variables as computed from Eqs. (2–4) (MMT method) and Eq. (9) (DIMM method) for (A) tissue and (B) phantom samples. Almost a similar level of agreement was observed for the retardance variables for both tissue and phantom samples.