Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging

Abstract

Depolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples.

Terahertz polarimetric imaging of biological tissues: Monte Carlo modeling of signal contrast mechanisms due to Mie scattering

“…which is in agreement with theoretical predictions resulted from assuming an ensemble of single scatterers each of them having a reciprocal Mueller-Jones matrix [79,80]. Therefore, this result is consistent with the PDFs shown in Fig.…”

Terahertz polarimetric imaging of biological tissue: Monte Carlo modeling of signal contrast mechanisms due to Mie scattering

“…Here, we note that M is a diagonal matrix and it complies with the additional condition that which agrees with theoretical predictions resulted from assuming an ensemble of single scatterers, each of them having a reciprocal Mueller-Jones matrix [ 80 , 81 ]. Therefore, this result is consistent with the PDFs shown in Fig.…”

Emerging Mueller matrix microscopy applications in biophysics and biomedicine

“…An early and notable application of confocal Mueller reflection microscope was for retinal diagnosis [93]. One has also to consider that the multiple reflection optics used as beamsplitters, Fresnel rhomb or Wollaston prism can be miniaturized thanks to the advance in designing and realizing metasurfaces [115][116][117]. More recently, a Mueller matrix polarimeter has been implemented into a nonlinear commercial transmission scanning microscope using simple motorized optical devices [118] allowing the acquisition of four images sequentially coded by four distinct polarization states (horizontal, vertical, 45°and right circular).…”