On the Q(M) depolarization metric

Abstract

In this work, we have derived a depolarization metric, named Q(M) here, from the nine bilinear constraints between the 16 Mueller-Jones matrix elements, reported previously by several authors following different approaches. This metric Q(M) is sensitive to the internal nature of the depolarization Mueller matrix and does not depend on the incident Stokes vector. Q(M) provides explicit information about the inner 3 • 3 internal matrix. Four bounds are associated to Q(M) for a totally depolarizing, partially depolarizing, non-depolarizing diattenuating or partially depolarizing, and non-depolarizing non-diattenuating optical system, respectively. To our best knowledge, Q(M) is the unique depolarization metric that provides such information in one single number.

Q(M) and the depolarization index scalar metrics

“…Observe that 1 ≤ QðMÞ < 3 and DIðMÞ < 1; it does follow that QðMÞ describes a partially depolarizing system, a result consistent with Eqs. (3) and (4) [13,16]. Figures 2(a) and 2(b) represent the DoPðM; SÞ and the gain, respectively, when all the incident Stokes vectors are taken from the Poincarè sphere [10].…”

“…The metric QðMÞ can be obtained from well established relations such as the nine bilinear constraints (a) (b) between the sixteen elements of the Mueller-Jones matrix [13] or from the degree of polarization (deduced here). In the following we discuss the properties of QðMÞ and the depolarization index DIðMÞ.…”

“…Observe that QðMÞ can be written in terms of the diattenuation and the polarizance parameters also [13]:…”

“…Now, in this work, a depolarization metric for Mueller matrices, denoted QðMÞ, is derived from the degree of polarization. This metric has been derived recently from the nine bilinear constraints between the sixteen elements of the Mueller-Jones matrix [13]. We apply a number of metrics, including QðMÞ, to several Mueller matrices to test our metric.…”

Characterization of porous media based on the polarimetric matrix models

“…All existing depolarization metrics can be divided into two classes. The first class is the metrics including only the elements of the Mueller matrix of the studied object, e.g., the depolarization metric [5], the Q -metric [6], the Cloude [7] and Lorentz [8] entropy. The second class is the metrics involving the scanning of all possible states of input polarizations, see, e.g., Ref.…”