A depolarization scalar metric for Mueller matrices, named QðMÞ, is derived from the degree of polarization. QðMÞ has been recently reported, and it has been deduced from the nine bilinear constraints between the sixteen elements of the Mueller-Jones matrix. We discuss the relations between QðMÞ and the depolarization index.

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.

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