Physical Significance of the Determinant of a Mueller Matrix

The determinant of a Mueller matrix M plays an important role in both polarization algebra and the interpretation polarimetric measurements. While certain physical quantities encoded admit direct interpretation, understanding geometric significance (detM) requires specific analysis, performed this work by using normal form M, as well indices purity (IPP) canonical depolarizer associated with M. We derive expression for detM terms diattenuation, polarizance parameter proportional to volume intrinsic ellipsoid likewise establish relation existing between rank covariance H determine lower upper bounds two types matrices taking advantage their representation IPP space.