Depolarization index and the average degree of polarization

Two single number metrics for depolarization of samples are contrasted: (1) the average degree of polarization of the exiting light averaged over the Poincaré sphere and (2) the depolarization index of Gill and Berhenau [Opt. Acta 32, 259-261 (1985); 33, 185-189 (1986)]. The depolarization index is a geometric measure that varies from 0 for the ideal depolarizer to 1 for nondepolarizing Mueller matrices. The average degree of polarization also varies from 0 to 1 and characterizes the typical level of depolarization. Although the depolarization index is very often close to the average degree of polarization, these two metrics can differ by more than 0.5 for certain Mueller matrices.