Degrees of freedom in depolarizing mueller matrices

Most measured Mueller matrices tend to be slightly non physical due to noise and calibration issues.¹ Based on a simple white noise model and higher dimensional geometrical considerations, only 1 out of 90 measured Mueller matrices for a non depolarizing sample should be physical, a number given by the relation ∫₀^π/4sin⁷ φ dφ/∫₀^πsin⁷ φ dφ≈0.0111 which describes the ratio of the 9-dimensional solid angle inside a 9-dimensional 45° cone to the 9-dimensional solid angle in the entire 9-dimensional hypersphere. The remaining majority of measured matrices would be expected to be slightly non physical.