Fractal correlation of fluctuations of primary differential polarization properties

In this work, we consider the properties of fractal correlation of fluctuations of primary differential polarization parameters. The spatial correlation function for isotropic light scattering is first generalized to light scattering by the anisotropic medium. It is then demonstrated that when there exist finite fractal correlations between fluctuations of the elementary polarization properties the elements of the differential Mueller matrix are functions of the thickness of the layer of the medium. Thus the differential Mueller matrices derived from the logarithm of measured macroscopic Mueller matrices can only be regarded as equivalent matrices. The results obtained in this work are helpful for correctly interpreting measured macroscopic Mueller matrices.