Statistics of normalized Stokes polarization parameters

The normalized Stokes parameters are formed from the ratio of the polarization components to the intensity component of light. Such ratio distributions are known to have an undefined mean and variance, and yet researchers in the polarization community work with these normalized parameters all the time. We show that while in theory the normalized parameters have a pathological probability density, in practice they are quite well-behaved. We provide expressions for their approximate densities and confirm the results with laboratory measurements. (C) 2018 Optical Society of America