Finding the field transfer matrix of scattering media

When illuminated by temporally coherent light, multiply scattering media produce speckle patterns that in many situations are unpolarized on spatial averaging. As a result, the underlying field statistics are assumed to be Gaussian and information about them can be extracted from intensity-intensity correlations. However, such an approach cannot be applied to any scattering medium where the interaction leads to partially developed speckle patterns. We present a general procedure to directly measure the field transfer matrix of a linear medium without regard to the scattering regime. Experimental results demonstrate the ability of our procedure to correctly measure field transfer matrices and use them to recover the polarization state of incident illumination.