Scattering-phase theorem

We derive two mathematical relations between quantitative phase images of thin slices of inhomogeneous media and the scattering parameters of the bulk, i.e., scattering mean free path, l_s, and anisotropy factor, g. The l_s turns out to be inversely proportional to the spatial variance of the phase shift, and g is related to the variance of the phase gradient. These formulas, referred collectively to as the scattering-phase theorem, allow for extracting l_s and g in a spatially resolved manner and across an entire tissue section, that is, mapping large cross sections of tissues in terms of l_s and g.