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.