Methods mapping a characteristic parameter of a specimen, such as a scattering mean free path and a scattering anisotropy factor, based on a quantitative phase shift measurement. The methods have steps of using spatial light interference microscopy (SLIM) to determine a quantitative phase shift as a function of position in a sample, and applying a generalized scatter-phase transformation to derive at least one of a scattering mean free path (MFP), a scattering anisotropy factor, and a thickness-independent parameter as a function of position in the sample. In some cases, the sample may be a slice of tissue or a cell.