A scattering medium is a material in which light does not travel in straight paths. The light travels a certain distance, changes direction, and has a chance of being absorbed by the medium. Three coefficients and a phase function determine the behaviour of light in this medium. The primary contribution of this thesis is an algorithm to determine these material coefficients and phase functions in a heterogeneous medium from a series of measurements. These measurements are the position, direction, and intensity of light exiting the medium, measured for various positions and directions of light entering the medium. Other contributions include a noise analysis for scattering media with multiplexed illumination, an experimental setup to scan photon distributions in a liquid scattering medium, and a distribution-based linear reconstruction approach.