Photon path distribution and optical responses of turbid media: theoretical analysis based on the microscopic Beer-Lambert law

A concise theoretical treatment has been developed to describe the optical responses of a highly scattering inhomogeneous medium using functions of the photon path distribution (PPD). The treatment is based on the microscopic Beer-Lambert law and has been found to yield a complete set of optical responses by time- and frequency-domain measurements. The PPD is defined for possible photons having a total zigzag pathlength of l between the points of light input and detection. Such a distribution is independent of the absorption properties of the medium and can be uniquely determined for the medium under quantification. Therefore, the PPD can be calculated with an imaginary reference medium having the same optical properties as the medium under quantification except for the absence of absorption. One of the advantages of this method is that the optical responses, the total attenuation, the mean pathlength, etc are expressed by functions of the PPD and the absorption distribution.