Photon path distribution in inhomogeneous turbid media: theoretical analysis and a method of calculation

The photon path distribution (PPD) is a measure that I have developed to express optical responses in inhomogeneous turbid media in the time and frequency domains. The PPD is defined by local photon pathlengths of possible photons having total zigzag pathlengths I between the points of light input and detection. Such a distribution is independent of absorption and is uniquely determined for the medium under quantification. I show that the PPD is derived through the local photon count of the possible photons arising from an optical impulse incident on an imaginary medium having the same optical properties as the medium under quantification, except for the absence of absorption. The formulas derived can be used to calculate the PPD simultaneously with, for example, the numerical calculation of a diffusion equation.