Definition: The Photon Measurement Density Function (PMDF) is a mathematical function that describes the probability distribution of photons reaching a particular detector or measurement point in a medium. It is obtained from the Green’s function of the diffusion equation. The Green’s function represents the response of the medium to a point source of light and can be used to calculate the photon density at any point in the medium. By integrating the photon density over the volume of the detector or measurement point, the PMDF can be obtained. The idea of a PMDF is an extension of the notions of a photon-sampling volume and a photon-hitting density. The mathematical formula for the photon-measurement density function (PMDF) depends on the specific measurement type and the properties of the medium being studied. However, in general, the PMDF can be expressed as:
where
is the photon-measurement density function at a point x and time t,
is the Green’s function of the diffusion equation, which describes the probability distribution of photons reaching point x at time t that originated at point
at time t=0,
is the photon density at point
and time t, and the integral is taken over the volume V of the detector or measurement point.
Alternative definition:
Synonym:
References: https://doi.org/10.1364/AO.34.007395
Related terms: Photon Transport
