DIRECT CALCULATION OF THE MOMENTS OF THE DISTRIBUTION OF PHOTON TIME-OF-FLIGHT IN TISSUE WITH A FINITE-ELEMENT METHOD

Modeling of the full temporal behavior of photons propagating in diffusive materials is computationally costly. Rather than deriving intensity as a function of time to fine sampling, we may consider methods that derive a transform of this function. To derive the Fourier transform involves calculation in the (complex) frequency domain and relates to intensity-modulated experiments. We consider instead the Mellin transform and show that this relates to the moments of the original temporal distribution. A derivation of the Mellin transform given the Fourier transform that permits closed-form derivations of the temporal moments for various simple geometries is presented. For general geometries a finite-element method is presented, and it is demonstrated that the computational cost to produce the nth moment is the same as producing the first n temporal samples of the original function.