Numerical diffusion modelling of interfering photon density waves for optical mammography

The interference between diffusive photon density waves in turbid media was studied. A finite-difference numerical method was employed to simulate the time-dependent diffusion of photons in the red and near-infrared region. In the model the time-dispersion curves following an illumination impulse were calculated for the light transmitted through a slab geometry along a line on the distal side of the slab. The time-dispersion curves were Fourier transformed to yield the amplitude and phase as a function of modulation frequency. The interference between photon density waves was studied by having two sources, one time-delayed as compared with the other, corresponding to 180 degrees out of phase for 200 MHz modulation frequency. The diffusing waves originating from the out-of-phase sources gave as expected an amplitude null and a sharp phase transition in the mid-plane. In order to establish the model, calculated curves were compared with experimental data. Furthermore, amplitude and phase data were acquired for various objects inside the slab to study the sensitivity and robustness of the technique.