Calculation of the weighting functions for the reconstruction of absorbing inhomogeneities in tissue by time-resolved optical projections

We report a new method for determining the weighting functions to reconstruct absorbing inhomogeneities in tissue by perturbation time-domain diffuse optical tomography using the transmission geometry of a flat layer. The method is based on an analytical approach to the calculation of the weighting functions for a semi-infinite scattering medium and on the use of the original method of an equivalent inverse source in order to obtain weight distributions for the flat layer geometry. The correctness of the proposed method of the weighting function calculation is evaluated by a numerical experiment on the reconstruction of absorbing inhomogeneities. It is shown that the perturbation reconstruction model based on the proposed weighting function calculation method allows the inhomogeneities smaller than 0.3 cm and ~0.4 cm, located respectively in the transverse and longitudinal directions to the probe light direction, to be resolved in the centre of an 8-cm-thick object.