Convolution picture of the boundary conditions in photon migration and its implications in time-resolved optical...

To model the effect of a tissue-air boundary on time-resolved optical measurements, a convolution picture is presented based on the photon migration picture. It is demonstrated that the boundary conditions (either index matched or index mismatched) can be formulated as a spatiotemporal convolution of two terms, with the first being identical to the solution in the infinite medium and the second being independent of the original light source. The conditions under which the spatial convolution part in the second term becomes negligible are also determined thus permitting the complete separation of the two terms by use of a temporal Laplace or Fourier transformation. This result is promising, since it, suggests a method of removing the effect of the boundary conditions in the applications of time-resolved optical imaging (in both the time domain and the frequency domain) in biological tissues.