Inverse radiation problem in one-dimensional slab by time-resolved reflected and transmitted signals

A time-domain inverse approach is proposed for estimating the distribution of absorbing and scattering coefficients in one-dimensional inhomogeneous media. The temporal reflected and transmitted signals are detected when an ultra-short pulse irradiates on the boundary of semi-transparent scattering media. Forward computation and inverse algorithm employ the least-squares finite element method and conjugate gradient method, respectively. As the prevalent diffusion approximation is not employed in our model, the present approach can be extended to more comprehensive application. The investigation about detected signals indicates that the reflected signals play a significant role in reconstructing optical properties; the signals in early sampling time are more important than those at long-time logarithm slope, and so, more attention should be paid to the early signals in the solution of inverse radiation problem. Three different inverse radiation problems are investigated to show the ability of the present approach to deal with the two-layer, three-layer and continuous inhomogeneous media. The effect of measured errors on the accuracy of reconstruction is investigated by adding artificial random errors. The results indicate that accurate reconstruction depends on not only precise numerical simulation but also quality of detected data.