Comparison of the filtered backpropagation and the filtered backprojection algorithms for quantitative tomography

We compare the filtered backpropagation algorithm with the filtered backprojection algorithm for reconstructing the complex refractive-index distribution of semitransparent, cylindrical objects. Before reconstruction, the recorded scattered light is propagated back to the reconstruction area by inverse diffraction. Our comparison is based on computer-simulated data, and experimental optical data obtained from fibers with step-index, graded-index, and uniform-index distributions. The results show that both the filtered backpropagation algorithm and the filtered backprojection algorithm can produce accurate reconstructions of the complex refractive-index distribution as long as the weak-scattering approximation is valid. The good agreement between the results obtained from these two reconstruction algorithms indicates that the errors introduced by the assumption of straight-line propagation inside the object are negligible compared with those introduced by the weak-scattering approximation.