On the data needed for the accurate reconstruction in 3D diffraction tomography

In this paper, the three dimensional (3D) extensions of the two well-known diffraction tomography algorithms, namely direct Fourier interpolation and filtered backpropagation (FBP) are presented. These algorithms solve the linearized version of the inverse scattering problem using either the Born or the Rytov approximations which are known to be valid for weak scatterers. We investigate the problem of the amount of data needed for a full 3D reconstruction. Previous attempts for 3D reconstruction using several inverse scattering algorithms were based on scattered field measurements with incident pulse directions restricted exclusively on the xy-plane. This results in ignoring the contribution of some spatial frequencies which are near the z-axis. This effect is studied here by comparing the results of reconstruction with and without data obtained from other incident directions which fill the spatial frequency domain. We conclude that for a class of objects presenting smooth variation along the z-axis, the use of data obtained for incident direction only in the xy-plane is sufficient to obtain a satisfactory quality of reconstruction while quick variations along the z-axis cannot be imagined.