Contour reconstruction in diffraction tomography

We address the problem of reconstructing the directional derivative and/or the Laplacian of an object function f characterizing a weakly inhomogeneous scatterer directly from data collected in a set of scattering experiments. We employ the Rytov approximation to model the complex phase of the scattered wavefields and show that a minimum‐norm least‐squares solution can be obtained from the well known filtered backpropagation algorithm of diffraction tomography with appropriate modification of the tomographic filters employed in the filtering step of the algorithm. The procedure is illustrated by a computer simulation study.