Three-dimensional diffraction tomography by two-dimensional sectioning

Abstract

The hybrid filtered backpropagation (HFBP) algorithm of diffraction tomography is a reconstruction algorithm that provides quantitative reconstructions of weakly scattering objects from scattered field data collected in a suite of scattering experiments employing incident plane waves. Although the HFBP algorithm is capable of reconstructing three-dimensional (3D) objects it is most often used in applications involving 2D objects (cylinders) since the data acquisition and computational requirements for full 3D objects are quite severe. In this paper we examine the feasibility of using the 2D HFBP algorithm to reconstruct weakly scattering three-dimensional (3D) objects cross-section by cross-section, so as to obtain substantial savings in computation and data acquisition. The method is tested in a computer simulation where a sphere is reconstructed section by section using the 2D HFBP algorithm applied to an exactly computed scattered field obtained using an eigenfunction expansion. The (computed) total field (incident plus scattered) is first backpropagated to the centre of the image area from which the 2D FBP algorithm is used to reconstruct different sections of the sphere. We show that sections of non-attenuating spheres can be reconstructed to the same accuracy as for circular cylinders of the same radius, except for sections very close to the top or bottom of the spheres. For sections of highly attenuating spheres we do not obtain quite as good results as for the corresponding circular cylinders.