The limited-view problem in diffraction tomography

The problem of reconstructing the complex index of refraction of a weakly scattering object from a limited data set is addressed within the framework of diffraction tomography (DT). This problem is cast into a form that includes the well studied limited-view problem of conventional computed tomography (CT) as a special case, obtained in the limit of vanishing wavelength. The theory is developed in detail for the case of plane-wave probes (parallel-beam case) in a manner completely parallel to that usually employed in studies of the limited-view problem in CT. An integral equation formulation is employed that leads directly to a number of results that include a theorem that states that any reconstruction that is convolutionally related to the exact object function can always be implemented in the form of a filtered backpropagation algorithm.