Diffraction tomographic imaging in a monostatic measurement geometry

Diffraction tomography (DT) is an imaging technique in which spatial variations in refractive index are reconstructed from measured data. The basis for DT is the generalized slice theorem (GST) relating a known function of the measured data to the spatially variable refractive index, subject to a weak scattering approximation. Forms of the GST have been developed for a number of measurement configurations based on bistatic geometries employing arrays of sources and receivers. The problem of imaging with scalar waves for a monostatic measurement geometry is considered. GSTs are derived for two dimensions employing several simplifying assumptions. The quality of the images and limitations of these simplifying assumptions are investigated for several two-dimensional algorithms using simulated data. It is found that one particular monostatic inversion formula yields good image quality and is not substantially limited by the necessary simplifying assumption