Unified reconstruction theory for diffraction tomography, with consideration of noise control

In diffraction tomography, the spatial distribution of the scattering object is reconstructed from the measured scattered data. For a scattering object that is illuminated with plane-wave radiation, under the condition of weak scattering one can invoke the Born (or the Rytov) approximation to linearize the equation for the scattered field (or the scattered phase) and derive a relationship between the scattered field (or the scattered phase) and the distribution of the scattering object. Reconstruction methods such as the Fourier domain interpolation methods and the filtered backpropagation method have been developed previously. However, the underlying relationship among and the noise properties of these methods are not evident. We introduce the concepts of ideal and modified sinograms. Analysis of the relationships between, and the noise properties of the two sinograms reveals infinite classes of methods for image reconstruction in diffraction tomography that include the previously proposed methods as special members. The methods in these classes are mathematically identical, but they respond to noise and numerical errors differently.