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 scatte ring object that is illuminated with plane-wave radiation, under the c ondition of weak scattering one can invoke the Born (or the Rytov) app roximation to linearize the equation for the scattered held (or the sc attered 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 metho ds and the filtered backpropagation method have been developed previou sly. However, the underlying relationship among and the noise properti es of these methods are not evident. We introduce the concepts of idea l and modified sinograms. Analysis of the relationships between, and t he noise properties of the two sinograms reveals infinite classes of m ethods for image reconstruction in diffraction tomography that include the previously proposed methods as special members. The methods in th ese classes are mathematically identical, but they respond to noise an d numerical errors differently. (C) 1998 Optical Society of America.