TABLE OF CONTENTS To study the approximations involved in the reconstruction process it is necessary to calculate scattered data assuming the forward approximations are valid. This can be done in one of two different ways. We have already discussed that the Born and Rytov approximations are valid for small objects and small changes in refractive index. Thus, if we calculate the exact scattered field for a small and weakly scattering object we can assume that either the Born or the Rytov approximation is exact.
A better approach is to recall the Fourier Diffraction Theorem, which says that the Fourier transform of the scattered field is proportional to the Fourier transform of the object along a semicircular arc. Since this theorem is the basis for our inversion algorithm, if we assume it is correct we can study the approximations involved in the reconstruction process.
If we assume that the Fourier Diffraction Theorem holds, the exact scattered field can be calculated exactly for objects that can be modeled as ellipses. The analytic expression for the Fourier transform of the object along an arc is proportional to the scattered fields. This procedure is fast and allows us to calculate scattered fields for testing reconstruction algorithms and experimental parameters.
To illustrate the accuracy of the interpolation-based algorithms, we will use the image in Fig. 6.24 as a test object for showing some computer simulation results. Fig. 6.24 is a modification...
