TABLE OF CONTENTS In our proof of the Fourier Diffraction Theorem, we showed that when an object is illuminated with a plane wave traveling in the positive y direction, the Fourier transform of the forward scattered fields gives values of the arc shown in Fig. 6.2. Therefore, if an object is illuminated from many different directions, we can, in principle, fill up a disk of diameter 
k in the frequency domain with samples of O( ? 1 , ? 2 ), which is the Fourier transform of the object, and then reconstruct the object by direct Fourier inversion. Therefore, we can say that diffraction tomography determines the object up to a maximum angular spatial frequency of 
k. To this extent, the reconstructed object is a low pass version of the original. In practice, the loss of resolution caused by this bandlimiting is negligible, being more influenced by considerations such as the aperture sizes of the transmitting and receiving elements, etc.
The fact that the frequency domain samples are available over circular arcs, whereas for convenient display it is desirable to have samples over a rectangular lattice, is a source of computational difficulty in reconstruction algorithms for diffracting tomography. To help the reader visualize the distribution of the available frequency domain information, we have shown in Fig. 6.8 the sampling points on a circular arc grid, each arc in this grid corresponding to the transform of one projection. It should also...
