In weak scattering diffraction tomography, there is a well-known Fourier relationship between the field scattered by an unknown object and the scattering potential that characterizes the object. For these weakly scattering objects, those that satisfy the Born or Rytov approximation, the scattered field generated from a sequence of different illumination directions complements Fourier data on the unknown scattering potential. A low-pass reconstruction is found by Fourier inversion. A simulation is presented in which the scattered far field from several strongly scattering penetrable two-dimensional cylinders is backpropagated into the object domain. For these more strongly scattering objects, a single wavelength and a single illumination direction are used to provide limited Fourier data on the product of the scattering potential and the total field. A nonlinear filtering technique, known as differential cepstral filtering, is used to isolate the scattering potential and to suppress artifacts introduced by the perturbing field component. Reconstructed images calculated by this technique from exact scattered-field data from cylindrically symmetric objects are shown.
© 1996 Optical Society of America
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