Diffraction tomography based on McCutchen’s theorem

An early paper by McCutchen [J. Opt. Soc. Am.54, 240 (1964)] relates the modulation of a convergent spherical wave front to the Fourier transform of the complex amplitude near the geometrical focal point. This implies additional useful Fourier relationships between the wave-front modulations and the cross sections of the diffracted field, which contain the geometrical focal point. We show how these relations can be applied to diffraction tomography. To make use of McCutchen’s relations, particular emphasis is given to the analysis of diffraction tomography with point-source illumination. We derive a sufficient condition under which linear tomographic reconstruction can be applied to arbitrary incident fields and synthetic apertures. This suggests a modified filtered backpropagation algorithm. In addition, we use the results of McCutchen’s paper to obtain information about the symmetry of the object from the scattered field.

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