Abstract

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.

© 1999 Optical Society of America

Analysis of the forward problem with diffuse photon density waves in turbid media by use of a diffraction tomography model

Charles L. Matson and Hanli Liu
J. Opt. Soc. Am. A 16(3) 455-466 (1999)

Minimal-scan filtered backpropagation algorithms for diffraction tomography

Xiaochuan Pan and Mark A. Anastasio
J. Opt. Soc. Am. A 16(12) 2896-2903 (1999)

Backpropagation in turbid media

Charles L. Matson and Hanli Liu
J. Opt. Soc. Am. A 16(6) 1254-1265 (1999)

Comparison of reconstruction algorithms for optical diffraction tomography

Pengyi Guo and Anthony J. Devaney
J. Opt. Soc. Am. A 22(11) 2338-2347 (2005)

Diffraction tomography using power extinction measurements

P. Scott Carney, E. Wolf, and G. S. Agarwal
J. Opt. Soc. Am. A 16(11) 2643-2648 (1999)