Spectral partitioning in diffraction tomography

Sean K. Lehman; David H. Chambers; James V. Candy

doi:10.1117/12.365713

15 October 1999 Spectral partitioning in diffraction tomography

Sean K. Lehman, David H. Chambers, James V. Candy

Proceedings Volume 3752, Subsurface Sensors and Applications; (1999) https://doi.org/10.1117/12.365713
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

The scattering mechanism of diffraction tomography is described by the integral form of the Helmholtz equation. The goal of diffraction tomography is to invert this equation in order to reconstruct the object function from the measured scattered fields. During the forward propagation process, the spatial spectrum of the object under investigation is 'smeared,' by a convolution in the spectral domain, across the propagating and evanescent regions of the received field. Hence, care must be taken in performing the reconstruct, as the object's spectral information has been moved into regions where it may be considered to be noise rather than useful information. This will reduce the quality and resolution of the reconstruction. We show how the object's spectrum can be partitioned into resolvable and non-resolvable parts based upon the cutoff between the propagating and evanescent fields. Operating under the Born approximation, we develop a beam- forming on transmit approach to direct the energy into either the propagating or evanescent parts of the spectrum. In this manner, we may individually interrogate the propagating and evanescent regions of the object spectrum.

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Sean K. Lehman, David H. Chambers, and James V. Candy "Spectral partitioning in diffraction tomography", Proc. SPIE 3752, Subsurface Sensors and Applications, (15 October 1999); https://doi.org/10.1117/12.365713

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KEYWORDS

Diffraction

Tomography

Near field

Convolution

Fourier transforms

Reconstruction algorithms

Scattering

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