Eliminating incident subtraction in diffraction tomography

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Title: Eliminating incident subtraction in diffraction tomography
Author(s): Huthwaite, P
Item Type: Journal Article
Abstract: Diffraction tomography is a powerful algorithm for producing high-resolution quantitative reconstructions across a wide range of applications. A major drawback of the method is that it operates on the scattered field, which cannot generally be directly measured, but must instead be calculated by subtracting the incident field, i.e. the equivalent field with no scatterer present. Unfortunately, often the incident field is not measurable and hence must be estimated, causing errors. This paper highlights an important, but not widely recognized, result: for particular widely used formulations of the algorithm, the subtraction of the incident field is unnecessary, and the algorithm can actually be applied directly to measured signals. The theory behind this is derived, showing that the incident field will vanish under far-field conditions, and the result is demonstrated in practice. Tests with subsampled arrays show that aliasing artefacts can appear, but can be removed with a filter at the expense of resolution. The incident field also has no effect for a variety of array configurations tested. Finally, the performance in the presence of both correlated and uncorrelated errors is confirmed, in all cases demonstrating that the incident field has a negligible effect on the final reconstruction.
Publication Date: 30-Nov-2016
Date of Acceptance: 3-Nov-2016
URI: http://hdl.handle.net/10044/1/43130
DOI: http://dx.doi.org/10.1098/rspa.2016.0707
ISSN: 1471-2946
Publisher: Royal Society, The
Journal / Book Title: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume: 472
Issue: 2195
Copyright Statement: © 2016 The Author(s). Published by the Royal Society. All rights reserved.
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Article Number: 20160707
Appears in Collections:Faculty of Engineering
Mechanical Engineering

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