Diffraction tomography on curved boundaries: A projection-based approach

TL;DR

This paper introduces a projection-based diffraction tomography method for 2D imaging of objects with arbitrarily-shaped boundaries, utilizing integral theorems and Green's functions to enable flexible data collection and image reconstruction.

Contribution

It develops a novel approach combining integral theorems and Green's functions for diffraction tomography on irregular boundaries, allowing flexible external field projections for improved imaging.

Findings

Method successfully reconstructs images from synthetic data.

Approach handles arbitrarily-shaped boundaries effectively.

Synthetic examples demonstrate the method's potential.

Abstract

An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the approach relies upon a valid choice of the Green's functions for selected conditions along the (possibly-irregular) boundary. This allows field projections from the receivers to an arbitrary external location. When performed over all source locations, it will be shown that the field caused by a hypothetical source at this external location is also known along the boundary. This field can then be projected to new external points that may serve as a virtual receiver. Under such a reformation, data may be put in a form suitable for image construction by synthetic aperture methods. Foundations of the approach are shown, followed by a mapping technique optimized for the approach. Examples formed from synthetic data are provided.