Raster Scan Diffraction Tomography

TL;DR

This paper extends diffraction tomography to include focused beam illumination by modeling incident fields as Herglotz waves, enabling more practical imaging in systems like medical ultrasound.

Contribution

It introduces a new Fourier diffraction relation for focused beams and analyzes the impact of scan geometries on reconstruction quality.

Findings

Derived a Fourier diffraction relation for focused beam illumination.

Analyzed effects of scan geometries on image reconstruction.

Extended diffraction tomography to more realistic imaging setups.

Abstract

Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This assumption, however, represents a simplification that often fails to reflect practical imaging systems such as medical ultrasound, where focused beams are used to scan a region of interest of the human body. Such measurement setups, combining focused illumination with scanning, have not yet been incorporated into the diffraction tomography framework. To bridge this gap, we extend diffraction tomography by modeling incident fields as Herglotz waves, thereby incorporating focused beams into the theory. Within this setting, we derive a new Fourier diffraction relation, which forms the basis for quantitative tomographic reconstruction from scanning data. Using this result, we systematically analyze how different scan geometries influence the reconstruction.