Work

Diffraction tomography for incident Herglotz waves

Year: 2024

Type: article

Abstract: Diffraction tomography (DT) is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional DT, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional DT by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. More specifically, we consider incident Herglotz waves and extend the classical Fourier diffraction theorem to this setting. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments.

Source: Inverse Problems

DOI: 10.1088/1361-6420/ad7d2d

Authors: Clemens Kirisits, Noemi Naujoks, Otmar Scherzer, Huidong Yang

Institutions: University of Vienna, Johann Radon Institute for Computational and Applied Mathematics

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funders: Austrian Science Fund, Christian Doppler Forschungsgesellschaft