TY - JOUR
T1 - Diffraction tomography for incident Herglotz waves
AU - Kirisits, Clemens
AU - Naujoks, Noemi
AU - Scherzer, Otmar
AU - Yang, Huidong
N1 - Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
PY - 2024/11
Y1 - 2024/11
N2 - 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.
AB - 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.
KW - backpropagation
KW - diffraction tomography
KW - focused beams
KW - Fourier diffraction theorem
KW - Herglotz wave functions
UR - http://www.scopus.com/inward/record.url?scp=85206217652&partnerID=8YFLogxK
U2 - 10.1088/1361-6420/ad7d2d
DO - 10.1088/1361-6420/ad7d2d
M3 - Article
SN - 0266-5611
VL - 40
JO - Inverse Problems
JF - Inverse Problems
IS - 11
M1 - 115007
ER -