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In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations with coherent light. Reconstruction algorithms such as the…

Numerical Analysis · Mathematics 2022-09-02 Robert Beinert , Michael Quellmalz

In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…

Numerical Analysis · Mathematics 2023-05-16 Florian Faucher , Clemens Kirisits , Michael Quellmalz , Otmar Scherzer , Eric Setterqvist

This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…

Numerical Analysis · Mathematics 2026-03-30 Clemens Kirisits , Michael Quellmalz , Eric Setterqvist

Optical Diffraction Tomography (ODT) is a powerful non-invasive imaging technique widely used in biological and medical applications. While significant progress has been made in transmission configuration, reflection ODT remains challenging…

Optics · Physics 2026-05-14 Thomas Wasik , Victor Barolle , Alexandre Aubry , Josselin Garnier

Optical diffraction tomography (ODT) is an emerging 3D imaging technique that is used for the 3D reconstruction of the refractive index (RI) for semi-transparent samples. Various inverse models have been proposed to reconstruct the 3D RI…

Optics · Physics 2022-06-13 Ahmed B. Ayoub , Amirhossein Saba , Carlo Gigli , Demetri Psaltis

Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…

Numerical Analysis · Mathematics 2026-03-11 Peter Elbau , Noemi Naujoks

Optical diffraction tomography (ODT) is a tomographic technique that can be used to measure the three-dimensional (3D) refractive index distribution within living cells without the requirement of any marker. In principle, ODT can be…

Quantitative Methods · Quantitative Biology 2018-01-03 Paul Müller , Mirjam Schürmann , Chii J. Chan , Jochen Guck

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

Computational Engineering, Finance, and Science · Computer Science 2017-09-01 Emmanuel Soubies , Thanh-An Pham , Michael Unser

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

Diffraction tomography 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…

Numerical Analysis · Mathematics 2024-03-26 Clemens Kirisits , Noemi Naujoks , Otmar Scherzer

Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…

Quantitative Methods · Quantitative Biology 2016-10-10 Paul Müller , Mirjam Schürmann , Jochen Guck

Optical diffraction tomography (ODT) provides three-dimensional refractive index (RI) tomograms of a transparent microscopic object. However, because of the finite numerical aperture of objective lenses, ODT has the limited access to…

Optics · Physics 2017-11-22 Moosung Lee , Seungwoo Shin , YongKeun Park

In optical diffraction tomography (ODT), a sample's 3D refractive-index (RI) is often reconstructed after illuminating it from multiple angles, with the assumption that the sample remains static throughout data collection. When the sample…

Optics · Physics 2024-12-13 Jeongsoo Kim , Shwetadwip Chowdhury

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…

Numerical Analysis · Mathematics 2026-03-11 Peter Elbau , Noemi Naujoks , Otmar Scherzer

Optical diffraction tomography (ODT) produces three dimensional distribution of refractive index (RI) by measuring scattering fields at various angles. Although the distribution of RI index is highly informative, due to the missing cone…

Image and Video Processing · Electrical Eng. & Systems 2021-07-20 Hyungjin Chung , Jaeyoung Huh , Geon Kim , Yong Keun Park , Jong Chul Ye

Many biological and soft matter processes occur at high speeds in complex 3D environments, and developing imaging techniques capable of elucidating their dynamics is an outstanding experimental challenge. Here, we introduce Fourier…

We report a computational 3D microscopy technique, termed Fourier ptychographic diffraction tomography (FPDT), that iteratively stitches together numerous variably illuminated, low-resolution images acquired with a low-numerical aperture…

Optics · Physics 2020-02-19 Chao Zuo , Jiasong Sun , Jiaji Li , Anand Asundi , Qian Chen

We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e. mass density and elastic Lam\'e parameters) of a weakly scattering medium from full-field data of scattered waves outside…

Analysis of PDEs · Mathematics 2022-12-07 Bochra Mejri , Otmar Scherzer

Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…

The ability to directly follow and time resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser induced electron diffraction can…

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