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This tutorial paper describes the problem of image reconstruction from interferometric data with a particular focus on the specific problems encountered at optical (visible/IR) wavelengths. The challenging issues in image reconstruction…

Instrumentation and Methods for Astrophysics · Physics 2011-04-20 Éric Thiébaut , Jean-François Giovannelli

Spectral domain optical coherence tomography (OCT) offers high resolution multidimensional imaging, but generally suffers from defocussing, intensity falloff and shot noise, causing artifacts and image degradation along the imaging depth.…

Image and Video Processing · Electrical Eng. & Systems 2021-08-04 Jonathan H. Mason , Yvonne Reinwald , Ying Yang , Sarah Waters , Alicia El Haj , Pierre O. Bagnaninchi

In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…

Numerical Analysis · Mathematics 2015-06-12 Keji Liu , Jun Zou

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

Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…

Numerical Analysis · Mathematics 2023-03-31 Barbara Kaltenbacher , William Rundell

Astronomical optical interferometers (OI) sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid atmospheric perturbations, the phases of the complex Fourier samples…

Instrumentation and Methods for Astrophysics · Physics 2015-03-06 Antony Schutz , André Ferrari , David Mary , Eric Thiébaut , Ferréol Soulez

Time-varying optical materials have attracted recent interest for their potential to enable frequency conversion, nonreciprocal physics, photonic time-crystals, and more. However, the description of time-varying materials has been primarily…

We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…

Analysis of PDEs · Mathematics 2023-08-01 Robert Lung , Nick Polydorides

Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent…

Computer Vision and Pattern Recognition · Computer Science 2013-10-31 Adriana Gonzalez , Laurent Jacques , Christophe De Vleeschouwer , Philippe Antoine

With the development of terahertz time-domain spectroscopy, methods have been proposed to precisely estimate the thickness, refractive index, and attenuation coefficient of a sample. In this article, we propose a new method to compute these…

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

Image reconstruction in optoacoustic tomography (OAT) is a trending learning task highly dependent on measured physical magnitudes present at sensing time. The large number of different settings, and also the presence of uncertainties or…

Image and Video Processing · Electrical Eng. & Systems 2023-05-17 Matias Vera , Martin G. Gonzalez , Leonardo Rey Vega

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

Dispersion is a common phenomenon in optics due to the frequency dependence of the refractive index in polychromatic light. This issue, if left untreated in optical coherence tomography (OCT) imaging, leads to signal broadening of the…

Image and Video Processing · Electrical Eng. & Systems 2022-01-03 Shangbang Luo , Guy Holland , Eric Mikula , Samantha Bradford , Reza Khazaeinezhad , James V Jester , Tibor Juhasz

Non-contact measurement of the refractive index and thickness of multilayer biological tissues is of great significance for biomedical applications and can greatly improve medical diagnosis and treatment. In this work, we introduce a…

Optics · Physics 2024-04-19 Yu-Lin Ku , Yao-Gen Shu

Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier…

Instrumentation and Methods for Astrophysics · Physics 2015-12-22 M. Jiang , J. N. Girard , J. -L. Starck , S. Corbel , C. Tasse

We propose a method to reconstruct the optical absorption of a highly-scattering medium probed by diffuse light. The method consists of learning the optical detection system and then using this result to reconstruct the absorption. Our…

Optics · Physics 2025-10-08 Zijian Wang , Andreas Hauptmann , Lu Lu , John C. Schotland

In this work, we investigate the recovery of a parameter in a diffusion process given by the order of derivation in time for a class of diffusion type equations, including both classical and time-fractional diffusion equations, from the…

Analysis of PDEs · Mathematics 2021-11-04 Bangti Jin , Yavar Kian

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 this work, we study an inverse problem of recovering information about the weight in distributed-order time-fractional diffusion from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of…

Numerical Analysis · Mathematics 2023-01-10 Bangti Jin , Yavar Kian