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We introduce and experimentally implement Fourier-plane phase synchronization for optical microscopy, and demonstrate its performance with interferometric scattering microscopy. By combining a photothermal phase plate and laser beam…

Linear-optical circuits are elementary building blocks for classical and quantum information processing with light. In particular, due to its monolithic structure, integrated photonics offers great phase-stability and can rely on the large…

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…

Analysis of PDEs · Mathematics 2021-12-08 Isaac Harris

The event camera, benefiting from its high dynamic range and low latency, provides performance gain for low-light image enhancement. Unlike frame-based cameras, it records intensity changes with extremely high temporal resolution, capturing…

Computer Vision and Pattern Recognition · Computer Science 2025-08-04 Chunyan She , Fujun Han , Chengyu Fang , Shukai Duan , Lidan Wang

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

In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…

Optimization and Control · Mathematics 2024-07-24 Jean-Jacques Godeme , Jalal Fadili

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

Optics · Physics 2024-09-10 Zhiyuan Hu , Julián Tachella , Michael Unser , Jonathan Dong

We deal with the geometrical inverse problem of the shape reconstruction of cavities in a bounded linear isotropic medium by means of boundary data. The problem is addressed from the point of view of optimal control: the goal is to minimize…

Analysis of PDEs · Mathematics 2022-07-26 Andrea Aspri

We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve…

Cosmology and Nongalactic Astrophysics · Physics 2019-10-16 Benjamin Horowitz , Uros Seljak , Grigor Aslanyan

Optical phase-spaces represent fields of any spatial coherence, and are typically measured through phase-retrieval methods involving a computational inversion, interference, or a resolution-limiting lenslet array. Recently, a weak-values…

Optics · Physics 2018-09-12 Samuel H. Knarr , Daniel J. Lum , James Schneeloch , John C. Howell

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the…

Light scattering within scattering media presents a substantial obstacle to optical transmission. A speckle pattern with random amplitude and phase distribution is observed when coherent light travels through strong scattering media.…

Optics · Physics 2022-09-01 Hui Liu , Xiangyu Zhu , Xiaoxue Zhang , Xudong Chen , Zhili Lin

We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…

Mathematical Physics · Physics 2026-05-25 John C. Schotland , Shenwen Yu

Wavefront shaping has revolutionized imaging deep in scattering media, being able to spatially and temporally refocus light through or inside the medium. However, wavefront shaping is not compatible yet with polarization-resolved microscopy…

Optics · Physics 2018-11-26 Hilton B. de Aguiar , Sylvain Gigan , Sophie Brasselet

In single molecule orientation localization microscopy, valuable information about the orientation and longitudinal position of each molecule is often encoded in the shape of the point spread function (PSF). This shape, though, can be…

The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…

Numerical Analysis · Mathematics 2014-02-04 Antonin Chambolle , Khalid Jalalzai

Optical phase-space functions describe spatial and angular information simultaneously; examples include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration…

Optics · Physics 2017-08-02 Hsiou-Yuan Liu , Jingshan Zhong , Laura Waller

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser

Nonlinear optical generation has been a well-established way to realize frequency conversion in nonlinear optics, whereas previous studies were just focusing on the scalar light fields. Here we report a concise yet efficient experiment to…

Optics · Physics 2018-11-20 Li Zhang , Fei Lin , Xiaodong Qiu , Lixiang Chen

Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various…

Optics · Physics 2021-08-11 Chao He , Honghui He , Jintao Chang , Binguo Chen , Hui Ma , Martin J. Booth