Related papers: Algorithmic Foundations for the Diffraction Limit

An important milestone for AI is the development of algorithms that can produce drawings that are indistinguishable from those of humans. Here, we adapt the 'diversity vs. recognizability' scoring framework from Boutin et al, 2022 and find…

There are many physical processes that have inherent discontinuities in their mathematical formulations. This paper is motivated by the specific case of collisions between two rigid or deformable bodies and the intrinsic nature of that…

We have studied atomic diffraction at normal incidence from an evanescent standing wave with a high resolution using velocity selective Raman transitions. We have observed up to 3 resolved orders of diffraction, which are well accounted for…

Scattering of light in complex media scrambles optical wavefronts and breaks the principles of conventional imaging methods. For decades, researchers have endeavored to conquer the problem by inventing approaches such as adaptive optics,…

Machine learning has become a premier tool in physics and other fields of science. It has been shown that the quantum mechanical scattering problem can not only be solved with such techniques, but it was argued that the underlying neural…

Visualization in the virtual image formed by dielectric microparticles has been shown to enable the distinction of objects that remain indistinguishable under direct observation. We perform the resolution analysis based on a full…

An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes…

Offset Rademacher complexities have been shown to provide tight upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that the offset complexity can be generalized…

We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to…

When mining large datasets in order to predict new data, limitations of the principles behind statistical machine learning pose a serious challenge not only to the Big Data deluge, but also to the traditional assumptions that data…

Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently,…

A variety of recent imaging techniques are able to beat the diffraction limit in fluorescence microcopy by activating and localizing subsets of the fluorescent molecules in the specimen, and repeating this process until all of the molecules…

This paper completes and comments on some aspects of our previous publications. In ref [1], we have derived a set of space-time transformations referred to as the extended space-time transformations. These transformations, which assume the…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

In this work we examine refraction of light by computing full solutions to axion electrodynamics. We also allow for the possibility of an additional plasma component. We then specialise to wavelengths which are small compared to background…

We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams,…

Accurate camera calibration is a fundamental task for 3D perception, especially when dealing with real-world, in-the-wild environments where complex optical distortions are common. Existing methods often rely on pre-rectified images or…

Filled arrays of bolometers are currently being employed for use in astronomy from the far-infrared through millimeter parts of the electromagnetic spectrum. Because of the large range of wavelengths for which such detectors are applicable,…