Related papers: Algorithmic Foundations for the Diffraction Limit
In a previous article we suggested a method to overcome the diffraction limit behind a telescope. We refer to theory and recent numerical simulations, and test whether it is indeed possible to use photon amplification to enhance the angular…
We proposed a method to achieve superresolved optical imaging without beating the diffraction limit of light. This is achieved by magnifying the ideal optical image of the object through higher-order spatial frequency generation while…
When subjected to monochromatic incident light a nanoparticle will emit light which then interferes with the incident beam. With sufficient contrast and sufficiently close to the particle this interference pattern may be recorded with a…
Diffraction limits the behaviour of light in optical systems and sets the smallest achievable line width at half the wavelength. With a novel subwavelength plasmonic lens to reduce the diffraction via an asymmetry and to generate and…
The manifestation of the wave nature of light through diffraction imposes limits on the resolution of optical imaging. For over a century, the Abbe-Rayleigh criterion has been utilized to assess the spatial resolution limits of optical…
Optical metrology has progressed beyond the Abbe-Rayleigh limit, unlocking (sub)atomic precision by leveraging nonlinear phenomena, statistical accumulation, and AI estimators trained on measurand variations. Here, we show that Fisher…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond…
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules…
We show why and when optics needs thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. Now…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks we demonstrate that…
Superresolution fluorescence microscopy techniques beat the diffraction limit, enabling ultra-high resolution imaging in biological physics and nanoscience. In all cases that have been studied experimentally, the resolution scales inversely…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…