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We derive the fundamental limit to the resolution of far-field optical imaging, and demonstrate that, while a bound to the resolution of a fundamental nature does exit, contrary to the conventional wisdom it is neither exactly equal to nor…

Optics · Physics 2019-03-14 Evgenii Narimanov

For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the…

Quantum Physics · Physics 2026-05-12 A. I. Lvovsky , Michael R. Grace , Saikat Guha , Mankei Tsang , Gerardo Adesso , Nicolas Treps

No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details…

Quantum Physics · Physics 2009-02-25 Vittorio Giovannetti , Seth Lloyd , Lorenzo Maccone , Jeffrey H. Shapiro

Fluorescence microscopy is a critical tool across various disciplines, from materials science to biomedical research, yet it is limited by the diffraction limit of resolution. Advanced super-resolution techniques such as localization…

Far-field super-resolution fluorescence microscopy has been rapidly developed for applications ranging from cell biology to nanomaterials. However, it remains a significant challenge to achieve super-resolution imaging at depth in opaque…

Optics · Physics 2024-05-01 Tengfei Wu , YoonSeok Baek , Fei Xia , Sylvain Gigan , Hilton B. de Aguiar

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…

Optics · Physics 2012-10-10 Alexander Small

Fluorescence fluctuations-based super-resolution microscopy (FF-SRM) is an emerging field promising low-cost and live-cell compatible imaging beyond the resolution of conventional optical microscopy. A comprehensive overview on how the…

Extending super-resolution imaging techniques to objects hidden in strongly scattering media potentially revolutionize the technical analysis for much broader categories of samples, such as biological tissues. The main challenge is the…

Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…

General Physics · Physics 2018-06-05 Stephane Perrin , Paul Montgomery

Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies…

Quantum Physics · Physics 2022-02-08 Mateusz Mazelanik , Adam Leszczyński , Michał Parniak

Super-resolution imaging refers to imaging techniques that surpass the Rayleigh resolution limit. One standard way to achieve super-resolution is by structuring the phase of the field illuminating the object. Although super-resolution…

Applied Physics · Physics 2025-11-13 Nilakshi Senapati , Abhinandan Bhattacharjee , Kedar Khare , Anand K Jha

In deep tissue photoacoustic imaging, the spatial resolution is inherently limited by acoustic diffraction. Moreover, as the ultrasound attenuation increases with frequency, resolution is often traded-off for penetration depth. Here we…

Here, we show that, contrary to the common opinion, the super-resolution optical fluctuation microscopy might not lead to ideally infinite super-resolution enhancement with increasing of the order of measured cumulants. Using information…

Fourier light-field microscopy (FLFM) uses a micro-lens array (MLA) to segment the Fourier Plane of the microscopic objective lens to generate multiple two-dimensional perspective views, thereby reconstructing the three-dimensional(3D)…

Optics · Physics 2022-08-29 Haixin Huang , Haoyuan Qiu , Hanzhe Wu , Yihong Ji , Heng Li , Bin Yu , Danni Chen , Junle Qu

I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…

Quantum Physics · Physics 2022-10-10 Mankei Tsang

Fluorescence microscopy is an important and extensively utilised tool for imaging biological systems. However, the image resolution that can be obtained has a limit as defined through the laws of diffraction. Demand for improved resolution…

Biological Physics · Physics 2007-08-27 James H. Rice

We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable…

Quantum Physics · Physics 2026-05-20 Joaquín López-Suárez , Michalis Skotiniotis

Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…

Image and Video Processing · Electrical Eng. & Systems 2021-10-27 Ping Liu , Hai Zhang

A priori information on the positivity of source intensities is ubiquitous in imaging fields and is also important for a multitude of super-resolution and deconvolution algorithms. However, the fundamental resolution limit of positive…

Image and Video Processing · Electrical Eng. & Systems 2023-08-01 Ping Liu , Yanchen He , Habib Ammari

Photon losses are intrinsic for any translationally invariant optical imaging system with a non-trivial Point Spread Function, and the relation between the transmission factor and the coherence properties of an imaged object is universal --…

Quantum Physics · Physics 2022-04-27 Stanislaw Kurdzialek