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Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially…

Quantum Physics · Physics 2016-09-07 Mankei Tsang , Ranjith Nair , Xiao-Ming Lu

The Rayleigh criterion is a widely known limit in the resolution of incoherent sources with classical measurements in the spatial domain. Unsurprisingly the estimation of the time delay between two weak incoherent signals is afflicted by an…

Quantum Physics · Physics 2026-02-12 Salvatore Muratore , Vincenzo Tamma

The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing…

Quantum Physics · Physics 2025-10-22 Junyan Li , Shengshi Pang

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,…

Quantum Physics · Physics 2019-01-09 Sisi Zhou , Liang Jiang

Abstract Superresolution has been demonstrated to overcome the limitation of the Rayleigh's criterion and achieve significant improvement of the precision in resolving the separation of two incoherent optical point sources. However, in…

Quantum Physics · Physics 2024-12-06 Junyan Li , Shengshi Pang

Using a semiclassical model of photodetection with Poissonian noise and insights from quantum metrology, we prove that linear optics and photon counting can optimally estimate the separation between two incoherent point sources without…

Quantum Physics · Physics 2016-11-08 Mankei Tsang , Ranjith Nair , Xiao-Ming Lu

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

We propose a scheme achieving the ultimate quantum precision for the estimation of the transverse displacement between two interfering photons. Such a transverse displacement could be caused, for example, by the refracting properties of the…

Quantum Physics · Physics 2025-03-19 Danilo Triggiani , Vincenzo Tamma

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…

Optics · Physics 2025-12-16 S. A. Wadood , Shaurya Aarav , Kevin Liang , Jason W Fleischer

Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have…

Quantum Physics · Physics 2024-07-08 Jian-Dong Zhang , Yiwen Fu , Lili Hou , Shuai Wang

We experimentally demonstrate the simultaneous estimation of the three parameters characterizing a pair of incoherent optical sources in the sub-Rayleigh regime, enabling super-resolved scene characterization. Using spatial-mode…

We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement, in which the phenomenon of induced coherence without induced emission…

Quantum Physics · Physics 2017-04-03 Armin Hochrainer , Mayukh Lahiri , Radek Lapkiewicz , Gabriela B. Lemos , Anton Zeilinger

Interferometric methods have been recently investigated to achieve sub-Rayleigh imaging and precision measurements of faint incoherent sources up to the ultimate quantum limit. Here we consider single-photon imaging of two point-like…

Quantum Physics · Physics 2024-02-28 Luigi Santamaria Amato , Fabrizio Sgobba , Cosmo Lupo

High-precision measurements implemented by means of light is desired in all fields of science. However, light is a wave and Rayleigh criterion gives us a diffraction limitation in classical optics which restricts to get arbitrary high…

Quantum Physics · Physics 2015-01-26 Ruifeng Liu , Pei Zhang , Yu Zhou , Hong Gao , Fuli Li

Multiparameter estimation theory offers a general framework to explore imaging techniques beyond the Rayleigh limit. While optimal measurements of single parameters characterizing a composite light source are now well understood,…

Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of…

Historically, the resolution of optical imaging systems was dictated by diffraction, and the Rayleigh criterion was long considered an unsurpassable limit. In superresolution microscopy, this limit is overcome by manipulating the emission…

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cram\'er-Rao bound that, contrary to the…

Quantum Physics · Physics 2016-11-29 Ranjith Nair , Mankei Tsang

Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially when it is smaller than or comparable to the Rayleigh length. In addition, the task of discriminating whether…

Quantum Physics · Physics 2025-06-23 Ugo Zanforlin , Cosmo Lupo , Peter W. R. Connolly , Pieter Kok , Gerald S. Buller , Zixin Huang

We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…

Quantum Physics · Physics 2019-11-07 Xiao-Ming Lu , Ranjith Nair , Mankei Tsang
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