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Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) in…

Quantum Physics · Physics 2025-04-01 Konrad Schlichtholz , Łukasz Rudnicki

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

Imaging systems measuring intensity in the far field succumb to Rayleigh's curse, a resolution limitation dictated by the finite aperture of the optical system. Many proof-of-principle and some two-dimensional imaging experiments have shown…

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…

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

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

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

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

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 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…

Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…

Quantum Physics · Physics 2024-07-23 Fattah Sakuldee , Łukasz Rudnicki

The Rayleigh's criterion infamously imposes a minimum separation between two incoherent sources for them to be distinguishable via classical methods. In this work, we demonstrate the emergence of two-photon beats from the interference of a…

Quantum Physics · Physics 2025-05-23 Salvatore Muratore , Danilo Triggiani , Vincenzo Tamma

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

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright…

Quantum Physics · Physics 2017-12-13 J. Rehacek , Z. Hradil , B. Stoklasa , M. Paur , J. Grover , A. Krzic , L. L. Sanchez-Soto

We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…

Quantum Physics · Physics 2016-11-09 Cosmo Lupo , Stefano Pirandola

Quantum-optimal discrimination between one and two closely separated light sources can be achieved by ideal spatial-mode demultiplexing, simply monitoring whether a photon is detected in a single antisymmetric mode. However, we show that…

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

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose the incoming radiation into orthogonal…

Quantum Physics · Physics 2021-02-10 J. O. de Almeida , J. Kołodyński , C. Hirche , M. Lewenstein , M. Skotiniotis

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

The Rayleigh diffraction limit imposes a fundamental restriction on the resolution of direct imaging systems, hindering the identification of incoherent optical sources, such as celestial bodies in astronomy and fluorophores in bioimaging.…

Quantum Physics · Physics 2025-12-12 Danilo Triggiani , Cosmo Lupo
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