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We demonstrate spectroscopy of incoherent light with sub-diffraction resolution. In a proof-of-principle experiment we analyze the spectrum of a pair of incoherent point-like sources whose separation is below the diffraction limit. The two…

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

We establish a simple method to assess the quantum Fisher information required for resolving two incoherent point sources with an imaging system. The resulting Cram\'er-Rao bound shows that the standard Rayleigh limit can be surpassed by…

Quantum Physics · Physics 2016-06-28 Martin Paur , Bohumil Stoklasa , Zdenek Hradil , Luis L. Sanchez-Soto , Jaroslav Rehacek

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

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

We solve the general problem of determining, through imaging, the three-dimensional positions of $N$ weak incoherent point-like emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a linear…

Quantum Physics · Physics 2021-03-25 Cosmo Lupo , Zixin Huang , Pieter Kok

We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations…

Quantum Physics · Physics 2019-04-17 Carmine Napoli , Samanta Piano , Richard Leach , Gerardo Adesso , Tommaso Tufarelli

We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter…

Quantum Physics · Physics 2026-03-12 Jernej Frank , George Brumpton , Tommaso Tufarelli , Gerardo Adesso , Samanta Piano

We investigate the resolution for imaging two pointlike entangled sources by using the method of the moments and the spatial-mode demultiplexing (SPADE), where the pointlike entangled sources can be generated by injecting single-mode…

Quantum Physics · Physics 2023-06-21 Huan Zhang , Wei Ye , Ying Xia , Zeyang Liao , Xue-hua Wang

Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of…

Quantum Physics · Physics 2022-07-26 M. T. DiMario , F. E. Becerra

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

We implement a general imaging method by measuring the complex degree of coherence using linear optics and photon number resolving detectors. In the absence of collective or entanglement assisted measurements, our method is optimal over a…

Quantum Physics · Physics 2019-10-09 L. A. Howard , G. G. Gillett , M. E. Pearce , R. A. Abrahao , T. J. Weinhold , P. Kok , A. G. White

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

The wave-particle duality of light introduces two fundamental problems to imaging, namely, the diffraction limit and the photon shot noise. Quantum information theory can tackle them both in one holistic formalism: model the light as a…

Quantum Physics · Physics 2020-04-10 Mankei Tsang

I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE…

Optics · Physics 2017-03-01 Mankei Tsang

Detecting if and when objects change is difficult in passive sub-diffraction imaging of dynamic scenes. We consider the best possible tradeoff between responsivity and accuracy for detecting a change from one arbitrary object model to…

Quantum Physics · Physics 2023-08-17 Michael R Grace , Saikat Guha , Zachary Dutton

We address the estimation problem of the separation of two arbitrarily close incoherent point sources from the quantum Bayesian point of view, i.e., when a prior probability distribution function (PDF) on the separation is available. For…

Quantum Physics · Physics 2024-12-09 Boyu Zhou , Saikat Guha , Christos N. Gagatsos

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

The problem of resolving point-like light sources not only serves as a benchmark for optical resolution but also holds various practical applications ranging from microscopy to astronomy. In this research, we aim to resolve two thermal…