Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Sub-Rayleigh-diffraction imaging via modulating classical light

Erfeng Zhang, Huizu Lin, Wei-Tao Liu, Quan Li, Ping‐Xing Chen

Published Dec 18, 2015• 17 citations
Publisher

Abstract

The spatial resolution of a traditional imaging system is restricted by the Rayleigh diffraction limit. In this paper, two types of classical light sources are generated by modulating the amplitude distribution and wavefront of a laser beam randomly, and the generated light sources can exhibit the features of the superposition of two-photon Fock states and the incoherent mixture of two-photon Fock states, respectively. With the generated light sources, the two-fold coherent and incoherent imaging schemes can be achieved, which lead to spatial resolution enhancement, and exceed the Rayleigh diffraction limit in the imaging system.

DOI
10.1364/oe.23.033506

Related papers

Sub-Rayleigh-diffraction-bound quantum imaging

Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone +1 more

The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some $N$-photon strategies that permit resolution of details that are smaller than this bound, attaining either a $1∕\sqrt{N}$ enhancement (standard quantum limit) or a $1∕N$ enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.

arXiv:0804.2875•Physical Review A•Jan 28, 2009•124 citations

Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source

De-Qin Xu, Xin-Bing Song, Hong-Guo Li +4 more

It has been theoretically predicted that N-photon quantum imaging can realize either an N-fold resolution improvement (Heisenberg-like scaling) or a N-fold resolution improvement (standard quantum limit) beyond the Rayleigh diffraction bound, over classical imaging. Here, we report the experimental study on spatial sub-Rayleigh quantum imaging using a two-photon entangled source. Two experimental schemes are proposed and performed. In a Fraunhofer diffraction scheme with a lens, two-photon Airy disk pattern is observed with subwavelength diffraction property. In a lens imaging apparatus, however, two-photon sub-Rayleigh imaging for an object is realized with super-resolution property. The experimental results agree with the theoretical prediction in the two-photon quantum imaging regime.

Applied Physics Letters•Apr 27, 2015•38 citations

Passive optical superresolution at the quantum limit

A. I. Lvovsky, Michael R. Grace, Saikat Guha +3 more

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 noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.

quant-pharXiv:2605.10767•Optica•May 12, 2026•0 citations

Temporal Resolution of Partially Coherent Sources

Syamsundar De, Jano Gil-López, Benjamin Brecht +4 more

In spatial imaging, it is well known that two incoherent sources with a separation less than the diffraction limit cannot be resolved, a phenomenon dubbed as Rayleigh’s curse. A recent information theoretic approach suggests that this curse can be avoided using optimal (here, mode-sensitive) measurements instead of the usual intensity-only measurements, which define the classical limit [1] . This quantum enhanced resolution has been realized in both the spatial [2] and temporal domain [3] . Nevertheless, the role of optical coherence on the resolution limit still remains elusive [4] , [5] , [6] . Here, we experimentally resolve this debate using time-domain measurements.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 21, 2021•0 citations

Sub-Rayleigh limit imaging via intensity correlation measurements

Xu‐Ri Yao, Longzhen Li, Xuefeng Liu +2 more

We demonstrate sub-Rayleigh limit imaging of an object via intensity correlation measurements. The image completely unaffected by the disturbance of diffraction-limit is achieved under the condition that the imaging system has an appropriate field of view. The resolution of this sub-Rayleigh limit imaging system is only tied to the lateral resolution of the illumination light.

Chinese Physics B•Mar 31, 2015•9 citations

Coherent Rabi oscillations in a molecular system and sub-diffraction-limited pattern generation

Zeyang Liao, M. Al-Amri, Muhammad Suhail Zubairy

Abstract The resolution of a photolithography and optical imaging system is restricted by the diffraction limit. Coherent Rabi oscillations have been shown to be able to overcome the diffraction limit in a simple two-level atomic system (Z Liao, M Al-amri, and M S Zubairy 2010 Phys. Rev. Lett. 105 183601 ). In this paper, we numerically calculate the wave packet dynamics of a molecular system interacting with an ultrashort laser pulse and show that coherent Rabi oscillations in a molecular system are also possible. Moreover, a sub-diffraction-limited pattern can be generated in this system by introducing spatially modulated Rabi oscillations. We also discuss several techniques to improve the visibility of the sub-diffraction-limited pattern. Our result may have important applications in super-resolution optical lithography and optical imaging.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 14, 2015•3 citations
The spatial resolution of a traditional imaging system is restricted by the Rayleigh diffraction limit. In this paper, two types of classical light sources are generated by modulating the amplitude distribution and wavefront of a laser beam randomly, and the generated light sources can exhibit the features of the superposition of two-photon Fock states and the incoherent mixture of two-photon Fock states, respectively. With the generated light sources, the two-fold coherent and incoherent imaging schemes can be achieved, which lead to spatial resolution enhancement, and exceed the Rayleigh diffraction limit in the imaging system.
The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some NNN-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1∕N1∕\sqrt{N}1∕N​ enhancement (standard quantum limit) or a 1∕N1∕N1∕N enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.
It has been theoretically predicted that N-photon quantum imaging can realize either an N-fold resolution improvement (Heisenberg-like scaling) or a N-fold resolution improvement (standard quantum limit) beyond the Rayleigh diffraction bound, over classical imaging. Here, we report the experimental study on spatial sub-Rayleigh quantum imaging using a two-photon entangled source. Two experimental schemes are proposed and performed. In a Fraunhofer diffraction scheme with a lens, two-photon Airy disk pattern is observed with subwavelength diffraction property. In a lens imaging apparatus, however, two-photon sub-Rayleigh imaging for an object is realized with super-resolution property. The experimental results agree with the theoretical prediction in the two-photon quantum imaging regime.
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 noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
In spatial imaging, it is well known that two incoherent sources with a separation less than the diffraction limit cannot be resolved, a phenomenon dubbed as Rayleigh’s curse. A recent information theoretic approach suggests that this curse can be avoided using optimal (here, mode-sensitive) measurements instead of the usual intensity-only measurements, which define the classical limit [1] . This quantum enhanced resolution has been realized in both the spatial [2] and temporal domain [3] . Nevertheless, the role of optical coherence on the resolution limit still remains elusive [4] , [5] , [6] . Here, we experimentally resolve this debate using time-domain measurements.
Abstract The resolution of a photolithography and optical imaging system is restricted by the diffraction limit. Coherent Rabi oscillations have been shown to be able to overcome the diffraction limit in a simple two-level atomic system (Z Liao, M Al-amri, and M S Zubairy 2010 Phys. Rev. Lett. 105 183601 ). In this paper, we numerically calculate the wave packet dynamics of a molecular system interacting with an ultrashort laser pulse and show that coherent Rabi oscillations in a molecular system are also possible. Moreover, a sub-diffraction-limited pattern can be generated in this system by introducing spatially modulated Rabi oscillations. We also discuss several techniques to improve the visibility of the sub-diffraction-limited pattern. Our result may have important applications in super-resolution optical lithography and optical imaging.