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

arXiv:2310.02585 · New Journal of Physics

Localising two sub-diffraction emitters in 3D using quantum correlation microscopy

Shuo Li, Wenchao Li, Qiang Sun, Bill Moran, Timothy C. Brown, Brant C. Gibson, Andrew D. Greentree

Published Mar 1, 2024• 3 citations
arXivHTMLPDF

Abstract

Abstract The localisation of fluorophores is an important aspect of determining the biological function of cellular systems. Quantum correlation microscopy (QCM) is a promising technique for providing diffraction unlimited emitter localisation that can be used with either confocal or widefield modalities. However, so far, QCM has not been applied to three dimensional localisation problems. Here we show that QCM provides diffraction-unlimited three-dimensional localisation for two emitters within a single diffraction-limited spot. By introducing a two-stage maximum likelihood estimator, our modelling shows that the localisation precision scales as 1 / t where t is the total detection time. Diffraction unlimited localisation is achieved using both intensity and photon correlation from Hanbury Brown and Twiss measurements at as few as four measurement locations. We also compare the results of (MC) simulations with the Cramér–Rao lower bound.

DOI
10.1088/1367-2630/ad31d4

Related papers

Quantum correlation microscopy localising sub-diffraction emitters in 3D

Shuo Li, Andrew D. Greentree

By applying the second order correlation of Hanbury Brown and Twiss (HBT) measurements in the quantum microscopy system we build the theory approach of localising two single-photon emitters in three dimensions under diffraction limit. The results shine light on 3D diffraction unlimited microscopy.

Imaging and Applied Optics•Jan 1, 2022•0 citations

Quantifying the advantage of quantum correlation microscopy using arrays of single-photon detectors

Jaret J. Vasquez-Lozano, Qiang Sun, Shuo Li +1 more

Quantum correlation microscopy is an emerging technique for improving optical resolution. By taking advantage of the quantum statistics from single-photon fluorophores, more information about the emitters (including number and location) is obtained compared with classical microscopy. Although it is known that the resolution can be improved by increasing detector numbers, as well as using quantum correlation, the quantitative relationship between these two approaches is not immediately clear. Here we explore widefield quantum correlation microscopy using arrays of single-photon detectors. We explicitly compare the use of $N$ detectors used in photon counting mode vs $N/2$ detectors used to measure quantum correlations. i.e., where there are $N/2$ Hanbury Brown and Twiss systems, using the same $N$ detectors, on randomly generated two-emitter systems. We find regimes where $N/2$ Hanbury Brown and Twiss detectors provide improved localisation compared to $N$ photon counting detectors, as a function of emitter position and number of photons sampled.

arXiv:2505.10794•May 16, 2025•0 citations

Quantifying the advantage of photon correlation microscopy using arrays of single-photon detectors

Jaret J. Vasquez-Lozano, Qiang Sun, Shuo Li +1 more

Correlation microscopy is an emerging technique for improving optical resolution. By taking advantage of the photon statistics from single-photon fluorophores, more information about the emitters (including number and location) is obtained compared with classical microscopy. Although it is known that the resolution can be improved by increasing detector numbers, as well as using photon correlations, the quantitative relationship between these two approaches is not immediately clear. Here we explore widefield photon correlation microscopy using arrays of single-photon detectors. We explicitly compare the use of N detectors used in photon counting mode vs N/2 detectors used to measure photon correlations. i.e., where there are N/2 Hanbury Brown and Twiss systems, using the same N detectors, on randomly generated two-emitter systems and triangular three-emitter systems. We find regimes where N/2 Hanbury Brown and Twiss detectors provide improved localisation compared to N photon counting detectors, as a function of emitter position and number of photons sampled.

Optics Express•Oct 1, 2025•0 citations

Scanning quantum correlation microscopy with few emitters

Jaret J. Vasquez-Lozano, Shuo Li, Andrew D. Greentree

Abstract Optical superresolution microscopy is an important field, where nonlinear optical processes or prior information is used to defeat the classical diffraction limit of light. Quantum correlation microscopy uses photon arrival statistics from single photon emitters to aid in the determination of properties including the number of emitters and their relative brightness. Here we model quantum correlation microscopy in the few emitter regime, i.e. around four single photon emitters below the diffraction limit. We use the Akaike Information Criterion to determine the number of emitters and we vary the relative contributions of intensity to quantum correlation information to determine contribution that provides optimal imaging. Our results show diffraction unlimited performance and a change in localisation scaling behaviour dependent on emitter closeness.

arXiv:2310.08007•New Journal of Physics•Mar 8, 2024•1 citation

Quantum diffraction unlimited protocol for single-photon fluorophores

Josef G. Worboys, Daniel W. Drumm, Andrew D. Greentree

Achieving higher resolution scales in optical microscopy allow a more rigorous investigation into the detailed components of cell systems. This higher resolution is typically achieved through super-resolution techniques utilizing methods inside the wave-like nature of light such as point spread function shaping and fluorophore switching. We wish to leverage both particle-like and wave-like natures of light to make a diffraction unlimited protocol. Our protocol uses the well known Hanbury Brown and Twiss (HBT) apparatus in combination with a customized second-order cross-correlation protocol. By performing least squares fitting of the HBT and intensity measurements we obtain diffraction unlimited localization for two particles of unknown relative brightness from few measurement locations. Our results show super-resolution enhancement by an order of magnitude after 5000 detection lifetimes.

Biophotonics Australasia•Dec 30, 2019•0 citations

Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics

Mikael P. Backlund, Yoav Shechtman, Ronald Lee Walsworth

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.

arXiv:1803.01776•Physical Review Letters•Jul 11, 2018•68 citations
Abstract The localisation of fluorophores is an important aspect of determining the biological function of cellular systems. Quantum correlation microscopy (QCM) is a promising technique for providing diffraction unlimited emitter localisation that can be used with either confocal or widefield modalities. However, so far, QCM has not been applied to three dimensional localisation problems. Here we show that QCM provides diffraction-unlimited three-dimensional localisation for two emitters within a single diffraction-limited spot. By introducing a two-stage maximum likelihood estimator, our modelling shows that the localisation precision scales as 1 / t where t is the total detection time. Diffraction unlimited localisation is achieved using both intensity and photon correlation from Hanbury Brown and Twiss measurements at as few as four measurement locations. We also compare the results of (MC) simulations with the Cramér–Rao lower bound.
Quantum correlation microscopy is an emerging technique for improving optical resolution. By taking advantage of the quantum statistics from single-photon fluorophores, more information about the emitters (including number and location) is obtained compared with classical microscopy. Although it is known that the resolution can be improved by increasing detector numbers, as well as using quantum correlation, the quantitative relationship between these two approaches is not immediately clear. Here we explore widefield quantum correlation microscopy using arrays of single-photon detectors. We explicitly compare the use of NNN detectors used in photon counting mode vs N/2N/2N/2 detectors used to measure quantum correlations. i.e., where there are N/2N/2N/2 Hanbury Brown and Twiss systems, using the same NNN detectors, on randomly generated two-emitter systems. We find regimes where N/2N/2N/2 Hanbury Brown and Twiss detectors provide improved localisation compared to NNN photon counting detectors, as a function of emitter position and number of photons sampled.
Correlation microscopy is an emerging technique for improving optical resolution. By taking advantage of the photon statistics from single-photon fluorophores, more information about the emitters (including number and location) is obtained compared with classical microscopy. Although it is known that the resolution can be improved by increasing detector numbers, as well as using photon correlations, the quantitative relationship between these two approaches is not immediately clear. Here we explore widefield photon correlation microscopy using arrays of single-photon detectors. We explicitly compare the use of N detectors used in photon counting mode vs N/2 detectors used to measure photon correlations. i.e., where there are N/2 Hanbury Brown and Twiss systems, using the same N detectors, on randomly generated two-emitter systems and triangular three-emitter systems. We find regimes where N/2 Hanbury Brown and Twiss detectors provide improved localisation compared to N photon counting detectors, as a function of emitter position and number of photons sampled.
Abstract Optical superresolution microscopy is an important field, where nonlinear optical processes or prior information is used to defeat the classical diffraction limit of light. Quantum correlation microscopy uses photon arrival statistics from single photon emitters to aid in the determination of properties including the number of emitters and their relative brightness. Here we model quantum correlation microscopy in the few emitter regime, i.e. around four single photon emitters below the diffraction limit. We use the Akaike Information Criterion to determine the number of emitters and we vary the relative contributions of intensity to quantum correlation information to determine contribution that provides optimal imaging. Our results show diffraction unlimited performance and a change in localisation scaling behaviour dependent on emitter closeness.
Achieving higher resolution scales in optical microscopy allow a more rigorous investigation into the detailed components of cell systems. This higher resolution is typically achieved through super-resolution techniques utilizing methods inside the wave-like nature of light such as point spread function shaping and fluorophore switching. We wish to leverage both particle-like and wave-like natures of light to make a diffraction unlimited protocol. Our protocol uses the well known Hanbury Brown and Twiss (HBT) apparatus in combination with a customized second-order cross-correlation protocol. By performing least squares fitting of the HBT and intensity measurements we obtain diffraction unlimited localization for two particles of unknown relative brightness from few measurement locations. Our results show super-resolution enhancement by an order of magnitude after 5000 detection lifetimes.
Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.