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Optics Express

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

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

Published Oct 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oe.568719

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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.
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.
Higher-order correlations of the radiation field improve resolution in stellar interferometers, as in the Hanbury-Brown–Twiss effect. It is also possible to improve microscopic resolution beyond the Rayleigh limit by using quantum light fields composed of entangled photons. Focusing on two photons, we distinguish two types of entanglement: frequency entanglement, where the photons in different paths are correlated in frequency, and path entanglement, where the correlation between paths is in photon number. Two paradigms of quantum microscopy are discussed: spectral microscopy, where path- and frequency-entangled photons produced in cascade decay of two atoms make possible sub-natural linewidth resolution of atomic levels, and spatial microscopy, where path-entangled photons emitted by an atomic array produce sub-wavelength diffraction resolution as compared to an equivalent classical grating. These scenarios require two-photon correlation or coincidence measurements. The connection between the two paradigms, and the two types of entanglement, highlights the link between the temporal and spatial aspects of quantum interferometry.
Typically, optical microscopy uses the wavelike properties of light to image a scene. However, photon arrival times provide more information about emitter properties than the classical intensity alone. Here we show that the Hanbury Brown and Twiss experiment (second-order correlation function) measures the relative brightness of two single-photon emitters. By combining the total number of detected photons with the zero-lag value of the correlation function, the positions and relative brightness of two emitters in two dimensions can be resolved from only three measurement positions: trilateration. This result is impossible to achieve on the basis of classical intensity measurements alone and represents a minimal demonstration of the advantage gained using quantum measurements over conventional classical microscopy. The effective point-spread function for imaging scales approximately as the inverse square root of the acquisition time.
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.
Techniques of optical superresolution imaging are vital for uncovering the complex dynamics of biochemistry in cellular environments. However the practical resolution for superresolution imaging is limited by the increased photon budget for superresolution, compared with conventional microscopy. For this reason it is important to determine the optimal methods for analysing all of the incoming information. Most approaches to microscopy use only the wave-like properties of light, but the particle-like nature of light provides extra information that is normally inaccessible and can be used to increase imaging resolution. Here we theoretically study the localisation of quantum emitters using higher-order quantum correlation functions to understand the resolution that is practically achievable for bio-imaging tasks. We show explicit imaging results for varying number of emitters as a function of correlation order to illustrate the necessary tradeoffs between imaging resolution and acquisition time.