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arXiv:2408.11654 · Optica

Quantum super-resolution microscopy by photon statistics and structured light

Fabio Picariello, Elena Losero, Sviatoslav Ditalia Tchernij, Pauline Boucher, Marco Genovese, Ivano Ruo Berchera, Ivo Pietro Degiovanni

Published Mar 6, 2025• 14 citations
arXivHTMLPDF

Abstract

Reaching high-resolution imaging of delicate samples at a low-intensity level is a major challenge in microscopy. Here, we present and experimentally implement an advanced quantum super-resolution imaging technique based on photon statistics measurement. Our reconstruction algorithm adapts to any kind of non-Poissonian emitters, outperforming the corresponding classical SOFI method, in particular in low-light conditions. It offers sub-diffraction resolution improvement that scales with the j , where j is the highest-order central moments of the photocounts. More remarkably, we show that in combination with structured illumination, an improvement of j + j can be reached, providing a promising avenue for non-invasive super-resolution microscopy.

DOI
10.1364/optica.540264

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Reaching high-resolution imaging of delicate samples at a low-intensity level is a major challenge in microscopy. Here, we present and experimentally implement an advanced quantum super-resolution imaging technique based on photon statistics measurement. Our reconstruction algorithm adapts to any kind of non-Poissonian emitters, outperforming the corresponding classical SOFI method, in particular in low-light conditions. It offers sub-diffraction resolution improvement that scales with the j , where j is the highest-order central moments of the photocounts. More remarkably, we show that in combination with structured illumination, an improvement of j + j can be reached, providing a promising avenue for non-invasive super-resolution microscopy.
We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far beyond the Rayleigh limit. Combining intensity measurements and intensity auto correlations up to order mmm creates an effective PSF with FWHM shrunk by the factor m\sqrt{m}m​. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as m+mm + \sqrt{m}m+m​ in dependence of the correlation order mmm. Hence, yielding this technique to be of interest in microscopy for imaging a variety of samples including biological ones. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.
We propose to use intensity correlation microscopy in combination with structured illumination to image quantum emitters that exhibit antibunching with a spatial resolution reaching far into the sub-classical regime. Combining intensity measurements and intensity auto correlations up to order m creates an effective PSF with FWHM shrunk by the factor p m. Structured Illumination microscopy on the other hand introduces a resolution improvement of factor 2 by use of the principle of moiré fringes. Here, we show that for linear low-intensity excitation and linear optical detection the simultaneous use of both techniques leads to an in theory unlimited resolution power with the improvement scaling favorably as m+sqrt m in dependence of the correlation order m. Hence, yielding this technique to be of the utmost interest for biological imaging. We present the underlying theory and simulations demonstrating the highly increased spatial superresolution, and point out requirements for an experimental implementation.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.
One of the main characteristics of optical imaging systems is spatial resolution, which is restricted by the diffraction limit to approximately half the wavelength of the incident light. Along with the recently developed classical super-resolution techniques, which aim at breaking the diffraction limit in classical systems, there is a class of quantum super-resolution techniques which leverage the non-classical nature of the optical signals radiated by quantum emitters, the so-called antibunching super-resolution microscopy. This approach can ensure a factor of [Formula: see text] improvement in the spatial resolution by measuring the n -th order autocorrelation function. The main bottleneck of the antibunching super-resolution microscopy is the time-consuming acquisition of multi-photon event histograms. We present a machine learning-assisted approach for the realization of rapid antibunching super-resolution imaging and demonstrate 12 times speed-up compared to conventional, fitting-based autocorrelation measurements. The developed framework paves the way to the practical realization of scalable quantum super-resolution imaging devices that can be compatible with various types of quantum emitters.
One of the main characteristics of optical imaging systems is the spatial resolution, which is restricted by the diffraction limit to approximately half the wavelength of the incident light. Along with the recently developed classical super-resolution techniques, which aim at breaking the diffraction limit in classical systems, there is a class of quantum super-resolution techniques which leverage the non-classical nature of the optical signals radiated by quantum emitters, the so-called antibunching super-resolution microscopy. This approach can ensure a factor of n\sqrt{n}n​ improvement in the spatial resolution by measuring the n-th order autocorrelation function. The main bottleneck of the antibunching super-resolution microscopy is the time-consuming acquisition of multi-photon event histograms. We present a machine learning-assisted approach for the realization of rapid antibunching super-resolution imaging and demonstrate 12 times speed-up compared to conventional, fitting-based autocorrelation measurements. The developed framework paves the way to the practical realization of scalable quantum super-resolution imaging devices that can be compatible with various types of quantum emitters.
Intensity correlation microscopy (ICM), which is prominently known through antibunching microscopy or super-resolution optical fluctuation imaging (SOFI), provides super-resolution through a correlation analysis of antibunching of independent quantum emitters or temporal fluctuations of blinking fluorophores. For correlation order m the PSF in the signal is effectively taken to the mth power, and is thus directly shrunk by the factor m. Combined with deconvolution, a close to linear resolution improvement of factor m can be obtained. Yet, analysis of high correlation orders is challenging, which limits the achievable resolutions. Here we propose to use three dimensional structured illumination along with mth-order correlation analysis to obtain an enhanced scaling of up to m + m = 2m. Including the stokes shift or plasmonic sub-wavelength illumination enhancements beyond 2m can be achieved. Hence, resolutions far below the diffraction limit in full 3D imaging and with already low correlation orders, can potentially be achieved. Since ICM operates in the linear regime our approach may be particularly promising for enhancing the resolution in biological imaging at low illumination levels.