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Biophotonics Australasia

Quantum diffraction unlimited protocol for single-photon fluorophores

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

Published Dec 30, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2541217

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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.
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.
Far-field optical microscopy beyond the Abbe diffraction limit, making use of nonlinear excitation (e.g. STED), or temporal fluctuations in fluorescence (PALM, STORM, SOFI) is already a reality. In contrast, overcoming the diffraction limit using non-classical properties of light is very difficult to achieve due to the fragility of quantum states of light. Here, we experimentally demonstrate superresolution microscopy based on quantum properties of light naturally emitted by fluorophores used as markers in fluorescence microscopy. Our approach is based on photon antibunching, the tendency of fluorophores to emit photons one by one rather than in bursts. Although a distinctively quantum phenomenon, antibunching is readily observed in most common fluorophores even at room temperature. This nonclassical resource can be utilized directly to enhance the imaging resolution, since the non-classical far-field intensity correlations induced by antibunching carry high spatial frequency information on the spatial distribution of emitters. Detecting photon statistics simultaneously in the entire field of view, we were able to detect non-classical correlations of the second and third order, and reconstructed images with resolution significantly beyond the diffraction limit. Alternatively, we demonstrate the utilization of antibunching for augmenting the capabilities of localization-based superresolution imaging in the presence of multiple emitters, using a novel detector comprised of an array of single photon detectors connected to a densely packed fiber bundle. These features allow us to enhance the spatial and temporal resolution with which multiple emitters can be imaged compared with other techniques that rely on CCD cameras.
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.
The classical optical diffraction limit can be overcome by exploiting the quantum properties of light in several theoretical studies; however, they mostly rely on an entangled light source. Recent experiments have demonstrated that quantum properties are preserved in many fluorophores, which makes it possible to add a new dimension of information for super-resolution fluorescence imaging. Here, we developed a statistical quantum coherence model for fluorescence emitters and proposed a new super-resolution method using fluorescence quantum coherence in fluorescence microscopy. In this study, by exploiting a single-photon avalanche detector (SPAD) array with a time-correlated single-photon-counting technique to perform spatial-temporal photon statistics of fluorescence coherence, the subdiffraction-limited spatial separation of emitters is obtained from the determined coherence. We numerically demonstrate an example of two-photon interference from two common fluorophores using an achievable experimental procedure. Our model provides a bridge between the macroscopic partial coherence theory and the microscopic dephasing and spectral diffusion mechanics of emitters. By fully taking advantage of the spatial-temporal fluctuations of the emitted photons as well as coherence, our quantum-enhanced imaging method has the significant potential to improve the resolution of fluorescence microscopy even when the detected signals are weak.