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arXiv:2411.19369

Stochastic Frequency Fluctuation Super-Resolution Imaging

Chen, Yifan, Tsao, Chieh, Hendrik Utzat

Published Nov 28, 2024• 0 citations
arXivHTMLPDF

Abstract

The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in Super-Resolution Optical Fluctuation Imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed Spectral Fluctuation Super-Resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-frequency correlation functions in the image plane can improve the imaging resolution by a factor of $\sqrt2$ in most cases and up to twofold for strictly two emitters. This improvement is achieved by quantifying the degree of correlation in spectral fluctuations across the spatial domain. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations with arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, where spectral diffusion is often more pronounced than emitter blinking.

DOI
10.48550/arxiv.2411.19369

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The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in Super-Resolution Optical Fluctuation Imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed Spectral Fluctuation Super-Resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-frequency correlation functions in the image plane can improve the imaging resolution by a factor of 2\sqrt22​ in most cases and up to twofold for strictly two emitters. This improvement is achieved by quantifying the degree of correlation in spectral fluctuations across the spatial domain. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations with arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, where spectral diffusion is often more pronounced than emitter blinking.
The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in super-resolution optical fluctuation imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed spectral fluctuation super-resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-frequency correlation functions in the image plane can improve the imaging resolution by a factor of 2 in most cases and up to twofold for strictly two emitters. This improvement is achieved by quantifying the degree of correlation in spectral fluctuations across the spatial domain. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations with arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, where spectral diffusion is often more pronounced than emitter blinking.
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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.
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.
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 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.