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arXiv:1806.00643 · Optics Express

Analysis of super-resolution via 3D structured illumination intensity correlation microscopy

Anton Classen, Joachim von Zanthier, G. S. Agarwal

Published Oct 5, 2018• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/oe.26.027492

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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.
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.
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.
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.
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.
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.
Super-resolution microscopy is crucial for imaging sub-wavelength biological structures. However, most techniques rely on nonlinear saturation or stochastic switching of emitters, limiting imaging speed and increasing phototoxicity. Here, we achieve deep super-resolution without employing saturation or stochastic dynamics, instead using a form of spatial mode demultiplexing. By shaping the point-spread function of the emitted light, our Structured Detection Microscope (SDM) redistributes information away from high shot-noise regions of the image, enhancing sensitivity to sub-diffraction emitter separations in two-dimensions and without mode-sorting optics. Implementing SDM within a high-numerical aperture total internal reflection fluorescence microscope, we demonstrate imaging of fluorophores attached to DNA nanorulers with separations as small as 50 nm at resolutions surpassing 40 nm - fivefold below the diffraction limit. This shows that spatial mode demultiplexing can achieve far sub-wavelength resolution and is applicable to biologically relevant samples. By enabling super-resolution biomolecular imaging without emitter saturation and stochasticity, our work opens the door to better understanding biological structure, function and dynamics.