Fourier interpolation stochastic optical fluctuation imaging

Cross-correlation increases sampling in diffusion-based super-resolution optical fluctuation imaging

Correlation signal processing of optical three-dimensional (x, y, t) data can produce super-resolution images. The second order cross-correlation function XC 2 has been documented to produce super-resolution imaging with static and blinking emitters but not for diffusing emitters. Here, we both analytically and numerically demonstrate cross-correlation analysis for diffusing particles. We then expand our fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) analysis to use cross-correlation as a post-processing computational technique to extract both dynamic and structural information of particle diffusion in nanoscale structures simultaneously. We further show how this method increases sampling rates and reduces aliasing for spatial information in both simulated and experimental data. Our work demonstrates how fcsSOFI with cross-correlation can be a powerful signal-processing tool to resolve the nanoscale dynamics and structure in samples relevant to biological and soft materials.

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Super-resolution SRS microscopy with A-PoD

Stimulated Raman scattering (SRS) offers the ability to image metabolic dynamics with high signal-to-noise ratio. However, its spatial resolution is limited by the numerical aperture of the imaging objective and the scattering cross-section of molecules. To achieve super-resolved SRS imaging, we developed a deconvolution algorithm, adaptive moment estimation (Adam) optimization-based pointillism deconvolution (A-PoD) and demonstrated a spatial resolution of lower than 59 nm on the membrane of a single lipid droplet (LD). We applied A-PoD to spatially correlated multiphoton fluorescence imaging and deuterium oxide (D2O)-probed SRS (DO-SRS) imaging from diverse samples to compare nanoscopic distributions of proteins and lipids in cells and subcellular organelles. We successfully differentiated newly synthesized lipids in LDs using A-PoD-coupled DO-SRS. The A-PoD-enhanced DO-SRS imaging method was also applied to reveal metabolic changes in brain samples from Drosophila on different diets. This new approach allows us to quantitatively measure the nanoscopic colocalization of biomolecules and metabolic dynamics in organelles.

PySOFI: an open source Python package for SOFI

Super-resolution optical fluctuation imaging (SOFI) is a highly democratizable technique that provides optical super-resolution without requirement of sophisticated imaging instruments. Easy-to-use open-source packages for SOFI are important to support the utilization and community adoption of the SOFI method, they also encourage the participation and further development of SOFI by new investigators. In this work, we developed PySOFI, an open-source Python package for SOFI analysis that offers the flexibility to inspect, test, modify, improve, and extend the algorithm. We provide complete documentation for the package and a collection of Jupyter Notebooks to demonstrate the usage of the package. We discuss the architecture of PySOFI and illustrate how to use each functional module. A demonstration on how to extend the PySOFI package with additional modules is also included in the PySOFI package. We expect PySOFI to facilitate efficient adoption, testing, modification, dissemination, and prototyping of new SOFI-relevant algorithms.

Rapid multi-plane phase-contrast microscopy reveals torsional dynamics in flagellar motion

High speed volumetric optical microscopy is an important tool for observing rapid processes in living cells or for real-time tracking of sub-cellular components. However, the 3D imaging capability often comes at the price of a high technical complexity of the imaging system and/or the requirement of demanding image analysis. Here, we propose a combination of conventional phase-contrast imaging with a customized multi-plane beam-splitter for enabling simultaneous acquisition of images in eight different focal planes. Our method is technically straightforward and does not require complex post-processing image analysis. We apply our multi-plane phase-contrast microscope to the real-time observation of the fast motion of reactivated Chlamydomonas axonemes with sub-µm spatial and 4 ms temporal resolution. Our system allows us to observe not only bending but also the three-dimensional torsional dynamics of these micro-swimmers.

Analysis of intensity correlation enhanced plasmonic structured illumination microscopy

We propose to enhance the performance of localized plasmon structured illumination microscopy (LP-SIM) via intensity correlations. LP-SIM uses sub-wavelength illumination patterns to encode high spatial frequency information. It can enhance the resolution up to three-fold before gaps in the optical transfer function (OTF) support arise. For blinking fluorophores or for quantum antibunching, an intensity correlation analysis induces higher harmonics of the illumination pattern and enlarges the effective OTF. This enables ultrahigh resolutions without gaps in the OTF support, and thus a fully deterministic imaging scheme. We present simulations that include shot and external noise and demonstrate the resolution power under realistic photon budgets. The technique has potential in light microscopy where low-intensity illumination is paramount while aiming for high spatial but moderate temporal resolutions.

Enhanced temporal and spatial resolution in super-resolution covariance imaging algorithm with deconvolution optimization

Based on the numerical analysis that covariance exhibits superior statistical precision than cumulant and variance, a new SOFI algorithm by calculating the n orders covariance for each pixel is presented with an almost 2n -fold resolution improvement, which can be enhanced to 2ⁿ via deconvolution. An optimized deconvolution is also proposed by calculating the (n + 1) order SD associated with each n order covariance pixel, and introducing the results into the deconvolution as a damping factor to suppress noise generation. Moreover, a re-deconvolution of the covariance image with the covariance-equivalent point spread function is used to further increase the final resolution by above 2-fold. Simulated and experimental results show that this algorithm can significantly increase the temporal-spatial resolution of SOFI, meanwhile, preserve the sample's structure. Thus, a resolution of 58 nm is achieved for 20 experimental images, and the corresponding acquisition time is 0.8 seconds.

Resolution enhanced photothermal imaging by high-order correlation

Laser scanning photothermal imaging offers a powerful non-destructive testing tool to visualize subsurface structures of opaque materials, but it suffers the resolution limit imposed by thermal diffusion. To overcome this physical obstacle, a tightly focused excitation beam with a high repetition rate is usually used to improve the spatial resolution. Here, we demonstrate that the resolution of photothermal imaging could be enhanced using the high-order correlation imaging method inspired by correlated optical imaging. By carefully designing the laser scanning and modulation behavior, we can individually control the statistical properties of isolated hotspots induced by lasers. Imaging reconstructions of subsurface structures are performed afterward by reading out time-fluctuated thermal images. Moreover, the resolution can be further enhanced by using the high-order correlation, which enables a new way for highly resolved thermal imaging and metrology applications.

An extended quantitative model for super-resolution optical fluctuation imaging (SOFI)

Super-resolution optical fluctuation imaging (SOFI) provides super-resolution (SR) fluorescence imaging by analyzing fluctuations in the fluorophore emission. The technique has been used both to acquire quantitative SR images and to provide SR biosensing by monitoring changes in fluorophore blinking dynamics. Proper analysis of such data relies on a fully quantitative model of the imaging. However, previous SOFI imaging models made several assumptions that can not be realized in practice. In this work we address these limitations by developing and verifying a fully quantitative model that better approximates real-world imaging conditions. Our model shows that (i) SOFI images are free of bias, or can be made so, if the signal is stationary and fluorophores blink independently, (ii) allows a fully quantitative description of the link between SOFI imaging and probe dynamics, and (iii) paves the way for more advanced SOFI image reconstruction by offering a computationally fast way to calculate SOFI images for arbitrary probe, sample and instrumental properties.

Moments reconstruction and local dynamic range compression of high order superresolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) offers a simple and affordable alternative to other super-resolution (SR) imaging techniques. The theoretical resolution enhancement of SOFI scales linearly with the order of cumulants, while the imaging conditions exhibit less photo-toxicity to the living samples as compared to other SR methods. High order SOFI could, therefore, be a method of choice for dynamic live cell imaging. However, due to the cusp-artifacts and dynamic range expansion of pixel intensities, this promise has not been materialized as of yet. Here we investigated and compared high order moments vs. high order cumulant SOFI reconstructions. We demonstrate that even-order moments reconstructions are intrinsically free of cusp artifacts, allowing for a subsequent deconvolution operation to be performed, hence enhancing the resolution even further. High order moments reconstruction performance was examined for various (simulated) conditions and applied to (experimental) imaging of QD labeled microtubules in fixed cells, and actin stress fiber dynamics in live cells.

Resolution-enhanced imaging through scattering media by high-order correlation

Super-resolution optical imaging is a rapidly emerging technology enabling many applications. Recently, correlation imaging has shown its capability in imaging beyond the diffraction limit, relying on quantum and statistical properties of light. High-order correlation imaging can further enhance resolution, however, at the expense of complicated algorithms. Here, we experimentally demonstrate a resolution-enhanced method of imaging through scattering media by exploiting high-order correlation of fluorescence light. Based on this method, individual fluorophores' temporal fluctuations are recorded and computed for their distinguished high-order correlations that enable super-resolution. Special designed time sequences are chosen to reduce computation time and memory. Such high-order correlation imaging exhibits reliable performance through scattering media with significant resolution enhancement and background noise reduction. This efficient imaging method paves the way for new biomedical applications.

Synergizing superresolution optical fluctuation imaging with single molecule localization microscopy

Single-molecule-localization-microscopy (SMLM) and superresolution-optical-fluctuation-imaging (SOFI) enable imaging biological samples well beyond the diffraction-limit of light. SOFI imaging is typically faster, yet has lower resolution than SMLM. Since the same (or similar) data format is acquired for both methods, their algorithms could presumably be combined synergistically for reconstruction and improvement of overall imaging performance. For that, we first defined a measure of the acquired-SNR for each method. This measure was ∼x10 to x100 higher for SOFI as compared to SMLM, indicating faster recognition and acquisition of features by SOFI. This measure also allowed fluorophore-specific optimization of SOFI reconstruction over its time-window and time-lag. We show that SOFI-assisted SMLM imaging can improve image reconstruction by rejecting common sources of background (e.g. out-of-focus emission and auto-fluorescence), especially under low signal-to-noise ratio conditions, by efficient optical sectioning and by shortening image reconstruction time. The performance and utility of our approach was evaluated by realistic simulations and by SOFI-assisted SMLM imaging of the plasma membrane of activated fixed and live T-cells (in isolation or in conjugation to antigen presenting cells). Our approach enhances SMLM performance under demanding imaging conditions and could set an example for synergizing additional imaging techniques.

Fluorescent Diarylethene Photoswitches-A Universal Tool for Super-Resolution Microscopy in Nanostructured Materials

Super-resolution fluorescence microscopy allows for unprecedented in situ visualization of biological structures, but its application to materials science has so far been comparatively limited. One of the main reasons is the lack of powerful dyes that allow for labeling and photoswitching in materials science systems. In this study it is shown that appropriate substitution of diarylethenes bearing a fluorescent closed and dark open form paves the way for imaging nanostructured materials with three of the most popular super-resolution fluorescence microscopy methods that are based on different concepts to achieve imaging beyond the diffraction limit of light. The key to obtain optimal resolution lies in a proper control over the photochemistry of the photoswitches and its adaption to the system to be imaged. It is hoped that the present work will provide researchers with a guide to choose the best photoswitch derivative for super-resolution microscopy in materials science, just like the correct choice of a Swiss Army Knife's tool is essential to fulfill a given task.

Correcting for photodestruction in super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging overcomes the diffraction limit by analyzing fluctuations in the fluorophore emission. A key assumption of the imaging is that the fluorophores are independent, though this is invalidated in the presence of photodestruction. In this work, we evaluate the effect of photodestruction on SOFI imaging using theoretical considerations and computer simulations. We find that photodestruction gives rise to an additional signal that does not present an easily interpretable view of the sample structure. This additional signal is strong and the resulting images typically exhibit less noise. Accordingly, these images may be mis-interpreted as being more visually pleasing or more informative. To address this uncertainty, we develop a procedure that can robustly estimate to what extent any particular experiment is affected by photodestruction. We also develop a detailed assessment methodology and use it to evaluate the performance of several correction algorithms. We identify two approaches that can correct for the presence of even strong photodestruction, one of which can be implemented directly in the SOFI calculation software.

Effect of probe diffusion on the SOFI imaging accuracy

Live-cell super-resolution fluorescence imaging is becoming commonplace for exploring biological systems, though sample dynamics can affect the imaging quality. In this work we evaluate the effect of probe diffusion on super-resolution optical fluctuation imaging (SOFI), using a theoretical model and numerical simulations based on the imaging of live cells labelled with photochromic fluorescent proteins. We find that, over a range of physiological conditions, fluorophore diffusion results in a change in the amplitude of the SOFI signal. The magnitude of this change is approximately proportional to the on-time ratio of the fluorophores. However, for photochromic fluorescent proteins this effect is unlikely to present a significant distortion in practical experiments in biological systems. Due to this lack of distortions, probe diffusion strongly enhances the SOFI imaging by avoiding spatial undersampling caused by the limited labeling density.

Live-cell monochromatic dual-label sub-diffraction microscopy by mt-pcSOFI

We present mt-pcSOFI, live-cell monochromatic sub-diffraction imaging and illustrate the method with existing RSFPs and the newly developed ffDronpa-F.

Statistical precision in super-resolution optical fluctuation imaging

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by calculating the spatiotemporal cross-cumulants of independent stochastic intensity fluctuations of emitters. Ideally, SOFI eliminates any noise that is not correlated over time, but in practice, due to limited data lengths, the statistical uncertainty of cumulants will affect the continuities and homogeneities of SOFI images. Since the variance and signal-to-noise ratio (SNR) characterize cumulant statistical uncertainty, we determined theoretical expressions for these based on a single dataset. From a simulation of temporal fluctuations of blinking fluorescent emitters, we calculated the quantitative relation between the SNR of cumulants and multiple parameters of the blinking signal, such as the on-time ratio, acquisition frame to average blinking rate ratio, sequence length, and photon amplitude, which not only provides a physical interpretation for SOFI phenomena but also theoretical guidance to achieve optimal practical outcomes.

Superior performance with sCMOS over EMCCD in super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) is a fast and low-cost live-cell optical nanoscopy for extracting subdiffraction information from the statistics of fluorescence intensity fluctuation. As SOFI is based on the fluctuation statistics, rather than the detection of single molecules, it poses unique requirements for imaging detectors, which still lack a systematic evaluation. Here, we analyze the influences of pixel sizes, frame rates, noise levels, and different gains in SOFI with simulations and experimental tests. Our analysis shows that the smaller pixel size and faster readout speed of scientific-grade complementary metal oxide semiconductor (sCMOS) enables SOFI to achieve high spatiotemporal resolution with a large field-of-view, which is especially beneficial for live-cell super-resolution imaging. Overall, as the performance of SOFI is relatively insensitive to the signal-to-noise ratio (SNR), the gain in pixel size and readout speed exceeds the loss in SNR, indicating sCMOS is superior to electron multiplying charge coupled device in context to SOFI in many cases. Super-resolution imaging of cellular microtubule structures with high-order SOFI is experimentally demonstrated at large field-of-view, taking advantage of the large pixel number and fast frame rate of sCMOS cameras.

Enhanced SOFI algorithm achieved with modified optical fluctuating signal extraction

In this paper, we present a modified SOFI algorithm with enhanced temporal resolution: the required number of raw images for SOFI is reduced from hundreds to tens. The modification is intended to eliminate the low-frequency fluctuation and readout noise from the raw image stack, and is achieved by separately utilizing two wavelet-based filters in the temporal and spatial domains of the raw image stack. The high-frequency stochastic fluctuating signal could be extracted effectively, and the efficiency of SOFI could be enhanced. The modified SOFI image could be generated with 25 frames of raw images, and the corresponding acquisition time was 1.25 s.

Model-free uncertainty estimation in stochastical optical fluctuation imaging (SOFI) leads to a doubled temporal resolution

Stochastic optical fluctuation imaging (SOFI) is a super-resolution fluorescence imaging technique that makes use of stochastic fluctuations in the emission of the fluorophores. During a SOFI measurement multiple fluorescence images are acquired from the sample, followed by the calculation of the spatiotemporal cumulants of the intensities observed at each position. Compared to other techniques, SOFI works well under conditions of low signal-to-noise, high background, or high emitter densities. However, it can be difficult to unambiguously determine the reliability of images produced by any superresolution imaging technique. In this work we present a strategy that enables the estimation of the variance or uncertainty associated with each pixel in the SOFI image. In addition to estimating the image quality or reliability, we show that this can be used to optimize the signal-to-noise ratio (SNR) of SOFI images by including multiple pixel combinations in the cumulant calculation. We present an algorithm to perform this optimization, which automatically takes all relevant instrumental, sample, and probe parameters into account. Depending on the optical magnification of the system, this strategy can be used to improve the SNR of a SOFI image by 40% to 90%. This gain in information is entirely free, in the sense that it does not require additional efforts or complications. Alternatively our approach can be applied to reduce the number of fluorescence images to meet a particular quality level by about 30% to 50%, strongly improving the temporal resolution of SOFI imaging.

Super-Resolution Optical Fluctuation Bio-Imaging with Dual-Color Carbon Nanodots

Success in super-resolution imaging relies on a proper choice of fluorescent probes. Here, we suggest novel easily produced and biocompatible nanoparticles-carbon nanodots-for super-resolution optical fluctuation bioimaging (SOFI). The particles revealed an intrinsic dual-color fluorescence, which corresponds to two subpopulations of particles of different electric charges. The neutral nanoparticles localize to cellular nuclei suggesting their potential use as an inexpensive, easily produced nucleus-specific label. The single particle study revealed that the carbon nanodots possess a unique hybrid combination of fluorescence properties exhibiting characteristics of both dye molecules and semiconductor nanocrystals. The results suggest that charge trapping and redistribution on the surface of the particles triggers their transitions between emissive and dark states. These findings open up new possibilities for the utilization of carbon nanodots in the various super-resolution microscopy methods based on stochastic optical switching.