Background: Super-resolution optical fluctuation imaging (SOFI) achieves 3D super-resolution by computing temporal cumulants or spatio-temporal cross-cumulants of stochastically blinking fluorophores. In contrast to localization microscopy, SOFI is compatible with weakly emitting fluorophores and a wide range of blinking conditions. The main drawback of SOFI is the nonlinear response to brightness and blinking heterogeneities in the sample, which limits the use of higher cumulant orders for improving the resolution. Balanced super-resolution optical fluctuation imaging (bSOFI) analyses several cumulant orders for extracting molecular parameter maps, such as molecular state lifetimes, concentration and brightness distributions of fluorophores within biological samples. Moreover, the estimated blinking statistics are used to balance the image contrast, i.e. linearize the brightness and blinking response and to obtain a resolution improving linearly with the cumulant order. Results: Using a widefield total-internal-reflection (TIR) fluorescence microscope, we acquired image sequences of fluorescently labelled microtubules in fixed HeLa cells. We demonstrate an up to five-fold resolution improvement as compared to the diffraction-limited image, despite low single-frame signal-to-noise ratios. Due to the TIR illumination, the intensity profile in the sample decreases exponentially along the optical axis, which is reported by the estimated spatial distributions of the molecular brightness as well as the blinking on-ratio. Therefore, TIR-bSOFI also encodes depth information through these parameter maps. Conclusions: bSOFI is an extended version of SOFI that cancels the nonlinear response to brightness and blinking heterogeneities. The obtained balanced image contrast significantly enhances the visual perception of super-resolution based on higher-order cumulants and thereby facilitates the access to higher resolutions. Furthermore, bSOFI provides microenvironment-related molecular parameter maps and paves the way for functional super-resolution microscopy based on stochastic switching.

A straightforward method to achieve super-resolution consists of taking an image sequence of stochastically blinking emitters using a standard wide-field fluorescence microscope. Densely packed single molecules can be distinguished sequentially in time using high-precision localization algorithms (e.g., PALM and STORM) or by analyzing the statistics of the temporal fluctuations (SOFI). In a face-to-face comparison of the two post-processing algorithms, we show that localization-based super-resolution can deliver higher resolution enhancements but imposes significant constraints on the blinking behavior of the probes, which limits its applicability for live-cell imaging. SOFI, on the other hand, works more consistently over different photo-switching kinetics and also delivers information about the specific blinking statistics. Its suitability for low SNR acquisition reveals SOFI's potential as a high-speed super-resolution imaging technique.

Super-resolution optical fluctuation imaging (SOFI) provides an elegant way of overcoming the diffraction limit in all three spatial dimensions by computing higher-order cumulants of image sequences of blinking fluorophores acquired with a classical widefield microscope. Previously, three-dimensional (3D) SOFI has been demonstrated by sequential imaging of multiple depth positions. Here we introduce a multiplexed imaging scheme for the simultaneous acquisition of multiple focal planes. Using 3D cross-cumulants, we show that the depth sampling can be increased. The simultaneous acquisition of multiple focal planes significantly reduces the acquisition time and thus the photobleaching. We demonstrate multiplane 3D SOFI by imaging fluorescently labelled cells over an imaged volume of up to 65 × 65 × 3.5 μm3 without depth scanning. In particular, we image the 3D network of mitochondria in fixed C2C12 cells immunostained with Alexa 647 fluorophores and the 3D vimentin structure in living Hela cells expressing the fluorescent protein Dreiklang.

Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. However, going `beyond the diffraction barrier' comes at a price since most far-field superresolution imaging techniques trade temporal for spatial super-resolution. We propose the combination of a novel label-free white light quantitative phase tomography with fluorescence imaging to provide high-speed imaging and spatial super-resolution. The non-iterative phase reconstruction relies on the acquisition of single images at each z-location and thus enables straightforward 3D phase imaging using a classical microscope. We realized multi-plane imaging using a customized prism for the simultaneous acquisition of 8 planes. This allowed us to not only image live cells in 3D at up to 200 Hz, but also to integrate fluorescence super-resolution optical fluctuation imaging within the same optical instrument.This 4D microscope platform unifies the sensitivity and high temporal resolution of phase tomography with the specificity and high spatial resolution of fluorescence imaging.

We present a novel concept for optical spectroscopy called nonlinear correlation spectroscopy (NLCS). NLCS analyses coherent field fluctuations of the second and third harmonic light generated by diffusing nanoparticles. Particles based on noncentrosymmetric nonlinear materials such as KNbO(3) show a strong second as well as third harmonic response. The method and the theory are introduced and experimental NLCS results in fetal calf serum are presented showing the promising selectivity of this technique for measurement in complex biological environments.

Super-resolution optical fluctuation imaging (SOFI) allows one to perform sub-diffraction fluorescence microscopy of living cells. By analyzing the acquired image sequence with an advanced correlation method, i.e. a high-order cross-cumulant analysis, super-resolution in all three spatial dimensions can be achieved. Here we introduce a software tool for a simple qualitative comparison of SOFI images under simulated conditions considering parameters of the microscope setup and essential properties of the biological sample. This tool incorporates SOFI and STORM algorithms, displays and describes the SOFI image processing steps in a tutorial-like fashion. Fast testing of various parameters simplifies the parameter optimization prior to experimental work. The performance of the simulation tool is demonstrated by comparing simulated results with experimentally acquired data.

Super-resolution optical fluctuation imaging provides a resolution beyond the diffraction limit by analysing stochastic fluorescence fluctuations with higher-order statistics. Using n th order spatio-temporal cross-cumulants the spatial resolution and the sampling can be increased up to n-fold in all spatial dimensions. In this study, we extend the cumulant analysis into the spectral domain and propose a multicolor super-resolution scheme. The simultaneous acquisition of two spectral channels followed by spectral cross-cumulant analysis and unmixing increases the spectral sampling. The number of discriminable fluorophore species is thus not limited to the number of physical detection channels. Using two color channels, we demonstrate spectral unmixing of three fluorophore species in simulations and experiments in fixed and live cells. Based on an eigenvalue/vector analysis, we propose a scheme for an optimized spectral filter choice. Overall, our methodology provides a route for easy-toimplement multicolor sub-diffraction imaging using standard microscopes while conserving the spatial super-resolution property.

We present a new method called optical coherence correlation spectroscopy (OCCS) using nanoparticles as reporters of kinetic processes at the single particle level. OCCS is a spectral interferometry based method, thus giving simultaneous access to several sampling volumes along the optical axis. Based on an auto-correlation analysis, we extract the diffusion coefficients and concentrations of nanoparticles over a large concentration range. The cross-correlation analysis between adjacent sampling volumes allows to measure flow parameters. This shows the potential of OCCS for spatially resolved diffusion and flow measurements.