Unveiling the limits of precision in iterative MINFLUX.

In single-molecule microscopy, a big question is how precisely we can estimate the location of a single molecule. Our research shows that by using iterative localisation microscopy and factoring in the prior information, we can boost precision and reduce the number of photons needed. Leveraging the Van Trees inequality aids in determining the optimal precision achievable. Our approach holds promise for wider application in discerning the optimal precision across diverse imaging scenarios, encompassing various illumination strategies, point spread functions and overarching control methodologies.

Site-Specific Integration of Hexagonal Boron Nitride Quantum Emitters on 2D DNA Origami Nanopores.

Optical emitters in hexagonal boron nitride (hBN) are promising probes for single-molecule sensing platforms. When engineered in nanoparticle form, they can be integrated as detectors in nanodevices, yet positional control at the nanoscale is lacking. Here we demonstrate the functionalization of DNA origami nanopores with optically active hBN nanoparticles (NPs) with nanometer precision. The NPs are active under three wavelengths of visible illumination and display both stable and blinking emission, enabling their accurate localization by using wide-field optical nanoscopy. Correlative opto-structural characterization reveals deterministic binding of bright, multicolor hBN NPs at the pore rim due to π-π stacking interactions at site-specific locations on the DNA origami. Our work provides a scalable, bottom-up approach toward deterministic assembly of solid-state emitters on arbitrary structural elements based on DNA origami. Such a nanoscale arrangement of optically active components can advance the development of single-molecule platforms, including optical nanopores and nanochannel sensors.

Image scanning microscopy: a vectorial physical optics analysis.

Image scanning microscopy (ISM) achieves resolution beyond the diffraction limit by a factor of 2. However, prior ISM research predominantly employs scalar diffraction theory, neglecting critical physical effects such as polarization, aberrations, and Stokes shift. This paper presents a comprehensive vectorial ISM point spread function (PSF) model that accounts for these phenomena. By considering the effect of polarization in emission and excitation paths, as well as aberrations and Stokes shift, our model provides a more accurate representation of ISM. We analyze the differences between scalar and vectorial theories in ISM and investigate the impact of pinhole size and aberration strength on resolution. At a numerical aperture of 1.2, the full width half maximum (FWHM) discrepancy between scalar and vectorial ISM PSFs can reach 45 nm, representing a 30% deviation from the vectorial model. Additionally, we explore multiphoton excitation in ISM and observe increased FWHM for 2-photon and 3-photon excitation compared to 1-photon excitation. The FWHM of the 2-photon excitation ISM PSF increases by 20% and the FWHM of the 3-photon excitation ISM PSF increases by 28% compared to the 1-photon excitation ISM. In addition, we found that the optimal sweep factor for 2-photon ISM is 1.22, and the optimal sweep factor of 3-photon ISM is 1.12 instead of the 2 predicted by the one-photon scalar ISM theory. Our work improves the understanding of ISM and contributes to its advancement as a high-resolution imaging technique.

Quantifying the minimum localization uncertainty of image scanning localization microscopy.

Modulation enhanced single-molecule localization microscopy (meSMLM), where emitters are sparsely activated with sequentially applied patterned illumination, increases the localization precision over single-molecule localization microscopy (SMLM). The precision improvement of modulation enhanced SMLM is derived from retrieving the position of an emitter relative to individual illumination patterns, which adds to existing point spread function information from SMLM. Here, we introduce SpinFlux: modulation enhanced localization for spinning disk confocal microscopy. SpinFlux uses a spinning disk with pinholes in its illumination and emission paths, to sequentially illuminate regions in the sample during each measurement. The resulting intensity-modulated emission signal is analyzed for each individual pattern to localize emitters with improved precision. We derive a statistical image formation model for SpinFlux and we quantify the theoretical minimum localization uncertainty in terms of the Cramér-Rao lower bound. Using the theoretical minimum uncertainty, we compare SpinFlux to localization on Fourier reweighted image scanning microscopy reconstructions. We find that localization on image scanning microscopy reconstructions with Fourier reweighting ideally results in a global precision improvement of 2.1 over SMLM. When SpinFlux is used for sequential illumination with three patterns around the emitter position, the localization precision improvement over SMLM is twofold when patterns are focused around the emitter position. If four donut-shaped illumination patterns are used for SpinFlux, the maximum local precision improvement over SMLM is increased to 3.5. Localization of image scanning microscopy reconstructions thus has the largest potential for global improvements of the localization precision, where SpinFlux is the method of choice for local refinements.

ZIMFLUX: Single molecule localization microscopy with patterned illumination in 3D.

Three dimensional modulation-enhanced single-molecule localization techniques, such as ModLoc, offer advancements in axial localization precision across the entire field of view and axial capture range, by applying phase shifting to the illumination pattern. However, this improvement is limited by the pitch of the illumination pattern that can be used and requires registration between separate regions of the camera. To overcome these limitations, we present ZIMFLUX, a method that combines astigmatic point-spread-function (PSF) engineering with a structured illumination pattern in all three spatial dimensions. In order to achieve this we address challenges such as optical aberrations, refractive index mismatch, supercritical angle fluorescence (SAF), and imaging at varying depths within a sample, by implementing a vectorial PSF model. In scenarios involving refractive index mismatch between the sample and immersion medium, the astigmatic PSF loses its ellipticity at greater imaging depths, leading to a deterioration in axial localization precision. In contrast, our simulations demonstrate that ZIMFLUX maintains high axial localization precision even when imaging deeper into the sample. Experimental results show unbiased localization of 3D 80 nm DNA-origami nanostructures in SAF conditions with a 1.5-fold improvement in axial localization precision when comparing ZIMFLUX to conventional SMLM methods that rely solely on astigmatic PSF engineering.

Bayesian posterior density estimation reveals degeneracy in three-dimensional multiple emitter localization.

Single-molecule localization microscopy requires sparse activation of emitters to circumvent the diffraction limit. In densely labeled or thick samples, overlap of emitter images is inevitable. Single-molecule localization of these samples results in a biased parameter estimate with a wrong model of the number of emitters. On the other hand, multiple emitter fitting suffers from point spread function degeneracy, which increases model and parameter uncertainty. To better estimate the model, parameters and uncertainties, a three-dimensional Bayesian multiple emitter fitting algorithm was constructed using Reversible Jump Markov Chain Monte Carlo. It reconstructs the posterior density of both the model and the parameters, namely the three-dimensional position and photon intensity, of overlapping emitters. The ability of the algorithm to separate two emitters at varying distance was evaluated using an astigmatic point spread function. We found that for astigmatic imaging, the posterior distribution of the emitter positions is multimodal when emitters are within two times the in-focus standard deviation of the point spread function. This multimodality describes the ambiguity in position that astigmatism introduces in localization microscopy. Biplane imaging was also tested, proving capable of separating emitters up to 0.75 times the in-focus standard deviation of the point spread function while staying free of multimodality. The posteriors seen in astigmatic and biplane imaging demonstrate how the algorithm can identify point spread function degeneracy and evaluate imaging techniques for three-dimensional multiple-emitter fitting performance.

Laser-Induced Cavitation for Controlling Crystallization from Solution.

We demonstrate that a cavitation bubble initiated by a Nd:YAG laser pulse below breakdown threshold induces crystallization from supersaturated aqueous solutions with supersaturation and laser-energy-dependent nucleation kinetics. Combining high-speed video microscopy and simulations, we argue that a competition between the dissipation of absorbed laser energy as latent and sensible heat dictates the solvent evaporation rate and creates a momentary supersaturation peak at the vapor-liquid interface. The number and morphology of crystals correlate to the characteristics of the simulated supersaturation peak.

Low-cost acoustic force trap in a microfluidic channel.

A low-cost glass-based microfluidic flow cell with a piezo actuator is built using off-the-shelf parts (total cost €9 per device) to apply acoustophoretic force on polystyrene micro-beads. The main challenge in the fabrication of these devices was to ensure their leak tightness, which we solved using double-sided tape and nail polish. Beads with 1.5 µm diameter flowing in a 100 µm deep channel were trapped at 7.5 MHz using a 23.7 peak-to-peak voltage (Vpp) sinusoidal input. The trap located at 50 ± 0.1 µm depth was measured to have a stiffness of approximately 0.6 pN/µm. With this simple device we can trap and control the axial position of micrometer scale objects, which allows for the manipulation of beads and cells. We intend to use the device for force spectroscopy on micro-bead tethered DNA. This can be combined with super-resolution imaging techniques to study mechanics and binding of protein structures along a DNA strand as a function of induced tension.

Low-cost fluorescence microscope with microfluidic device fabrication for optofluidic applications.

Optofluidic devices have revolutionized the manipulation and transportation of fluid at smaller length scales ranging from micrometers to millimeters. We describe a dedicated optical setup for studying laser-induced cavitation inside a microchannel. In a typical experiment, we use a tightly focused laser beam to locally evaporate the solution laced with a dye resulting in the formation of a microbubble. The evolving bubble interface is tracked using high-speed microscopy and digital image analysis. Furthermore, we extend this system to analyze fluid flow through fluorescence-Particle Image Velocimetry (PIV) technique with minimal adaptations. In addition, we demonstrate the protocols for the in-house fabrication of a microchannel tailored to function as a sample holder in this optical setup. In essence, we present a complete guide for constructing a fluorescence microscope from scratch using standard optical components with flexibility in the design and at a lower cost compared to its commercial analogues.

Adaptive optics in single objective inclined light sheet microscopy enables three-dimensional localization microscopy in adult Drosophila brains.

Single-molecule localization microscopy (SMLM) enables the high-resolution visualization of organelle structures and the precise localization of individual proteins. However, the expected resolution is not achieved in tissue as the imaging conditions deteriorate. Sample-induced aberrations distort the point spread function (PSF), and high background fluorescence decreases the localization precision. Here, we synergistically combine sensorless adaptive optics (AO), in-situ 3D-PSF calibration, and a single-objective lens inclined light sheet microscope (SOLEIL), termed (AO-SOLEIL), to mitigate deep tissue-induced deteriorations. We apply AO-SOLEIL on several dSTORM samples including brains of adult Drosophila. We observed a 2x improvement in the estimated axial localization precision with respect to widefield without aberration correction while we used synergistic solution. AO-SOLEIL enhances the overall imaging resolution and further facilitates the visualization of sub-cellular structures in tissue.

SOLEIL: single-objective lens inclined light sheet localization microscopy.

High-NA light sheet illumination can improve the resolution of single-molecule localization microscopy (SMLM) by reducing the background fluorescence. These approaches currently require custom-made sample holders or additional specialized objectives, which makes the sample mounting or the optical system complex and therefore reduces the usability of these approaches. Here, we developed a single-objective lens-inclined light sheet microscope (SOLEIL) that is capable of 2D and 3D SMLM in thick samples. SOLEIL combines oblique illumination with point spread function PSF engineering to enable dSTORM imaging in a wide variety of samples. SOLEIL is compatible with standard sample holders and off-the-shelve optics and standard high NA objectives. To accomplish optimal optical sectioning we show that there is an ideal oblique angle and sheet thickness. Furthermore, to show what optical sectioning delivers for SMLM we benchmark SOLEIL against widefield and HILO microscopy with several biological samples. SOLEIL delivers in 15 µm thick Caco2-BBE cells a 374% higher intensity to background ratio and a 54% improvement in the estimated CRLB compared to widefield illumination, and a 184% higher intensity to background ratio and a 20% improvement in the estimated CRLB compared to HILO illumination.

Precision in iterative modulation enhanced single-molecule localization microscopy.

Modulation enhanced single-molecule localization microscopy (meSMLM) methods improve the localization precision by using patterned illumination to encode additional position information. Iterative meSMLM (imeSMLM) methods iteratively generate prior information on emitter positions, used to locally improve the localization precision during subsequent iterations. The Cramér-Rao lower bound cannot incorporate prior information to bound the best achievable localization precision because it requires estimators to be unbiased. By treating estimands as random variables with a known prior distribution, the Van Trees inequality (VTI) can be used to bound the best possible localization precision of imeSMLM methods. An imeSMLM method is considered, where the positions of in-plane standing-wave illumination patterns are controlled over the course of multiple iterations. Using the VTI, we analytically approximate a lower bound on the maximum localization precision of imeSMLM methods that make use of standing-wave illumination patterns. In addition, we evaluate the maximally achievable localization precision for different illumination pattern placement strategies using Monte Carlo simulations. We show that in the absence of background and under perfect modulation, the information content of signal photons increases exponentially as a function of the iteration count. However, the information increase is no longer exponential as a function of the iteration count under non-zero background, imperfect modulation, or limited mechanical resolution of the illumination positioning system. As a result, imeSMLM with two iterations reaches at most a fivefold improvement over SMLM at 8 expected background photons per pixel and 95% modulation contrast. Moreover, the information increase from imeSMLM is balanced by a reduced signal photon rate. Therefore, SMLM outperforms imeSMLM when considering an equal measurement time and illumination power per iteration. Finally, the VTI is an excellent tool for the assessment of the performance of illumination control and is therefore the method of choice for optimal design and control of imeSMLM methods.

Theoretical minimum uncertainty of single-molecule localizations using a single-photon avalanche diode array.

Single-photon avalanche diode (SPAD) arrays can be used for single-molecule localization microscopy (SMLM) because of their high frame rate and lack of readout noise. SPAD arrays have a binary frame output, which means photon arrivals should be described as a binomial process rather than a Poissonian process. Consequentially, the theoretical minimum uncertainty of the localizations is not accurately predicted by the Poissonian Cramér-Rao lower bound (CRLB). Here, we derive a binomial CRLB and benchmark it using simulated and experimental data. We show that if the expected photon count is larger than one for all pixels within one standard deviation of a Gaussian point spread function, the binomial CRLB gives a 46% higher theoretical uncertainty than the Poissonian CRLB. For typical SMLM photon fluxes, where no saturation occurs, the binomial CRLB predicts the same uncertainty as the Poissonian CRLB. Therefore, the binomial CRLB can be used to predict and benchmark localization uncertainty for SMLM with SPAD arrays for all practical emitter intensities.

Drift correction in localization microscopy using entropy minimization.

Localization microscopy offers resolutions down to a single nanometer but currently requires additional dedicated hardware or fiducial markers to reduce resolution loss from the drift of the sample. Drift estimation without fiducial markers is typically implemented using redundant cross correlation (RCC). We show that RCC has sub-optimal precision and bias, which leaves room for improvement. Here, we minimize a bound on the entropy of the obtained localizations to efficiently compute a precise drift estimate. Within practical compute-time constraints, simulations show a 5x improvement in drift estimation precision over the widely used RCC algorithm. The algorithm operates directly on fluorophore localizations and is tested on simulated and experimental datasets in 2D and 3D. An open source implementation is provided, implemented in Python and C++, and can utilize a GPU if available.

Structured illumination microscopy with noise-controlled image reconstructions.

Super-resolution structured illumination microscopy (SIM) has become a widely used method for biological imaging. Standard reconstruction algorithms, however, are prone to generate noise-specific artifacts that limit their applicability for lower signal-to-noise data. Here we present a physically realistic noise model that explains the structured noise artifact, which we then use to motivate new complementary reconstruction approaches. True-Wiener-filtered SIM optimizes contrast given the available signal-to-noise ratio, and flat-noise SIM fully overcomes the structured noise artifact while maintaining resolving power. Both methods eliminate ad hoc user-adjustable reconstruction parameters in favor of physical parameters, enhancing objectivity. The new reconstructions point to a trade-off between contrast and a natural noise appearance. This trade-off can be partly overcome by further notch filtering but at the expense of a decrease in signal-to-noise ratio. The benefits of the proposed approaches are demonstrated on focal adhesion and tubulin samples in two and three dimensions, and on nanofabricated fluorescent test patterns.

Selective dendritic localization of mRNA in Drosophila mushroom body output neurons.

Memory-relevant neuronal plasticity is believed to require local translation of new proteins at synapses. Understanding this process requires the visualization of the relevant mRNAs within these neuronal compartments. Here, we used single-molecule fluorescence in situ hybridization to localize mRNAs at subcellular resolution in the adult Drosophila brain. mRNAs for subunits of nicotinic acetylcholine receptors and kinases could be detected within the dendrites of co-labeled mushroom body output neurons (MBONs) and their relative abundance showed cell specificity. Moreover, aversive olfactory learning produced a transient increase in the level of CaMKII mRNA within the dendritic compartments of the γ5ß'2a MBONs. Localization of specific mRNAs in MBONs before and after learning represents a critical step towards deciphering the role of dendritic translation in the neuronal plasticity underlying behavioral change in Drosophila.

Anisoplanatic adaptive optics in parallelized laser scanning microscopy.

Inhomogeneities in the refractive index of a biological microscopy sample can introduce phase aberrations, severely impairing the quality of images. Adaptive optics can be employed to correct for phase aberrations and improve image quality. However, conventional adaptive optics can only correct a single phase aberration for the whole field of view (isoplanatic correction) while, due to the highly heterogeneous nature of biological tissues, the sample induced aberrations in microscopy often vary throughout the field of view (anisoplanatic aberration), limiting significantly the effectiveness of adaptive optics. This paper reports on a new approach for aberration correction in laser scanning confocal microscopy, in which a spatial light modulator is used to generate multiple excitation points in the sample to simultaneously scan different portions of the field of view with completely independent correction, achieving anisoplanatic compensation of sample induced aberrations, in a significantly shorter time compared to sequential isoplanatic correction of multiple image subregions. The method was tested in whole Drosophila brains and in larval Zebrafish, each showing a dramatic improvement in resolution and sharpness when compared to conventional isoplanatic adaptive optics.