Subnanometer localization accuracy in widefield optical microscopy

Traceable localization enables accurate integration of quantum emitters and photonic structures with high yield

In a popular integration process for quantum information technologies, localization microscopy of quantum emitters guides lithographic placement of photonic structures. However, a complex coupling of microscopy and lithography errors degrades registration accuracy, severely limiting device performance and process yield. We introduce a methodology to solve this widespread but poorly understood problem. A new foundation of traceable localization enables rapid characterization of lithographic standards and comprehensive calibration of cryogenic microscopes, revealing and correcting latent systematic effects. Of particular concern, we discover that scale factor deviation and complex optical distortion couple to dominate registration errors. These novel results parameterize a process model for integrating quantum dots and bullseye resonators, predicting higher yield by orders of magnitude, depending on the Purcell factor threshold as a quantum performance metric. Our foundational methodology is a key enabler of the lab-to-fab transition of quantum information technologies and has broader implications to cryogenic and correlative microscopy.

Large-FOV 3D localization microscopy by spatially variant point spread function generation

Accurate characterization of the microscopic point spread function (PSF) is crucial for achieving high-performance localization microscopy (LM). Traditionally, LM assumes a spatially invariant PSF to simplify the modeling of the imaging system. However, for large fields of view (FOV) imaging, it becomes important to account for the spatially variant nature of the PSF. Here, we propose an accurate and fast principal components analysis-based field-dependent 3D PSF generator (PPG3D) and localizer for LM. Through simulations and experimental three-dimensional (3D) single-molecule localization microscopy (SMLM), we demonstrate the effectiveness of PPG3D, enabling super-resolution imaging of mitochondria and microtubules with high fidelity over a large FOV. A comparison of PPG3D with a shift-variant PSF generator for 3D LM reveals a threefold improvement in accuracy. Moreover, PPG3D is approximately 100 times faster than existing PSF generators, when used in image plane-based interpolation mode. Given its user-friendliness, we believe that PPG3D holds great potential for widespread application in SMLM and other imaging modalities.

Motion screening of fiducial marker for improved localization precision and resolution in SMLM

Single-molecule localization microscopy (SMLM) provides unmatched high resolution but relies on accurate drift correction due to the long acquisition time for each field of view. A popular drift correction is implemented via referencing to fiducial markers that are assumed to be firmly immobilized and remain stationary relative to the imaged sample. However, there is so far lack of efficient approaches for evaluating other motions except sample drifting of immobilized markers and for addressing their potential impacts on images. Here, we developed a new approach for quantitatively assessing the motions of fiducial markers relative to the sample via mean squared displacement (MSD) analysis. Our findings revealed that over 90% of immobilized fluorescent beads in the SMLM imaging buffer exhibited higher MSDs compared to stationary beads in dry samples and displayed varying degrees of wobbling relative to the imaged field. By excluding extremely high-MSD beads in each field from drift correction, we optimized drift correction and experimentally measured localization precision. In SMLM experiments of cellular microtubules, we also found that including only relatively low-MSD beads for drift correction significantly improved the image resolution and quality. Our study presents a simple and effective approach to assess the potential relative motions of fiducial markers and emphasizes the importance of pre-screening fiducial markers for improved image quality and resolution in SMLM imaging.

Unmasking the Resolution-Throughput Tradespace of Focused-Ion-Beam Machining

Focused-ion-beam machining is a powerful process to fabricate complex nanostructures, often through a sacrificial mask that enables milling beyond the resolution limit of the ion beam. However, current understanding of this super-resolution effect is empirical in the spatial domain and nonexistent in the temporal domain. This article reports the primary study of this fundamental tradespace of resolution and throughput. Chromia functions well as a masking material due to its smooth, uniform, and amorphous structure. An efficient method of in-line metrology enables characterization of ion-beam focus by scanning electron microscopy. Fabrication and characterization of complex test structures through chromia and into silica probe the response of the bilayer to a focused beam of gallium cations, demonstrating super-resolution factors of up to 6 ± 2 and improvements to volume throughput of at least factors of 42 ± 2, with uncertainties denoting 95% coverage intervals. Tractable theory models the essential aspects of the super-resolution effect for various nanostructures. Application of the new tradespace increases the volume throughput of machining Fresnel lenses by a factor of 75, enabling the introduction of projection standards for optical microscopy. These results enable paradigm shifts of sacrificial masking from empirical to engineering design and from prototyping to manufacturing.

Photon-free (s)CMOS camera characterization for artifact reduction in high- and super-resolution microscopy

Modern implementations of widefield fluorescence microscopy often rely on sCMOS cameras, but this camera architecture inherently features pixel-to-pixel variations. Such variations lead to image artifacts and render quantitative image interpretation difficult. Although a variety of algorithmic corrections exists, they require a thorough characterization of the camera, which typically is not easy to access or perform. Here, we developed a fully automated pipeline for camera characterization based solely on thermally generated signal, and implemented it in the popular open-source software Micro-Manager and ImageJ/Fiji. Besides supplying the conventional camera maps of noise, offset and gain, our pipeline also gives access to dark current and thermal noise as functions of the exposure time. This allowed us to avoid structural bias in single-molecule localization microscopy (SMLM), which without correction is substantial even for scientific-grade, cooled cameras. In addition, our approach enables high-quality 3D super-resolution as well as live-cell time-lapse microscopy with cheap, industry-grade cameras. As our approach for camera characterization does not require any user interventions or additional hardware implementations, numerous correction algorithms that rely on camera characterization become easily applicable.

Sub-picoliter Traceability of Microdroplet Gravimetry and Microscopy

Gravimetry typically lacks the resolution to measure single microdroplets, whereas microscopy is often inaccurate beyond the resolution limit. To address these issues, we advance and integrate these complementary methods, introducing simultaneous measurements of the same microdroplets, comprehensive calibrations that are independently traceable to the International System of Units (SI), and Monte-Carlo evaluations of volumetric uncertainty. We achieve sub-picoliter agreement of measurements of microdroplets in flight with volumes of approximately 70 pL, with ensemble gravimetry and optical microscopy both yielding 95% coverage intervals of ±0.6 pL, or relative uncertainties of ±0.9%, and root-mean-square deviations of mean values between the two methods of 0.2 pL or 0.3%. These uncertainties match previous gravimetry results and improve upon previous microscopy results by an order of magnitude. Gravimetry precision depends on the continuity of droplet formation, whereas microscopy accuracy requires that optical diffraction from an edge reference matches that from a microdroplet. Applying our microscopy method, we jet and image water microdroplets suspending fluorescent nanoplastics, count nanoplastic particles after deposition and evaporation, and transfer volumetric traceability to the number concentrations of single microdroplets. We expect that our methods will impact diverse fields involving dimensional metrology and volumetric analysis of microdroplets, including inkjet microfabrication, disease transmission, and industrial sprays.

Accurate measurement of the photonic crystal slab period using diffraction in the Littrow configuration

Photonic crystal slab devices with subwavelength periods can be tailored to provide remarkable functionality, such as ultrahigh reflectivity in a structure only 200 nm in thickness. Accurate measurement of the characteristics of these structures is essential to compare their performance to theoretical expectations and to better understand the origin of unexpected behavior. In this work, we present a simple non-invasive method employing diffraction of a visible wavelength reference in the Littrow configuration for measuring the period of a photonic crystal slab. We have measured periods of our devices with uncertainty below 0.5 nm and expect that the uncertainty could easily be improved by an order of magnitude. In addition to facilitating development, our approach can be used to explore possible variations in the period of the photonic crystal due to its operating environment and aging.

Accurate localization microscopy by intrinsic aberration calibration

A standard paradigm of localization microscopy involves extension from two to three dimensions by engineering information into emitter images, and approximation of errors resulting from the field dependence of optical aberrations. We invert this standard paradigm, introducing the concept of fully exploiting the latent information of intrinsic aberrations by comprehensive calibration of an ordinary microscope, enabling accurate localization of single emitters in three dimensions throughout an ultrawide and deep field. To complete the extraction of spatial information from microscale bodies ranging from imaging substrates to microsystem technologies, we introduce a synergistic concept of the rigid transformation of the positions of multiple emitters in three dimensions, improving precision, testing accuracy, and yielding measurements in six degrees of freedom. Our study illuminates the challenge of aberration effects in localization microscopy, redefines the challenge as an opportunity for accurate, precise, and complete localization, and elucidates the performance and reliability of a complex microelectromechanical system.

Characterizing and correcting camera noise in back-illuminated sCMOS cameras

With promising properties of fast imaging speed, large field-of-view, relative low cost and many others, back-illuminated sCMOS cameras have been receiving intensive attention for low light level imaging in the past several years. However, due to the pixel-to-pixel difference of camera noise (called noise non-uniformity) in sCMOS cameras, researchers may hesitate to use them in some application fields, and sometimes wonder whether they should optimize the noise non-uniformity of their sCMOS cameras before using them in a specific application scenario. In this paper, we systematically characterize the impact of different types of sCMOS noise on image quality and perform corrections to these types of sCMOS noise using three representative algorithms (PURE, NCS and MLE_sCMOS). We verify that it is possible to use appropriate correction methods to push the non-uniformity of major types of camera noise, including readout noise, offset, and photon response, to a satisfactory level for conventional microscopy and single molecule localization microscopy. We further find out that, after these corrections, global read noise becomes a major concern that limits the imaging performance of back-illuminated sCMOS cameras. We believe this study provides new insights into the understanding of camera noise in back-illuminated sCMOS cameras, and also provides useful information for future development of this promising camera technology.

Microscope calibration protocol for single-molecule microscopy

Single-molecule microscopy allows for the investigation of the dynamics of individual molecules and the visualization of subcellular structures at high spatial resolution. For single-molecule imaging experiments, and particularly those that entail the acquisition of multicolor data, calibration of the microscope and its optical components therefore needs to be carried out at a high level of accuracy. We propose here a method for calibrating a microscope at the nanometer scale, in the sense of determining optical aberrations as revealed by point source localization errors on the order of nanometers. The method is based on the imaging of a standard sample to detect and evaluate the amount of geometric aberration introduced in the optical light path. To provide support for multicolor imaging, it also includes procedures for evaluating the geometric aberration caused by a dichroic filter and the axial chromatic aberration introduced by an objective lens.

Quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy

The resolution and accuracy of single-molecule localization microscopes (SMLMs) are routinely benchmarked using simulated data, calibration rulers, or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of reconstructed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm.

Standard benchmarking of single-molecule localization microscopy cannot quantify nanoscale accuracy of arbitrary datasets. Here, the authors present Wasserstein-induced flux, a method using a chosen perturbation and knowledge of the imaging system to measure confidence of individual localizations.

Strongly confined atomic localization by Rydberg coherent population trapping

We investigate the possibility to attain strongly confined atomic localization using interacting Rydberg atoms in a coherent population trapping ladder configuration, where a standing-wave is used as a coupling field in the second leg of the ladder. Depending on the degree of compensation for the Rydberg level energy shift induced by the van der Waals interaction, by the coupling field detuning, we distinguish between two antiblockade regimes, i.e., a partial antiblockade (PA) and a full antiblockade. While a periodic pattern of tightly localized regions can be achieved for both regimes, the PA allows much faster convergence of spatial confinement, yielding a high-resolution Rydberg state-selective superlocalization regime for higher-lying Rydberg levels. In comparison, for lower-lying Rydberg levels, the PA leads to an anomalous change of spectra linewidth, confirming the importance of using a stable uppermost state to achieve a superlocalization regime.

Correcting Artifacts in Single Molecule Localization Microscopy Analysis Arising from Pixel Quantum Efficiency Differences in sCMOS Cameras

Optimal analysis of single molecule localization microscopy (SMLM) data acquired with a scientific Complementary Metal-Oxide-Semiconductor (sCMOS) camera relies on statistical compensation for its pixel-dependent gain, offset and readout noise. In this work we show that it is also necessary to compensate for differences in the relative quantum efficiency (RQE) of each pixel. We found differences in RQE on the order of 4% in our tested sCMOS sensors. These differences were large enough to have a noticeable effect on analysis algorithm results, as seen both in simulations and biological imaging data. We discuss how the RQE differences manifest themselves in the analysis results and present the modifications to the Poisson maximum likelihood estimation (MLE) sCMOS analysis algorithm that are needed to correct for the RQE differences.

Nanomotor tracking experiments at the edge of reproducibility

The emerging field of self-propelling micro/nanorobots is teeming with a wide variety of novel micro/nanostructures, which are tested here for self-propulsion in a liquid environment. As the size of these microscopic movers diminishes into the fully nanosized region, the ballistic paths of an active micromotor become a random walk of colloidal particles. To test such colloidal samples for self-propulsion, the commonly adopted "golden rule" is to refer to the mean squared displacement (MSD) function of the measured particle tracks. The practical significance of the result strongly depends on the amount of collected particle data and the sampling rate of the particle track. Because micro/nanomotor preparation methods are mostly low-yield, the amount of used experimental data in published results is often on the edge of reproducibility. To address the situation, we perform MSD analysis on an experimental as well as simulated dataset. These data are used to explore the effects of MSD analysis on limited data and several situations where the lack of data can lead to insignificant results.

3D super-resolution microscopy performance and quantitative analysis assessment using DNA-PAINT and DNA origami test samples

Assessment of the imaging quality in localisation-based super-resolution techniques relies on an accurate characterisation of the imaging setup and analysis procedures. Test samples can provide regular feedback on system performance and facilitate the implementation of new methods. While multiple test samples for regular, 2D imaging are available, they are not common for more specialised imaging modes. Here, we analyse robust test samples for 3D and quantitative super-resolution imaging, which are straightforward to use, are time- and cost-effective and do not require experience beyond basic laboratory and imaging skills. We present two options for assessment of 3D imaging quality, the use of microspheres functionalised for DNA-PAINT and a commercial DNA origami sample. A method to establish and assess a qPAINT workflow for quantitative imaging is demonstrated with a second, commercially available DNA origami sample.

Geometric-Phase Microscopy for Quantitative Phase Imaging of Isotropic, Birefringent and Space-Variant Polarization Samples

We present geometric-phase microscopy allowing a multipurpose quantitative phase imaging in which the ground-truth phase is restored by quantifying the phase retardance. The method uses broadband spatially incoherent light that is polarization sensitively controlled through the geometric (Pancharatnam-Berry) phase. The assessed retardance possibly originates either in dynamic or geometric phase and measurements are customized for quantitative mapping of isotropic and birefringent samples or multi-functional geometric-phase elements. The phase restoration is based on the self-interference of polarization distinguished waves carrying sample information and providing pure reference phase, while passing through an inherently stable common-path setup. The experimental configuration allows an instantaneous (single-shot) phase restoration with guaranteed subnanometer precision and excellent ground-truth accuracy (well below 5 nm). The optical performance is demonstrated in advanced yet routinely feasible noninvasive biophotonic imaging executed in the automated manner and predestined for supervised machine learning. The experiments demonstrate measurement of cell dry mass density, cell classification based on the morphological parameters and visualization of dynamic dry mass changes. The multipurpose use of the method was demonstrated by restoring variations in the dynamic phase originating from the electrically induced birefringence of liquid crystals and by mapping the geometric phase of a space-variant polarization directed lens.

Particle Tracking of Microelectromechanical System Performance and Reliability

Microelectromechanical systems (MEMS) that require contact of moving parts to implement complex functions exhibit limits to their performance and reliability. Here, we advance our particle tracking method to measure MEMS motion in operando at nanometer, microradian, and millisecond scales. We test a torsional ratcheting actuator and observe dynamic behavior ranging from nearly perfect repeatability, to transient feedback and stiction, to terminal failure. This new measurement capability will help to understand and improve MEMS motion.