Twin-Airy Point-Spread Function for Extended-Volume Particle Localization

Advances in Axial Resolution Strategies for Super-Resolution Imaging Systems

3D fluorescence super-resolution imaging technology can reconstruct the 3D structure of biological cells in space, which is crucial for observing the intricate internal structures of cells and studying the organization and function of tissues and organs. However, even with super-resolution imaging techniques that surpass the diffraction limit, the axial resolution typically only reaches one-third to one-half of the lateral resolution. Achieving true axial or 3D super-resolution imaging of samples remains a significant challenge. In light of this, this review summarizes the research progress in axial super-resolution imaging techniques, with a focus on the principles, developments, and characteristics of these techniques, and provides an outlook on their future development directions. This paper aims to provide valuable reference material for researchers in the field.

Tracking the extensive three-dimensional motion of single ions by an engineered point-spread function

Three-dimensional (3D) imaging of individual atoms is a critical tool for discovering new physical phenomena and developing new technologies in microscopic systems. However, the current single-atom-resolved 3D imaging methods are limited to static circumstances or a shallow detection range. Here, we demonstrate a generic dynamic 3D imaging method to track the extensive motion of single ions by exploiting the engineered point-spread function (PSF). We show that the image of a single ion can be engineered into a helical PSF, thus enabling single-snapshot acquisition of the position information of the ion in the trap. A preliminary application of this technique is demonstrated by recording the 3D motion trajectory of a single trapped ion and reconstructing the 3D dynamical configuration transition between the zig and zag structures of a 5-ion crystal. This work opens the path for studies on single-atom-resolved dynamics in both trapped-ion and neutral-atom systems.

Simultaneous spectral differentiation of multiple fluorophores in super-resolution imaging using a glass phase plate

By engineering the point-spread function (PSF) of single molecules, different fluorophore species can be imaged simultaneously and distinguished by their unique PSF patterns. Here, we insert a silicon-dioxide phase plate at the Fourier plane of the detection path of a wide-field fluorescence microscope to produce distinguishable PSFs (X-PSFs) at different wavelengths. We demonstrate that the resulting PSFs can be localized spatially and spectrally using a maximum-likelihood estimation algorithm and can be utilized for hyper-spectral super-resolution microscopy of biological samples. We produced superresolution images of fixed U2OS cells using X-PSFs for dSTORM imaging with simultaneous illumination of up to three fluorophore species. The species were distinguished only by the PSF pattern. We achieved ∼21-nm lateral localization precision (FWHM) and ∼17-nm axial precision (FWHM) with an average of 1,800 - 3,500 photons per PSF and a background as high as 130 - 400 photons per pixel. The modified PSF distinguished fluorescent probes with ∼80 nm separation between spectral peaks.

Airy-Gaussian vector beam and its application in generating flexible optical chains

In recent years, the manipulation of structured optical beam has become an attractive and promising area. The Gaussian beam is the most common beam as the output beam of the laser, and the Airy beam is recently proposed with fascinating properties and applications. In this paper, for the first time to our knowledge, the polarization is used as a tool to design a new kind of Airy-Gaussian vector beam by connecting the Gaussian and Airy functions, which opens a new avenue in designing new beams based on the existed beams. We realize the Airy-Gaussian vector beam with space-variant polarization distribution in theory and experiment, and find that the vector beam can autofocus twice during propagation. The optical chains with flexible intensity peaks are achieved with the Airy-Gaussian vector beam, which can be applied in trapping and delivering particles including biological cells and Rydberg atoms. Such optical chains can significantly improve the trapping efficiency, reduce the heat accumulation, and sweep away the impurity particles.

Double helix point spread function with variable spacing for precise 3D particle localization

To extend the axial depth of nanoscale 3D-localization microscopy, we propose here a splicing-type vortex singularities (SVS) phase mask, which has been meticulously optimized with a Fresnel approximation imaging inverse operation. The optimized SVS DH-PSF has proven to have high transfer function efficiency with adjustable performance in its axial range. The axial position of the particle was computed by using both the main lobes' spacing and the rotation angle, an improvement of the localization precision of the particle. Concretely, the proposed optimized SVS DH-PSF, with a smaller spatial extent, can effectively reduce the overlap of nanoparticle images and realize the 3D localization of multiple nanoparticles with small spacing, with respect to PSFs for large axial 3D localization. Finally, we successfully conducted extensive experiments on 3D localization for tracking dense nanoparticles at 8µm depth with a numerical aperture of 1.4, demonstrating its great potential.

Towards optimal point spread function design for resolving closely spaced emitters in three dimensions

The past decade has brought many innovations in optical design for 3D super-resolution imaging of point-like emitters, but these methods often focus on single-emitter localization precision as a performance metric. Here, we propose a simple heuristic for designing a point spread function (PSF) that allows for precise measurement of the distance between two emitters. We discover that there are two types of PSFs that achieve high performance for resolving emitters in 3D, as quantified by the Cramér-Rao bounds for estimating the separation between two closely spaced emitters. One PSF is very similar to the existing Tetrapod PSFs; the other is a rotating single-spot PSF, which we call the crescent PSF. The latter exhibits excellent performance for localizing single emitters throughout a 1-µm focal volume (localization precisions of 7.3 nm in x, 7.7 nm in y, and 18.3 nm in z using 1000 detected photons), and it distinguishes between one and two closely spaced emitters with superior accuracy (25-53% lower error rates than the best-performing Tetrapod PSF, averaged throughout a 1-µm focal volume). Our study provides additional insights into optimal strategies for encoding 3D spatial information into optical PSFs.

Snapshot volumetric imaging with engineered point-spread functions

The biological world involves intracellular and intercellular interactions that occur at high speed, at multiple scales and in three dimensions. Acquiring 3D images, however, typically requires a compromise in either spatial or temporal resolution compared to 2D imaging. Conventional 2D fluorescence imaging provides high spatial resolution but requires plane-by-plane imaging of volumes. Conversely, snapshot methods such as light-field microscopy allow video-rate imaging, but at the cost of spatial resolution. Here we introduce 3D engineered point-spread function microscopy (3D-EPM), enabling snapshot imaging of real-world 3D extended biological structures while retaining the native resolution of the microscope in space and time. Our new computational recovery strategy is the key to volumetrically reconstructing arbitrary 3D structures from the information encapsulated in 2D raw EPM images. We validate our technique on both point-like and extended samples, and demonstrate its power by imaging the intracellular motion of chloroplasts undergoing cyclosis in a sample of Egeria densa. Our technique represents a generalised computational methodology for 3D image recovery which is readily adapted to a diverse range of existing microscopy platforms and engineered point-spread functions. We therefore expect it to find broad applicability in the study of rapid biological dynamics in 3D.

Phase optimization algorithm for 3D particle localization with large axial depth

We propose an optimization algorithm based on Fresnel approximation (FA) imaging to optimize an extended-axial-depth point spread function (PSF) for 3D particle localization. The transfer function efficiency of the PSF is improved by repeatedly imposing constraints in the object plane, the spatial domain, and the Fourier domain. During the iterative calculation, the effective photon number or Cramer-Rao lower bound is used as the termination condition of the iteration. The algorithm allows flexible adjustment of the peak intensity ratio of the two main lobes. Moreover, the transfer function efficiency can be balanced by increasing the weight of the modulation function of the expected PSF at each axial position. The twin-Airy (TA) PSF optimized by the FA optimization algorithm does not require complex post-processing, whereas post-processing is an essential step for the unoptimized TA-PSF. The optimization algorithm is significant for extended-axial-depth PSFs used for 3D particle localization, as it improves localization precision and temporal resolution.

Three-dimensional diffusion coefficient measurement by a large depth-of-field rotating point spread function

A prominent challenge in single-molecule localization microscopy is the real-time, fast, and accurate localization of nano-objects moving in three-dimensional (3D) samples. A well-established method for 3D single-molecule localization is the double-helix pointspread-function (DH-PSF) engineering, which uses additional optical elements to make the PSF exhibit different rotation angles with different nanoparticle depths. However, the compact main lobe size, effective detection depth, and precise conversion between rotation angle and depth are necessary, posing challenges to the DH-PSF generation method. Here we generate a more compact DH-PSF using Fresnel-zone-based spiral phases, and the pure phase mask achieves high transmission efficiency. The final generated DH-PSFs have a linear rotation rate at each axial position, showing a more accurate rotation angle and depth conversion. The Cramer-Rao lower limit calculation results show that the axial depth of DH-PSF extends to ∼11µm with an axial localization precision of ∼45nm at 3000 photons and average background noise of 15. We measured the diffusion coefficient of nanospheres in different concentrations of glycerol using the generated DH-PSF. The measured results are within 6% error from the theoretical values, indicating the superior performance of the DH-PSF for nanoparticle diffusion coefficient measurements.

Splicing exponential point spread function design for localization of nanoparticles

We propose a point spread function for three-dimensional localization of nanoparticles. The axial detection range of the point spread function can be simply changed by adjusting the design parameters. In addition, the spatial extent of the point spread function can also be changed by adjusting the design parameters, which is an advantage other point spread functions do not have. We used our point spread functions and the existing point spread functions for dense multi-particle imaging, which proved the advantage that the point spread function with a smaller spatial extent we designed can effectively reduce the overlap between the point spread functions. The three-dimensional process of the fluorescent microsphere penetrating HT-22 cell membrane was successfully recorded, which verified the effectiveness of this method.

Particles 3D tracking with large axial depth by using the 2π-DH-PSF

We propose a 2π-double-helix point spread function (2π-DH-PSF) using the Fresnel zone approach that can rotate 2π rad. When 16 Fresnel zones are used, the particles can be tracked in the axial range of 10 µm in a 100× microscopy imaging system (NA=1.4, λ=514nm). We measured the diffusion coefficient of nanospheres in different concentrations of glycerol with the 2π-DH-PSF, and the error between the measured results and theoretical value was within 10%, indicating the superior performance of 2π-DH-PSF in 3D localization imaging of nanoparticles. When combined with the defocus phase, the rotation angle can reach 4π rad, four times that of the conventional DH-PSF.

Refractive Index Modulation in Monolayer Molybdenum Diselenide

Two-dimensional transition metal dichalcogenides are promising candidates for ultrathin light modulators due to their highly tunable excitonic resonances at visible and near-infrared wavelengths. At cryogenic temperatures, large excitonic reflectivity in monolayer molybdenum diselenide (MoSe₂) has been shown, but the permittivity and index modulation have not been studied. Here, we demonstrate large gate-tunability of complex refractive index in monolayer MoSe₂ by Fermi level modulation and study the doping dependence of the A and B excitonic resonances for temperatures between 4 and 150 K. By tuning the charge density, we observe both temperature- and carrier-dependent epsilon-near-zero response in the permittivity and transition from metallic to dielectric near the A exciton energy. We attribute the dynamic control of the refractive index to the interplay between radiative and non-radiative decay channels that are tuned upon gating. Our results suggest the potential of monolayer MoSe₂ as an active material for emerging photonics applications.

Axially resolved volumetric two-photon microscopy with an extended field of view using depth localization under mirrored Airy beams

It is a great challenge in two-photon microscopy (2PM) to have a high volumetric imaging speed without sacrificing the spatial and temporal resolution in three dimensions (3D). The structure in 2PM images could be reconstructed with better spatial and temporal resolution by the proper choice of the data processing algorithm. Here, we propose a method to reconstruct 3D volume from 2D projections imaged by mirrored Airy beams. We verified that our approach can achieve high accuracy in 3D localization over a large axial range and is applicable to continuous and dense sample. The effective field of view after reconstruction is expanded. It is a promising technique for rapid volumetric 2PM with axial localization at high resolution.

Ultraprecise Rydberg atomic localization using optical vortices

We propose a robust localization of the highly-excited Rydberg atoms interacting with doughnut-shaped optical vortices. Compared with the earlier standing-wave (SW)-based localization methods, a vortex beam can provide an ultraprecise two-dimensional localization solely in the zero-intensity center, within a confined excitation region down to the nanometer scale. We show that the presence of the Rydberg-Rydberg interaction permits counter-intuitively much stronger confinement towards a high spatial resolution when it is partially compensated by a suitable detuning. In addition, applying an auxiliary SW modulation to the two-photon detuning allows a three-dimensional confinement of Rydberg atoms. In this case, the vortex field provides a transverse confinement, while the SW modulation of the two-photon detuning localizes the Rydberg atoms longitudinally. To develop a new subwavelength localization technique, our results pave a path one step closer to reducing excitation volumes to the level of a few nanometers, representing a feasible implementation for the future experimental applications.