Double-helix Point Spread Function Research Articles

Long-Axial-Range Double-Helix Point Spread Functions for 3D Volumetric Super-Resolution Imaging.

Single-molecule localization microscopy (SMLM) is a powerful tool for observing structures beyond the diffraction limit of light. Combining SMLM with engineered point spread functions (PSFs) enables 3D imaging over an extended axial range, as has been demonstrated for super-resolution imaging of various cellular structures. However, super-resolving structures in 3D in thick samples, such as whole mammalian cells, remains challenging as it typically requires acquisition and postprocessing stitching of multiple slices to cover the entire sample volume or more complex analysis of the data. Here, we demonstrate how the imaging and analysis workflows can be simplified by 3D single-molecule super-resolution imaging with long-axial-range double-helix (DH)-PSFs. First, we experimentally benchmark the localization precisions of short- and long-axial-range DH-PSFs at different signal-to-background ratios by imaging fluorescent beads. The performance of the DH-PSFs in terms of achievable resolution and imaging speed was then quantified for 3D single-molecule super-resolution imaging of mammalian cells by DNA-PAINT imaging of nuclear lamina protein lamin B1 in U-2 OS cells. Furthermore, we demonstrate how the use of a deep-learning-based algorithm allows the localization of dense emitters, drastically improving the achievable imaging speed and resolution. Our data demonstrate that using long-axial-range DH-PSFs offers stitching-free, 3D super-resolution imaging of whole mammalian cells, simplifying the experimental and analysis procedures for obtaining volumetric nanoscale structural information.

2π double-helix point spread function based on ring segmentation method for nanoparticle tracking technique

2π double-helix point spread function based on ring segmentation method for nanoparticle tracking technique

Single-Shot 3D Imaging Meta-Microscope.

Three-dimensional (3D) imaging enables high-precision and high-resolution axial positioning, which is crucial for biological imaging, semiconductor defect monitoring, and other applications. Conventional implementations rely on bulky optical elements or scanning mechanisms, resulting in low speed and complicated setups. Here, we generate the double-helix (DH) point spread function with an all-dielectric metasurface and thus innovate the 3D imaging microscope (hence dubbed meta-microscope), both in 4f and 2f imaging systems. The 4f-meta-microscope with a numerical aperture of 0.7 achieves an axial localization accuracy below 0.12 μm within a 15.47 μm detection range, while the 2f-DH meta-microscope with a numerical aperture of 0.3 shows a 1.12 μm accuracy within a 227.33 μm range. We also demonstrate single-shot and accurate 3D biological imaging of the mouse kidney tissue and peach anther, providing a comprehensive and efficient approach for 3D bioimaging and other applications through a single-shot 3D meta-microscope.

3D-3C measurements of flow reversal in small sessile drops in shear flow

Sessile drops play an important role in nature and the operation of many technical and biological systems as for instance fuel cells, cleaning processes, lab-on-a-chip devices and single-cell analysis. Nonetheless, their dynamic behaviour in a shear flow is still not fully understood (e. g. detachment mechanism). Challenges exist regarding the precise simulation of two-phase flows as well as difficulties in conducting flow measurements with sufficient temporal resolution of more than 1 kHz. In this article, we present the first three-dimensional flow measurements in strongly oscillating drops stemming from a shear flow by using a monocular 3D localization microscope based on a Double-Helix Point Spread Function combined with Particle Tracking Velocimetry. The high temporal resolution and the large measurement volume - in terms of microscopy - make it possible to measure the time- and phase-averaged flow in small drops with Bond numbers (Bo) smaller than 1. Water drops were placed in an air flow channel and measurements were conducted for Reynolds numbers (Red) from about 750 to 1700. Our measurements show that the results of previous investigations for drops with Bo>1 concerning vortex pattern and flow reversal inside the drop apply for smaller drops as well. In addition, we are able to reveal the three-dimensional flow structure and multiple vortex-pattern in time and space. We discover a periodic 3D vortical flow pattern that corresponds to the first and second eigenfrequency of the drop. Moreover, we demonstrate the potential of adaptive optics to correct measurement errors stemming from time-varying light refraction when conducting measurements through the fluctuating drop surface, in particular for opaque substrates. The results may help in understanding the coupling of inner and outer flow for sessile drops in shear flow which allows for an analysis of the onset motion of these drops, i.e. drop removal. Removal of sessile drops plays a crucial role in many applications, which includes among other things the water management of fuel cells where small drops with Bo<1 predominantly occur.

One-dimensional photonic crystal enhancing spin-to-orbital angular momentum conversion for single-particle tracking

Single-particle tracking (SPT) is an immensely valuable technique for studying a variety of processes in the life sciences and physics. It can help researchers better understand the positions, paths, and interactions of single objects in systems that are highly dynamic or require imaging over an extended time. Here, we propose an all-dielectric one-dimensional photonic crystal (1D PC) that enhances spin-to-orbital angular momentum conversion for three-dimensional (3D) SPTs. This well-designed 1D PC can work as a substrate for optical microscopy. We introduce this effect into the interferometric scattering (iSCAT) technique, resulting in a double-helix point spread function (DH-PSF). DH-PSF provides more uniform Fisher information for 3D position estimation than the PSFs of conventional microscopy, such as encoding the axial position of a single particle in the angular orientation of DH-PSF lobes, thus providing a means for 3D SPT. This approach can address the challenge of iSCAT in 3D SPT because DH-PSF iSCAT will not experience multiple contrast inversions when a single particle travels along the axial direction. DH-PSF iSCAT microscopy was used to record the 3D trajectory of a single microbead attached to the flagellum, facilitating precise analysis of fluctuations in motor dynamics. Its ability to track single nanoparticles, such as 3D diffusion trajectories of 20 nm gold nanoparticles in glycerol solution, was also demonstrated. The DH-PSF iSCAT technique enabled by a 1D PC holds potential promise for future applications in physical, biological, and chemical science.

Revealing the 3D nanoscale organization of MyosinH in the apical complex of toxoplasma gondii through single-molecule localization microscopy with the double-helix point spread function

Revealing the 3D nanoscale organization of MyosinH in the apical complex of toxoplasma gondii through single-molecule localization microscopy with the double-helix point spread function

PS 2 F: Polarized Spiral Point Spread Function for Single-Shot 3D Sensing.

We propose a compact snapshot monocular depth estimation technique that relies on an engineered point spread function (PSF). Traditional approaches used in microscopic super-resolution imaging such as the Double-Helix PSF (DHPSF) are ill-suited for scenes that are more complex than a sparse set of point light sources. We show, using the Cramér-Rao lower bound, that separating the two lobes of the DHPSF and thereby capturing two separate images leads to a dramatic increase in depth accuracy. A special property of the phase mask used for generating the DHPSF is that a separation of the phase mask into two halves leads to a spatial separation of the two lobes. We leverage this property to build a compact polarization-based optical setup, where we place two orthogonal linear polarizers on each half of the DHPSF phase mask and then capture the resulting image with a polarization-sensitive camera. Results from simulations and a lab prototype demonstrate that our technique achieves up to 50% lower depth error compared to state-of-the-art designs including the DHPSF and the Tetrapod PSF, with little to no loss in spatial resolution.

Multifocus double-helix point spread function microscopy for 3D single particle tracking

Double-helix point spread function (DH-PSF) microscopy can realize three-dimensional single particle tracking (3D SPT) on a nanoscale, and is widely used in life sciences and other fields. However, its imaging depth-of-field (DOF) and localization accuracy are limited, which hinders its application in thick samples in vivo. To address this issue, this paper proposes a z-splitter prism-based multifocus DH-PSF microscopy (ZPMDM) method and system to improve the DOF and localization accuracy of DH-PSF microscopy without scanning. It solves the problem of large DOF detection of 3D SPT in whole living cells. By means of systematic calibration, the average 3D localization accuracies of three channels of ZPMDM are determined to be &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;L(&lt;i&gt;x, y, z&lt;/i&gt;)&lt;/sub&gt; = (4.4 nm, 4.6 nm, 10.5 nm), &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;M(&lt;i&gt;x, y, z&lt;/i&gt;)&lt;/sub&gt; = (4.3 nm, 4.2 nm, 8.2 nm), and &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;R(&lt;i&gt;x, y, z&lt;/i&gt;)&lt;/sub&gt; = (4.8 nm, 4.4 nm, 10.3 nm). And the effective DOF of the system is extended to 6 μm. Furthermore, the ZPMDM system is used to track fluorescent microspheres in a glycerol-water mixture across a large depth-of-field range. The Brownian motion of the fluorescent microspheres in the mixture solution is also investigated. The experimental results demonstrate that the errors between the experimentally obtained diffusion coefficients and the theoretically calculated diffusion coefficients are all within 10%. The reliability of the ZPMDM system in achieving single-particle 3D tracking imaging is verified in this study. The validity of the method is further verified by preliminarily investigating the phagocytosis phenomenon of live macrophages. It is of significance for the development and application of nanoscale 3D SPT. The ZPMDM system is shown in the attached figure.

Similarly slow diffusion of BAM and SecYEG complexes in live E. coli cells observed with 3D spt-PALM

The β-barrel assembly machinery (BAM) complex is responsible for inserting outer membrane proteins (OMPs) into the Escherichia coli outer membrane. The SecYEG translocon inserts inner membrane proteins into the inner membrane and translocates both soluble proteins and nascent OMPs into the periplasm. Recent reports describe Sec possibly playing a direct role in OMP biogenesis through interactions with the soluble polypeptide transport-associated (POTRA) domains of BamA (the central OMP component of BAM). Here we probe the diffusion behavior of these protein complexes using photoactivatable super-resolution localization microscopy and single-particle tracking in live E. coli cells of BAM and SecYEG components BamA and SecE and compare them to other outer and inner membrane proteins. To accurately measure trajectories on the highly curved cell surface, three-dimensional tracking was performed using double-helix point-spread function microscopy. All proteins tested exhibit two diffusive modes characterized by “slow” and “fast” diffusion coefficients. We implement a diffusion coefficient analysis as a function of the measurement lag time to separate positional uncertainty from true mobility. The resulting true diffusion coefficients of the slow and fast modes showed a complete immobility of full-length BamA constructs in the time frame of the experiment, whereas the OMP OmpLA displayed a slow diffusion consistent with the high viscosity of the outer membrane. The periplasmic POTRA domains of BamA were found to anchor BAM to other cellular structures and render it immobile. However, deletion of individual distal POTRA domains resulted in increased mobility, suggesting that these domains are required for the full set of cellular interactions. SecE diffusion was much slower than that of the inner membrane protein PgpB and was more like OMPs and BamA. Strikingly, SecE diffused faster upon POTRA domain deletion. These results are consistent with the existence of a BAM-SecYEG trans-periplasmic assembly in live E. coli cells.

Combining CdTe/CdS/ZnS Quantum Dot Fluorescence Temperature Measurements with Double-Helix Point Spread Function Axial Location for Intracellular 3D Thermograms

Combining CdTe/CdS/ZnS Quantum Dot Fluorescence Temperature Measurements with Double-Helix Point Spread Function Axial Location for Intracellular 3D Thermograms

Imaging and positioning through scattering media with double-helix point spread function engineering.

Double-helix point spread function (DH-PSF) microscopy has been developed for three-dimensional (3D) localization and imaging at super-resolution but usually in environments with no or weak scattering. To date, super-resolution imaging through turbid media has not been reported. We aim to explore the potential of DH-PSF microscopy in the imaging and localization of targets in scattering environments for improved 3D localization accuracy and imaging quality. The conventional DH-PSF method was modified to accommodate the scanning strategy combined with a deconvolution algorithm. The localization of a fluorescent microsphere is determined by the center of the corresponding double spot, and the image is reconstructed from the scanned data by deconvoluting the DH-PSF. The resolution, i.e., the localization accuracy, was calibrated to 13nm in the transverse plane and 51nm in the axial direction. Penetration thickness could reach an optical thickness (OT) of 5. Proof-of-concept imaging and the 3D localization of fluorescent microspheres through an eggshell membrane and an inner epidermal membrane of an onion are presented to demonstrate the super-resolution and optical sectioning capabilities. Modified DH-PSF microscopy can image and localize targets buried in scattering media using super-resolution. Combining fluorescent dyes, nanoparticles, and quantum dots, among other fluorescent probes, the proposed method may provide a simple solution for visualizing deeper and clearer in/through scattering media, making in situ super-resolution microscopy possible for various demanding applications.

Monocular depth sensing using metalens

Abstract3-D depth sensing is essential for many applications ranging from consumer electronics to robotics. Passive depth sensing techniques based on a double-helix (DH) point-spread-function (PSF) feature high depth estimation precision, minimal power consumption, and reduced system complexity compared to active sensing methods. Here, we propose and experimentally implemented a polarization-multiplexed DH metalens designed using an autonomous direct search algorithm, which utilizes two contra-rotating DH PSFs encoded in orthogonal polarization states to enable monocular depth perception. Using a reconstruction algorithm that we developed, concurrent depth calculation and scene reconstruction with minimum distortion and high resolution in all three dimensions were demonstrated.

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.

Multi-target 3D single-molecule super resolution imaging throughout mammalian cells with a single-objective tilted light sheet.

Single-molecule based super-resolution fluorescence microscopy offers an approach to sub-diffraction-limited imaging of biological samples. While these approaches have proved significant to understanding subcellular structures, numerous super-resolution systems suffer from drawbacks such as decreased localization precision due to high background fluorescence, lack of control of the extracellular environment, decreased multi-target accuracy due to chromatic offsets in multicolor imaging, and the inability to image structures in three dimensions (3D). Light sheet fluorescence microscopy, which involves illuminating the sample with a thin sheet of light, offers a gentle illumination scheme that greatly reduces photobleaching, photodamage, and out of focus background fluorescence, thereby improving the localization precision. Here, we present a single-objective tilted light sheet super-resolution setup with five added innovations: (i) a microfluidic chip with reflective sidewalls and transparent top, (ii) sequential DNA Point Accumulation for Imaging in Nanoscale Topography (DNA-PAINT) known as Exchange-PAINT, (iii) deep learning for high density single emitter localization, (iv) double helix point spread functions for 3D imaging, and (iv) galvanometric dithering of the illumination beam to reduce scattering artifacts and provide homogenous sample illumination. By utilizing light sheet illumination in conjunction with Exchange-PAINT and deep learning, this setup allows for the use of high concentrations of imager strands given that background fluorescence is drastically reduced and sparse emitters are no longer necessary for accurate localization. Furthermore, sequential washes of imager strands are enabled through the use of microfluidics, which allows for accurate, multi-target reconstructions that are not subject to chromatic offsets. Thus, we demonstrate a setup that offers improved localization precision, extracellular environment control, multi-target information, and 3D imaging that can easily be implemented for fast, accurate, and precise multi-target super-resolution whole cell imaging.

Fourier-Domain Phase Retardation Vortex Measurement

Optical vortices have found a wide range of applications thanks to their helical phase topology allowing to carry the orbital angular momentum. In this work, self-interfering vortex beams are utilized in a new single-shot holographic method for the circular phase retardation measurement. The vortices carrying information about the phase retardation introduced between two orthogonal circular polarization modes are generated by the spin to orbital angular momentum conversion. The phase retardation is stored in off-axis holographic records acquired in a common-path setup using a geometric-phase grating. In the proposed method, the circular phase retardation is reconstructed in the Fourier domain, surpassing the measurement precision provided by methods restoring the retardation from the rotation of a Double-Helix Point Spread Function (DH PSF). The developed method can be adapted for application to polarimetry, orientation imaging and diagnostics of nano-emitters.

Axial accuracy in localization microscopy with 3D point spread function engineering.

Single-molecule localization microscopy has developed into a widely used technique to overcome the diffraction limit and enables 3D localization of single-emitters with nanometer precision. A widely used method to enable 3D encoding is to use a cylindrical lens or a phase mask to engineer the point spread function (PSF). The performance of these PSFs is often assessed by comparing the precision they achieve, ignoring accuracy. Nonetheless, accurate localization is required in many applications, such as multi-plane imaging, measuring and modelling of physical processes based on volumetric data, and 3D particle averaging. However, there are PSF model mismatches in the localization schemes due to how reference PSFs are obtained, look-up-tables are created, or spots are fitted. Currently there is little insight in how these model mismatches give rise to systematic axial localization errors, how large these errors are, and how to mitigate them. In this theoretical and simulation work we use a vector PSF model, which incorporates super-critical angle fluorescence (SAF) and the appropriate aplanatic correction factor, to analyze the errors in z-localization. We introduce theory for defining the focal plane in SAF conditions and analyze the predicted axial errors for an astigmatic PSF, double-helix PSF, and saddle-point PSF. These simulations indicate that the absolute axial biases can be as large as 140 nm, 250 nm, and 120 nm for the astigmatic, saddle-point, and double-helix PSF respectively, with relative errors of more than 50%. Finally, we discuss potential experimental methods to verify these findings and propose a workflow to mitigate these effects.

Particle Tracking Velocimetry With Dynamic Aberration Correction For 3D Flow Measurements Through Fluctuating Phase Boundaries

Imaging based flow measurements allow the observation of complex three-dimensional flows with a high temporal resolution. However, at least one optical access with a good imaging quality is needed. In fluids with a dynamic phase boundary, often the only optical access is the dynamic surface (e. g. droplet on opaque surface). In this case, temporally varying aberrations are introduced that can increase the measurement uncertainty significantly. Additionally, many flows in technical systems are three-dimensional and turbulent so that volumetric measurements are desirable. In this contribution, we present the first 3D-3C flow measurement system with dynamic aberration correction and a single optical access. By using a deformable mirror with 69 actuators, a laser guide star and a wavefront sensor, the dynamic aberrations that are introduced by the fluctuating phase boundary can be corrected. By introducing a double-helix point spread function (DH-PSF) with a spatial light modulator (SLM) we achieve three-dimensional flow measurements with only one camera. For demonstration purposes, the flow in a microchannel was measured through an oscillating puddle-like droplet. By applying the adaptive-optics system, the measurement uncertainty could be lowered by 58 % relative to measurements through a static droplet. The technique has the potential to allow three-dimensional flow measurements in droplets on opaque surfaces (e. g. membrane of fuel cell). Thus, new insights about the movement of droplets (e. g. in fuel cells) are made possible.

Reconfigurable Metalens with Phase-Change Switching between Beam Acceleration and Rotation for 3D Depth Imaging.

Depth imaging is very important for many emerging technologies, such as artificial intelligence, driverless vehicles and facial recognition. However, all these applications demand compact and low-power systems that are beyond the capabilities of most state-of-art depth cameras. Recently, metasurface-based depth imaging that exploits point spread function (PSF) engineering has been demonstrated to be miniaturized and single shot without requiring active illumination or multiple viewpoint exposures. A pair of spatially adjacent metalenses with an extended depth-of-field (EDOF) PSF and a depth-sensitive double-helix PSF (DH-PSF) were used, using the former metalens to reconstruct clear images of each depth and the latter to accurately estimate depth. However, due to these two metalenses being non-coaxial, parallax in capturing scenes is inevitable, which would limit the depth precision and field of view. In this work, a bifunctional reconfigurable metalens for 3D depth imaging was proposed by dynamically switching between EDOF-PSF and DH-PSF. Specifically, a polarization-independent metalens working at 1550 nm with a compact 1 mm2 aperture was realized, which can generate a focused accelerating beam and a focused rotating beam at the phase transition of crystalline and amorphous Ge2Sb2Te5 (GST), respectively. Combined with the deconvolution algorithm, we demonstrated the good capabilities of scene reconstruction and depth imaging using a theoretical simulation and achieved a depth measurement error of only 3.42%.

3D Imaging with Double-Helix Point Spread Function and Dynamic Aberration Correction Using a Deformable Mirror

Imaging-based measurements through fluctuating phase boundaries such as free water surfaces or droplets have usually a higher uncertainty due to the changing refraction of light at the boundary. In this paper, a novel measurement system is presented for both 3D imaging with only one camera and aberration correction of light propagation through one boundary. 3D imaging is achieved by introducing a Double-Helix Point Spread Function (DH-PSF). The dynamically introduced aberrations of the phase boundary are measured with a Fresnel Guide Star (FGS) and are corrected with a deformable mirror in a closed-loop system with low latency. The measurement system and the adaptive optics image correction were characterized by means of a linear actuator and a demonstration measurement through an oscillating droplet. For the latter, the uncertainty of a reference flow could be lowered by 58 % using adaptive optics. The technique has the potential to measure complex three-dimensional flows that are optically difficult to access without modification of the experimental setup. Possible applications are optimizations of fuel cells for reducing the consumption of fossil energy.

Four-dimensional multi-particle tracking in living cells based on lifetime imaging

Abstract Research on dynamic events in living cells, such as intracellular transportation, is important for understanding cell functions. As movements occur within cells, the microenvironment of the moving vesicles or biomacromolecules may affect the behavior of them. Herein, we propose a method of simultaneously monitoring changes in spatial positions and the local environment related to the fluorescence lifetime, i.e., four-dimensional (4D) multi-particle parallel-tracking in living cells. Based on double-helix point spread function (DH-PSF) microscopy and streak camera, the method combines three-dimensional (3D) localization methods and fluorescence lifetime imaging. By modifying the PSF of the system, the 3D positions and fluorescence lifetime information for several molecules within a depth of a few microns can be acquired simultaneously from a single snapshot. The feasibility of this method is verified by simulating the real-time tracking of a single particle with a given trajectory. In addition, a proof-of-concept 4D tracking system based on the DH-PSF and streak camera was built. The experimental results show that the 3D localization and lifetime precision are σ(x, y, z) = (26 nm, 35 nm, 53 nm) and σ(τ) = 103 ps, respectively, and the effective depth of field is approximately 4 μm. Finally, intracellular endocytosis in a living cell was observed using the system, which demonstrated the successful 4D tracking of two microspheres moving within an axial depth of 4 μm. This work opens a new perspective for research of dynamic processes, by providing information about the chemical (microenvironments) and physical (positions) changes of moving targets in living cells.