Astigmatic Imaging Research Articles

Dynamic three-dimensional tracking of single fluorescent nanoparticles deep inside living tissue

Three-dimensional (3D) spatial information can be encoded in two-dimensional images of fluorescent nanoparticles by astigmatic imaging. We combined this method with light sheet microscopy for high contrast single particle imaging up to 200 µm deep within living tissue and real-time image analysis to determine 3D particle localizations with nanometer precision and millisecond temporal resolution. Axial information was instantly directed to the sample stage to keep a moving particle within the focal plane in an active feedback loop. We demonstrated 3D tracking of nanoparticles at an unprecedented depth throughout large cell nuclei over several thousand frames and a range of more than 10 µm in each spatial dimension, while simultaneously acquiring optically sectioned wide field images. We conclude that this 3D particle tracking technique employing light sheet microscopy presents a valuable extension to the nanoscopy toolbox.

Relaxation in Thin Polymer Films Mapped across the Film Thickness by Astigmatic Single-Molecule Imaging.

We have studied relaxation processes in thin supported films of poly(methyl acrylate) at the temperature corresponding to 13 K above the glass transition by monitoring the reorientation of single perylenediimide molecules doped into the films. The axial position of the dye molecules across the thickness of the film was determined with a resolution of 12 nm by analyzing astigmatic fluorescence images. The average relaxation times of the rotating molecules do not depend on the overall thickness of the film between 20 and 110 nm. The relaxation times also do not show any dependence on the axial position within the films for the film thickness between 70 and 110 nm. In addition to the rotating molecules we observed a fraction of spatially diffusing molecules and completely immobile molecules. These molecules indicate the presence of thin (<5 nm) high-mobility surface layer and low-mobility layer at the interface with the substrate.

Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton

By combining astigmatism imaging with a dual-objective scheme, we improved the image resolution of stochastic optical reconstruction microscopy (STORM) and obtained <10 nm lateral resolution and <20 nm axial resolution when imaging biological specimens. Using this approach, we resolved individual actin filaments in cells and revealed three-dimensional ultrastructure of the actin cytoskeleton. We observed two vertically separated layers of actin networks with distinct structural organizations in sheet-like cell protrusions.

Three Dimensional Single Molecule Localization using Phase Retrieved Pupil Functions

Single particle tracking and single-molecule localization based super-resolution techniques rely on the precise and accurate localization of single fluorescent molecules. For two dimensional imaging, relatively simple models of a microscope point spread function (PSF), such as the two dimensional Gaussian, are adequate for most common imaging approaches. However, three dimensional localization is hampered by the fact that the image of a molecule near the focal plane contains little information about its axial position. In recent years, several three dimensional (3D) imaging techniques have been demonstrated that improve the localization of single fluorescent molecules along the axial direction, such as astigmatic imaging[1], a double helix point spread function (DH-PSF)[2], and dual focal plane methods[3]. Although these methods implement very different optical setups, they use either a simple Gaussian models, theoretical PSFs that do not account imaging system aberrations, or large, unwieldy, experimentally acquired 3D PSFs that can be prone to artifacts. Here we introduce a localization algorithm based on phase retrieved pupil functions. Pupil functions can contain information about specific aberrations present in the imaging system and can be used to calculate realistic 3D PSFs from a small set of Zernike polynomial coefficients that describe the pupil magnitude and phase. This compact representation of the 3D PSF allows the PSF to be efficiently calculated as needed in an iterative update method implemented on GPU hardware. We demonstrate the use of phase retrieved pupil functions for 3D localization in both the astigmatic and dual focal plane setups.Reference[1] Bo Huang, Science, 2008[2] Pavani, App.Phy.Sci, 2009[3] Manuel F Juette, NMETH, 2008

Off-plane anastigmatic imaging in Offner spectrometers

In this paper, the imaging performance of an Offner concentric imaging spectrometer is analyzed when the spectrometer entrance slit is disposed arbitrarily on the plane that is parallel to the grating grooves and contains the common center of curvature. Astigmatism-corrected designs are obtained for off-plane incidence on the grating if one point on the slit is located on the Rowland circle of the primary mirror. In this case, the combined system of primary mirror plus diffraction grating provides two astigmatic line images oriented parallel and orthogonal to the plane of diffraction, with the former located on the same plane as the slit. Consequently, these images can be brought to a single focus on this plane by the tertiary mirror if its radius of curvature is chosen properly. In addition, coma aberration is simultaneously removed. These results can be applied to the design of two-mirror or three-mirror spectrometers, generalizing the concept of the best imaging circle and providing solutions to get anastigmatic imaging for two object points and two wavelengths.

基于像散与理想光源成像原理的高亮度半导体激光器光纤耦合设计方法

A high-brightness fiber-coupled diode laser system is designed,based on the principle of astigmatism and ideal light source imaging theory.As an example,details of the calculation methods and design steps of the fiber coupled laser diode are given whose wavelength is 808 nm and output power is 10 W.Semiconductor laser beam can be coupled into the 50 μm core diameter optical fiber with a numerical aperture of 0.22.It is found that this fiber-coupled system has an output power of 9.712 W,a coupling efficiency of 97.12% and a power density of 1.1224×106 W/cm2.The proposed method is simple in principle,and the designed fiber-coupled system has high coupling efficiency,small size and strong practical value.

Apparent shape of a swimming pool

The apparent depth of a pool depends on the angle between the normal to the pool surface and the ray that reaches the observer’s eye. For small angles, the ratio of apparent to actual depth is 1/n, where n is the index of refraction of the water. As the angle increases, the image of a point on the bottom becomes astigmatic giving rise to two principal images. For both images, the apparent depth becomes smaller as the angle becomes larger. I show that the appearance of a typical gymnasium pool is significantly different depending on whether the observer is standing at the shallow or the deep end of the pool. In either case, one of the principal astigmatic images will be much more apparent than the other.

Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane

Wide-field microscopy with a double-helix point spread function (DH-PSF) provides three-dimensional (3D) position information beyond the optical diffraction limit. We compare the theoretical localization precision for an unbiased estimator of the DH-PSF to that for 3D localization by astigmatic and biplane imaging using Fisher information analysis including pixelation and varying levels of background. The DH-PSF results in almost constant localization precision in all three dimensions for a 2 μm thick depth of field while astigmatism and biplane improve the axial localization precision over smaller axial ranges. For high signal-to-background ratio, the DH-PSF on average achieves better localization precision.

Performance limits on three-dimensional particle localization in photon-limited microscopy

We present the performance limits on three-dimensional (3D) localization accuracy of currently used methods of wide-field superlocalization microscopy. The three methods investigated are double-helix microscopy, astigmatic imaging, and biplane detection. In the shot-noise limit, Cramer-Rao lower bound calculations show that, among these techniques, the double-helix microscope exhibits the best axial and 3D localization accuracy over short as well as long depth-of-field systems. The fundamental advantage of engineered point-spread function systems, like the double-helix, stems from the additional degrees of freedom available to control diffraction in three dimensions over variable regions of interest.

LTP-V with EPICS controls system for efficient quality assessment of KB-bender systems

We present a new approach for efficient bender calibration and quality assessment on the example of a KB-mirror system for the refocusing stage at the new Phoenix beamline of the Swiss Light Source. To reach the target focus of about 2 μ m FWHM with the strong astigmatic imaging ratio of 70:1 in the vertical- and 50:1 in the horizontal direction the bender system of the mirror has to be carefully calibrated to reach the desired elliptic shape. We use off-line slope measurements with the Long Trace Profiler LTP-V from Ocean Optics in our metrology laboratory. The proprietary controls system of the LTP has been replaced by EPICS to allow automatic synchronized measurements over the whole parameter space of the benders. The data acquisition is implemented as four-dimensional scan using the standard EPICS sscan record. The controls of the hardware has been realized with a genSub record for the CCD detector and a stream device for the motion of the LTP head.

Three-dimensional Super-resolution Fluorescence Microscopy and Its Application to Clathrin Mediated Endocytosis

The recent invention of super-resolution fluorescence microscopy allows nanoscopic investigation of cellular structures. Among these techniques, the Stochastic Optical Reconstruction Microscopy (STORM) is based on precise single molecule localization of photoswitchable fluorescent probes. By stochastically activating, imaging and deactivating subsets of fluorophores, it makes their images optically resolvable and determines their positions with nanometer precision. A super-resolution image is then reconstructed using these localizations. We now extend this approach to three-dimensional (3D) microscopy by determining the 3D coordinates of activated probes through astigmatism imaging: a cylindrical lens is inserted into the imaging optical path such that the image of individual molecules appear elliptical with the ellipticity depending on its z-position. Using this approach, we have achieved an optical resolution of 20-30 nm in the x-y direction and 50-60 nm in the z direction, representing an order of magnitude improvement over conventional fluorescence microscopy in all three dimensions. We have resolved the nanoscopic morphology of cellular structures that was previously deemed impossible by light microscopy.As a specific application, we use STORM to study the mechanism of clathrin mediated endocytosis in an in vitro reconstituted system. Proteins of interest in this system are directly labeled with photoswitchable fluorescent probes. This procedure is facilitated by covalently linking the two components of the probe, an activator dye and a photoswitchable reporter fluorophore, to form a single chemical unit prior to protein labeling. Using multicolor 3D STORM, we have characterized the spatial organization of plasma membrane, clathrin, actin and tubule forming proteins dynamin at the site of clathrin mediated endocytosis. These results reveal the molecular architecture of the nascent clathrin-coated pits at the nanometer scale and help to establish the role of actin and dynamin in membrane invagination, scission and vesicle formation.

Radial averages of astigmatic TEM images

The Contrast Transfer Function (CTF) of an image, which modulates images taken from a Transmission Electron Microscope (TEM), is usually determined from the radial average of the power spectrum of the image (Frank, J., Three-dimensional Electron Microscopy of Macromolecular Assemblies, Oxford University Press, Oxford, 2006). The CTF is primarily defined by the defocus. If the defocus estimate is accurate enough then it is possible to demodulate the image, which is popularly known as the CTF correction. However, it is known that the radial average is somewhat attenuated if the image is astigmatic (see Fernando, K.V., Fuller, S.D., 2007. Determination of astigmatism in TEM images. Journal of Structural Biology 157, 189-200) but this distortion due to astigmatism has not been fully studied or understood up to now. We have discovered the exact mathematical relationship between the radial averages of TEM images with and without astigmatism. This relationship is determined by a zeroth order Bessel function of the first kind and hence we can exactly quantify this distortion in the radial averages of signal and power spectra of astigmatic images. The argument to this Bessel function is similar to an aberration function (without the spherical aberration term) except that the defocus parameter is replaced by the differences of the defoci in the major and minor axes of astigmatism. The ill effects due this Bessel function are twofold. Since the zeroth order Bessel function is a decaying oscillatory function, it introduces additional zeros to the radial average and it also attenuates the CTF signal in the radial averages. Using our analysis, it is possible to simulate the effects of astigmatism in radial averages by imposing Bessel functions on idealized radial averages of images which are not astigmatic. We validate our theory using astigmatic TEM images.

Compact 1.9 THz BWO local-oscillator for the GREAT heterodyne receiver

The 1.9THz local-oscillator (LO) of the GREAT heterodyne receiver is presented. The LO is based on a frequency tripled backward-wave oscillator source. The frequency stabilization system is described and an astigmatic imaging system, developed for improved beam coupling, is presented. Allan variances and temperature dependent power drifts are analyzed. The LO is designed as a stand-alone system and fits into GREAT’s local-oscillator compartments. It produces more than 1.5μW of stable output power to pump the hot electron bolometer mixers of the GREAT instrument.

Determination of astigmatism in TEM images

We have developed a new two-step algorithm to determine the astigmatism of images from transmission electron microscopes (TEMs). Instead of computing the radial average of the power spectrum, we divide the power spectrum of a TEM image 1 to m (typically 32) sectors. We use a technique based on perturbation analysis of the contrast transfer function (CTF) to assimilate sector averages of the power spectrum of an image, which are incoherent in the presence of astigmatism, to a coherent radial average corresponding to a nominal defocus value. This is based on the fact that small defocus change from a nominal value can be considered to be equivalent to a perturbation on the spatial frequency spectra. Thus, instead of measuring the angular defocus variations, we optimise the frequency change required to obtain a coherent radial average. Numerically, this is achieved by minimizing σ 2/ σ 1 of a matrix formed from the sector averages, where σ i denotes the ith singular value of the matrix. After the minimisation procedure, the second singular value should be very small compared with the first singular value, indicating that the matrix is nearly rank unity. In the second step, the nominal defocus can be obtained from the coherent radial average using any good defocus estimation program, which assumes zero astigmatism. The defocus value at a sector can be obtained from this nominal defocus value and one of the parameters from the unconstrained optima. Our algorithm is tested on astigmatic images of carbon film, 2D crystals of bacteriorhodopsin and cryo-images of HIV cores.

Astigmatic electron diffraction imaging: a novel mode for structure determination

In a conventional transmission electron microscope, stigmators are used to correct for the effects of axial astigmatism in the diffraction lens. It seems feasible that these same stigmators could also be used to form a series of 'astigmatic' diffraction patterns. It is shown how this series of diffraction patterns could then be used to perform exit-surface wavefunction reconstruction. This has the advantage that the diffraction patterns are not resolution limited by the objective aperture as are images when performing exit-surface wavefunction reconstruction from a focal series. A scheme for carrying out phase reconstruction from a series of astigmatic diffraction patterns in an electron microscope is presented.

Easy spectrally tunable highly efficient X-ray backlighting schemes based on spherically bent crystals

New easy spectrally tunable backlighting schemes based on a spherically bent crystal are considered. Contrary to traditional backlighting scheme, in which the investigated objects should be placed between the backlighter and the crystal, for the considered schemes an object is placed downstream of the crystal, before the tangential or after the sagittal focus and an image of the object is recorded at the distance from the object corresponding to the needed magnification. The magnification is defined by the ratio of the distances from the sagittal focus to the detector and from the object to the sagittal focus. A ray-tracing modeling and experimental images of test meshes, obtained at incidence angles of the backlighter radiation of 10° and 22°, are presented. It is demonstrated that a simple linear transformation of the obtained astigmatic images allows reconstructing them as a stigmatic with an accuracy of 5–15%. For the spectral range around 9 Å a spatial resolution about 10 μm in a field of view of some square millimeters is achieved experimentally and confirmed by ray-tracing simulations.

A method for estimating the CTF in electron microscopy based on ARMA models and parameter adjustment

In this work, a powerful parametric spectral estimation technique, 2D-auto regressive moving average modeling (ARMA), has been applied to contrast transfer function (CTF) detection in electron microscopy. Parametric techniques such as auto regressive (AR) and ARMA models allow a more exact determination of the CTF than traditional methods based only on the Fourier transform of the complete image or parts of it and performing some average (periodogram averaging). Previous works revealed that AR models can be used to improve CTF estimation and the detection of its zeros. ARMA models reduce the model order and the computing time, and more interestingly, achieve increased accuracy. ARMA models are generated from electron microscopy (EM) images, and then a stepwise search algorithm is used to fit all the parameters of a theoretical CTF model in the ARMA model previously calculated. Furthermore, this adjustment is truly two-dimensional, allowing astigmatic images to be properly treated. Finally, an individual CTF can be assigned to every point of the micrograph, by means of an interpolation at the functional level, provided that a CTF has been estimated in each one of a set of local areas. The user need only know a few a priori parameters of the experimental conditions of his micrographs, for turning this technique into an automatic and very powerful tool for CTF determination, prior to CTF correction in 3D-EM. The programs developed for the above tasks have been integrated into the X-Windows-based Microscopy Image Processing Package (Xmipp) software package, and are fully accessible at www.biocomp.cnb.uam.es.

A robust focusing and astigmatism correction method for the scanning electron microscope

AbstractThis paper discusses a new approach to focusing and astigmatism correction based on the fast fourier transforms (FFTs) of scanning electron microscopy (SEM) images. From the FFTs, it is possible to obtain information on the severity of the defocus and astigmatism. This information is then processed by an algorithm to perform real‐time focusing and astigmatism correction on the SEM. The algorithm has been tested on defocused and astigmatic images of different samples, including those with highly directional features. Experiments show that the images obtained after running the algorithm can be as good as those that an experienced SEM operator can achieve.

Structure projection retrieval by image processing of HREM images taken under non-optimum defocus conditions

A direct method for retrieval of the projected potential from a single HREM image of a thin sample is presented. Both out-of-focus and astigmatic images can be restored. The defocus and astigmatism values are first determined from the Fourier transform of the digitised HREM image. Then a filter is applied which reverts the phases of those Fourier components which have been reversed by the Contrast Transfer Function (CTF). The method has been incorporated into the CRISP image processing system. It can be applied on any sample, crystalline or amorphous. From thin crystalline areas the projected symmetry can be determined and a further improvement achieved by imposing the symmetry exactly. This compensates for the effects of crystal tilt. Five HREM images of a thin crystal of K 8− x Nb 16− x W 12+ x O 80 ( x ≈ 1), different defocus and astigmatism values, were processed. Only one, taken near Scherzer defocus, was directly interpretable before image processing. After processing, all images showed the projected potential of the structure. Using data to 2.77 Å resolution, all heavy ( Nb W ) atom positions were found in every image, within on average 0.15 Å of the positions determined by single crystal X-ray diffraction. In the HREM images taken under non-optimum defocus conditions, also the potassium atoms in the tunnels of the structure were found.

Interferometric Measurements of Phase Singularities in the Output of a Visible Laser

We report the use of a simple interferometric technique which allows direct identification of phase singularities in laser fields. Phase singularities are observed in families of optical patterns formed via cooperative frequency mode locking in a continuous single longitudinal mode Na2 ring laser. The interferometric technique complements a previously reported astigmatic imaging method, and is superior in that it can be used to elucidate the structure of the higher order stationary patterns.