Diffractive imaging of nanoparticles on a substrate.
Explore the source record for details and available documents.
Retraction Notice↗
Biomedical subjects
U Weierstall
Publications and source records attributed to U Weierstall.
Damped and thermal motion of laser-aligned hydrated macromolecule beams for diffraction.
We consider a monodispersed Rayleigh droplet beam of water droplets doped with proteins. An intense infrared laser is used to align these droplets. The arrangement has been proposed for electron- and x-ray-diffraction studies of proteins which are difficult to crystallize. This paper considers the effect of thermal fluctuations on the angular spread of alignment in thermal equilibrium, and relaxation phenomena, particularly the damping of oscillations excited as the molecules enter the field. The possibility of adiabatic alignment is also considered. We find that damping times in a high-pressure gas cell as used in x-ray-diffraction experiments are short compared with the time taken for molecules to traverse the beam and that a suitably shaped field might be used for electron-diffraction experiments in vacuum to provide adiabatic alignment, thus obviating the need for a damping gas cell.
Chemistry, Physical↗
Diffractive electron imaging of nanoparticles on a substrate.
The observation of the detailed atomic arrangement within nanostructures has previously required the use of an electron microscope for imaging. The development of diffractive (lensless) imaging in X-ray science and electron microscopy using ab initio phase retrieval provides a promising tool for nanostructural characterization. We show that it is possible experimentally to reconstruct the atomic-resolution complex image (exit-face wavefunction) of a small particle lying on a thin carbon substrate from its electron microdiffraction pattern alone. We use a modified iterative charge-flipping algorithm and an estimate of the complex substrate image is subtracted at each iteration. The diffraction pattern is recorded using a parallel beam with a diameter of approximately 50 nm, illuminating a gold nanoparticle of approximately 13.6 nm diameter. Prior knowledge of the boundary of the object is not required. The method has the advantage that the reconstructed exit-face wavefunction is free of the aberrations of the objective lens normally used in the microscope, whereas resolution is limited only by thermal vibration and noise.
Algorithms↗
Diffraction and imaging from a beam of laser-aligned proteins: resolution limits.
The effect of the limited alignment of hydrated molecules is considered in a laser-aligned molecular beam, on diffraction patterns taken from the beam. Simulated patterns for a protein beam are inverted using the Fienup-Gerchberg-Saxton phasing algorithm, and the effect of limited alignment on the resolution of the resulting potential maps is studied. For a typical protein molecule (lysozyme) with anisotropic polarizability, it is found that up to 1 kW of continuous-wave near-infrared laser power (depending on dielectric constant), together with cooling to liquid-nitrogen temperatures, may be needed to produce sufficiently accurate alignment for direct observation of the secondary structure of proteins in the reconstructed potential or charge-density map. For a typical virus (TMV), a 50 W continuous-wave laser is adequate for subnanometre resolution at room temperature. The dependence of resolution on laser power, temperature, molecular size, shape and dielectric constant is analyzed.
Algorithms↗
Iterative phase retrieval without support.
An iterative phase retrieval method for nonperiodic objects has been developed from the charge-flipping algorithm proposed in crystallography. A combination of the hybrid input-output (HIO) algorithm and the flipping algorithm has greatly improved performance. In this combined algorithm the flipping algorithm serves to find the support (object boundary) dynamically, and the HIO part improves convergence and moves the algorithm out of local minima. It starts with a single intensity measurement in the Fourier domain and does not require a priori knowledge of the support in the image domain. This method is suitable for general image recovery from oversampled diffuse elastic x-ray and electron-diffraction intensities. The relationship between this algorithm and the output-output algorithm is elucidated.
Journal Article↗
Phasing diffuse scattering. Application of the SIR2002 algorithm to the non-crystallographic phase problem.
A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV energy. The reconstructed image fits well with a scanning-electron-microscope (SEM) image of the same sample. The algorithm, which uses only the density modification portion of the SIR2002 program, is compared with the results obtained via the Gerchberg-Saxton-Fienup HiO algorithm. The new algorithm requires no knowledge of the object's boundary and proceeds from low to high resolution. In this way, the relationship between density modification in crystallography and the HiO algorithm used in signal and image processing is elucidated.
Journal Article↗
Coherence and sampling requirements for diffractive imaging.
Coherent Diffractive Imaging (CDI) allows images to be reconstructed from diffraction patterns by solving the non-crystallographic phase problem for isolated nanostructures. We show that the Shannon sampling of diffraction intensities needed in CDI requires a coherence width about twice the lateral dimensions of the object, and that the linear number of detector pixels fixes the energy spread needed in the beam. The Shannon sampling, defined by the transform of the periodically repeated autocorrelation of the object, is related to Bragg scattering from an equivalent crystal, and shown to be consistent with the sampling of Young's fringes established by scattering from extreme points in the object. The results are relevant to the design of diffraction cameras for CDI and plans for femotosecond X-ray diffraction from individual proteins.
Models, Theoretical↗
Experimental lensless soft-X-ray imaging using iterative algorithms: phasing diffuse scattering.
Images of randomly placed two-dimensional arrays of gold balls have been reconstructed from their soft-X-ray transmission diffraction patterns. An iterative hybrid input-output (HiO) algorithm was used to solve the phase problem for the continuous distribution of diffuse X-ray scattering. Knowledge of the approximate size of the clusters was required. The images compare well with scanning electron microscope (SEM) images of the same sample. The use of micrometre-sized silicon nitride window supports is suggested, and absorption filters have been used to allow collection of low spatial frequencies often obscured by a beam stop. This method of phasing diffuse scattering may have application to scattering from individual inorganic nanostructures or single macromolecules.
Journal Article↗
Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction.
Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.
Algorithms↗
Ordering energies and occupancies in doped TiAl, and dedicated ALCHEMI instrumentation.
Alloy design has been a lifelong interest of Gareth Thomas, and modern design algorithms include atomistic parameters which are obtainable from new electron microscope techniques such as ALCHEMI. In this paper, we discuss the relevance of ALCHEMI site occupancy measurements to intermetallic alloys, and summarize prior work. The results are found to lie in regions of a site-occupancy diagram (SOC) relating ordering energies to occupancy, as predicted by the Bragg-Williams theory of short-range order. These predictions also explain previous inconsistencies in the ALCHEMI measurements. A diffraction camera and X-ray detector system of novel design is proposed for dedicated ALCHEMI analysis for substitutional and interstitial dopant site-occupancy measurement, and details of the design given. Using this novel hardware design, the data-collection times for two-dimensional ALCHEMI patterns should be reduced by an order of magnitude or more, and the full data collection process automated. The resulting occupancy information can provide essential input parameters for atomistic alloy design algorithms, and can provide entirely new information on interstitial occupancies in minerals, ceramics, semiconductors, and alloys.
Algorithms↗
Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation.
The hybrid input-output iterative algorithm, which solves the phase problem for scattering from non-periodic objects, is reviewed for application to X-ray and electron diffraction data. Desirable convex constraints, including the sign of the scattering potential for electrons, and compact support, are discussed. The cases of complex and real exit-face wavefunctions, strong and weak phase objects, various supports, and the use of coherent focussed radiation are reviewed. Reconstruction of general complex objects requires accurate knowledge of the support, which should consist of two holes or a triangle in an opaque mask. The support boundaries should be as sharp as possible. Strong phase objects without absorption can be recovered if the support consists of one hole, is accurately known and has sufficiently sharp boundaries. Real and weak phase objects with absorption can be recovered without accurate knowledge of the support area if the support boundaries are sufficiently sharp and the support consists of one or more holes. A sign constraint on the scattering potential is used to recover weak phase objects. The experimental realization of theoretically desirable support conditions is discussed. A two-stage method of finding the support for complex objects is proposed. Experimental results from applying the Gerchberg-Saxton-Fienup HiO-algorithm to coherent electron diffraction patterns are presented, using specially made e-beam lithographed support structures. Images with a resolution of about 5 nm are thus recovered from the intensities alone in coherent electron diffraction patterns from non-periodic objects. Limitations of the present experiments are identified and suggestions made for development of both X-ray and electron work.
Journal Article↗
Surface structural sensitivity of convergent-beam RHEED: Si (0 0 1) 2 x 1 models compared with dynamical simulations
The aim of this work is to evaluate the sensitivity of convergent-beam RHEED for the refinement of surface atomic structure. We have compared experimental and theoretical convergent-beam RHEED patterns from the silicon (0 0 1) reconstructed surface. The experiment was carried out in a custom designed UHV diffraction camera,using a micron sized probe. Both experimental and theoretical CB-RHEED patterns show complex details, highly sensitive to the surface structure. The multiple scattering simulations were based on two experimental structural models which make different assumptions for dimer tilt, one derived from X-ray diffraction results, and another from LEED data. The simulated CB-RHEED patterns using the X-ray model were found to be in closer agreement with our experiment than the LEED model. However, the agreement is not entirely satisfactory, suggesting that further improvement on this model is necessary.
Journal Article↗
Transmission Electron Diffraction at 200 eV and Damage Thresholds below the Carbon K Edge.
Transmission electron diffraction patterns from ultra-thin aromatic and aliphatic organic films at beam energies of 200 eV-1 keV have been recorded in a custom low energy electron transmission (LEET) chamber. A significant reduction of the molecular damage cross-section, measured by fading of diffraction spots, was found for thin films of the aromatic perylene when the beam energy was reduced from 400 to 200 eV. The corresponding measurements for the aliphatic tetracontane showed a smaller "threshold energy" and the differences are discussed. Electron beam damage from other aromatic materials has also been studied at low energy. Comparison of the carbon K shell ionization cross-section and the measured damage cross-sections show that carbon K-shell ionization is strongly correlated with the damage observed in aromatics at beam energies higher than 284 eV. Calculation of the minimum number of unit cells needed for imaging a single molecule, and comparison of calculated elastic with measured damage cross-sections both indicate new possibilities for imaging biomolecules with low energy electrons.
Journal Article↗
Three-dimensional diffractive imaging for crystalline monolayers with one-dimensional compact support.
The use of a compact support constraint along the beam direction is considered as a solution to the phase problem for diffraction by two-dimensional protein crystals. Specifically we apply the iterative Gerchberg-Saxton-Fienup algorithm to simulated three-dimensional transmission electron diffraction data from monolayer organic crystals. We find that oversampling along the reciprocal-lattice rods (relrods) normal to the monolayer alone does not solve the phase problem in this geometry in general. However, based on simulations for a crystalline protein monolayer (lysozyme), we find that convergence is obtained in three dimensions if phases are supplied from a few high resolution electron microscope images recorded at small tilts to the beam direction. In the absence of noise, amplitude-weighted phase residuals of around 5 degrees, and a cross-correlation coefficient of 0.96 between the true and estimated potential are obtained if phases are included from images at tilts of up to 15 degrees. The performance is almost as good in the presence of noise at a level that is comparable to that commonly observed in electron crystallography of proteins. The method should greatly reduce the time and labor needed for data acquisition and analysis in cryo-electron microscopy of organic thin crystals by avoiding the need to record images at high tilt angles.
Algorithms↗