Biomedical subjects

L J Allen

Publications and source records attributed to L J Allen.

At least 19 recordsLinked to original sources

PubMed2006

Modelling high-resolution electron microscopy based on core-loss spectroscopy.

There are a number of factors affecting the formation of images based on core-loss spectroscopy in high-resolution electron microscopy. We demonstrate unambiguously the need to use a full nonlocal description of the effective core-loss interaction for experimental results obtained from high angular resolution electron channelling electron spectroscopy. The implications of this model are investigated for atomic resolution scanning transmission electron microscopy. Simulations are used to demonstrate that core-loss spectroscopy images formed using fine probes proposed for future microscopes can result in images that do not correspond visually with the structure that has led to their formation. In this context, we also examine the effect of varying detector geometries. The importance of the contribution to core-loss spectroscopy images by dechannelled or diffusely scattered electrons is reiterated here.

Journal Article↗

PubMed2006

Spatial incoherence in phase retrieval based on focus variation.

We investigate the effect of spatial incoherence on two methods of phase retrieval based on focus variation: the transport of intensity equation and iterative wave function reconstruction. Spatial incoherence provides an upper bound on the defocus step size which should be used in each case. The requirement that phase information manifests itself in sufficient variation in the defocused images provides a lower bound on the defocus step size which should be used in each case. The scaling of these upper and lower bounds with object size and imaging resolution differs in such a way that, given the spatial incoherence properties of the source, for sufficiently low resolutions neither technique can retrieve phase information. The regions of applicability of the two techniques are discussed.

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PubMed2005

Nonlocality in imaging.

We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schrödinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.

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PubMed2005

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.

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PubMed2005

Modelling imaging based on core-loss spectroscopy in scanning transmission electron microscopy.

Recent experimental realizations of atomic column resolution core-loss spectroscopy in the scanning transmission electron microscope have increased the importance of routinely modelling core-loss images. We discuss different approaches to wave function simulation and how they may be used in conjunction with the mixed dynamic form factor model to simulate images resulting from such inelastic scattering events. It is shown that, as resolution improves and in situations where the degree of thermal scattering is high, detailed quantitative comparisons will require the thermal scattering of electrons to be adequately modelled. Indeed, for sufficiently strong thermal scattering even qualitative interpretation may be affected: we give an example where this leads to a contrast reversal. We describe two methods suited to this purpose, the frozen lattice model and the scattering factor model, and explain how they may be combined with the mixed dynamic form factor approach.

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PubMed2005

Quantitative structure retrieval at atomic resolution.

The ability to determine the structure of a sample at atomic resolution is crucial for the development of nanotechnology and materials science. Consequently, structure retrieval must become a quantitative rather than a qualitative exercise. A method to retrieve the projected potential of a crystalline sample by inversion from an exit-surface wavefunction in high-resolution electron microscopy is proposed. This method accounts for both multiple scattering and absorption.

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PubMed2005

The spatial resolution of imaging using core-loss spectroscopy in the scanning transmission electron microscope.

The 'delocalization' of inelastic scattering is an important issue for the ultimate spatial resolution of core-loss spectroscopy in the electron microscope. This paper investigates the resolution of scanning transmission electron microscopy images for single, isolated atoms. Images are simulated from first principles using a nonlocal model for electron core-loss spectroscopy. The role of the width of the probe relative to the delocalization of the underlying ionization interaction is considered.

Calcium↗

PubMed2004

Retrieval of a complex-valued object from its diffraction pattern.

It is commonly understood that the retrieval of a complex-valued object from its diffraction pattern using a support constraint is a difficult problem, the more so if the support is symmetric. In this Letter we show that, for just such a symmetric support, use of an iterative algorithm in which the basic iteration is specified by a difference map converges routinely. All that is required is sufficient oversampling in the diffraction pattern coupled with judicious choices of the parameters defining the difference map.

Journal Article↗

PubMed2004

Spectroscopic imaging of single atoms within a bulk solid.

The ability to localize, identify, and measure the electronic environment of individual atoms will provide fundamental insights into many issues in materials science, physics, and nanotechnology. We demonstrate, using an aberration-corrected scanning transmission electron microscope, the spectroscopic imaging of single La atoms inside CaTiO3. Dynamical simulations confirm that the spectroscopic information is spatially confined around the scattering atom. Furthermore, we show how the depth of the atom within the crystal may be estimated.

Journal Article↗

PubMed2004

Exit wave reconstruction at atomic resolution.

An iterative method for exit wave function reconstruction based on wave function propagation in free space is presented. The method, which has the potential for application to many forms of microscopy, has been tailored to work with a through focal series of images measured in a high-resolution transmission electron microscope. Practical difficulties for exit wave reconstruction which are pertinent in this experimental environment are the slight incoherence of the electron beam, sample drift and its effect upon the defocus step size that can be utilised, and the number of image measurements that need to be made. To gauge the effectiveness of the method it is applied to experimental data that has been analysed previously using a maximum likelihood formalism (the MAL method).

Crystallography↗

PubMed2004

Investigation of the effects of partial coherence on exit wave reconstruction.

In a recent work we presented an iterative wave function reconstruction (IWFR) method that reconstructs a wave function from measurements of its amplitude taken as it propagates in free space (a focal series of images). Although the ideal environment for application of the IWFR method is in a coherent imaging system, it has been developed so that it can be applied in a partially coherent imaging system, in particular for a high-resolution transmission electron microscope using a field-emission gun. In this paper we investigate the effects of partial coherence on the accuracy of results obtained using the IWFR method. We then show how results obtained under such conditions can be improved by estimating and subtracting components from the amplitude measurements of the wave function that derive from incoherence in the electron beam.

Journal Article↗

PubMed2004

Phase imaging with a half-plane aperture.

A method that effects phase reconstruction from a single image of a phase object is presented. The method, which is founded on the iterative transform algorithm, more specifically the error reduction version of this algorithm, applies this algorithm in an unusual way, in that it attempts to solve the phase problem from the measurement of a single image of the object taken by using a half-plane aperture rather than its diffraction pattern. A description of the method, an analysis of its performance, and suggestions as to its potential application are given.

Journal Article↗

PubMed2003

Atomic-resolution electron energy loss spectroscopy imaging in aberration corrected scanning transmission electron microscopy.

The "delocalization" of inelastic scattering is an important issue for the ultimate spatial resolution of innershell spectroscopy in the electron microscope. It is demonstrated in a nonlocal model for electron energy loss spectroscopy (EELS) that delocalization of scanning transmission electron microscopy (STEM) images for single, isolated atoms is primarily determined by the width of the probe, even for light atoms. We present experimental data and theoretical simulations for Ti L-shell EELS in a [100] SrTiO3 crystal showing that, in this case, delocalization is not significantly increased by dynamical propagation. Issues relating to the use of aberration correctors in the STEM geometry are discussed.

Journal Article↗

PubMed2003

Lattice-resolution contrast from a focused coherent electron probe. Part I.

To develop a Bloch wave framework for lattice-resolution contrast derived from coherent or incoherent scattering of an electron probe focused onto a crystal, boundary conditions which influence the propagation of an arbitrarily distorted coherent electron probe are addressed. These boundary conditions are particularly relevant for a probe focused within a unit cell, and lead to a general theory which hinges on Bloch wave excitation amplitudes being written as a function of beam position and focus. Whereas antisymmetric Bloch states are not excited for an incident plane wave at an exact zone axis orientation, these states may be strongly excited depending on probe focus and position within the unit cell. Equations for both coherent and incoherent lattice image contrast in scanning transmission electron microscopy are derived for any detector configuration in the Bloch wave framework. An equivalent expression amenable to evaluation via multislice techniques is also described. It is shown explicitly how mixed dynamic form factors for incoherent scattering should be taken into account for annular dark field or backscattered electron detectors, as well as for characteristic losses detected by X-ray emissions or by electron energy loss spectroscopy. A background contribution from "absorbed" electrons is included in the theory. The contribution of cross-talk from neighbouring columns to incoherent contrast is examined within the context of this theoretical framework.

Algorithms↗

PubMed2003

Lattice-resolution contrast from a focused coherent electron probe. Part II.

In the previous paper, boundary conditions matching the probe to the crystal wave function in scanning transmission electron microscopy were applied by matching the whole wave function across the boundary. It is shown here how that approach relates to previous Bloch wave formulations using (phase-linked) plane wave boundary conditions for wave vectors implied by the range of transverse momentum components in the incident probe. Matching the whole wave function across the boundary, and including a suitably fine mesh in the reciprocal space associated with the crystal to allow matching of transverse momentum components within the probe, leads to a structure matrix A containing many elements which would normally be excluded for plane wave incidence. For perfect crystals, the A-matrix may be block diagonalised. This leads to a considerable increase in the computational efficiency of the model and yields important insights into the physics of convergent probes in perfect crystals-reciprocity in coherent imaging and the small aperture limit for coherent and incoherent contrast are considered. The numerical equivalence of the incoherent lattice contrast calculated in this Bloch wave method and the multislice method using mixed dynamic form factors will be demonstrated. Comparison between both these methods and the frozen phonon model, a prevalent multislice method for annular dark field simulation which has the theoretical advantage of handling double channelling, will be made.

Algorithms↗

PubMed2003

Channelling effects in atomic resolution STEM.

A Bloch wave theory for incoherent scattering of an incident plane wave has proved successful in predicting the fine detail in 2-D zone axis channelling patterns formed by ADF, BSE and characteristic X-ray detection in beam rocking mode. A previously published example of polarity determination of GaAs by channelling contrast is compared with simulations in order to illustrate the applicability of the theory. Modification of boundary conditions for a focused coherent probe allows lattice-resolution incoherent contrast based on ADF and EELS detection as well as X-ray emissions to be catered for within a similar theoretical framework. Mixed dynamic form factors constitute an integral part of this theory, where quantum-mechanical phase is a core issue. Simulations of lattice-resolution ADF and EELS are discussed with reference to various zone axis projections of GaAs. Issues of single versus double channelling conditions, and local versus nonlocal interactions, are discussed in relation to X-ray, ADF and EELS detection.

Journal Article↗

PubMed2001

Atomic scattering factors for K-shell electron energy-loss spectroscopy.

Atomic scattering factors for K-shell electron energy-loss spectroscopy (EELS) have been calculated for elements in the range Z = 6 (carbon) to Z = 50 (tin). The calculations are based on relativistic Hartree-Fock wave functions for the atomic bound states and Hartree-Slater wave functions for the continuum states. The results are presented in parameterized form so that accurate values of the scattering factors can be obtained for incident electron energies between 50 and 400 keV, collection semi-angles between 10 and 40 mrad, and energy windows between 25 and 100 eV. The parameterizations are for scattering vectors with magnitude s = sin theta/lambda up to 2.5 A(-1) (2 theta is the scattering angle and lambda is the wavelength of the incident electrons).

Journal Article↗

PubMed2001

Computational aberration correction for an arbitrary linear imaging system.

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schrödinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.

Journal Article↗