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M P Oxley

Publications and source records attributed to M P Oxley.

9 recordsLinked to original sources
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↗
PubMed2001

Phase retrieval from images in the presence of first-order vortices.

We discuss retrieval of the phase of quantum-mechanical and classical wave fields in the presence of first-order vortices. A practical method of phase retrieval is demonstrated which is robust in the presence of noise. Conditions for the uniqueness of the retrieved phase are discussed and we show that determination of the phase in a given plane requires a series of at least three two-dimensional intensity images at different propagation distances. The method is applicable to a wide range of scenarios such as the imaging of imperfect crystals, quantitative determination of the strength of vortex filaments in high-temperature superconductors, and x-ray and electron holography.

Journal Article↗
PubMed2001

Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy.

We discuss phase retrieval and the correction of images for aberrations, in particular defocus and spherical aberration, in high-resolution transmission electron microscopy. Non-interferometric phase retrieval requires at least two intensity measurements in different planes. Vortices in the phase may occur in the image plane or the other planes involved in the phase retrieval. We discuss the performance of various methods of phase retrieval in that case. After retrieval of the phase, the aberrations can be corrected in the Fraunhofer diffraction space (the wave function in the diffraction space is related to that in the image space by a Fourier transform). The aberration-corrected image is obtained from the aberration-corrected wave function in the diffraction plane by inverse Fourier transformation.

Journal Article↗
PubMed2001

Structure determination at the atomic level from dynamical electron diffraction data under systematic row conditions.

We discuss a method to obtain structural information on crystals at the atomic level in high-resolution transmission electron microscopy from dynamical diffraction data under systematic row conditions. Working at a fixed incident energy and within an N-beam approximation, data is required at a well defined set of N incident beam orientations to determine the scattering matrix, one orientation for each column in the matrix. At each orientation the corresponding column of the scattering-matrix is obtained by Fourier transformation of the exit surface wave function. Thus, in addition to each exit surface image, we must recover the phase of the wave function for that orientation in the image plane. We show that retrieval of the phase using algorithms based on conservation of flux, which assume continuity of the phase, can yield incorrect solutions for the phase. This is because singularities can occur in the phase of the wave field at points where the intensity is zero, which can lead to edge dislocations in the phase. We demonstrate, using a model example, how these edge dislocations arise. We will show that phase retrieval from a through focal series of measurements or using the Gerchberg-Saxton algorithm (starting from measurements of an image and the corresponding diffraction pattern), correctly retrieves the phase and hence the exit surface wave function for all the orientations required to obtain the scattering-matrix. The dynamical (multiple) scattering can then be inverted to uniquely obtain the projected potential.

Journal Article↗