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.

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.

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.

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.

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).