Linear image processing and anomalous scattering

Abstract

The complete analytical image model for bright field transmission electron micrographs contains several nonlinear image components as well as several linear image components all of which are degraded by noise and an instrumental transfer function. When these small nonlinear image components are neglected it is possible, using linear processing, to recover the complete complex ideal unaberrated image from a series of micrographs taken at different defocus. The imaginary part of this ideal image is due to the so called “anomalous” part of the elastic electron-atom scattering amplitudes. In this paper the effects of neglecting the nonlinear terms are tested qualitatively and quantitatively. A theoretical phase grating calculation (including nonlinear imaging effects) of a hypothetical specimen of sixteen single atoms with varying atomic number, Z, is used to simulate a defocus series which is subsequently processed with a linear image reconstruction procedure. Quantitative agreement of the reconstructed image with the ideal unaberrated image of comparable resolution is excellent. The real part of the reconstructed image is accurate to 0.68% and the imaginary part of the reconstructed image is accurate to 3.10%. The contrast variation in the reconstructed image is found to be roughly proportional to Z 0.67 for the real part of the image and roughly proportional to Z 1.29 for the imaginary part of the image.