Quantitative criteria for the matching of simulations with experimental HREM images

Abstract

We propose a quantitative way of distinguishing between proposed structural models by the comparison of simulations with experimental high resolution images. The comparison is divided into three parts: the comparison of the mean intensity, the contrast and the pattern. We define a cross-correlation coefficient for the assessment of the differences in pattern. The effect of noise is characterised and it is shown that the cross-correlation chosen responds linearly to errors in the simulation parameters. This is shown theoretically by Fourier analysis of the image and by using simulations. From this analysis it is shown that an iterative method can be used to determine the values of several of the parameters in combination.