Maximum likelihood estimation of structure parameters from high resolution electron microscopy images. Part I: a theoretical framework.

This paper is the first part of a two-part paper on maximum likelihood (ML) estimation of structure parameters from electron microscopy images. In principle, electron microscopy allows structure determination with a precision that is orders of magnitude better than the resolution of the microscope. This requires, however, a quantitative, model-based method. In our opinion, the ML method is the most appropriate one since it has optimal statistical properties. This paper aims to provide microscopists with the necessary tools to apply this method so as to determine structure parameters as precisely as possible. It reviews the theoretical framework, including model assessment, the derivation of the ML estimator of the parameters, the limits to precision and the construction of confidence regions and intervals for ML parameter estimates. In a companion paper [Van Aert et al., Ultramicroscopy, this issue, 2005], a practical example will be worked out.