Improvement of resolution by maximum entropy linear image restoration for NiSi₂/Si interface

A linear imaging constrained-maximum entropy method has been developed to extend the resolution from a series of defocused high-resolution images and one diffraction pattern. Our method is basically the Gerchberg-Saxton algorithm, which restores spatial information by imposing real space and Fourier space constraints cyclically. A constrained-maximum entropy method (constrained-MEM) was developed for real space constraints. This constrained-MEM finds an optimum solution of phases such that simulated images resemble the experimental image under some constraints in real space. These constraints include conservation of charge as well as a minimum of the χ² function, which is a measure of the level of satisfaction between simulated images and experimental images. For the Fourier space constraint, the square root intensities of diffraction spots were substituted. In this paper, we demonstrate that this method is able to extend the resolution from a series of high-resolution images and one diffraction pattern from a periodic NiSi₂/Si interface. The atomic structure of the NiSi₂/Si interface can be directly read out from the MEM image without a priori knowledge of the interface.