Theoretical consideration of the optimal performance of atomic resolution holography

Abstract

The recording of holograms with atomic resolution is usually affected by distortions, e.g., due to the finite size of the source and detector, twin images and various imperfections of the instrument some of which have already been analyzed in detail. Amongst others in the present paper we discuss the effect of statistical noise. It is shown that the level of statistical noise of the reconstructed image is not influenced by the number of data points in the hologram and their individual counting statistics but is determined by the total number of counts collected in the experiment. The effects of instrumental resolution, filtering methods and symmetry operations on the signal-to-noise ratio of the reconstructed image are investigated as well. These achievements form the basis of the optimization method for the signal-to-noise ratio of the reconstructed holographic image.