High resolution electron microscopy (HREM) is a primary tool for studying the atomic structure of defects in crystals. However, the quantitative analysis of defect structures is often seriously limited by specimen noise due to contamination or oxide layers on the surfaces of a thin foil.For simple monatomic structures such as fcc or bcc metals observed in directions where the crystal projects into well-separated atomic columns, HREM image interpretation is relatively simple: under weak phase object, Scherzer imaging conditions, each atomic column is imaged as a black dot. Variations in intensity and position of individual image dots can be due to variations in composition or location of atomic columns. Unfortunately, both types of variation may also arise from random noise superimposed on the periodic image due to an amorphous oxide or contamination film on the surfaces of the thin foil. For example, image simulations have shown that a layer of amorphous oxide (random noise) on the surfaces of a thin foil of perfect crystalline Si can lead to significant shifts in image intensities and centroid positions for individual atomic columns.
On the spectrum of noisy blown-up matrices
