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A new method for restoration and sharpening of scanning tunneling microscopy (STM) data is presented. According to the STM theory of Tersoff and Hamann it is assumed that the response of the STM can be approximated by the convolution of a localized atomic density of states of the sample and a Gaussian, which limits the resolution. Therefore, one must find the solution of an inverse problem, which is done by minimizing the mean square deviation between the measured and the reconstructed image using entropy as a regularization functional. This nonlinear method is shown to be superior to linear filters such as the Wiener filter in that the solution carries as minimal information as is necessary to fit the data and is not constrained to low frequencies. On metals, where atomically resolved STM images show mainly geometrical information, the centers of mass of the resulting peaks are taken as the atomic positions which are compared to those estimated visually from the STM images. The method has been applied to both the periodic Cu(111) surface and to the nonperiodic shifted row reconstruction of Pt10Ni90(100).
Corresponding author: S.D. Böhmig; reprints available from M. Schmid (schmid).