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**Enhancement of STM images and estimation of atomic positions based on maximum entropy deconvolution**

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S. D. Böhmig, M. Schmid, H. Störi

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Institut für Allgemeine Physik,
Technische Universität Wien, A-1040 Wien, Austria
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*Surf. Sci. 313 (1994) 6-16*

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 Pt_{10}Ni_{90}(100).

Corresponding author: S.D. Böhmig; reprints available from M. Schmid (schmid).