Analysis of roughness of Cs surfaces via evaluation of the autocorrelation function

At low temperature prepared quench-condensed Cs surfaces are analysed on a nanometer scale via scanning tunneling microscopy. The analysis of surface roughness is presented with the help of the evaluation of their autocorrelation function. In order to extract the correct autocorrelation function we present the requirement regarding the scan resolution of scanning probe microscopy (SPM) images in general. This is supported by a 'numerical experiment'. Furthermore, we present some methods of deducing higher orders of autocorrelation lengths, which are needed to evaluate SPM images with non-random distribution of roughness amplitudes. These characteristic values of the autocorrelation function could play the key role in further statistical calculations, e.g., on how surface roughness alters the wetting behaviour of liquid helium adsorbed on the cesium surfaces.