INFLUENCE OF TIP GEOMETRY ON FRACTAL ANALYSIS OF ATOMIC-FORCE MICROSCOPY IMAGES

Fractal analysis of data from atomic force microscopy (AFM) is often n ecessary for studying surfaces with scale-invariant roughness. However , the fractal parameters are influenced by the finite-sized tip geomet ry of the AFM stylus. We make an extended study of such little-known e ffects. The so-called successive random algorithm is used to generate by computer ideal fractal surfaces with known fractal dimensions and v arying height magnitudes. Tip-distorted AFM images are simulated from the ideal surfaces for the case of a strictly geometrical interaction between surface and tip. The AFM-induced error, taken as the differenc e in estimated parameters between ideal and distorted images, is shown to be largest for small scan sizes and high fractal dimensions. The d ependence on AFM tip radius and surface height magnitude is analyzed b y the structure function, variance and a Fourier method. The latter is shown to be unreliable for analyzing AFM images. We exemplify how the results can be applied to AFM images of real surfaces.