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A direct method of evaluating the scaling exponent H of a self‐affine fractal surface from a single topographic image recorded by using scanning probe microscopy is presented. This method uses the fact that for these surfaces the root‐mean‐square roughness increases with length as LH. The method is applied to study the fractal nature of silver films of different thicknesses and it is observed that the variation in the scaling exponent H is in correlation with the surface roughness and the observed growth mode.