Finite resolution effects in the analysis of the scaling behavior of rough surfaces

Abstract

We investigate the influence of finite spatial resolution in the analysis of the scaling behavior of rough surfaces. We analyze such an effect for two usual measurement methods: the local width and the height-height correlation function. We show that while the correlation function is insensitive to finite resolution effects for practical purposes, the local width presents correction terms to the scaling law, leading to an effective value of the local roughness exponent smaller than the theoretically expected. We also show that a functional scaling relation can only be properly formulated in terms of the height-height correlation function.