Robust evaluation of statistical surface topography parameters using focus-variation microscopy
Erich N. Grossman, Martin Gould, Natalie P. Mujica-Schwahn
Spatial bandwidth limitations frequently introduce large biases into the estimated values of RMS roughness and autocorrelation length that are extracted from topography data on random rough surfaces. The biases can be particularly severe for focus-variation microscopy data because of the reduced lateral resolution (and therefore dynamic range) inherent in the technique. In this paper, we describe a measurement protocol - essentially a super-resolution algorithm - that greatly reduces these biases. The measurement protocol is developed for the case of surfaces that are isotropic, and whose topography displays an autocovariance function that Is exponential, with a single autocorrelation length. The protocol Is first validated against Monte Carlo-generated mock surfaces of this form that have been filtered so as to simulate the lateral resolution and field-of-view limits of a commercial focus-variation microscope. It is found that accurate values of roughness and autocorrelation length can be extracted over a four octave range in autocorrelation length by applying the protocol, whereas errors without applying the protocol are a minimum of 30% even at the absolute optimum autocorrelation length. Then, microscopy data on eleven examples of rough, outdoor building materials are analyzed using the protocol. Even though the samples were not in any way selected to conform to the model's assumptions, we find that applying the protocol yields extracted values of roughness and autocorrelation length for each surface that are highly consistent among datasets obtained at different magnifications (i.e. datasets obtained with different spatial bandpass limits).