Focus-variation microscopy for measurement of surface roughness and autocorrelation length

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 technique’s spatial bandwidth limitations (limited lateral resolution and field-of-view). We recently developed a measurement protocol that greatly reduces the bias due to limited resolution[1]. In the present paper, we describe an extension of the protocol to correct for limited field-of-view, and present measurements on a series of commercial surface roughness comparator samples to validate the protocol. The protocol strictly applies to the case of surfaces that are isotropic, and whose topography displays an autocovariance function that is exponential, with a single autocorrelation length. However, we find that applying the protocol yields extracted values of roughness and autocorrelation length for each surface that are accurate and consistent among datasets obtained at different magnifications (i.e. among datasets obtained with different spatial bandpass limits), even for samples that are not in any way selected to conform to the model’s assumptions.