Topographic information from multiple beam interferometry in the surface forces apparatus

This paper shows how multiple-beam interferometry can be used to unambiguously determine the topography of both surfaces in the surface farces apparatus at nanometer resolution. The conventional fringe pattern which is widely used to determine surface separations exhibits a fine background modulation. Under favorable conditions, i.e., low mirror reflectivity and unlike layer thickness (asymmetry), these background variations, which consist of a number of superimposed but distinguishable fringe patterns, provide valuable additional information about surface topography. This allows one to determine the surface topography in contact and noncontact. We present the results of extensive numerical calculations for the three-layer interferometer system using a generalized numerical algorithm. The comparison of measured and simulated interference patterns illustrates the influence of various parameters such as refractive index, layer thickness, mirror reflectivity, asymmetry, and topographic features on specific fringe properties such as their visibility, position, and shape. We also demonstrate the new method by analyzing experimental data of a mica-polymer contact.