How shadows shape our impression of rough surfaces

Abstract

The aim here is to shape our impression of rough surfaces based on the formation of shadows. The shadows blackout some parts of the surface leading us to state that rough surfaces are not always quite the way they seem. In fact, it is the angle of view that proves the size of the shadows. In surface profilometry, the scanned image is produced by a vertical shot. While in nature, a vertical sighting of events is not always possible or preferred, therefore readings by various observers would depend on the angle of their line of sight. In the present work, owing to the statistical properties of rough surfaces, the relation between a vertical and angular line of site view of a surface is obtained. This enables the estimation of how the surface really looks like, even though the observer has an non vertical line of sight. To be most illustrative, a comparison between wave scattering from an actual surface and that from an observed surface is performed. The shadowing effects which are shown to be inversely proportional to the Hurst exponent, cause the height correlation function to posses a bi-scaling behaviour. We also illustrate how the correlation develops its efficiency as the line of sight angle tends to zero, making the surface look smooth.