Applicability of the Singular-Optics Concept for Diagnostics of Random and Fractal Rough Surfaces

We introduce the singular-optics approach for classification of rough surfaces with large-scale inhomogeneities into random and fractal surfaces. The maps of amplitude zeros of a field versus the parameters of the rough surfaces and the position of the observation zone are obtained and analyzed. It is shown that the local density of amplitude zeros in the scattered field serves as an appropriate parameter with which to classify the surface of interest into a surface with a height distribution that can be described as a random or a fractal process.