Abstract: A method of characterizing a surface topography includes determining scale-dependent parameters. Each of the scale-dependent parameters represents a statistical characterization of a distribution of at least one of a first-order or higher-order derivative of surface height or h determined from one or more measurements of the surface at each of multiple distance scales. For at least one of the one or more measurements, the first-order or higher-order derivative of surface height is determined at the multiple distance scales in real space defined via a scaling factor ? which is greater than or equal to 1 and which is multiplied by the smallest possible distance scale or resolution provided by the at least one of the one or more measurements.