Oscillating and non-oscillating contributions in the Porod law

Abstract
Experimental Ih⁴ plots often show damped oscillating terms. The first non-oscillating term describing the interface curvature effects is given by the Kirste-Porod formula for regular surfaces. It provides a positive h^-2 contribution to Ih⁴. In the presence of sharp edges and vertices on otherwise planar interfaces an additional negative h^-2 term occurs. A cylinder cutted following a planar section parallel to its axis provides the simplest situation where oscillating, positive and negative h^-2 terms have to be simultaneously taken into account. The three additional asymptotic contributions to Ih⁴ are evaluated. The exact correlation function is calculated. The difference between its fourier transform and the asymptotic intensity yields an estimate of the neglected contribution using the asymptotic expansion. The modification of the oscillating Ih⁴ pattern resulting from the positive and negative h^-2 contributions is examined.