In Eq. 1 I0-I3 are scaling pre-factors, and bkg is a constant background component. The first term in the sum describes region I, and is a surface fractal expression by refs . Ds is a surface fractal dimension value, which assumes a value of 2 for smooth surfaces, and <3 for very rough surfaces, and A = 6-Ds (see intensity region I). The I0 scaling constant is proportional to the surface area, and Γ is a gamma function.