(Top) The scattering from one island along the perpendicular direction can be treated in the DWBA using, as an unperturbed state, (a) the bare substrate or (b) the graded interface and its full profile of refraction index n(z). In case (a), the particle form factor includes the reflection effect of the incident and scattered radiation on the substrate surface alone, as if the particle were isolated. In case (b), the scattering is from an upward or downward to an upward or downward propagating wave inside the particle layer. (Bottom) Schematics of the morphology corresponding to the various approximations used to calculate X-ray diffuse scattering. Particles are placed following (c) the DA, (d) the LMA, without or with correlation, and (e) the SSCA. Figures reprinted with permission from Lazzari, Renaud et al. (2007). Copyright (2007) the American Physical Society.