Rough layer interfaces

There are two main effects of rough interfaces in the DWBA calculation:

• Correction of Fresnel coefficients: this will be handled in the presentation on reflectivity
• Off-specular scattering from the rough interface

Rough interfaces can be seen as perturbations to a perfectly smooth layer interface. These roughness profiles can also be correlated between different interfaces:

In BornAgain, we use a model of the roughness where the height-height correlation function is:

$$\left\langle \phi(r)\phi(r+R) \right\rangle = \sigma^2 \exp(-\left| \frac{R}{\xi} \right|^{2h})$$

where $\sigma^2$ is the variance of the height perturbation, $\xi$ is the lateral correlation length and the Hurst parameter $h$ determines the jaggedness of the profile (a value of $h=1$ gives a smooth profile). The influence of this parameter can be seen in the following picture.

In BornAgain, an exponentially decaying correlation between roughness profiles of different interfaces is also supported. The correlation is modeled as follows:

$$\large{\left\langle \sigma_i(r)\sigma_j(r)\right\rangle = e^{-\frac{\left| z_i - z_j \right|}{L}}}$$