Distributed Error-Function Roughness in Refl1d Reflectometry Fitting Program

The Refl1d program is used for modeling and fitting data from neutron and X-ray reflectometry experiments. The model of the (thin-film) samples is typically constructed of discrete layers of different scattering-length densities (SLD). Interlayer roughness is represented as an error-function transition from one layer to the next. Previous versions of the software truncated this error-function at the next interface. This strategy has the advantage of preventing layers with unbounded effective extent, but it can also result in SLD depth profiles that do not conform to the physical expectations of the users (such as introducing sharp transitions) whenever the layer roughness approaches the thickness of the layer. In this article we introduce a new version of the software in which the option is provided to extend the roughness of each layer over the entire structure; the resulting SLD profiles often more closely resemble the physical models intended by the user. Most importantly no sharp transitions are introduced by truncating the roughness, when a smooth transition is often desired when adding rough layers together.