Gaussian deconvolution: a useful method for a form-free modeling of scattering data from mono- and multilayered planar systems

A new method for analysis of scattering data from lamellar bilayer systems is presented. The method employs a form-free description of the cross-section structure of the bilayer and the fit is performed directly to the scattering data, introducing also a structure factor when required. The cross-section structure (electron density profile in the case of X-ray scattering) is described by a set of Gaussian functions and the technique is termed Gaussian deconvolution. The coefficients of the Gaussians are optimized using a constrained least-squares routine that induces smoothness of the electron density profile. The optimization is coupled with the point-of-inflection method for determining the optimal weight of the smoothness. With the new approach, it is possible to optimize simultaneously the form factor, structure factor and several other parameters in the model. The applicability of this method is demonstrated by using it in a study of a multilamellar system composed of lecithin bilayers, where the form factor and structure factor are obtained simultaneously, and the obtained results provided new insight into this very well known system.