Unbiased analysis of neutron and X-ray reflectivity data by an evolution strategy

A new method for the unbiased determination of scattering length density (SLD) profiles from neutron or X-ray reflectograms is presented, based on an evolution strategy. In contrast to existing methods, the new approach uses no constraints that could influence the fit result improperly. While it is widely agreed that SLD profile oscillations with small wavelength and small amplitude cannot be resolved, randomly occurring long-wavelength oscillations have been neglected to date despite the fact that such oscillations can tremendously affect the calculated SLD profile. No easy remedy exists for this problem within the framework of conventional reflectogram analysis methods. The analytical approach proposed in this work offers a solution based on the recognition that each perturbation which leads to an indistinguishable reflectivity has a negative pendant. Averaging of numerous different, randomly perturbed, profiles therefore cancels out random deviations and accentuates reliable features. Moreover, the resulting averaged free-form fit has maximum (information) entropy. The performance of the novel approach is demonstrated by analysing complex molecular arrangements at an air-water interface and comparing the results with prior evaluations.