Model-independent reconstruction of smooth electron density profiles from reflectivity data of liquid surfaces

Abstract

A smoothed groove-tracking method (SGTM) is developed for the construction of the electron density profiles of liquid surfaces from reflectivity data. This work is based on improving the groove-tracking method (GTM) previously published by one of us (X.-L. Zhou) [X.-L. Zhou and S. H. Chen, Phys. Rev. E 47, 3174 (1993)] by imposing the requirement that the electron density profile be smooth. Application of the method is demonstrated on both simulated reflectivity data with model density profiles and experimental data from liquid metal, liquid crystal, and water surfaces. Comparisons are made among results obtained by the SGTM, the original GTM, and published model density functions for both monotonic and layered density profiles. We find that the requirement for a smooth profile leads to more physically reasonable profiles than the often jagged, discontinuous profiles generated by the GTM. Although model-independent methods, by their nature, cannot yield unique density profiles and may converge to local minima, these techniques are quite useful for suggesting new profiles when little a priori information is available.