Model-independent method for reconstruction of scattering-length-density profiles using neutron or x-ray reflectivity data

A model-independent method is developed for the reconstruction of the scattering-length-density profile of a film on top of a known substrate or bulk from the measured reflectivity data. The method is first tested on simulated reflectivity data calculated from profiles resembling those used in real experiments. It is shown that the method is effective in faithfully reproducing the original profiles from the simulated data. The method is then tested on experimental data from four different surface films. It is found again that the method is capable of generating physically reasonable profiles whose calculated reflectivities agree to within ${\mathrm{\chi }}^2$=1 with the measured data. In the tests, detailed descriptions are also given for the implementation of the method. Finally, a discussion is given with regard to the application of the method and the precautions needed for using this method.