A comparison of modern data analysis methods for X-ray and neutron specular reflectivity data

Data analysis methods for specular X-ray or neutron reflectivity are compared. The methods that have been developed over the years can be classified into different types. The so-called classical methods are based on Parrat's or Abelès' formalism and rely on minimization using more or less evolved Levenberg-Marquardt or simplex routines. A second class uses the same formalism, but optimization is carried out using simulated annealing or genetic algorithms. A third class uses alternative expressions for the reflectivity, such as the Born approximation or distorted Born approximation. This makes it easier to invert the specular data directly, coupled or not with classical least-squares or iterative methods using over-relaxation or charge-flipping techniques. A fourth class uses mathematical methods founded in scattering theory to determine the phase of the scattered waves, but has to be coupled in certain cases with (magnetic) reference layers. The strengths and weaknesses of a number of these methods are evaluated using simulated and experimental data. It is shown that genetic algorithms are by far superior to traditional and advanced least-squares methods, but that they fail when the layers are less well defined. In the latter case, the methods from the third or fourth class are the better choice, because they permit at least a first estimate of the density profile to be obtained that can be refined using the classical methods of the first class. It is also shown that different analysis programs may calculate different reflectivities for a similar chemical system. One reason for this is that the representation of the layers is either described by chemical composition or by scattering length or electronic densities, between which the conversion of the absorptive part is not straightforward. A second important reason is that routines that describe the convolution with the instrumental resolution function are not identical.