Relevance of Default Models on Maximum Entropy Regularization of Spectroscopy Data

R. Fischer, W. von der Linden and V. Dose
Max-Plank-Institut für Plasmaphysik
D-85740 Garching


The quantified maximum entropy method is used to infer the relative intensity and lineshape of backscattered ion-energy distributions from the system Pd/Ru(001). The 13 isotopes of the system cause a broad unresolved structure which is not decomposable with simple model functions. In addition to the regularization of the under-determined problem the incorporation of prior knowledge is essential for getting reliable results.

A flat default model results in bad ringing of the reconstruction with overwhelming uncertainties in the structures. To refine the default model, the moments of the experimental data was used for the cases of the clean Ru(001) surface and the thick Pd film. For the mixed cases the reconstructions of the extreme cases are chosen for the default model.

Our experiences with applications of the maximum entropy method to ion-scattering-spectroscopy, ultraviolet-photoemission-spectroscopy and scanning-tunnelling-microscopy data show that it is far beyond a method which be used as a black box. Careful examination of the uncertainies of the reconstruction as well as the supplement of prior knowledge in the form of a soft constraint is essential for reliable conclusions. Last not least the intuition of the experimentalist sets a prior which can not be neglected.

MaxEnt 94 Abstracts /