Deconvolution of Rutherford backscattering spectra: An inverse problem

摘要

We review the problems associated with resolution correction and discuss some of the most promising procedures to solve them. We select four methods to deconvolute heavy particle backscattering spectra: (i) parametrization of the theoretical function, (ii) using histograms with variable bin width, (iii) modified Land-weber iterations, and (iv) using mollifiers. To judge the quality of the methods, we treat simulated backscattering spectra as obtained in Rutherford backscattering measurements with solid-state detectors. Our results are as follows: When a priori information on the shape of the spectra is available, parametrization of the problem is superior to all other methods. When information on high-frequency components of the spectrum (e.g., on sharp edges) is of primary interest, the use of histograms with variable-bin width might provide good results. In all other cases, the choice of the best procedure depends on the specific problem and our ability to optimize the adjustable parameter of the specific method.