SPECTRAL RESTORATION IN HREELS

The spectral resolution of HREELS is determined by both instrumental and sample-related factors. Despite substantial progress in electron optic design, these factors ate still a limitation in assigning the vibrational modes of complex molecules and in determining linewidths. To the extent that all spectral features are broadened in the same way and within signal to noise limitations, currently available spectral restoration methods may provide a reliable solution. In principle, the measured elastic peak provides a template for deconvolution of these factors from the observed lineshapes. We compare results of a direct deconvolution method, in which division in the Fourier domain is followed by a linearised maximum entropy filter, with iterative methods based on maximum likelihood, maximum entropy and Bayesian principles involving only multiplication (i.e. convolution) in the Fourier domain. These methods are applicable both to spectra of modest resolution (intrinsic linewidths << instrumental linewidth) and to high resolution spectra (linewidths approximate to instrumental resolution) in which spectral lineshapes are measurably different. The asymmetry and tailing of the elastic peak, which are critical to restoration of low frequency features, are determined by a number of processes such as multiple scattering, the thermal population of vibrational states, and low energy continuum excitations (e-h pairs, phonons) of the substrate. These factors, as well as practical considerations, are discussed in relation to measuring data for optimal spectral restoration.