SPECTRAL RESTORATION IN HREELS

The spectral resolution of HREELS is determined by both instrumental a nd sample-related factors. Despite substantial progress in electron op tic design, these factors ate still a limitation in assigning the vibr ational modes of complex molecules and in determining linewidths. To t he extent that all spectral features are broadened in the same way and within signal to noise limitations, currently available spectral rest oration methods may provide a reliable solution. In principle, the mea sured elastic peak provides a template for deconvolution of these fact ors from the observed lineshapes. We compare results of a direct decon volution method, in which division in the Fourier domain is followed b y 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 m ethods 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 l ineshapes are measurably different. The asymmetry and tailing of the e lastic peak, which are critical to restoration of low frequency featur es, are determined by a number of processes such as multiple scatterin g, the thermal population of vibrational states, and low energy contin uum excitations (e-h pairs, phonons) of the substrate. These factors, as well as practical considerations, are discussed in relation to meas uring data for optimal spectral restoration.