AVS 49th International Symposium
    Applied Surface Science Monday Sessions
       Session AS-MoA

Paper AS-MoA5
Wavelets: A New Technique for Spectral Processing in Surface Science - Applications to Filtering and Deconvoluting HREELS and XPS Data

Monday, November 4, 2002, 3:20 pm, Room C-106

Session: Quantification & Accuracy in Surface Analysis
Presenter: J.J. Pireaux, Facultés Universitaires Notre-Dame de la Paix, Belgium
Authors: C. Charles, Facultés Universitaires Notre-Dame de la Paix, Belgium
J.P. Rasson, Facultés Universitaires Notre-Dame de la Paix, Belgium
G. Leclerc, Facultés Universitaires Notre-Dame de la Paix, Belgium
P. Louette, Facultés Universitaires Notre-Dame de la Paix, Belgium
J.J. Pireaux, Facultés Universitaires Notre-Dame de la Paix, Belgium
Correspondent: Click to Email
Last decade has witnessed the emergence of new powerful signal analysis tools: the wavelet transform is one of them.@footnote 1@ By simultaneously taking into account both the time and frequency domains, a wavelet analysis is a priori more efficient and covers a larger spectrum of applications than the Fourier Transform. The wavelet theory will be briefly presented, with comparison to Fourier analysis. Three applications for HREELS (High Resolution Electron Energy Loss Spectroscopy) and XPS (X-Ray Photoelectron Spectroscopy) will follow: noise filtering, peak detection and deconvolution. We first use synthetic data, a quite common practice in statistics: the correct answer is indeed known; it is thus possible to assess the validity and robustness of the algorithms, under clear hypotheses; errors can be calculated. The filtering algorithm proceeds with an original ‘Local in Time and Frequency Translation Invariant Poisson Smoothing’ code, that adapts itself to a spectrum containing peaks of very different amplitudes. Regions with a local maximum is then automatically detected with wavelets, allowing a Localized Least Squares method to precisely locate and determine the intensity of a peak. Different applications on real HREELS and XPS data are illustrated; they are particularly encouraging. @FootnoteText@ @footnote 1@ I. Daubechies, Ten lectures on wavelets. Philadelphia, PA, SIAM, 1992