An analytical approach is presented for correlating modulated reflectance spectra and complex surface structure. A response function is constructed of specular reflectance from metal surfaces that are both rough and spatially dispersive. The method of analysis is based on a response function formulation that entails a windowing operation. This windowing operation is not ad hoc and is theoretically well founded for providing a statistical interpretation of the permittivity function. The initial analysis indicates that the windowing operation provides for a robust formulation that is conveniently adaptable to a wide range of frequencies, spanning regimes characterized by different response characteristics. A prototype case using this windowed response function formulation is applied to the electroreflectivity spectra, from 1.5 to 4.5 eV, of roughened silver electrodes. The electrode is modeled by a two-interface system as the basis of a parameterization of experimentally measured response functions, which are partitioned into reflectivity and transparent regimes by the windowing operation. The bulk plasmons and defect polaritons are characterized by our robust formulation. In addition, we present a discussion of the general significance of our approach with respect to the application of statistical pattern recognition to the analysis of modulated reflectivity data.
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