“…The Pointwise Unconstrained Minimization Approach (PUMA) numerical method (Birgin et al, 1999;Mulato et al, 2000;Erarslan & Gungor, 2010;Ventura et al, 2005) and algebraic methods (Peng & Desu, 1994;Birgin et al, 1999), based on approximate equations derived from reasonable assumptions, were widely used to extract spectral dispersion of optical constants of a film and its geometric thickness from normal-incidence -and/or -spectra of its air-supported {thin film/thick substrate}-stack, both of which do not require in prior a dispersion functional model. An algebraic method in this category is the envelope method, developed and refined by a number of authors ( Manifacier et al, 1976;Swanepoel, 1983;Minkov, 1990;El-Naggar et al, 2009;Epstein et al, 1987;González-Leal et al, 1998;Tigau, 2006;Poelman & Smet, 2003), whose viability is based on the presence of many interference-fringe maxima and minima on transmittance (reflectance) spectra in transparent and weak absorption regions of the film, and cannot be applied to spectra displaying few interference fringes. This is not a problem in optical analysis based on PUMA program or curve-fitting softwares that can be used to analyze transmittance and reflectance spectra of multi-layered structures, irrespective of the number of observed interference-fringe extrema.…”