Determination of optical parameters in general film-substrate systems:: a reformulation based on the concepts of envelope extremes and local magnitudes

We present a reformulation of the determination of optical parameters in general film-substrate systems. Developed for interferential films in terms of photometric magnitudes (R, T), the formalism introduced allows us to establish how many parameters can be extracted from a set of measurements and fro which type of sample model. These parameters are the refractive index and the absorption of both film and substrate (i.e., (n) over tilde(1) = n(1) - jk(1) and (n) over tilde(2) = n(2) - jk(2)), the thickness of the film (d), the inhomogeneity of the film (Delta n(1)), and the surface roughness of the interfaces (sigma(1), sigma(2)) delimiting the film. The new formalism leads to some new analytical results and confirms others. Among the new results we have the following: (a) The mathematical condition commonly related with extremes (maxima and minima) in an interference pattern defines in fact a condition for envelope extremes. (b) The refractive index of a film can be obtained without prior knowledge of the thickness or the refractive index of the substrate (provided we have an optical interference film). (c) Absorption can he directly extracted from an interference-free magnitude T/(1 - R). (d) Roughness at the inner surface, inhomogeneity in the film, and absorption are correlated in reflection spectral measurements. (C) 2000 Optical Society of America OCIS codes: 120.4530, 120.5240, 240.6700, 240.0310, 240.5770, 310.6860, 310.1620.