Original research articleDevelopment of algorithm for computer drawing envelopes of interference reflectance spectra for thin film specimens

An algorithm is proposed for computer drawing accurate envelopes of reflectance spectra R(λ), for specimens representing a thin transmitting film on a substrate. The algorithm uses only one-step smoothing the spectrum, and piecewise cubic Hermite polynomial interpolation, which is shown to be superior to cubic spline interpolation for constructing envelopes of such R(λ) spectra. Boundary points are formulated and included at both ends of each of the two envelopes of the R(λ) spectrum. The boundary point at the longest wavelength accounts for the substrate absorption, which is notable e.g. for glass substrates at λ > 2000 nm. The boundary point at the shortest wavelength represents the convergence point for the two converging there envelopes. The performance of the algorithm is shown by comparing the true and the computer drawn envelopes for a model specimen, representing one relatively thin film, and two times thicker film, respectively, on a glass substrate. Examples are given for computer drawing envelopes of experimental spectra of two a-Si films, with disparate thicknesses, on different kind of glass substrates.