Multi-layer structures described with the help of the superposition of two-layer solutions

For multi-layer systems consisting of e. g. three different layers, a solution method is proposed which relies on the superposition of two-layer solutions, determined separately from the two relative extrema of the inverse calibrated modulated IR phases. Starting from the two-layer solutions, the inverse calibrated IR phases are iteratively approximated using a three-layer model, whereby first the approximation for the relative extremum at low modulation frequencies is improved, while the solution for the extremum at high modulation frequencies is maintained constant. In the next step, the solution for the extremum at high modulation frequencies is improved, while the solution at low modulation frequencies remains constant. If the two relative extrema are measured at rather different modulation frequencies, this alternate iteration procedure rapidly converges, e. g. after six iterations, and the final solutions are found in the neighborhood of the initial two-layer solutions.