Fourier description of analysis and synthesis operations for a stack of thin films of equal optical thickness

Analysis and synthesis operations for a stack of dielectric layers with equal optical thickness are described in terms of the Wiener-Khintchine theorem with variables reflectance R and distribution of optical paths f. The method yields an infinite sequence of refractive indices that converge to a substrate index. An iterative process is used to determine the minimum phase solution, and all practical solutions are constructed from it by a root-shifting procedure. Realizability and practicability conditions are discussed.