Resolution of two problems in the Fourier analysis of thin films

The most common approaches to the application of the Fourier transform method to the synthesis of thin films suffer from two difficulties. The function of reflectance or transmittance to be transformed has been variously approximated, but none of the approximations has been recognized as giving accurate results for all cases. The transformed results for high-reflectance cases have what appear to be distortions in the frequency and in the amplitude scales. These problems and their solutions are the subjects of this paper. It is shown that the reflectance amplitude is the function that should be transformed and that the inclusion of multiple reflections eliminates the distortions in frequency and amplitude.