Understanding and Using Fourier Transform Thin Film Design Without Advanced Calculus

A desired reflectance profile versus frequency (wavenumber) can be directly Fourier transformed into the index of refraction profile as a function of thickness which would produce the desired spectral reflectance profile. This tool has existed for some years now but does not seem to be in common use. This paper lays out some of the principles to aid in making the process more understandable, intuitive, and useful without recourse to higher mathematics. If nothing else, the Fourier transform technique can provide a good starting point for further design optimization with commonly used techniques. It can be very valuable for new and unusual thin film design problems for which previous experience is of little guidance. It can also add insight into underlying principles of common designs of longstanding.