Non-destructive Optical Characterization Tools: Spectral Interferometry Using Minimum-phase Functions

Fourier transform theory is one of the most widely used tools in physical sciences to retrieve vital information about various physical phenomena. In general, because a Fourier transform is a complex quantity, both its phase and magnitude are required for a unique representation of the function of interest. However, in many applications, only the magnitude of the Fourier transform can be measured, and a direct measurement of its phase is rather difficult. This constitutes a fundamental limitation in many fields, since the function of interest cannot be recovered uniquely from its Fourier transform magnitude measurement alone. In this book, a special family of functions, so called the minimum-phase functions, for which the Fourier transform phase can be recovered from the Fourier transform magnitude alone, is discussed. We apply this concept to several important fields of physics, and show in each case that with a simple magnitude spectrum measurement and data processing, we can recover the function of interest unambiguously. In all cases, this approach has led to significant breakthroughs, as well as simpler and faster measurements and processing.