Disintegration of multiple-beam Fizeau fringes in transmission using FFT analysis

An investigation of fast Fourier transformation (FFT) spectrum appears from multiple-beam Fizeau fringes is presented. It is proven theoretically and demonstrated experimentally that the number of the appeared peaks is related to the interfered rays’ number. In addition, a detailed interpretation of (FFT) yields from multiple-beam Fizeau fringes analyses is illustrated. This interpretation proved that every peak of the FFT spectrum represents a set of two-beam interference. Therefore, the higher order FFT peaks are not an error. It is found that the frequencies of the appeared peaks are separated by a constant increment. Therefore, when we apply the inverse fast Fourier transformation (IFFT) on a selected peak we can get a two-beam intensity distribution image with a fringe frequency depending on the peak order number. This study removes confusion and answers some important questions concerning the multiple-beam interference. The presented analysis leads to disintegrate multiple-beam interferogram to its components of two-beam interferograms. This could facilitate recovering the phase map and provides more information from one multiple-beam interferogram.