Disintegration of multiple-beam Fizeau fringes in transmission using FFT analysis
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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.
The author would like to thank Prof. Dr. A. A. Hamza the leader of optics research in Mansoura and Damietta Universities for his kind encouragement. Also, many thanks to optics research group members in Damietta University for their sincere collaborations.
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