Fractional derivative applied to the retrieval of phase distribution from an interferogram

Abstract

This paper proposes a new method for determining the phase distribution of a 2D fringe pattern using 2D fractional derivatives. The fractional derivative of order r (real 0≤r≤3), in the θ direction (θ∈[0,2π]) is defined by the Fourier transform and its inverse and gives as result a phase distribution. The fractional derivative of order r produces a phase displacement of rπ/2 without significantly changes in normalized amplitude distribution. There are optimum values of r and θ for which the phase distribution given by the fractional derivative represents the phase distribution for the fringe pattern. Also, we demonstrate the usefulness of a method based on four fractional derivatives to determine the phase and intensity distribution from a single interferogram and highlights small objects located in the fringe pattern. We demonstrate the proposed method using both numerical simulated and experimental interferograms.