Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm.

We propose a simple and robust polynomial-based phase-fitting (PPF) technique for single interferogram demodulation. Based on the smoothness assumption, the method employs a set of Zernike polynomials (ZPs) to fit the phase and estimates the expansion coefficients using a global optimization algorithm, i.e., differential evolution. The fitting order of the ZPs and the bounds of the coefficients can be intuitively determined according to the shape and number of fringes of the interferogram. Different from classical methods that need predefined scanning paths to guide the phase estimator, the PPF demodulates an interferogram globally and is insensitive to local defects, which allows it to deal with very noisy interferograms. Moreover, as the PPF gives the reconstructed phase by use of the ZPs, no further phase-unwrapping or wavefront-fitting procedures are needed. Experimental results have demonstrated the robustness and effectiveness of the method.