Demodulation of a single closed-fringe interferogram with symmetric wavefront and tilt

A phase recovery method from a single fringe pattern with closed fringes is developed. The interferogram is first normalized and then rotated to create a new fringe pattern. Both interference images are multiplied which results in the sum of the cosines of the symmetric and asymmetric components of the phase respect to the rotating axis. If the original phase contains tilt and also possesses a high degree of symmetry respect to the rotating axis, the cosine of the asymmetric term will be composed of tilt and a small asymmetric term. In this case, the Fourier transform of the multiplication will be given by two high intensity peaks localized symmetrically respect to the origin and a broader lobule centered at the origin. The asymmetric component of the phase is then recovered with a Fourier method and used to calculate the phase of the original interferogram. The above procedure may serve as an alternative to other methods that works iteratively to recover the phase from a single interferogram with closed fringes as it is demonstrated in experimental and simulated data.