A phase recovery procedure using interferograms acquired in highly noisy environments as severe vibrations is described. This method may be implemented when disturbances do not allow obtaining equidistant phase shifts between consecutive interferograms due to tilt-shift and nonlinearity errors introduced by the vibrating conditions. If the amount of the tilt-shift is greater than π radians, it will lead a sign change in the phase estimation. This situation cannot be handled correctly by algorithms that consider small errors or non-equidistant phase shifts during the phase shifting process under moderate disturbances. In experimental applications, it is observed that the tilt-shift is often the most dominant error in phase differences that one must deal with. In this work, a Fourier technique is used for the processing and recovering of the cosine of the phase differences. Once the phase differences are obtained, the phase encoded in the interferograms is determined. The proposed algorithm is tested in two sets of interferograms obtained from the analysis of an optical component, finding an rms error in the phase reconstructions of 0.1388 rad.