An a posteriori method to cancel out atmospheric optical path fluctuations to achieve accurate phase restoration and spectral analysis of interferograms is presented in this paper. The correction algorithm is based on classical noise reduction methods. The consequence of piston noise is twofold: 1) loss of spectral information; 2) loss of visibility phase. A method to measure the modulus and the phase gradient of visibilities is explained and examples of restoration of simulated spectra and visibilities for various ratios are presented.