We have recently shown that a posteriori co-phasing of multi-spectral interferograms was possible. 1 In this contribution, we extend our approach so that it can be applied to actual data as provided by Amber 2 or Matisse instruments. The main advantage of the proposed post-processing technique is that it requires no modifications of the instruments and yields interferometric observables with higher SNR and much fewer unknowns (in particular for the Fourier phase) than conventional measurements. In order to perform the co-phasing of a complete sequence of interferograms, we jointly estimate a global phase template and the frame dependent optical path errors due to the turbulence. We show that this strategy is effective for very low SNR data. We assess the effectiveness of our method on simulated and actual AMBER data. We also compare the lowest SNR that can be achieved to the theoretical bounds and estimate the gain in sensitivity compared to usual interferometric data. To overcome turbulence effects and yet reach a reasonable signal to noise ratio (SNR), interferometric observables require to integrate information over many short exposure frames computed from the so-called coherent fluxes. 3, 4 Our objective is to compensate for the variable phase changes during a given sequence so that it is possible to perform a direct integration of the coherent fluxes over many short exposures, before the computation of the long exposure chromatic complex visibilities. 1.1 Maximum Likelihood Criterion Let c ,m ∈ C be the coherent flux measured in-th spectral channel and m-th frame; it is related to the complex visibility c obj ∈ C of the observed object at the wavelength λ of the spectral channel by: 3, 4 c ,m = c atm ,m c inst c obj + n ,m , (1) where c inst ∈ C is a static instrumental complex visibility, c atm ,m ∈ C is a variable complex factor mainly due to atmospheric effects and n ,m accounts for the noise. Our objective is to provide an estimator closely related to c stat def = c inst c obj , the static part of the coherent flux. Getting rid of the c inst factor is a matter of calibrating this term either by means of internal calibration sources or by observing a calibrator whose complex visibility is known. Since we are interested in compensating for variable phase shifts, we rewrite the direct model in Eq. (1) as: c ,m = ρ ,m e i (ϕ +ψ ,m) + n ,m , (2)