Interferometric Closure Phase (CP) yields information on the asymmetries of the source brightness distribu tion. While accurate closure phases are the key for detecting, odeling and imaging low contrast features, their experimental accuracy is usually far from what it could be: in the case of the AMBER/VLTI instrument, the guaranteed accuracy calibration is between 3 and 5 degrees, while the theoretical limit is better than 0.01 deg for bright sources. Closure phase should first be corrected for detection artifacts (mainly drifts in the detector and optics), using in our case the AMBER Beam Commutation Device. We show that closure phase is nevertheless contaminated by the pistons drifts of each baseline. This effect is attributed to a cross-talk between the fringes peaks, which cannot be completely avoided in a multi-axial beam combiner with a limited readout window. We show that the variable bias on CP is a linear function of the external pistons. This relationship can be determined from the calibration source data and applied for correcting the science data. The global process both unbiases and stabilizes the average CP, yielding, with our measurements, an accuracy of 0.3 deg for 1 minute exposures with ATs, which is close to the fundamental limit for our K=4 source. It also allows to correct the chromatic OPD effect by comparison with a well chosen calibrator, displaying a CP vs. wavelength curve with aRMS error of 0.1 deg per spectral channel, about a factor 3 to 4 better than with a straight calibration.
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