  A new "self-calibrated" statistical analysis method has been developed for
the reduction of nulling interferometry data. The idea is to use the
statistical distributions of the fluctuating null depth and beam intensities to
retrieve the astrophysical null depth (or equivalently the object's visibility)
in the presence of fast atmospheric fluctuations. The approach yields an
accuracy much better (about an order of magnitude) than is presently possible
with standard data reduction methods, because the astrophysical null depth
accuracy is no longer limited by the magnitude of the instrumental phase and
intensity errors but by uncertainties on their probability distributions. This
approach was tested on the sky with the two-aperture fiber nulling instrument
mounted on the Palomar Hale telescope. Using our new data analysis approach
alone-and no observations of calibrators-we find that error bars on the
astrophysical null depth as low as a few 10-4 can be obtained in the
near-infrared, which means that null depths lower than 10-3 can be reliably
measured. This statistical analysis is not specific to our instrument and may
be applicable to other interferometers.
