Figure 9: Error introduced in the pseudo correction when the geometric mean
of 
and 
is replaced by the arithmetic mean
Much of the data reduction procedure detailed in this paper can be applied
even if the photometric signals 
and 
cannot be measured (if for
example the fiber unit contains only a single X coupler), provided that the
scintillation noise and the fringe signal do not overlap in the spectrum of
I(x). In that case Sect. 4 (click here) is no longer relevant
and a simple filtering can separate the high frequency fringe signal
from the low frequency scintillation noise
. We can then build a ``pseudo corrected''
interferometric signal 
as:
The pseudo correction consists in approximating the geometric mean of
and 
by the
arithmetic mean. The ratio of the geometric mean to the arithmetic mean is
plotted in Fig. 9 (click here). The approximation leads to
a systematic underestimate of the coherence factor, the amount of which
depends on the statistics of the scintillation.
By extension, the same procedure can be used for any pupil plane
interferometer, provided that the data be obtained by recording a scan
around the zero OPD. It represents then an approach complementary to what
was proposed by Benson et al. (1995). In a dioptric
interferometer (using mirrors and beamsplitters) the photometric signals,
affected only by atmospheric scintillation, are equal in average (assuming
identical pupils) and much more stable than in a fiber interferometer. Then
the bias introduced by the approximation in Eq. (75 (click here))
is usually negligible. Indeed the error is less than 1% if 
and
do not differ by more than 30%. With a dioptric interferometer
however, an atmospheric transfer function 
is
involved between the measured coherence factor and the object visibility
(Eq. 1 (click here)), and the classical calibration problems
remain.