  Nulling interferometry aims to detect faint objects close to bright stars.
Its principle is to produce a destructive interference along the line-of-sight
so that the stellar flux is rejected, while the flux of the off-axis source can
be transmitted. In practice, various instrumental perturbations can degrade the
nulling performance. Any imperfection in phase, amplitude, or polarization
produces a spurious flux that leaks to the interferometer output and corrupts
the transmitted off-axis flux. One of these instrumental pertubations is the
crosstalk phenomenon, which occurs because of multiple parasitic reflections
inside transmitting optics, and/or diffraction effects related to beam
propagation along finite size optics. It can include a crosstalk of a beam with
itself, and a mutual crosstalk between different beams. This can create a
parasitic interference pattern, which degrades the intrinsic transmission map -
or intensity response - of the interferometer. In this context, we describe how
this instrumental effect impairs the performance of a Bracewell interferometer.
A simple formalism is developed to derive the corresponding modified intensity
response of the interferometer, as a function of the two parameters of
interest: the crosstalk level (or contamination rate) and the phase shift
between the primary and secondary - parasitic - beams. We then apply our
mathematical approach to a few scientific cases, both analytically and using
the GENIEsim simulation software, adapted to handle coherent crosstalk. Our
results show that a coherent crosstalk level of about 1% implies a 20% drop of
the SNR at most. Careful attention should thus be paid to reduce the crosstalk
level inside an interferometric instrument and ensure an instrumental stability
that provides the necessary sensitivity through calibration procedures.
