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.
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