The observable quantities in optical interferometry, which are the modulus and the phase of the complex visibility, may be corrupted by parasitic fringes superimposed on the genuine fringe pattern. These fringes are due to an interference phenomenon occurring from straylight effects inside an interferometric instrument. We developed an analytical approach to better understand this phenomenon when straylight causes crosstalk between beams. We deduced that the parasitic interference significantly affects the interferometric phase and thus the associated observables including the differential phase and the closure phase. The amount of parasitic flux coupled to the piston between beams appears to be very influential in this degradation. For instance, considering a point-like source and a piston ranging from $lambda/500$ to $lambda/5$ in L band ($lambda=3.5:mu$m), a parasitic flux of about 1% of the total flux produces a parasitic phase reaching at most one third of the intrinsic phase. The piston, which can have different origins (instrumental stability, atmospheric perturbations, ...), thus amplifies the effect of parasitic interference. According to specifications of piston correction in space or at ground level (respectively $lambda/500approx 2$nm and $lambda/30approx 100$nm), the detection of hot Jupiter-like planets, one of the most challenging aims for current ground-based interferometers, limits parasitic radiation to about 5% of the incident intensity. This was evaluated by considering different types of hot Jupiter synthetic spectra. Otherwise, if no fringe tracking is used, the detection of a typical hot Jupiter-like system with a solar-like star would admit a maximum level of parasitic intensity of 0.01% for piston errors equal to $lambda$/15. If the fringe tracking specifications are not precisely observed, it thus appears that the allowed level of parasitic intensity dramatically decreases and may prevent the detection. In parallel, the calibration of the parasitic phase by a reference star, at this accuracy level, seems very difficult. Moreover, since parasitic phase is an object-dependent quantity, the use of a hypothetical phase abacus, directly giving the parasitic phase from a given parasitic flux level, is also impossible. Some instrumental solutions, implemented at the instrument design stage for limiting or preventing this parasitic interference, appears to be crucial and are presented in this paper.
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