Photobombing for the Large Interferometer For Exoplanets (LIFE). A new criterion for target confusion and application to a MIR rotating nulling interferometer

One of the primary objectives in modern astronomy is to discover and study planets with characteristics similar to Earth. This pursuit involves analyzing the spectra of exoplanets and searching for biosignatures. Contamination of spectra by nearby objects (e.g., other planets and moons in the same system) is a significant concern and must be addressed for future exo-Earth searching missions. The aim is to estimate, for habitable planets, the probability of spectral contamination by other planets within the same star system. This investigation focuses on the Large Interferometer for Exoplanets (LIFE). Since the Rayleigh criterion is inapplicable to interferometers such as those proposed for LIFE, we present new criteria based on the principle of parsimony, which take into account two types of issues: contamination or blending of point sources, and cancellation of point sources due to destructive interference. We define a new spatial resolution metric associated with contamination or cancellation that generalizes to a broader family of observing instruments. In the current baseline design, LIFE is an X-array architecture nulling interferometer. Our investigation reveals that its transmission map introduces the potential for two point sources to appear as one, even if they do not appear in close proximity. We find that LIFE has a spatial resolution comparable to that of a traditional telescope with a diameter of $D = 600\,\text{m}$, observing at $λ= 4 \,μ\text{m}$. Our survey of a star system population shows that, out of 73.4 expected habitable planets detected, 71.3 are not contaminated on average.