Definition of the instrumental setup. The observed astrophysical scene consists of the star, the planet, the exozodiacal dust (exozodi; ellipse) and the local zodiacal dust (local zodi; shaded area). The four collectors are shown in the X-array configuration, rotating around the line of sight, which is centered on the star to null its light. The shorter baseline between two collectors is called the nulling baseline, while the longer one is called the imaging baseline. Amplitude, phase, and polarization angle perturbations are introduced in the input beams. The beams are combined in the beam combiner to form different outputs. For a double Bracewell nuller, four inputs are combined into two bright (left and right) and two dark (bottom) outputs. The dark outputs are spatially filtered using a single mode fiber (SMF), fed into a spectrograph and measured on the detectors. The measured signals are then combined in post-processing to form the so-called differential output. This figure is adapted from O. P. Lay (2004).