Simple Fourier optics formalism for high-angular-resolution systems and nulling interferometry

Reviewed are various designs of advanced, multiaperture optical systems dedicated to high-angular-resolution imaging or to the detection of exoplanets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing their basic theoretical relationships to be derived as convolution or cross-correlation products suitable for fast and accurate computation. Several unusual designs, such as a "superresolving telescope" utilizing a mosaicking observation procedure or a free-flying, axially recombined interferometer are examined, and their performance in terms of imaging and nulling capacity are assessed. In all considered cases, it is found that the limiting parameter is the diameter of the individual telescopes. A final section devoted to nulling interferometry shows an apparent superiority of axial versus multiaxial recombining schemes. The entire study is valid only in the framework of first-order geometrical optics and scalar diffraction theory. Furthermore, it is assumed that all entrance subapertures are optically conjugated with their associated exit pupils.