Optimal beam combiner design for nulling interferometers

A scheme to optimally design a beam combiner is discussed for any predetermined fixed geometry nulling interferometer aimed at detection and characterization of exoplanets with multiple telescopes or a single telescope (aperture masking).We show that considerably higher order nulls can be achieved with 1D (one-dimensional) interferometer geometries than possible with 2D (two-dimensional) geometries with the same number of apertures. Any 1D interferometer with N apertures can achieve a 2{eth}N 1{Thorn}-order null, while the order of the deepest null for a random 2D aperture geometry interferometer is the order of the Nth term in the Taylor expansion of e^i(x2+y2) around x = 0, y = 0 (2nd order null for N = 2; 3; 4th order null for N = 4; 5; 6).We also show that an optimal beam combiner for nulling interferometry relies on only 0 or π phase shifts. Examples of nulling interferometer designs are shown to illustrate these findings.