  We discuss the theory of the Bracewell nulling interferometer and explicitly
demonstrate that the phase of the "white light" null fringe is the same as the
phase of the bright output from an ordinary stellar interferometer. As a
consequence a "closure phase" exists for a nulling interferometer with three or
more telescopes. We calculate the phase offset as a function of baseline length
for an Earth-like planet around the Sun at 10 pc, with a contrast ratio of
$10^{-6}$ at 10 $\mu$m. The magnitude of the phase due to the planet is $\sim
10^{-6}$ radians, assuming the star is at the phase center of the array.
Although this is small, this phase may be observable in a three-telescope
nulling interferometer that measures the closure phase. We propose a simple
non-redundant three-telescope nulling interferometer that can perform this
measurement. This configuration is expected to have improved characteristics
compared to other nulling interferometer concepts, such as a relaxation of
pathlength tolerances, through the use of the "ratio of wavelengths" technique,
a closure phase, and better discrimination between exodiacal dust and planets.

Astrophysics