  We provide a complete theory of the phase closure of a binary system in which
a small, feeble, and unresolved companion acts as a perturbing parameter on the
spatial frequency spectrum of a dominant, bright, resolved source. We
demonstrate that the influence of the companion can be measured with precision
by measuring the phase closure of the system near the nulls of the primary
visibility function. In these regions of phase closure nulling, frequency
intervals always exist where the phase closure signature of the companion is
larger than any systematic error and can then be measured.We show that this
technique allows retrieval of many astrophysically relevant properties of faint
and close companions such as flux, position, and in favorable cases, spectrum.
We conclude by a rapid study of the potentialities of phase closure nulling
observations with current interferometers and explore the requirements for a
new type of dedicated instrument.
