  System equivalent flux density (SEFD) is an important figure of merit of a
radio telescope. This paper aims to derive a general expression for SEFD of a
polarimetric tripole interferometer. The derivation makes only two basic and
reasonable assumptions. First, the noise under consideration is zero mean and
when expressed in complex phasor domain, has independent and identically
distributed (iid) real and imaginary components. Correlated and non-identically
distributed noise sources are allowed as long as the real and imaginary
components remain iid. Second, the system noise is uncorrelated between the
elements separated by a baseline distance. The SEFD expression is derived from
first principles, that is the standard deviation of the noisy flux estimate in
a target direction due to system noise. The resulting SEFD expression is
expressed as a simple matrix operation that involves a mixture of the system
temperatures of each antenna and the Jones matrix elements. It is not limited
to tripoles, but rather, fully extensible to multipole antennas; it is not
limited to mutually orthogonal antennas. To illustrate the usefulness of the
expression and how the formula is applied, we discuss an example calculation
based on a tripole interferometer on lunar orbit for ultra-long wavelengths
observation. We compared the SEFD results based on a formula assuming short
dipoles and the general expression. As expected, the SEFDs converge at the
ultra-long wavelengths where the dipoles are well-approximated as short
dipoles. The general SEFD expression can be applied to any multipole antenna
systems with arbitrary shapes.
