System Equivalent Flux Density of a Polarimetric Tripole Radio Interferometer

Abstract

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.