System equivalent flux density of Stokes I, Q, U, V of a polarimetric interferometer

TL;DR

This paper derives formulas for the system equivalent flux density (SEFD) for all four Stokes parameters in polarimetric interferometry, enabling better sensitivity analysis for radio telescopes.

Contribution

It extends previous SEFD derivations for Stokes I to include Q, U, V, providing a unified matrix-based framework for all polarization states.

Findings

Derived explicit SEFD formulas for Q, U, V based on matrix trace representations.

Validated formulas with simulations and observations from the Murchison Widefield Array.

Demonstrated applicability to phased array and multipole interferometers.

Abstract

We present the system equivalent flux density (SEFD) expressions for all four Stokes parameters: I, Q, U, V. The expressions were derived based on our derivation of SEFD I (for Stokes I) and subsequent extensions of that work to phased array and multipole interferometers. The key to the derivation of the SEFD Q, U, V expressions is to recognize that the noisy estimates of Q, U, V can be written as the trace of a matrix product. This shows that the SEFD I is a special case, where the general case involves a diagonal or anti-diagonal 2x2 matrix interposed in the matrix multiplication. Following this step, the relation between the SEFD for I and Q, U, V becomes immediately evident. We present example calculations for a crossed dipole based on the formulas derived and the comparison between simulation and observation using the Murchison Widefield Array (MWA).