Generalized formalisms of the radio interferometer measurement equation

The radio interferometer measurement equation (RIME) is a matrix-based mathematical model that describes the response of a radio interferometer. The Jones calculus it employs is not suitable for describing the analogue components of a telescope. This is because it does not consider the effect of impedance mismatches between components. This paper aims to highlight the limitations of Jones calculus, and suggests some alternative methods that are more applicable. We reformulate the RIME with a different basis that includes magnetic and mixed coherency statistics. We present a microwave network inspired 2N-port version of the RIME, and a tensor formalism based upon the electromagnetic tensor from special relativity. We elucidate the limitations of the Jones-matrix-based RIME for describing analogue components. We show how measured scattering parameters of analogue components can be used in a 2N-port version of the RIME. In addition, we show how motion at relativistic speed affects the observed flux. We present reformulations of the RIME that correctly account for magnetic field coherency. These reformulations extend the standard formulation, highlight its limitations, and may have applications in space-based interferometry and precise absolute calibration experiments.