Generalized Formalisms of the Radio Interferometer Measurement Equation

Abstract

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.

arXiv commentAccepted for publication in MNRAS

References in corpus (7)

• Revisiting the radio interferometer measurement equation. I. A full-sky Jones formalism
• A lower limit of dz > 0.06 for the duration of the reionization epoch
• Absolute calibration of a wideband antenna and spectrometer for sky noise spectral index measurements
• Stokes Parameters as a Minkowskian Four-vector
• A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
• Jones-matrix Formalism as a Representation of the Lorentz Group
• Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism

Cited by in corpus (5)

• Robust sparse image reconstruction of radio interferometric observations with purify
• Calibration errors in interferometric radio polarimetry
• A fast and exact $w$-stacking and $w$-projection hybrid algorithm for wide-field interferometric imaging
• $w$-stacking $w$-projection hybrid algorithm for wide-field interferometric imaging: implementation details and improvements
• Distributed and parallel sparse convex optimization for radio interferometry with PURIFY