The Effect of $w-term$ on Visibility Correlation and Power Spectrum Estimation

TL;DR

This paper investigates how the $w$-term affects visibility correlation and power spectrum estimation in large field of view radio interferometry, revealing that it modifies the aperture function and impacts measurements at certain baselines.

Contribution

It demonstrates that the $w$-term causes a Gaussian-envelope oscillation in the aperture function, affecting power spectrum estimation beyond a specific baseline, especially at larger wavelengths.

Findings

The $w$-term modifies the primary aperture to an oscillating function with a Gaussian envelope.

Visibility correlation can recover the power spectrum beyond a baseline determined by the aperture width.

The maximum baseline affected by the $w$-term is independent of observation frequency.

Abstract

Visibility-visibility correlation has been proposed as a technique for the estimation of power spectrum, and used extensively for small field of view observations, where the effect of $w-term$ is usually ignored. We consider power spectrum estimation from the large field of view observations, where the $w-term$ can have a significant effect. Our investigation shows that a nonzero $w$ manifests itself as a modification of the primary aperture function of the instrument. Using a gaussian primary beam, we show that the modified aperture is an oscillating function with a gaussian envelope. We show that the two visibility correlation reproduces the power spectrum beyond a certain baseline given by the width, $U_{w}$ of the modified aperture. Further, for a given interferometer, the maximum $U_{w}$ remains independent of the frequencies of observation. This suggests that, the incorporation of large field of view in radio interferometric observation has a greater effect for larger observing wavelengths.