Imaging on a Sphere with Interferometers: the Spherical Wave Harmonic Transform

TL;DR

This paper introduces an exact solution for radio interferometer imaging on a spherical surface, enabling accurate wide-field imaging and spherical harmonic analysis, especially useful for non-coplanar arrays and future multi-spacecraft interferometers.

Contribution

It provides a novel explicit solution to the interferometer imaging equation on a sphere, removing the need for $w$-term corrections and facilitating direct spherical harmonic identification.

Findings

Exact solution for spherical interferometer imaging equation.

Applicable to non-coplanar and wide-field configurations.

Enables direct spherical harmonic analysis of sky signals.

Abstract

I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is comparable to $w$-term imaging algorithms, but by using a spherical rather than a Cartesian formulation this term has no special significance. The solution presented also allows direct identification of the scalar (spin 0 weighted) spherical harmonics on the sky. The method should be of interest for future multi-spacecraft interferometers, wide-field imaging with non-coplanar arrays, and CMB spherical harmonic measurements using interferometers.