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

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.

(Fixed references missing in previous arxiv version). This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review

References in corpus (5)

• A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
• 3DEX: a code for fast spherical Fourier-Bessel decomposition of 3D surveys
• Simulating full-sky interferometric observations
• Complex Visibilities of Cosmic Microwave Background Anisotropies
• Direct reconstruction of spherical harmonics from interferometer observations of the CMB polarization

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• The Role of the Instrumental Response in 21 cm EoR Power Spectrum Gridding Analyses
• Robust Foregrounds Removal for 21-cm Experiments
• Imaging the Southern Sky at 159MHz using Spherical Harmonics with the Engineering Development Array 2