Simulating full-sky interferometric observations

Abstract

Aperture array interferometers, such as that proposed for the Square Kilometre Array (SKA), will see the entire sky, hence the standard approach to simulating visibilities will not be applicable since it relies on a tangent plane approximation that is valid only for small fields of view. We derive interferometric formulations in real, spherical harmonic and wavelet space that include contributions over the entire sky and do not rely on any tangent plane approximations. A fast wavelet method is developed to simulate the visibilities observed by an interferometer in the full-sky setting. Computing visibilities using the fast wavelet method adapts to the sparse representation of the primary beam and sky intensity in the wavelet basis. Consequently, the fast wavelet method exhibits superior computational complexity to the real and spherical harmonic space methods and may be performed at substantially lower computational cost, while introducing only negligible error to simulated visibilities. Low-resolution interferometric observations are simulated using all of the methods to compare their performance, demonstrating that the fast wavelet method is approximately three times faster that the other methods for these low-resolution simulations. The computational burden of the real and spherical harmonic space methods renders these techniques computationally infeasible for higher resolution simulations. High-resolution interferometric observations are simulated using the fast wavelet method only, demonstrating and validating the application of this method to realistic simulations. The fast wavelet method is estimated to provide a greater than ten-fold reduction in execution time compared to the other methods for these high-resolution simulations.

16 pages, 9 figures, replaced to match version accepted by MNRAS (major additions to previous version including new fast wavelet method)

References in corpus (14)

• Maps of Dust IR Emission for Use in Estimation of Reddening and CMBR Foregrounds
• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Extrapolation of Galactic Dust Emission at 100 Microns to CMBR Frequencies Using FIRAS
• Wavelets, ridgelets and curvelets on the sphere
• Interferometric Observation of Cosmic Microwave Background Anisotropies
• Exact reconstruction with directional wavelets on the sphere
• Correspondence principle between spherical and Euclidean wavelets
• Applications of Wavelets to the Analysis of Cosmic Microwave Background Maps
• Testing the Gaussianity of the COBE-DMR data with spherical wavelets
• Observability of secondary Doppler peaks in the CMBR power spectrum by experiments with small fields
• Complex Visibilities of Cosmic Microwave Background Anisotropies
• Mosaicking with cosmic microwave background interferometers
• Full-sky correlation functions for CMB experiments with asymmetric window functions

Cited by in corpus (28)

• Compressed sensing imaging techniques for radio interferometry
• All-Sky Interferometry with Spherical Harmonic Transit Telescopes
• Coaxing Cosmic 21cm Fluctuations from the Polarized Sky using m-mode Analysis
• HI as a Probe of the Large Scale Structure in the Post-Reionization Universe
• Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods
• Compressed sensing for wide-field radio interferometric imaging
• Robust sparse image reconstruction of radio interferometric observations with purify
• Spread spectrum for imaging techniques in radio interferometry
• A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
• Localisation of directional scale-discretised wavelets on the sphere
• Software Holography: Interferometric Data Analysis for the Challenges of Next Generation Observatories
• Sky reconstruction from transit visibilities: PAON-4 and Tianlai Dish Array
• Second-Generation Curvelets on the Sphere
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• Directional spin wavelets on the sphere
• Deconvolving the Wedge: Maximum-Likelihood Power Spectra via Spherical-Wave Visibility Modeling
• Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
• SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
• Revisiting the spread spectrum effect in radio interferometric imaging: a sparse variant of the w-projection algorithm
• A fast and exact $w$-stacking and $w$-projection hybrid algorithm for wide-field interferometric imaging
• Sparse image reconstruction on the sphere: analysis and synthesis
• The w-effect in interferometric imaging: from a fast sparse measurement operator to super-resolution
• Imaging on a Sphere with Interferometers: the Spherical Wave Harmonic Transform
• Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs
• $w$-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
• Scale-discretised ridgelet transform on the sphere
• All-Sky Imaging with Vector Sensor Interferometry