The standard wide-field imaging technique, the w-projection, allows
correction for wide-fields of view for non-coplanar radio interferometric
arrays. However, calculating exact corrections for each measurement has not
been possible due to the amount of computation required at high resolution and
with the large number of visibilities from current interferometers. The
required accuracy and computational cost of these corrections is one of the
largest unsolved challenges facing next generation radio interferometers such
as the Square Kilometre Array. We show that the same calculation can be
performed with a radially symmetric w-projection kernel, where we use one
dimensional adaptive quadrature to calculate the resulting Hankel transform,
decreasing the computation required for kernel generation by several orders of
magnitude, whilst preserving the accuracy. We confirm that the radial
w-projection kernel is accurate to approximately 1% by imaging the
zero-spacing with an added w-term. We demonstrate the potential of our
radially symmetric w-projection kernel via sparse image reconstruction, using
the software package PURIFY. We develop a distributed w-stacking and
w-projection hybrid algorithm. We apply this algorithm to individually
correct for non-coplanar effects in 17.5 million visibilities over a 25 by
25 degree field of view MWA observation for image reconstruction. Such a
level of accuracy and scalability is not possible with standard w-projection
kernel generation methods. This demonstrates that we can scale to a large
number of measurements with large image sizes whilst still maintaining both
speed and accuracy.Comment: 9 Figures, 19 Pages. Accepted to Ap
