  With the development of modern radio interferometers, wide-field continuum
surveys have been planned and undertaken, for which accurate wide-field imaging
methods are essential. Based on the widely-used W-stacking method, we propose a
new wide-field imaging algorithm that can synthesize visibility data from a
model of the sky brightness via degridding, able to construct dirty maps from
measured visibility data via gridding. Results carry the smallest approximation
error yet achieved relative to the exact calculation involving the direct
Fourier transform. In contrast to the original W-stacking method, the new
algorithm performs least-misfit optimal gridding (and degridding) in all three
directions, and is capable of achieving much higher accuracy than is feasible
with the original algorithm. In particular, accuracy at the level of single
precision arithmetic is readily achieved by choosing a least-misfit convolution
function of width W=7 and an image cropping parameter of x0=0.25. If the
accuracy required is only that attained by the original W-stacking method, the
computational cost for both the gridding and FFT steps can be substantially
reduced using the proposed method by making an appropriate choice of the width
and image cropping parameters.
