spheroidal wavefunctions. This means that the imaging performance of the two approaches is essentially the same (except for the errors in truncating the Taylor series of the FGT) and the support size of the convolution functions is also easily computed.

We assume standard $w$ projection computes the convolution functions in advance and stores them in memory. We assume a convolution function of 1-D size for the $k$th $w$-plane $M_{\rm k} = k \Delta w$, where $k$ is an integer, and $\Delta w$ difference in size between different $w$ planes. Usually the cached convolution function is oversampled by a factor $\kappa$ of 4–8 in order to accurately grid visibilities whose coordinates are not exactly in the center of a $uv$ cell.

We assume that we truncate the convolution function when the real envelope reaches a value $\epsilon$, which is at a distance $t_\epsilon = \sqrt{- \delta_R \log \epsilon}$ from the centre of the convolution function. Therefore, the 1D support size in pixels, of the $k$th $w$-plane is (by substituting Equation \[eq:deltar\])

$$\begin{aligned}
M_{k} & = &2 t_\epsilon \nonumber \\
& = & 2 \sqrt{\log \epsilon \left (\delta_A + \frac{k^2 \Delta w^2}{\pi^2 \delta_A}  \right )}\end{aligned}$$

### Operations count

Gridding a visibility requires 