a 2D fast Fourier transform (FFT) can be used to estimate the sky brightness distribution [@Taylor99 p. 134ff]. Mathematically, the grid is evaluated at a point $(u_c, v_c)$ by multiplying each visibility by a shifted convolution function according to:

$$F(u_c, v_c) = \sum_{k=1}^{M}{C(u_c - u_k, v_c - v_k, w_k) V(u_k, v_k, w_k)} \label{eq:gridsum}$$

where $M$ is the number of visibilities in to be gridded, $u$, $v$, and $w$ are the coordinates of the projected baseline (in wavelengths), $C(u, v, w)$ is a convolution function and $V(u, v, w)$ is the measured visibility weight. Typically, $C$ is assumed to be zero outside some region of support (6–8 pixels). If we take no account for the $w$ term, then the convolution function is chosen to be an anti-aliasing function, and is independent of $w$, i.e. $C(u,v,w) = A(u,v)$. If we account for the $w$ term using $w$-projection of @Cornwell08, then the convolution function is given by

$$C(u, v, w) = A(u, v) * G(u, v, w) \label{eq:convfunc}$$

where $*$ denotes convolution, $A(u, v)$ is an anti-aliasing function, and

$$G(u, v, w) = \frac{i}{w} \exp \left (-\pi i [u^2 + v^2]/w \right ) \label{eq:fresnel}$$

is the Fresnel diffraction term required by the $w$ 