Link between image size and $uv$ cell size

The gridding requires at least Nyquist sampling of the $uv$ plane to avoid the artifact known as aliasing. For the signal, the Nyquist sampling in the $uv$ plane is obtained with a size of the grid cells equal to half the size of the antenna diameter (this is the smallest spatial frequency that the interferometer can be sensitive to, i.e. the natural resolution in the $uv$ plane). In the image plane, this implies to make an image at least twice as large as the primary beam size (see Fourier transform property #2 in appendix). Unfortunately, the spatial frequencies of the noise are not bounded: Noise aliasing can not be avoided, i.e. the noise increases at the edges of the produced image.