There isn’t really any perfect choice for images with a square lattice of sample points. With a one-dimensional signal you don’t get the same annoying patterns from the interaction of the two grids along different dimensions.
If you use a equilateral triangle grid (if you like, think of hexagonal pixels) you can do better.
I don't think it is exactly the same as the Airy disc, but it's a good question. http://mathworld.wolfram.com/SincFunction.html