Airy disk
Rayleigh's resolution limit is reached when the two stars are separated by the theoretical radius of the first dark interval around the Airy disk, which is larger than the disk's apparent radius, so that a distinct dark gap appears between the two disks. Most astronomers say they can still distinguish the two stars when they are closer than Rayleigh's resolution limit. Sparrow's Resolution Limit is reached when the combined light from two overlapping and equally bright Airy disks is constant along a line between the central peak brightness of the two Airy disks. However, at the Sparrow resolution limit the two Airy disks will appear to be just touching at their edges, which according to Sparrow is due to a brightness contrast response of the eye. The same reasoning applies to the resolution of two wavelengths in a spectroscope, where lines of emission or absorption will have a diffraction induced width analogous to the diameter of an Airy disk.