The resolution of a telescope is its ability to separate two point sources into separate images. Under ideal conditions, such as above the atmosphere where there is no turbulence (seeing), the resolving power is limited by diffraction effects.
For a circular aperture, such as the objective lens of a refracting telescope or the primary mirror of a reflecting telescope, a point source will appear as a disk surrounded by many thin, faint rings. These rings are produced by Fraunhofer diffraction, and the shape of the rings is given by the equation:
where I(θ) is the irradiance at an angle θ, I(0) is the peak irradiance at the centre of the diffraction pattern, D=2a is the diameter of the aperture, k is the wave number and J1(u) is the first order Bessel function.
using the small angle approximation, sin θ ≈ θ for small θ.
If we look at the combined profile of the diffraction patterns produced by two point sources, we can see that when the Rayleigh criterion is satisfied, there is a dip between the two peaks. In practice, a telescope is able to resolve sources that are closer together than
so an alternative criterion for resolution was proposed by C. Sparrow (the Sparrow criterion). The minimum resolvable case now occurs when the central dip in the combined diffraction pattern just disappears.