The Rayleigh criterion for optical resolution suggests that the closest two resolvable objects are separated by a distance $r \sim \frac{\lambda}{2NA}$, where $\lambda$ is the wavelength of my light source and $NA$ is the numerical aperture of the lens. This condition for optical resolution is based on the Fraunhofer diffraction pattern formed at the focus of our lens.
Since the Fraunhofer diffraction scheme assumes that the source is temporally coherent (one wavelength) and spatially coherent (well-defined phase front), does the Rayleigh criterion generalize to incoherent light? Should my theoretical resolution be better or worse if I use a coherent source?