On super-resolution in astronomical imaging

Our work is an attempt to fulfil one of the aims of astronomical imaging, that is, to obtain information at high angular resolution. Stars as point sources can be represented by Dirac δ -functions whose Fourier transforms contain information about the position and the (integrated) intensity at all angular frequencies. Thus, we can deconvolve unresolved images of star fields even at angular distances smaller than the diffraction limit of the telescope with which the observations are performed. We give an example of reconstruction of the image of two stars with an angular separation of a factor 2.5 less than $\alpha_\mathrm{Ra}=1.22\times\lambda/D$. However, we find that super-resolution is feasible only for point sources. For extended objects the information about intensity fluctuations at angular frequencies $u>u_\mathrm{max}=D/\lambda=1/\alpha_\mathrm{min}$ is irretrievably lost. We discuss the impossibility of super-resolution for the Sun using a numerically simulated image of solar granulation. However, one can enhance the contrast of solar images, though without increasing angular resolution beyond the diffraction limit.