A super-resolution telescope. A target is illuminated with at least three laser beams, each beam having a slightly different frequency so as to produce an illumination pattern comprised of several sets of straight interference fringes which sweep across the target. The frequencies of the illumination beams are chosen so that each pair of beams has a unique beat frequency, and the corresponding fringe pattern for each pair sweeps over the target at a unique speed. By collecting a series of images, and demodulating them at the various beat frequencies, the downshifted spatial frequencies can be identified, correctly up-shifted, and fitted together with a set of special Fourier transform based algorithms to reconstruct high-resolution images. Applicants have performed laboratory experiments that this invention can provide resolution substantially better than diffraction limited resolution.