We propose a new approach, based on the Hanbury Brown and Twiss intensity interferometry, to transform a Cherenkov telescope to its equivalent optical telescope. We show that, based on the use of photonics components borrowed from quantum-optical applications, we can recover spatial details of the observed source down to the diffraction limit of the Cherenkov telescope, set by its diameter at the mean wavelength of observation. For this, we propose to apply aperture synthesis techniques from pairwise and triple correlation of sub-pupil intensities, in order to reconstruct the image of a celestial source from its Fourier moduli and phase information, despite atmospheric turbulence. We examine the sensitivity of the method, i.e. limiting magnitude, and its implementation on existing or future high energy arrays of Cherenkov telescopes. We show that despite its poor optical quality compared to extremely large optical telescopes under construction, a Cherenkov telescope can provide diffraction limited imaging of celestial sources, in particular at the visible, down to violet wavelengths.