The highest resolution images ever taken in the visible were obtained by combining Lucky Imaging and low order adaptive optics. This paper describes a new instrument to be deployed on the WHT 4.2m and GTC 10.4 m telescopes on La Palma, with particular emphasis on the optical design and the expected system performance. A new design of low order wavefront sensor using photon counting CCD detectors and multi-plane curvature wavefront sensor will allow dramatically fainter reference stars to be used, allowing virtually full sky coverage with a natural guide star. This paper also describes a significant improvements in the efficiency of Lucky Imaging, important advances in wavefront reconstruction with curvature sensors and the results of simulations and sensitivity limits. With a 2 x 2 array of 1024 x 1024 photon counting EMCCDs, AOLI is likely to be the first of the new class of high sensitivity, near diffraction limited imaging systems giving higher resolution in the visible from the ground than hitherto been possible from space.