The Adaptive Optics Lucky Imager (AOLI) is a new instrument under development to demonstrate near diffraction limited imaging in the visible on large ground-based telescopes. We present the adaptive optics system being designed for the instrument comprising a large stroke deformable mirror, fixed component non-linear curvature wavefront sensor and photon-counting EMCCD detectors. We describe the optical design of the wavefront sensor where two photoncounting CCDs provide a total of four reference images. Simulations of the optical characteristics of the system are discussed, with their relevance to low and high order AO systems. The development and optimisation of high-speed wavefront reconstruction algorithms are presented. Finally we discuss the results of simulations to demonstrate the sensitivity of the system.