In order to further reduce the volume of optical correlator, an optical correlator for folding reflective 2f system is designed. The optical path adopts folding reflective structure. Digital micro lens replaces physical lens in the traditional correlator to reduce the volume of the structure and improve the system integration. The structural design conditions and structural parameters of the folding reflective 2f correlator are given theoretically based on equivalent optical path method. The optimal trade-off share duplexed filter (SDF) is designed for the correlator, and the simulation analysis is performed by a self-compiled program. Simulation results indicate that the correlator still has good distortion invariant recognition performance when the target is subject to scaling and rotation distortion.