Realization of a sign-distinguishable higher-order optical differentiation

A differential operation, which can highlight features of images, is of significant importance in fields such as machine vision. As a front-end action, optical differentiation can overcome the shortcomings of traditional computer differentiation and runs at the speed of light. Compared with the conventional first-order optical differentiation technique, a higher-order one with the correct sign of a differential field obtained can facilitate the recognition of finer features, although relevant studies are relatively scarce. Here, we propose a method to realize sign-distinguishable arbitrary-order optical differentiation by coupling the momentum and polarization of a light field, the feasibility of which is further confirmed by a proof-of-principle experiment. We hope our method will promote the development of optical analog computing, image recognition, and other relevant applications.