There are significant recent interests in using nanophotonic structures to perform computations in the optical domain. Specifically in optical image processing, there have been a number of demonstrations using nanophotonic structures to perform edge detection and spatial filtering operations on images without the bulky 4f systems. These structures have the advantage of being compact, fast and low power. However, all previous works using nanophotonic structures, can only operate with coherent light. Here we introduce a hybrid optoelectronic approach that enables one to use nanophotonic structures to perform differentiation operation with spatially incoherent light. As a demonstration we consider a photonic crystal slab structure, and show that differentiation operation with incoherent light can be achieved by subtracting the two output images at two different frequencies, after passing through the designed structure. Both second order and first order differentiation are demonstrated with corresponding structure design. Our method is robust to noise compared to exact differentiation computation, and directly integrable into existing image sensors. This approach points to a new avenue for improving image sensors using nanophotonic structures, and has potential applications in real scene image processing and object recognition.
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