Incoherent Optoelectronic Differentiation Based on Optimized Multilayer Films

Fourier-based optical computing operations, such as spatial differentiation, have recently been realized in compact form factors using flat optics. Experimental demonstrations, however, have been limited to coherent light requiring laser illumination and leading to speckle noise and unwanted interference fringes. Here, the use of an optimized multilayer film, combined with dual color image subtraction, is demonstrated to realize differentiation with unpolarized incoherent light. Global optimization is achieved by employing neural networks combined with the reconciled level set method to optimize the optical transfer function of a multilayer film at wavelengths of 532 and 633 nm. Spatial differentiation is then achieved by subtracting the normalized incoherent images at these two wavelengths. The optimized multilayer film is experimentally demonstrated to achieve incoherent differentiation with a resolution of 6.2 mu$\umu$m. The use of a multilayer film allows for scalable lithography-free fabrication and results in a system that could open the door to high-speed processing for a wide variety of incoherent, and coherent, imaging systems.