Inverse design of incoherent multiple image differentiation with spatial multiplexing optical convolution

Optical edge detection has shown attractive research interests in target recognition and machine vision, due to the low computational power, parallel operation, and high speed. However, the incoherent optical imaging systems are linear with respect to light intensity; thus, it is nearly unachievable to directly design an incoherent bipolar point spread function (PSF) for edge detection. In this work, we proposed and experimentally demonstrated incoherent multiple image differentiation via spatial multiplexing optical convolution. A differentiable light field model was utilized to establish the response relationship between the optimization parameters of the phase mask and the target PSF field, enabling the desired phase mask to be iteratively optimized by the inverse design method. As a proof of concept, the PSF of the optical system is designed to implement four specially constructed spatial tiling non-negative optical convolutional kernels, and the spatial differentiation along x and y directions, as well as isotropic edge detection, can be simultaneously realized after digital subtraction. Our proposed method possesses the advantages of facilitating intelligent design, reducing device complexity, and increasing scalability. Meanwhile, a single optimized phase mask acts as a convolution processor, greatly promoting optical system integration. This scheme provides a flexible and intelligent approach for achieving multifunctional imaging processors with a compact, low-consumption optical system under incoherent illumination.