Universal linear intensity transformations using spatially incoherent diffractive processors

Under spatially coherent light,a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view(FOVs)if the total number(N)of optimizable phase-only diffractive features is≥~2N_(i)N_(o),where Ni and No refer to the number of useful pixels at the input and the output FOVs,respectively.Here we report the design of a spatially incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs.Under spatially incoherent monochromatic light,the spatially varying intensity point spread function(H)of a diffractive network,corresponding to a given,arbitrarily-selected linear intensity transformation,can be written as H(m,n;m′,n′)=|h(m,n;m′,n′)|^(2),where h is the spatially coherent point spread function of the same diffractive network,and(m,n)and(m′,n′)define the coordinates of the output and input FOVs,respectively.Using numerical simulations and deep learning,supervised through examples of input-output profiles,we demonstrate that a spatially incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N≥~2N_(i)N_(o).We also report the design of spatially incoherent diffractive networks for linear processing of intensity information at multiple illumination wavelengths,operating simultaneously.Finally,we numerically demonstrate a diffractive network design that performs all-optical classification of handwritten digits under spatially incoherent illumination,achieving a test accuracy of>95%.Spatially incoherent diffractive networks will be broadly useful for designing all-optical visual processors that can work under natural light.