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_iN_o, where N_i and N_o 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_iN_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.

在空间相干光下，如果可优化仅相位衍射特征的总数 （N） 为 ≥~2N_O ，其中 N 和 N_o，则可以设计由结构化表面组成的衍射光学网络在其输入和输出视场 （FOV） 之间执行任意复值线性变换分别指输入和输出 FOV 处的有用像素数。在这里，我们报告了一种空间非相干衍射光学处理器的设计，该处理器可以近似其输入和输出 FOV 之间时间平均强度的任何任意线性变换。在空间非相干单色光下，衍射网络的空间变化强度点扩散函数 （H） 对应于给定的、任意选择的线性强度变换，可以写成 H（m， n;m′， n′） = |h（m， n;m′， n′）|²，其中 h 是同一衍射网络的空间相干点扩散函数，（m， n） 和 （m′， n′） 分别定义输出和输入 FOV 的坐标。使用数值模拟和深度学习，通过输入输出剖面示例进行监督，我们证明了如果 N ≥ ~2N_{N o}，则可以训练空间非相干衍射网络在其输入和输出之间执行任意线性强度变换。 我们还报道了空间非相干衍射网络的设计，用于在多个照明波长下对强度信息进行线性处理，同时运行。最后，我们数值演示了一种衍射网络设计，该设计在空间非相干照明下对手写数字进行全光学分类，测试精度达到 >95%。空间非相干衍射网络对于设计可以在自然光下工作的全光学视觉处理器将广泛有用。