Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet realizing nonlinear mappings in optical hardware remains challenging due to the weak nonlinearity of optical materials and the large intensities required to induce nonlinear interactions. This challenge is further amplified in many systems that operate with incoherent illumination, motivating a coherence-aware framework for scalable optical nonlinear processing. Here, we show that linear optical systems, in particular, optimized diffractive processors comprising passive surfaces, can perform large-scale nonlinear function approximation under spatially incoherent or partially coherent illumination, when preceded by intensity-only input encoding. We quantify how the accuracy of the nonlinear function approximation varies with the degree of parallelism, the number of diffractive layers, and the number of trainable diffractive features. Numerical results demonstrate snapshot computation of up to one million distinct nonlinear functions in a single forward pass through a diffractive processor, with the function outputs spatially multiplexed and read out using densely packed detectors at the output. We further provide a proof-of-concept experimental demonstration under incoherent illumination from a liquid crystal display (LCD), enabled by a model-free in situ learning strategy that jointly optimizes the diffractive profile and detector readout geometry in the presence of hardware imperfections and misalignments. Our findings establish diffractive processors as a massively parallel universal function approximator for both spatially incoherent and partially coherent illumination.

翻译：非线性计算对于各类信息处理任务至关重要。光学实现方案极具吸引力，因为无源光传播能以极高吞吐量和并行性操控高维信号；然而，由于光学材料的弱非线性以及诱导非线性相互作用所需的高强度，在光学硬件中实现非线性映射仍具挑战性。这一挑战在众多使用非相干照明的系统中更为突出，从而催生了对可扩展光学非线性处理中相干性感知框架的需求。本文证明，线性光学系统（特别是由无源表面构成的优化衍射处理器）在仅通过强度编码输入后，能够在空间非相干或部分相干照明下执行大规模非线性函数逼近。我们量化了非线性函数逼近精度随并行度、衍射层数及可训练衍射特征数量的变化规律。数值结果表明，通过衍射处理器的单次前向传播，可瞬时计算多达一百万个不同的非线性函数，其函数输出通过空间复用并在输出端使用高密度探测器阵列读取。我们进一步提供了基于液晶显示器（LCD）非相干照明的概念验证实验演示，该实验采用无模型原位学习策略，在存在硬件缺陷和未对准的情况下联合优化衍射分布和探测器读出几何结构。我们的研究确立了衍射处理器作为空间非相干和部分相干照明的海量并行通用函数逼近器的地位。