As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees-of-freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are non-negative, acting on diffraction-limited optical intensity patterns at the input field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

翻译：作为一种光学处理器，衍射深度神经网络利用通过机器学习设计的工程化衍射表面，实现全光学信息处理，其任务完成速度取决于光波在薄光学层中的传播速度。在拥有足够自由度的情况下，衍射深度神经网络可使用空间相干光执行任意复值线性变换。类似地，衍射深度神经网络在空间非相干照明条件下也可执行任意线性强度变换；然而，在空间非相干光下，这些变换具有非负性，作用于输入视场内受衍射限制的光学强度模式。本文拓展了空间非相干衍射深度神经网络在复值信息处理中的应用，使其能够利用空间非相干光执行任意复值线性变换。通过仿真实验表明：当优化后的衍射特征数量超过由输入与输出空间带宽乘积决定的阈值时，空间非相干衍射视觉处理器可近似任何复值线性变换，并可用于非相干照明下的全光学图像加密。该研究成果对基于衍射表面型光学处理器在自然光条件下实现全光学信息处理具有重要意义。