Coherence Awareness in Diffractive Neural Networks

Diffractive neural networks hold great promise for applications requiring intensive computational processing. Considerable attention has focused on diffractive networks for either spatially coherent or spatially incoherent illumination. Here we illustrate that, as opposed to imaging systems, in diffractive networks the degree of spatial coherence has a dramatic effect. In particular, we show that when the spatial coherence length on the object is comparable to the minimal feature size preserved by the optical system, neither the incoherent nor the coherent extremes serve as acceptable approximations. Importantly, this situation is inherent to many settings involving active illumination, including reflected light microscopy, autonomous vehicles and smartphones. Following this observation, we propose a general framework for training diffractive networks for any specified degree of spatial and temporal coherence, supporting all types of linear and nonlinear layers. Using our method, we numerically optimize networks for image classification, and thoroughly investigate their performance dependence on the illumination coherence properties. We further introduce the concept of coherence-blind networks, which have enhanced resilience to changes in illumination conditions. Our findings serve as a steppingstone toward adopting all-optical neural networks in real-world applications, leveraging nothing but natural light.