Partially coherent diffractive optical neural network

Since their proposal, diffractive optical neural networks (DONNs) have attracted significant interest for their potential in information processing. However, current research on DONNs primarily focuses on coherent light, limiting their applications in practical environments. Although it is possible to realize DONNs under partially coherent light conditions by considering DONNs with both coherent and incoherent light simultaneously, the structures of coherence have been ignored. To overcome this limitation, we propose the partially coherent diffractive optical neural network (PC-DONN) by introducing the coherence length of light $l$ for the Gauss-Schell model. The effectiveness of PC-DONN is demonstrated by recognizing handwritten digits in the visible spectrum both numerically and experimentally. Results show that, for our PC-DONNs trained with $l=0.2\mathrm{m}\mathrm{m}$, the accuracy keeps over 82% as the coherence of light diminishes to $l=0.05\mathrm{m}\mathrm{m}$, and it can reach 90% with further optimization. In contrast, the accuracy of conventional coherent DONNs experiences a drop from 91% to 26%. The physics of this strong robustness of PC-DONN are revealed in exploring the influence of interlayer distance $d$, the total number of random screens $M$, and the coherence to the network. PC-DONNs pave the way for the practical application of DONN, especially in low coherence or incoherent conditions, and shed new light on the understanding of DONN.