Deep empirical neural network for optical phase retrieval over a scattering medium

Supervised learning, a popular tool in modern science and technology, thrives on huge amounts of labeled data. Physics-enhanced deep neural networks offer an effective solution to alleviate the data burden by incorporating an analytical model that interprets the underlying physical processes. However, it completely fails in tackling systems without analytical solution, where wave scattering systems with multiple input multiple output are typical examples. Herein, we propose a concept of deep empirical neural network (DENN) that is a hybridization of a deep neural network and an empirical model, which enables seeing through an opaque scattering medium in an untrained manner. The DENN does not rely on labeled data, all while delivering as high as 58% improvement in fidelity compared with the supervised learning using 30000 data pairs for achieving the same goal of optical phase retrieval. The DENN might shed new light on the applications of deep learning in physics, information science, biology, chemistry and beyond.