Referenceless characterisation of complex media using physics-informed neural networks

In this work, we present a method to characterise the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to upto 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalised to characterise a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing.