  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.

Optics;Computational Physics