Single-ended Recovery of Optical fiber Transmission Matrices using Neural Networks

Ultra-thin multimode optical fiber imaging technology promises next-generation medical endoscopes that provide high image resolution deep in the body (e.g. blood vessels, brain). However, this technology suffers from severe optical distortion. The fiber's transmission matrix (TM) calibrates for this distortion but is sensitive to bending and temperature so must be measured immediately prior to imaging, i.e. \emph{in vivo} and thus with access to a single end only. We present a neural network (NN)-based approach that quickly reconstructs transmission matrices based on multi-wavelength reflection-mode measurements. We introduce a custom loss function insensitive to global phase-degeneracy that enables effective NN training. We then train two different NN architectures, a fully connected NN and convolutional U-Net, to reconstruct $64\times64$ complex-valued fiber TMs through a simulated single-ended optical fiber with $\leq 4\%$ error. This enables image reconstruction with $\leq 8\%$ error. This TM recovery approach shows advantages compared to conventional TM recovery methods: 4500 times faster; robustness to 6\% fiber perturbation during characterization; operation with non-square TMs and no requirement for prior characterization of reflectors.