  Multimode fibers (MMF) are an example of a highly scattering medium which
scramble the coherent light propagating within them and produce seemingly
random patterns. Thus, for applications such as imaging and image projection
through a MMF, careful measurements of the relationship between inputs and
outputs of the fiber are required. We show, as a proof of concept, that a deep
learning neural network can learn the input-output relationship in a 0.75 m
long MMF. Specifically, we demonstrate that a deep convolutional neural network
(CNN) can learn the non-linear relationships between the amplitude of the
speckle pattern obtained at the output of the fiber and the phase or amplitude
at the input of the fiber. Effectively the network performs a non-linear
inversion task. We obtained image fidelity (correlation) of ~98% compared with
the image obtained using the measured matrix of the system. We further show
that the network can be trained for transfer learning, i.e. it can transmit
images through the MMF which belongs to another class which were not used for
training/testing.
