Deep, complex, invertible networks for inversion of transmission effects in multimode optical fibres

We use complex-weighted, deep networks to invert the effects of multimode optical fibre distortion of a coherent input image. We generated experimental data based on collections of optical fibre responses to greyscale input images generated with coherent light, by measuring only image amplitude (not amplitude and phase as is typical) at the output of \SI{1}{\metre} and \SI{10}{\metre} long, \SI{105}{\micro\metre} diameter multimode fibre. This data is made available as the {\it Optical fibre inverse problem} Benchmark collection. The experimental data is used to train complex-weighted models with a range of regularisation approaches. A {\it unitary regularisation} approach for complex-weighted networks is proposed which performs well in robustly inverting the fibre transmission matrix, which fits well with the physical theory. A key benefit of the unitary constraint is that it allows us to learn a forward unitary model and analytically invert it to solve the inverse problem. We demonstrate this approach, and show how it can improve performance by incorporating knowledge of the phase shift induced by the spatial light modulator.