Needle-thin optical fibre imaging systems using multimode fibre show considerable potential for facilitating advanced medical endoscopes that can capture high-resolution images in challenging regions of the body, such as the brain or blood vessels. However, these systems experience significant optical distortion whenever the fibre is disturbed. To address this, it is crucial to calibrate the fibre transmission matrix (TM) in vivo immediately before conducting the imaging process since TM is highly sensitive to temperature variations and bending. We therefore present a reflection-mode TM reconstruction model using U-net based convolutional neural networks with a custom loss function used for arbitrary global phase compensation, which reduced computational time to ~1s. We demonstrated this model by reconstructing 64 × 64 complex-valued fibre TMs through a reflection-mode optical fibre system and tested by reconstructing widefield images with ≤ 9% image error. We anticipate this neural network-based TM reconstruction model with the custom loss function designed will lead to new AI models that deal with phase information, for example in imaging through optical fibre, holographic imaging and projection, where both phase control and speed are required.
Holographic imaging and projection are increasingly used for important applications such as augmented reality,1 3D microscopy2 and imaging through optical fibres.3 However, there are emerging applications that require control or detection of phase, where deep learning techniques are used as faster alternatives to conventional hologram generation algorithms or phase-retrieval algorithms.4 Although conventional mean absolute error (MAE) loss function or mean squared error (MSE) can directly compare complex values for absolute control of phase, there is a class of problems whose solutions are degenerate within a global phase factor, but whose relative phase between pixels must be preserved. In such cases, MAE is not suitable because it is sensitive to global phase differences. We therefore develop a ‘global phase insensitive’ loss function that estimates the global phase factor between predicted and target outputs and normalises the predicted output to remove this factor before calculating MAE. As a case study we demonstrate ≤ 0.1% error in the recovery of complex-valued optical fibre transmission matrices via a neural network. This global phase insensitive loss function will offer new opportunities for deep learning-based holographic image reconstruction, 3D holographic projection for augmented reality and coherent imaging through optical fibres.
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