Machine learning method to measure the transmission matrix of a multimode optical fiber without reference beam for 3D beam tailoring

We report a new reference-free method for measuring the complex Transmission Matrix (TM) of a Multimode Fiber (MMF), without the need of an interferometric setup, employing a two-step supervised machine learning framework. By using a deformable mirror at the proximal end of the MMF, and a camera at its distal end, we first retrieve the TM of the MMF that predicts the intensity pattern of the output beam. In a second step, with only some random additional images of the output far field, the TM is corrected to predict the true complex field at the distal end of the MMF. We experimentally validate our method by controlling the output optical field from a standard 50/125 step-index multimode fiber with 140 LP modes per polarization, using a segmented deformable mirror of 952 actuators at 1064 nm. We demonstrate the validity of the retrieved complex transmission matrix by tailoring the laser beam from the MMF simultaneously at two distal planes. These results open new avenues for complete control of the optical field using solely intensity measurements, which could be of major interest for endoscopic or telecommunication applications.