Feedback-assisted transmission matrix measurement of a multimode fiber in a referenceless system

Recent development in wavefront shaping shows the promise to employ multimode fibers (MMFs) to deliver images in endoscopy. In these applications, retrieving the transmission matrix (TM) of the MMF is especially important. Among existing non-holographic approaches, feedback-based wavefront shaping requires a large number of measurements, while directly measuring the TM can be easily trapped into local optimums if the constraints are insufficient. To reduce the required number of measurements, we combine the concepts of these two approaches and develop a scheme termed feedback-assisted TM measurements. We show that under such a hybrid scheme, less than 3N intensity measurements are sufficient to accurately retrieve one row of the TM that contains N unknown complex elements. As a proof of concept, we experimentally demonstrated retrieving multiple rows of the TM of an MMF using the proposed scheme with high fidelity. In particular, a single focus and dual foci through the MMF with enhancements larger than 75% of the theoretical values were reported.