Fast transmission matrix measurement of a multimode fiber with common path reference

We report an improved scheme for the measurement of the transmission matrix of multimode waveguides in which the reference field co-propagates with the signal wave. The performance of the technique is demonstrated with the measurement of a 1.6 m long multimode optical fiber guiding 104 LP modes at 1064nm. The transmission matrix permitted efficient focusing of the light delivered at the fiber exit as well as shaping in the fiber transmission channels.