Measuring the transmission matrix of a multimode fiber: on-axis vs off-axis holography

The transmission matrix (TM) measurement is a powerful and well-known tool for characterizing scattering media such as multimode fibers (MMF). Access to the phase of the optical field based on the results of intensity measurements is a long-standing problem known as the phase retrieval problem. To obtain the complex optical field and therefore phase information, it is necessary to use interferences with a known wavefront. In this work, we compare two interferometric methods: on-axis holography with a speckle reference beam propagating through the same optical path and off-axis holography with a plane wave reference beam propagating via an additional arm. These methods, combined with a DMD, provide a fast and accurate way to measure the TM. We present results and a detailed comparison of the two methods of TM measurements of the same system.