Transmission matrix of a multimode fiber: In-line vs off-axis holography

Multimode fibers (MMFs) hold great promise for a variety of imaging applications.
However, controlling the complex propagation of light through thousands of modes
in MMFs remains a challenging task. To enable precise wavefront control, the MMF
transmission matrix (TM) must be accurately measured. In this paper, we compare
in-line and off-axis holography as phase retrieval techniques for TM measurement
within a single optical setup. The quality of wavefront shaping is analyzed for different target shapes, including single-mode and complex free-form projections. Our
findings reveal a trade-off in wavefront shaping: while in-line holography achieves
superior focus quality for single-mode targets, off-axis holography excels in projecting
complex-shaped targets. These experimental findings provide a basis for choosing
and optimizing holographic techniques in MMF-based imaging setups.