Controlling and understanding light propagation through a multimode fiber (MMF) requires knowledge of an optical Transmission Matrix (TM). Holography is essential for extracting phase information from intensity measurements, enabling the TM measurement. Usually, complex optical fields are retrieved through its interferences with a plane wavefront. Here we demonstrate and study TM measurements of an MMF using a self-reference approach, emphasizing its strengths and limitations. We focus on compensating for phase fluctuations to enhance image quality. The efficiency of this approach in precise TM measurements is experimentally confirmed by demonstrating high-quality light focusing, as well as complex patterns transmission through an MMF. This work enhances the understanding of self-reference holography in complex scattering media and its practical applications, particularly in studying and controlling light within MMFs.
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