Retrieving the optical transmission matrix of a multimode fiber using the extended Kalman filter

Abstract

Characterizing the transmission matrix (TM) of a multimode fiber (MMF) benefits many fiber-based applications and allows in-depth studies on the physical properties. For example, by modulating the incident field, the knowledge of the TM allows one to synthesize any optical field at the distill end of the MMF. However, the extraction of optical fields usually requires holographic measurements with interferometry, which complicates the system design and introduces additional noise. In this work, we developed an efficient method to retrieve the TM of the MMF in a referenceless optical system. With pure intensity measurements, this method uses the extended Kalman filter (EKF) to recursively search for the optimum solution. To facilitate the computational process, a modified speckle-correlation scatter matrix (MSSM) is constructed as a low-fidelity initial estimation. This method, termed EKF-MSSM, only requires 4N intensity measurements to precisely solve for N unknown complex variables in the TM. Experimentally, we successfully retrieved the TM of the MMF with high precision, which allows optical focusing with the enhancement (>70%) close to the theoretical value. We anticipate that this method will serve as a useful tool for studying physical properties of the MMFs and potentially open new possibilities in a variety of applications in fiber optics.

Seeing through multimode fibers with real-valued intensity transmission matrices

“…Last, the experimental setup with our method is simpler compared to those of holographical methods which usually require optical reference arms that increase the complexity and can degrade the stability of the system. Several algorithms were reported for TM characterization in reference-arm-free setups [ 14 , 24 , 29 , 30 , 45 – 48 ], however, these works were mainly focused on producing incident wavefronts based on the achieved TM to focus light through fibers or diffusers. The lack of phase information in output speckles made it challenging to retrieve images directly from the measured TM and speckle intensities.…”

Speckle-Correlation Scattering Matrix Approaches for Imaging and Sensing through Turbidity

“…Huang et al proposed a method to calibrate the TM based on the SSM and an iterated extended Kalman filter [52]. Conceptually, they switch the role of the input field and the TM of a conventional SSM.…”

“…Secondly, it utilizes the universal statistical property of the speckle phenomenon without a priori information or volumetric data correction. Recent studies have shown that the SSM methods achieve holographic imaging and sensing through turbidity [51,52], which will pave the way for new applications in various spectral domains.…”

“…EKF: extended Kalman filter; MSSM: modified speckle-correlation scattering matrix. Adapted with permission from[52], OSA Publishing.…”

Focusing light through multimode fibres using a digital micromirror device: a comparison study of non-holographic approaches

“…Digital optical phase conjugation (DOPC) was also studied for WS with a LC-SLM [ 7 ], in which a laser beam was focused at the target position at one end of a MMF and the conjugated field of the transmitted light at the other end was projected back to focus at the original focusing point. TM-based methods were also studied [ 1 , 3 , 6 , 27 , 28 ], in which the light transport characteristics of a disordered medium was modelled as a complex-valued TM, which was then estimated in a characterisation measurement. Subsequently an optimal input field was determined to correct for the light field changes according to the estimated TM to generate an optical focus.…”