Optical refocusing through perturbed multimode fiber using Cake-Cutting Hadamard encoding algorithm to improve robustness

•A Cake-Cutting Hadamard encoding algorithm was first used to counteract the fiber's perturbation in multimode fiber imaging to help improve the robustness of the system.•The proposed method can have a fast convergence rate and high enhancement.•The proposed method does not require the adjustment of parameters.•The proposed method improves the robustness of multimode fiber imaging systems regardless of the intensity of noise and random fiber bending. Multimode fibres offer the advantages of high resolution and miniaturization over single-mode fibers in optical imaging. However, multimode fibre's imaging is susceptible to perturbations of MMF that can lead to secondary spatial distortions in the transmitted image. Perturbations include random disturbances in the fiber as well as environmental noise. Here, we exploit the fast focusing capability of the Cake-Cutting Hadamard algorithm to counteract the effects of perturbations and improve the system's robustness. Simulation shows that it can approach the theoretical enhancement at 2000 measurements. Experimental results show that the algorithm can help the system to refocus in a short time when MMFs are perturbed. This research will further contribute to using multimode fibres in medicine, communication, and detection.