A Comparative Study of Polynomial-Based Disorder Avoidance in Multimode Fiber Propagation

This study explores and evaluates various polynomial-based methods for signal reconstruction, including Zernike, Seidel, Fourier, Chebyshev, Legendre, and orthonormal polynomials. Our objective is to improve upon existing reconstruction approaches, particularly the technique described in [1]. Experimental results demonstrate that Seidel polynomials outperform all others, yielding the highest reconstruction accuracy. These findings propose Seidel-based reconstruction as a new benchmark for signal fidelity in complex systems. Through rigorous experimentation and analysis, we illustrate the strengths and weaknesses of each polynomial basis in modeling spatial features and recovering original signals from distorted or noisy observations. These findings could inform future developments in fields such as optical imaging, signal processing, and machine learning where efficient and accurate reconstruction is essential.