Çok modlu fiberlerde ışık odaklama için gürültüye dayanıklı dalgacephesi şekillendirme

Multimode optical fibers (MMFs) offer unique advantages for high-resolution imaging, optical communication, and power delivery. However, their complex modal structure poses significant challenges for the precise prediction of light propagation. This thesis explores the upper bounds of intensity enhancement achievable in light focusing through multimode fibers (MMFs) using phase-only wavefront shaping techniques designed to be robust against noise. We begin with a theoretical analysis of modal propagation and introduce the transmission matrix (TM) formalism as a foundation for describing input-output field relationships in MMFs. We then explore digital optical phase conjugation (DOPC) and feedback-based wavefront shaping strategies, emphasizing their performance limitations under realistic experimental constraints. A central contribution of this thesis is the introduction of a generalized expression for the enhancement factor, incorporating both the input participation ratio and the phase error coefficient. We demonstrate that enhancement is strongly influenced by the choice of input basis and the presence of experimental noise. Using common-path interferometric transmission matrix (TM) measurements, we demonstrate that the Dual Reference Algorithm (DRA) implemented in the Hadamard basis outperforms the widely used Stepwise Sequential Algorithm (SSA) operating in the canonical (SLM pixel) basis. Our experimental results confirm that Hadamard-based wavefront shaping offers superior noise resilience, yielding intensity enhancement factors approaching the theoretical upper bound. We further conduct a detailed analysis of experimentally measured transmission matrices (TMs), revealing that the segment size on the SLM significantly influences modal coupling and focusing performance. Finally, we introduce an operator-based framework that encodes the radial memory effect for a focused beam, extending beyond the conventional rotational memory effect in multimode fibers (MMFs). This approach enables beam scanning via controlled shifts of the input SLM pattern, paving the way for advanced applications in fiber-optic imaging and beam steering. Overall, this thesis presents a unified framework that bridges theory and experiment to optimize wavefront shaping in multimode fibers (MMFs), with direct implications for endoscopic imaging, clean-beam fiber amplification, and programmable fiber-based optical systems.