Toward Micro-Endoscopy: Distal-Free, Configuration-Agnostic Focusing Through Multimode Fiber

Technical Summary: Toward Micro-Endoscopy: Distal-Free, Configuration-Agnostic Focusing Through Multimode Fiber

Problem Statement
Multimode fibers (MMFs) offer a promising platform for high-resolution biomedical imaging and optical communication due to their ability to support multiple spatial modes simultaneously. This capability allows for significant miniaturization of endoscopic probes, enabling access to confined biological regions with minimal tissue damage. However, the practical application of MMFs is hindered by complex modal behavior. In real-world conditions, environmental perturbations such as temperature fluctuations, fiber bending, and mechanical stress induce mode coupling. This coupling scrambles the phase relations between eigenmodes, distorting the transmitted field and rendering the transmission matrix (TM) dependent on the instantaneous fiber configuration.

Conventional wavefront shaping strategies, such as closed-loop feedback optimization and transmission matrix (TM) characterization, typically require direct access to the distal (output) facet of the fiber to measure the transmitted field. This requirement makes them impractical for in-situ applications like endoscopy, where the distal end is inaccessible. Furthermore, existing deep learning approaches that rely solely on input wavefronts lack the conditional information necessary to generalize across varying, dynamic fiber configurations, leading to failure when the fiber is perturbed.

Methodology
The authors propose a deep learning-based framework that enables focusing through an MMF without requiring distal feedback. The core principle relies on the physical coupling between the fiber's transmission matrix ($T$) and its reflection matrix ($R$). Since both matrices are determined by the same underlying fiber configuration, the reflected signal encodes the instantaneous state of the fiber.

The methodology involves the following components:

1. Reflection-Informed Deep Neural Network (DNN): The authors designed a U-Net architecture with three separate encoder branches. These branches process three distinct input modalities:
   • The spatial phase pattern applied by a Spatial Light Modulator (SLM) at the proximal end.
   • The intensity of the reflected signal measured in the image plane.
   • The intensity of the reflected signal measured in the Fourier plane.
     The outputs of these encoders are concatenated and fed into a single decoder to reconstruct the estimated intensity distribution of the transmitted field at the distal end.
2. Training Dataset: The model was trained on a comprehensive dataset comprising 4.5 million image sets collected from 1,200 distinct fiber configurations. Each configuration was generated using a motorized stage to induce controlled mechanical bending. For each configuration, 10 independent focusing processes were performed using a genetic algorithm to optimize the SLM phase mask. During these processes, the system captured the SLM phase mask, the reflected intensities (image and Fourier planes), and the ground-truth transmitted intensities.
3. Indirect Feedback Focusing: To validate the system, the authors implemented an indirect feedback loop. The DNN predicts the transmitted field based on the SLM pattern and reflected signals. A "Focus Strength" (FS) metric is calculated from this prediction and used to guide a genetic algorithm in updating the SLM phase pattern. This process iterates without any direct measurement of the transmitted field.

Key Results
The study demonstrates robust performance across several metrics:

• Generalization to Unseen Configurations: The model was tested on 240 fiber configurations that were not present in the training set. It successfully predicted the transmitted speckle patterns, capturing the salient features and overall structure despite significant mode coupling.
• Quantitative Accuracy: The model achieved an average Focus Deviation (FD) of 14% across the test configurations. This metric represents the relative difference between the focus strength calculated from the ground truth and the model's prediction.
• Superiority over Baselines: When compared to a baseline U-Net trained only on SLM input patterns (without reflection data), the reflection-informed model showed superior performance across all metrics, including Structural Similarity Index (SSIM), Pearson correlation, and Mean Squared Error (MSE). The inclusion of reflection data was critical for maintaining accuracy under mechanical perturbations.
• Distal-Free Focusing: In 100 independent focusing experiments on random, unseen fiber configurations, the indirect feedback loop successfully drove the real physical transmitted field to a high-intensity focus. The ground-truth focus strength increased monotonically, converging to a strong focus, validating that the model's predictions accurately reflect the physical reality of the fiber's output.

Significance and Claims
The paper claims that this framework represents a significant step toward deploying MMFs in dynamic, real-world environments where distal access is impossible. By decoupling the wavefront optimization process from the need for distal feedback, the approach addresses a major bottleneck in MMF-based micro-endoscopy and optical communications.

The authors emphasize that their method enables robust, high-contrast focusing in arbitrary and unknown fiber configurations. They posit that this learning-based technique paves the way for efficient, non-invasive focusing in practical applications. While the current implementation relies on an iterative genetic algorithm for optimization, the authors note that the framework establishes the foundation for future single-shot, real-time focusing by potentially training inverse-design networks to directly map reflections to required phase masks. The work underscores the potential of leveraging reflected signals to decode complex fiber states, offering a viable solution for adaptive control in photonics and biomedical imaging.