Physics-Informed Deep Learning for Demodulating Phase and Optical Properties in Polymer Fibers from complex Interference Patterns

Abstract This study addresses the critical need for accurate, real-time phase demodulation in the opto-mechanical characterization of polymer fibers. Existing methods face significant limitations, including difficulties in handling noise, non-stationary patterns, reliance on simulated data or limited real-world samples, and computational inefficiency. To overcome these challenges, we propose a novel deep learning approach based on a refined U-Net architecture that directly extracts phase maps from complex interference patterns. Our methodology employs a diverse dataset of 460 high-resolution experimental patterns captured under various conditions of illumination, contrast, and distortion using Pluta polarizing microscopes and Mach-Zehnder interferometers, ensuring robust performance across real-world scenarios. The network architecture integrates encoder-decoder blocks with transposed convolutions and is trained end-to-end, eliminating the need for intermediate preprocessing steps such as fringe normalization. Data augmentation techniques including random rotations and flips further enhance the model's generalization capability. Through Adam optimization minimizing mean squared error (MSE), the model achieves a remarkable 98.6% reduction in error, reaching a final MSE of 0.00434 after 220 training iterations. Applied to isotactic polypropylene (iPP) and polypropylene (PP) fibers, the method demonstrates real-time capability in mapping birefringence and refractive index changes during mechanical stretching, revealing dynamic structural phenomena like core-shell formation and necking. This work bridges advanced machine learning with optical metrology, offering a scalable solution for industrial fiber characterization.