Fractional Fourier Transform for Phase Demodulation and Characterizing Optical Heterogeneity in Nano-Composite Fiber Interference Patterns with Random Nanoparticle Distributions

Nano-composite materials enable advanced material engineering by strategically incorporating nanoscale reinforcements to enhance material properties. However, characterizing these materials, particularly those with randomly distributed nanoparticles, presents significant analytical challenges. So, this study introduces an advanced phase demodulation technique using two-dimensional fractional Fourier transform (2D FrFT) specifically tailored for analyzing interference patterns from nano-composite fibers with complex nanoparticle distributions. The proposed 2D FrFT method offers enhanced flexibility by adaptively handling complex optical interactions in heterogeneous material systems. Through comprehensive computational and experimental investigations using recycled polyethylene terephthalate (PET) reinforced with titanium dioxide (TiO₂) nanoparticles, we demonstrate the method’s remarkable capabilities in demodulating phase maps from both stationary and non-stationary interference patterns. Quantitative assessments reveal that the 2D FrFT approach achieves superior phase extraction accuracy, with standard deviation as low as 0.111% compared to traditional Fourier transform methods, which exhibited deviations of 21.5%. Furthermore, the technique successfully mapped intricate refractive index variations, revealing complex optical heterogeneities in nano-composite fibers. The method’s versatility enables precise analysis of interferometric patterns in nanostructured materials, connecting microscopic structures to macroscopic optical behaviors.