FBG demodulation methods include cross-correlation, centroid, polynomial fitting, Hilbert transform, fast phase correlation, wavelet-based filtering, digital filtering, and neural network approaches.

Classical and Signal-Based Methods

Cross-Correlation Methods: These involve comparing the measured FBG spectrum with a reference spectrum to determine the wavelength shift. Variants include iterative cross-correlation and FFT-based cross-correlation, which improve accuracy and reduce peak-locking effects . Centroid Algorithms: The centroid method calculates the center of mass of the reflected spectrum to estimate the Bragg wavelength, providing a simple and computationally efficient approach . Polynomial Peak Tracking: Second-order or higher-order polynomial fitting is applied to the spectral peak to track wavelength shifts, often used for multiple FBGs or overlapping spectra . Hilbert Transform and Zero-Crossing: The Hilbert transform converts the resonance peak into a zero-crossing curve, which can then be analyzed to determine the wavelength shift. This method is often combined with cross-correlation for enhanced precision . Fast Phase Correlation: This method uses phase information of the spectrum to quickly and accurately determine wavelength shifts, suitable for real-time applications .

Filtering and Numerical Approaches

Wavelet Transform: Wavelet-based filtering is used to denoise the FBG spectrum before demodulation, improving measurement accuracy . Digital Filtering: Classical digital filters or matched filtering techniques can enhance the signal-to-noise ratio and extract the Bragg wavelength from noisy spectra . Karhunen–Loève Transform (KLT): KLT is applied to represent the measured spectrum in an orthogonal basis, facilitating precise wavelength estimation . Gaussian Curve Fitting: For distorted spectra, fitting a Gaussian function to the reflection peak allows accurate determination of the Bragg wavelength . Cumulative Sum and Empirical Mode Decomposition: These preprocessing methods reduce noise influence and simplify subsequent wavelength shift calculations .

Advanced and AI-Based Methods

Artificial Neural Networks: Machine learning algorithms can model complex spectral distortions and perform demodulation with high accuracy, especially in multi-FBG systems . Dynamic Statistical Threshold Detection and Wavelet Packet Decomposition: These methods are used to minimize noise effects and improve the reliability of wavelength shift detection .

Summary

FBG demodulation methods can be broadly categorized into signal transformation techniques, numerical fitting approaches, filtering and denoising methods, and AI-based algorithms. The choice of method depends on the application requirements, including accuracy, computational complexity, noise robustness, and the number of FBGs being interrogated. Combining multiple methods, such as cross-correlation with Hilbert transform or wavelet filtering with centroid calculation, is common to enhance precision and reliability .