Robust Demodulation Algorithm for Multimode Sapphire Fiber Bragg Grating High-Temperature Sensors Based on Analytic Envelope Extraction

Multimode sapphire fiber Bragg gratings (SFBGs) are essential for high-temperature monitoring in aerospace and energy sectors. However, their unclad structure inherently causes spectral broadening and severe modal asymmetry. Intense thermal blackbody radiation further degrades the signal-to-noise ratio at extreme temperatures. These combined factors render conventional single-peak demodulation methods highly unreliable. To resolve these challenges, this study proposes a three-stage demodulation framework tailored for multimode SFBG sensors. The process begins with an optimized 201-point moving-average filter. This filter suppresses detector shot noise and intermodal ripples while strictly preserving the steep cut-off edges of the spectrum. A Hilbert transform applied in the linear power domain then extracts the analytic envelope to adaptively isolate the dominant 3 dB reflection sub-band without relying on fixed intensity thresholds. A localized zero-centered parabolic fitting operator subsequently resolves the continuous resonant peak with picometer-level precision. We evaluated this framework through static and long-term isothermal sensing experiments from 23 °C to 1400 °C. The extracted Bragg wavelengths maintain a polynomial fitting correlation exceeding 0.9981 across the entire calibrated range. During 60 min continuous isothermal dwelling at 1000 °C, 1200 °C, and 1400 °C, the standard deviations of the measurements reached 0.186 nm, 0.098 nm, and 0.158 nm respectively. These stability metrics substantially outperform conventional centroid, direct maximum, and Gaussian fitting techniques. The proposed framework directly mitigates multimodal spectral distortion and thermal noise, offering a highly accurate and computationally efficient demodulation protocol for harsh-environment optical fiber sensing.