Research Progress in High-Temperature Sensing Demodulation Technologies for Sapphire Fiber Bragg Gratings

doi:10.16553/j.cnki.issn1000-985x.2026.0110

Abstract

Abstract: Sapphire fiber Bragg gratings （SFBG） can realize in-situ， multipoint， and high-accuracy temperature measurement above 1 800 ℃， making them important sensors for extreme-environment monitoring in aerospace engines， nuclear energy systems， and industrial furnaces. However， the strong multimode characteristics of sapphire fibers lead to broadband reflection spectra， overlapping multiple peaks， and high sensitivity to coupling and packaging conditions， making their demodulation mechanisms significantly different from those of conventional silica fiber Bragg grating （FBG）. Focusing on the wavelength demodulation requirements of SFBG， this paper systematically reviews and compares technical routes including direct spectral measurement by optical spectrum analyzers （OSA） or array spectrometers， as well as optical frequency domain reflectometry （OFDR） demodulation. Representative progress is summarized in terms of key performance indicators such as demodulation speed， resolution/accuracy， measurement range， multiplexing capability， and robustness. Engineering and algorithmic approaches for improving signal-to-noise ratio and stability are further summarized， including mode filtering， mode reduction， single-mode operation and mode stabilization， end-face and coupling optimization， high-temperature packaging， cross-correlation algorithms， and machine-learning-assisted algorithms. Finally， future development trends of SFBG demodulation systems are discussed from three perspectives： miniaturized demodulation based on arrayed waveguide gratings （AWG）， high-speed demodulation based on swept-laser schemes， and high-precision demodulation based on interferometric methods. This review provides a reference for the engineering development of real-time demodulation in high-temperature and strain sensing using optical fibers.

Key words: sapphire fiber; sapphire fiber Bragg grating; wavelength demodulation; high-temperature sensing; spectrometer; signal-to-noise ratio; demodulation algorithm

CLC Number:

TP212

ZHANG Jingwei, QIN Zhiwei, LI Zhuoda, CHANG Xinyu, CHEN Xiaole, BAI Zhiyong, XU Xizhen, WANG Yiping, HE Jun. Research Progress in High-Temperature Sensing Demodulation Technologies for Sapphire Fiber Bragg Gratings[J]. Journal of Synthetic Crystals, 2026, 55(8): 1155-1191.

Figures/Tables 20

Fig.1 Schematic diagram of an FBG sensor

Table 1 Summary of figures related to FBG interrogation systems

Fiber Bragg grating demodulation system	Schematic diagram of the FBG demodulation system	Research progress in related studies
基于光谱仪直读式的解调方法		Wang和Tang基于光谱仪直读的FBG传感解调系统通过实时获取FBG/LPFG反射或透射谱的波长漂移，实现温度、应变和液位等参量的解调^［31］
基于InGaAs光电二极管线阵图像传感器的解调方法		Li等采用InGaAs光电二极管线阵替代传统CCD的FBG阵列解调结合BFBG实现了适用于1.55 μm波段的FBG解调系统^［35］
基于波长扫频光纤激光器的解调方法		Wang等将波长扫频光纤激光用于FBG传感系统，实现了静态与动态信号的同步测量^［41］
基于边缘滤波器的解调方法		Ogawa等实现了采用光学边缘滤波器的无线便携式FBG解调系统^［55］
基于LVF的解调方法		Liu等建立了基于LVF的FBG解调模型，说明LVF与线阵探测器结合可将波长漂移转换为位置或强度分布变化，并通过质心法实现高分辨率波长解调^［37］
基于扫描式FP滤波器/Mach-Zehnder干涉仪的解调方法		Todd等构建的基于扫描式FP滤波器与3×3耦合器Mach-Zehnder干涉仪的FBG解调系统^［80］
基于FP可调滤波器的解调方法		Allan等采用MEMS FP可调滤波器实现复用FBG阵列解调系统^［95］
基于AWG相对强度解调的解调方法		Li等实现了AWG与光电探测器单片集成的解调芯片，实验表明该器件可达到约6.79 pm的解调精度、1 pm的分辨率和1.56 nm的动态范围^［114］
基于OFDR的解调方法		Wang等提出基于混沌的iOFDR方法，实现了高密度FBG阵列的有效解调^［125］
基于FMCW的解调方法		Perez-Herrera等针对FMCW光纤传感解调系统，研究了参考、复用及性能优化方法^{［136-137］}

Fig.2 Three mainstream sapphire fiber Bragg grating interrogation systems for high-temperature measurements and their typical reflection spectra［9，32，138］. （a） FBG interrogation setup；（b） optical signal acquisition system and reflection spectra of an SFBG array；（c） schematic diagram of the SFBG array optical signal acquisition system， including the SFBG temperature sensor， optical unit， and electrical signal-processing unit；（d） measured reflection spectra of five SFBG in the array；（e） amplitude distribution of sapphire FBG reflection spectra at different fiber-length positions measured by a Luna fiber grating interrogator based on the OFDR principle

Fig.3 Reflection spectra of SFBG［154］. （a） Single grating；（b） grating array

Fig.4 SEM images showing the surface topography of three sapphire fiber samples S1~S3 after long-time high-temperature annealing. （a1）~（a3） 1 530 ℃；（b1）~（b3） 1 560 ℃；（c1）~（c3） 1 600 ℃；（d1）~（d3） evolutions of the feature size of lossy spots and feature width of the etched lines on the surface of the fiber samples （S1， unpackaged sample； S2， packaged sample； S3， packaged sample with stress relaxation）［146］

Fig.5 Morphology of sapphire fiber end faces and corresponding SFBG spectra［15］. （a） Sapphire fiber end face obtained by cleaving with a Miller clamp； sapphire fiber end faces polished using diamond lapping films with particle sizes of 30 μm （b）， 9 μm （c）， 5 μm （d）， 3 μm （e）， and 1 μm （f）， respectively；（g） SFBG spectra under different end-face processing conditions. Sample abbreviations are given as ［sample name， coupling face， end face， lapping-film particle size］：［S1， 0°， index matching］，［S2， 8°， fractured end face］，［（S3， S4， S5， S6， S7）， 8°， 30°，（30， 9， 5， 3， 1 μm）］， and ［S8， 8°， 30°， index matching］， the inset shows a microscopic image of the sapphire fiber

Fig.6 Microscopic images and reflection spectra of multilayer SFBG fabricated by multilayer line-by-line writing［151］. （a） Cross-sectional microscopic images of single-layer， bilayer， and three-layer SFBGs with one， two， and three written layers， respectively；（b） corresponding side-view microscopic images of the SFBG；（c） reflection spectra of the single-layer， bilayer， and three-layer SFBG

Fig.7 Microscopic images and spectral comparison of HSFBG with different periods and helical diameters［163］. （a），（b） Microscopic images of HSFBG with a period of 1.332 μm and helical diameters of 15 and 30 μm， respectively；（c），（d） microscopic images of HSFBG with a period of 6.66 μm and helical diameters of 15 and 30 μm， respectively；（e） spectral comparison of HSFBG with helical diameters of 15， 20， 25， 30， and 35 μm. The inset shows a magnified view over a 20 nm wavelength range

Fig.8 Near-field transmission mode fields of sapphire fibers and optical characterization setup under different AMMF lengths［15］. （a） Schematic diagram of the optical characterization setup， including measurements of the near-field transmission mode distribution of the sapphire fiber and the SFBG reflection spectrum；（b） measured near-field transmission mode fields of sapphire fibers for AMMF lengths of 1， 50， 500， and 1 000 m， respectively；（c） SFBG reflection peak profiles under different AMMF lengths

Fig.9 Three mode-filtering techniques for sapphire fiber Bragg gratings and their effects on reflection-spectrum optimization［139，144，151］. （a） Experimental setup of the proposed sapphire fiber FBG sensing system， the inset images show microscopic views of the splicing point and the FBG structure；（b） measured FBG spectrum at room temperature， the blue curve represents the conventional case， where the multimode fiber （MMF） is directly connected to the OSA； the red curve shows the result obtained using the proposed system， and the dashed curves indicate the Gaussian fitting results；（c1） schematic diagram of offset coupling between the bilayer SFBG and the input MMF along the y-axis；（c2） Schematic diagram of offset coupling along the x-axis；（d） reflection spectra of the bilayer SFBG without offset （0 μm）， with a 20 μm offset along the y-axis， and with a 20 μm offset along the x-axis；（e） diagram of the three-step multi-layer WBG fabrication process；（f） experimentally measured reflection spectrum of the single-modes SFBG

Fig.10 Schematic diagrams of the helically tapered depressed-cladding waveguide （HTDCW） and SFBG structure fabricated by femtosecond-laser direct writing［14］. （a） Simulated mode fields （up） and optical paths （down） for forward and backward propagation in the helical-trajectory depressed-cladding waveguide （HTDCW）， cross-sectional structure of the HTDCW （right）；（b） reflection spectra of the SFBG measured through butt-coupling to MMF， SMF， and HTDCW， inset： schematic diagram of the SFBG butt-coupled to MMF， SMF， and HTDCW；（c） wavelength dispersion obtained from 65 repeated measurements under no-vibration and 20 Hz vibration conditions

Fig.11 Fabrication and characterization of a micro-SFBG［12，138］. （a） Optical microscopic image of the fabricated micro-SFBG with a diameter of 9.6 μm， where the FBG is visualized by injecting 638 nm red light into the fiber；（b） reflection spectra of the air-clad SFBG under different diameters （d）

Fig.12 Cross-sectional morphology， refractive-index distribution， and near-field output of depressed-cladding waveguides （DCWs） inscribed in bulk sapphire by femtosecond laser writing［172，174-175］. （a） Cross-sectional image of the DCW inscribed in sapphire；（b），（c） near-field intensity distributions measured at the output end of the DCW for transmitted light at a wavelength of 2 850 nm；（d） schematic diagram of the sapphire sensor；（e） coupling into the single-mode sapphire waveguide core， spectrum after successful splicing from the optimized position， and image of the splicing joint after successful splicing；（f） schematic of an HBGW fabricated in sapphire fiber using femtosecond laser direct writing， insets： cross-sectional schematics of the HBGW inscribed with and without a slit；（g） corresponding transmission and reflection spectra of three fabricated HBGW samples， S1， S2， and S3， in sapphire fibers with decreasing diameters of 30， 20， and 14 μm， respectively

Table 2 Summary of six traditional FBG demodulation algorithms［177］

Algorithm	Demodulationaccuracy	Anti-noiseperformance	Evaluation
Direct peak-finding	Low	Low	Higher requirements on the number of sampled spectral points
Power weighting algorithm（centroid method）	Low	Low	Peak-seeking error will be reduced in the case of low noise
General polynomial fitting	Middle	Low	Accuracy is with regard to the observed data. If the peak value is not within the sampling point， the error will be large
Gaussian fitting algorithm	High	High	Strict requirements on spectrum
Gaussian-polynomial fitting algorithm	Middle	Low	Accuracy is with regard to the observed data. If the peak value is not within the sampling point， the error will be large
Gaussian nonlinear curve fittingalgorithm	High	High	Be not applicable to actual situation

Fig.13 Comparison of reflection spectra analysis and peak-detection stability of SFBG using different interrogation algorithms［178-179］.（a） Asymmetric reflection peak of the SFBG， the symbols represent the measured reflection intensities in arbitrary units， and the solid lines represent the peak functions fitted using Eq. （2） strain release in the fiber causes the Bragg wavelength to shift by 0.5 nm toward shorter wavelengths， as indicated by the arrows；（b） temperature dependence of the coefficient of thermal expansion （CTE） of the steel pad used in this study， as determined by the SFBG-based sensing device （green line） and by a dilatometer （blue line）， temperature calibration results of an SFBG sensor from 19 ℃ to 650 ℃；（c） wavelength dispersion；（d） temperature response and its polynomial fitting curve

Fig.14 Flowchart of the multi-peak detection algorithm［32］

Table 3 Performance comparison of nine machine learning algorithms on FBG demodulation［177］

Model	Interrogation range	R²	RMSE	Training time
Net2	2 nm	0.99	14.7 pm	—
BPNN	2 nm	—	1.291 5 pm	200.4 s
Adam	8 nm	0.999 7	9.47 pm	15.46 min
Lorentzian fitting	1.6 nm	—	3.7 pm	—
Liner fitting	13.5 nm	—	20 pm	—
Liner fitting	1.6 nm	—	2.1 pm	—
Gauss fitting	1.56 nm	—	6.79 pm	—
BPNN	49.35 nm	0.999 64	0.83~0.85 pm	—
Polynomial regression	24 nm	0.999 99	0.48~0.99 pm	10.757 s

Fig.15 DNN-based SFBG demodulation algorithm［144］. （a） Structure of the DNN model used in the experiment；（b） performance of the DNN model under stationary conditions， together with the error histogram of 2 720 input spectra， loss graph of the raining and validation datasets

Fig.16 High-temperature sensing applications of SFBG［32，138，187，189］. （a） Sensor deployment in a coal-fired boiler reported by Yang et al.， including the schematic diagram of the sensor configuration and the photograph of the deployment site；（b） ultrahigh-temperature blackbody radiation furnace temperature-distribution measurement based on an SFBG array sensor reported by Tan et al.， including the measurement principle， field deployment， and temperature distributions under different thermal conditions；（c） experimental setup for testing the performance of an SFBG array during heating and cooling cycles；（d） high-temperature monitoring in liquid-sodium systems for sodium-cooled fast reactors using regenerated FBG sensors

Fig.17 Examples of strain-sensing applications of SFBG［178，185］. （a） Design diagram of the SFBG strain sensor；（b） strain response of the SFBG at 25， 800， and 1 100 ℃， linear fitting relationship between Bragg wavelength and strain；（c） discrete distribution of Bragg wavelength during the strain test

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