
人工晶体学报 ›› 2026, Vol. 55 ›› Issue (8): 1155-1191.DOI: 10.16553/j.cnki.issn1000-985x.2026.0110
• 专题·综合评述 • 下一篇
张景威1,2(
), 覃志威1,2, 李卓达1,2, 常馨予1,2, 陈晓乐1,2, 白志勇1,2, 徐锡镇1,2(
), 王义平1,2, 何俊1,2
收稿日期:2026-06-04
出版日期:2026-08-20
发布日期:2026-08-26
通信作者:
徐锡镇,博士,副教授。E-mail:xizhenxu@szu.edu.cn作者简介:张景威(2002—),男,广东省人,硕士研究生。E-mail:2510232193@mails.szu.edu.cn基金资助:
ZHANG Jingwei1,2(
), QIN Zhiwei1,2, LI Zhuoda1,2, CHANG Xinyu1,2, CHEN Xiaole1,2, BAI Zhiyong1,2, XU Xizhen1,2(
), WANG Yiping1,2, HE Jun1,2
Received:2026-06-04
Online:2026-08-20
Published:2026-08-26
摘要: 蓝宝石光纤布拉格光栅(SFBG)可在1 800 ℃以上实现原位、多点高精度测温,是航空发动机、核能与工业炉等极端环境监测的重要传感器。然而,蓝宝石光纤的强多模特性导致反射谱宽带、多峰叠加且对耦合与封装高度敏感,使其解调机理与传统石英光纤布拉格光栅(FBG)显著不同。本文围绕SFBG波长解调需求,系统梳理并对比光谱分析仪(OSA)阵列光谱仪直接测量及光学频域反射(OFDR)解调等技术路线,从解调速度、分辨率/精度、量程、复用能力与鲁棒性等关键指标总结代表性进展。进一步归纳提升信噪比与稳定性的工程与算法研究,包括模式滤除、模式减少、单模化与稳模、端面与耦合优化、高温封装、互相关算法及机器学习辅助算法等。最后从阵列波导光栅(AWG)小型化解调、扫频激光路线快速解调与干涉型高精度解调三方面展望SFBG解调系统的发展方向,为光纤高温及应变传感工程化实时解调的发展提供参考。
中图分类号:
张景威, 覃志威, 李卓达, 常馨予, 陈晓乐, 白志勇, 徐锡镇, 王义平, 何俊. 蓝宝石光纤布拉格光栅高温传感解调技术研究进展[J]. 人工晶体学报, 2026, 55(8): 1155-1191.
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.
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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
表1 FBG 解调系统相关图示
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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
| 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[ |
图2 面向高温测量的三种主流蓝宝石光纤布拉格光栅解调系统及其典型反射光谱[9,32,138]。(a)FBG解调装置;(b)SFBG阵列光信号采集系统及反射光谱;(c)SFBG阵列光信号采集系统示意图,包括SFBG温度传感器、光学单元和电信号处理单元;(d)五个SFBG阵列的实测反射光谱;(e)基于OFDR原理的Luna光纤光栅解调仪不同光纤长度位置处SFBG反射光谱幅值分布
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
图4 三种蓝宝石光纤样品S1~S3在长期高温退火后的表面形貌SEM照片。(a1)~(a3)1 530 ℃;(b1)~(b3)1 560 ℃;(c1)~(c3)1 600 ℃;(d1)~(d3)光纤样品表面损伤斑特征尺寸和刻蚀线特征宽度的变化情况,其中,S1为未封装样品,S2为封装样品,S3为经过应力释放处理的封装样品[146]
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]
图5 蓝宝石光纤端面处理后的形貌及SFBG光谱[15]。(a)采用Miller钳压断得到的蓝宝石光纤端面;采用粒径为30 μm(b)、9 μm(c)、5 μm(d)、3 μm(e)和1 μm(f)的金刚石研磨膜抛光后的蓝宝石光纤端面;(g)不同端面处理方式下的SFBG光谱。样品信息缩写为[样品名称,耦合面,端面,研磨膜粒径]、[S1,0°,折射率匹配]、[S2,8°,断裂端面]、[(S3,S4,S5,S6,S7),8°,30°,(30,9,5,3,1 μm)]、[S8,8°,30°,折射率匹配],插图为蓝宝石光纤显微图
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
图6 多层逐线写入多层SFBG的显微图像及反射光谱[151]。(a)分别具有1层、2层和3层刻写结构的单层、双层和三层SFBG截面显微图像;(b)对应SFBG的侧向显微图像;(c)单层、双层和三层SFBG的反射光谱
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
图7 不同周期和螺旋直径HSFBG的显微图像及光谱对比[163]。(a)、(b)周期为1.332 μm、螺旋直径分别为15和30 μm的HSFBG显微图像;(c)、(d)周期为6.66 μm、螺旋直径分别为15和30 μm的 HSFBG显微图像;(e)螺旋直径分别为15、20、25、30和35 μm的HSFBG光谱对比。插图为20 nm波长范围内的局部放大图
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
图8 不同长度AMMF条件下蓝宝石光纤近场传输模式场及光学表征装置[15]。(a)光学特性表征实验装置示意图,包括蓝宝石光纤近场传输模式分布和SFBG反射光谱的测量;(b)不同AMMF长度下蓝宝石光纤近场传输模式场测量结果,分别对应1、50、500和1 000 m;(c)不同长度AMMF条件下SFBG反射峰形貌
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
图9 三种蓝宝石光纤布拉格光栅滤模技术及其反射光谱优化效果[139,144,151]。(a)所提出的蓝宝石光纤FBG传感系统的实验装置图,插图展示了熔接点和FBG结构的显微图像;(b)室温下测得的FBG光谱,蓝色曲线表示传统连接方式,即多模光纤(multimode fiber, MMF)直接连接到OSA;红色曲线表示所提出系统的测试结果;虚线表示高斯拟合结果;(c1)双层SFBG与入射MMF沿y轴偏置耦合示意图;(c2)沿x轴偏置耦合示意图;(d)无偏置(0 μm)、沿y轴偏置20 μm和沿x轴偏置20 μm时双层SFBG的反射光谱;(e)三步多层WBG制备工艺示意图;(f)单模SFBG的实验测量反射光谱
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
图10 螺旋锥形凹陷包层波导(HTDCW)飞秒激光直写制备的HTDCW与SFBG结构示意图[14]。(a)光在螺旋轨迹凹陷包层波导(HTDCW)中正向和反向传播时的模拟模式场(上)及光路示意图(下),HTDCW的截面结构示意图(右);(b)通过与MMF、SMF和HTDCW对接耦合测得的SFBG反射光谱,插图:SFBG与MMF、SMF和HTDCW对接耦合的结构示意图;(c)在无振动和20 Hz振动条件下65次测量的波长离散分布
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
图11 微型SFBG及表征[12,138]。(a)制备得到的9.6 μm直径微型SFBG的光学显微图像,其中通过向光纤中注入638 nm红光实现FBG的可视化;(b)不同直径(d)下空气包层 SFBG的反射光谱
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)
图12 在块体蓝宝石中利用飞秒激光写入凹陷包层波导蓝宝石中凹陷包层波导(DCWs)的截面形貌、折射率分布及近场输出[172,174-175]。(a)蓝宝石中刻写的DCW截面图像;(b)、(c)波长为2 850 nm的透射光在DCW波导输出端测得的近场强度分布;(d)蓝宝石传感器示意图;(e)耦合进入单模蓝宝石波导芯;从优化位置成功熔接后的光谱图,以及成功熔接后的熔接接头图像与光谱图;(f)采用飞秒激光直写技术在蓝宝石光纤中制备的HBGW结构示意图,插图为带狭缝和不带狭缝的HBGW横截面结构示意图;(g)蓝宝石光纤中制备的三个HBGW样品S1、S2和S3的相应透射和反射光谱,其中S1、S2和S3的直径依次减小,分别为30、20和14 μm
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
| 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 |
表2 6种传统FBG解调算法总结[177]
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 |
图13 不同解调算法下SFBG的反射光谱分析与寻峰稳定性对比[178-179]。(a)SFBG的非对称反射峰,图中符号表示实测反射强度,单位为任意单位,实线表示采用式(2)拟合得到的峰函数,光纤中的应变释放导致Bragg波长向较短波长方向移动0.5 nm,如箭头所示;(b)所用钢基底热膨胀系数(CTE)随温度的变化,其中绿色曲线为基于SFBG的传感装置测得的结果,蓝色曲线为膨胀仪测得的结果,SFBG传感器在19~650 ℃的温度标定结果;(c)波长稳定性;(d)温度响应及其多项式拟合曲线
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
| 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 |
表3 9种机器学习算法对FBG解调效果对比[177]
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 |
图15 基于DNN的SFBG解调算法[144]。(a)实验中所采用的DNN模型结构;(b)DNN模型在静止条件下的性能表现及2 720组输入光谱的误差直方图,训练集和验证集的损失曲线图
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
图16 SFBG高温传感应用示例[32,138,187,189]。(a)Yang等在燃煤锅炉中的传感器部署,包括传感器配置方案示意图和现场部署照片;(b)Tan等基于SFBG阵列传感器的超高温黑体辐射炉温度分布测量,包括高温黑体辐射源温度分布测量原理、现场部署照片及不同热工况下的温度分布结果;(c)用于测试SFBG阵列在加热和冷却循环下性能的实验装置;(d)基于再生FBG传感器的液态钠系统高温监测,适用于钠冷快堆等核能装备
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
图17 SFBG应变传感应用示例[178,185]。(a) SFBG应变传感器设计图;(b)SFBG在25、800和1 100 ℃下的应变响应,布拉格波长与应变之间的线性拟合关系;(c)应变测试过程中布拉格波长的离散分布
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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