短双折射光纤环镜应变传感器在线测量方法研究

江莺; 段峥

doi:doi:10.19453/j.cnki.1005-488x.2020.02.012

光电子技术, 2020, 40 (2): 134, 网络出版: 2020-08-13

短双折射光纤环镜应变传感器在线测量方法研究下载： 514次

Research on the On⁃line Measurement of the Short Birefringence Fiber Loop Mirror Strain Sensors

论文大纲

江莺段峥

作者单位

College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037，CHN

短双折射光纤环镜应变传感器在线测量干扰测量精度 short birefringence fiber loop mirror strain sensor on-line measurement noises measurement accuracy

摘要

为了实现短双折射光纤环镜(Bi?FLM)应变传感器的在线测量，理论推导得出通过任意连续的2个相邻波谷波长、2个相邻波峰波长及其双折射光纤初始长度、初始双折射率和初始双折射应变系数计算双折射光纤所受应变大小的方法。选取典型通讯波长1 550 nm附近的波长，波长分辨率分别为0.01 nm、0.001 nm、0.000 1 nm时，应用提出的计算方法计算应变和误差。结果表明：波长分辨率越小，测量精度越高。波长分辨率为0.000 1 nm时，最大绝对误差为0.39%，最小绝对误差为0.01%，平均绝对误差为0.15%。进一步选取典型通讯波长1 310 nm附近的3组不同波长组合，计算的应变均与给定应变基本吻合。根据干涉光谱波谷波长、波峰波长的相对位置蕴含着应变信息的特点，与初始相角无关，可以剔除外界干扰，提高测量精度。该方法无需人为判断，有助于实现计算机在线测量；需要的信息量较小，可以实现短Bi?FLM传感器的在线测量。研究结果对Bi?FLM各类传感器实现计算机在线测量，提高测量精度具有指导意义。

Abstract

In order to realize the on-line measurement of the short birefringence fiber (BF) loop mirror (Bi-FLM) strain sensors, the method of calculating the BF strain by random continuous two-adjacent-wave-valley wavelengths, two-adjacent-wave-peak wavelengths, the initial BF length, the initial BF birefringence and the initial strain dependent birefringence coefficient were deduced theoretically. The wavelengths near 1 550 nm were chosen and used to calculate the strain by the presented theoretical method when the wavelength resolution was 0.01 nm, 0.001 nm and 0.000 1 nm, respectively. The results show that the smaller the wavelength resolution is, the higher the measurement accuracy is. When the wavelength resolution is 0.000 1 nm, the maximum absolute error is 0.39%, the minimum absolute error is 0.01%, and the average absolute error is 0.15%. Three groups of different wavelength combinations near 1 310 nm are also chosen and used to calculate the strain by the theoretical method. The calculated strains are basically consistent with the given strains. According to the characteristics of strain information contained in the relative positions of two-adjacent-wave-valley wavelengths and two-adjacent-wave-peak wavelengths, which are independent of the initial phase angle, the external noises could be eliminated and the measurement accuracy could be improved. This method does not need human judgment and is helpful to realize on-line measurement by computer. In addition, this method requires less information. So it could realize online measurement of the short Bi-FLM sensors. The results could provide guidance for realizing the on-line measurement and improving the measurement accuracy of the Bi-FLM sensors.

1 引言

双折射光纤环镜（Birefringence fiber loop mirror，Bi⁃FLM）传感器具有低成本、易于制造、极化独立、不受电磁干扰等优点 [1, 2] ，已成功应用于应变 [3, 4, 5] 、振动 [6, 7] 、扭矩 [8, 9] 等各类传感器。目前，该传感器多通过波长解调的方法实现离线测量，即根据Bi⁃FLM干涉光谱波长的相对变化量来推算传感量的大小 [10, 11, 12, 13, 14, 15, 16, 17] 。由于干涉光谱是周期性信号，需要人为判断外界传感量的变化会导致干涉光谱左移还是右移，需要人为判断是较小外界传感量产生较小相角变化导致的干涉光谱平移，还是较大外界传感量产生较大相角的周而复始的干涉光谱，不利于实施传感器的在线测量。且在测试过程中外界干扰容易改变干涉光谱的初始相角，导致干涉光谱平移，从而改变波长的相对变化量，基于波长解调的方法无法区分是干扰还是外界传感量的变化导致的波长相对变化，致使测量精度下降。也有学者基于强度解调原理 [18, 19, 20] 实现Bi⁃FLM传感器在线测量，即将Bi⁃FLM传感器的光信号强度通过光电转换器转换为电信号，通过监测电信号的变化反推光信号的变化，从而反推外界传感量的变化。由于强度解调受光源稳定性影响较大，因此该方法精度较低。

作者根据Bi⁃FLM干涉光谱任意4个相邻波谷波长相对位置蕴含着应变信息的特点，曾研究通过任意4个相邻波谷波长及双折射光纤初始条件计算应变大小，该方法无需人为判断，有助于促进传感器与计算机有效对接，实现在线测量。且与初始相角无关，因此可以剔除外界干扰，提高测量精度 [21] 。但该方法需要4个相邻波谷的波长，包含3个周期的干涉波形，需要的信息量较多。双折射光纤长度越短，Bi⁃FLM干涉光谱周期越大，在一定的光源波长范围内，光纤长度较短的Bi⁃FLM可能没有足够的波谷点，导致无法计算。文中在继承该方法优点的同时，提出通过任意连续不间断的2个相邻波谷波长、2个相邻波峰波长及双折射光纤初始条件计算应变大小，该方法需要包含1.5个周期的干涉波形，需要的信息量较小，能够解决光纤长度较短的Bi⁃FLM传感器蕴含的信息量不够的问题。

1 理论分析

Bi⁃FLM传感器原理图如 图1 所示，入射光从端口1经光隔离器进入3 dB光纤耦合器，按1∶1分成从端口3顺时针和端口4逆时针相向传输的两束光，最后汇聚在端口2，由于双折射光纤具有双折射效应，汇聚在端口2的两束光发生干涉。当双折射光纤受到应变时，导致双折射光纤双折射率和双折射光纤长度发生变化，从而导致干涉光谱随之改变，以此实现应变测量。

图 1. 双折射光纤环镜传感器原理图

Fig. 1. Principle schematic of Bi-FLM

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Bi⁃FLM传感器初始干涉光谱表达式为 [18] ：

T (λ) = \frac{1 - c o s (\frac{2 π L_{0} B_{0}}{λ})}{2} = \frac{1 - c o s θ}{2}

(1)

λ

Δ θ

Δ θ = \frac{2 π L_{0}}{λ} (B_{0} + k) ε_{z}

(2)

ε_{z} = Δ L / L_{0} = (L' - L_{0}) / L_{0}

L'

Δ θ = \frac{2 π}{λ} (B_{0} + k) \times (L' - L_{0})

(3)

ε_{z}

T' (λ) = \frac{1 - c o s (θ + Δ θ)}{2} = \frac{1 - c o s [\frac{2 π L_{0} B_{0}}{λ} + \frac{2 π L_{0}}{λ} (B_{0} + k) ε_{z}]}{2}

(4)

ε_{z}

L'

T' (λ) = \frac{1 - c o s (θ + Δ θ)}{2} = \frac{1 - c o s [\frac{2 π L_{0} B_{0}}{λ} + \frac{2 π}{λ} (B_{0} + k) (L' - L_{0})]}{2}

(5)

T' (λ)

\frac{2 π L_{0} B_{0}}{λ_{n}} + \frac{2 π}{λ_{n}} (B_{0} + k) (L' - L_{0}) = 2 n π

(6)

n

λ_{n} = \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{n}

(7)

由(7)式可得：

λ_{n + 1} - λ_{n} = - \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{n (n + 1)}

(8)

由(8)式可得：

L' = - \frac{n (n + 1) (λ_{n + 1} - λ_{n}) - L_{0} k}{B_{0} + k}

(9)

T' (λ)

\frac{2 π L_{0} B_{0}}{λ'_{n}} + \frac{2 π}{λ'_{n}} (B_{0} + k) (L' - L_{0}) = (2 n + 1) π

(10)

λ'_{n}

由(10)式解出:

λ'_{n} = \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{n + 0.5}

(11)

由(11) 式可得:

λ'_{n + 1} - λ'_{n} = - \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{(n + 1.5) (n + 0.5)}

(12)

由(12)式可得:

L' = - \frac{(n + 0.5) (n + 1.5) (λ'_{n + 1} - λ'_{n}) - L_{0} k}{B_{0} + k}

(13)

由(9)式、(13)式可得:

L' = - \frac{n (n + 1) (λ_{n + 1} - λ_{n}) - L_{0} k}{B_{0} + k} = - \frac{(n + 0.5) (n + 1.5) (λ'_{n + 1} - λ'_{n}) - L_{0} k}{B_{0} + k}

(14)

根据(14)式，经编程验证可得:

n = \frac{2 (λ'_{n + 1} - λ'_{n}) - (λ_{n + 1} - λ_{n}) - \sqrt[]{(λ_{n + 1} - λ_{n})^{2} + (λ'_{n + 1} - λ'_{n})^{2} - (λ_{n + 1} - λ_{n}) (λ'_{n + 1} - λ'_{n})}}{2 (λ_{n + 1} - λ_{n}) - 2 (λ'_{n + 1} - λ'_{n})}

(15)

λ_{n}

θ + Δ θ = 2 n π

λ_{n} = \frac{L_{0} [B_{0} + (B_{0} + k) ε_{z}]}{n}

(16)

λ'_{n} = \frac{L_{0} [B_{0} + (B_{0} + k) ε_{z}]}{n + 0.5}

(17)

ε_{z}

ε_{z} < \frac{- B_{0}}{(B_{0} + k)}

(18)

L_{0} = 0.1 m

2 结果与讨论

2.1　算法的验证

λ_{n}

L_{0} = 0.1 m

图 2. 长度为0.1 m的1 550 nm波长附近Bi-FLM干涉光谱

Fig. 2. Bi-FLM sensor interference spectrum near 1 550 nm when BF is 0.1 m

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L_{0} = 0.1 m

定义表中误差为：

误 差 = \frac{(计 算 应 变 - 给 定 应 变)}{给 定 应 变} \times 100 %

其它应变和误差的计算以此类推。计算应变和误差流程图如下：

λ

表 1. 1 550 nm波长附近的计算应变和误差的结果

Table 1. 1 550 nm波长附近的计算应变和误差的结果

给定应变 $/ μ ε$	$λ'_{n} / n m$	$λ'_{n + 1} / n m$	$λ_{n} / n m$	$λ_{n + 1} / n m$	$步长 / n m$	计算应变 $/ μ ε$	$误差 / (%)$
100	1 580.34	1 490.03	1 629.73	1 533.86	0.01	118.10	18.10
	1 580.339	1 490.034	1 629.725	1 533.859	0.001	100.69	0.69
	1 580.339 4	1 490.034 3	1 629.725 0	1 533.858 8	0.000 1	99.61	-0.39
200	1 584.92	1 494.35	1 634.45	1 538.31	0.01	288.82	44.41
	1 584.921	1 494.354	1 634.450	1 538.306	0.001	202.35	1.18
	1 584.921 2	1 494.354 3	1 634.450 0	1 538.305 9	0.000 1	199.87	-0.06
300	1 589.50	1 498.67	1 639.18	1 542.75	0.01	222.29	-25.90
	1 589.503	1 498.674	1 639.175	1 542.753	0.001	304.01	1.34
	1 589.503 0	1 498.674 3	1 639.175 0	1 542.752 9	0.000 1	298.93	-0.36
400	1 594.08	1 502.99	1 643.90	1 547.20	0.01	392.71	-1.82
	1 594.085	1 502.994	1 643.900	1 547.200	0.001	405.67	1.42
	1 594.084 8	1 502.994 3	1 643.900 0	1 547.200 0	0.000 1	399.19	-0.20
500	1 598.67	1 507.31	1 648.63	1 551.65	0.01	574.48	14.90
	1 598.667	1 507.314	1 648.625	1 551.647	0.001	507.33	1.47
	1 598.666 7	1 507.314 3	1 648.625 0	1 551.647 1	0.000 1	500.73	0.15
600	1 603.25	1 511.63	1 653.35	1 556.09	0.01	626.41	4.40
	1 603.248	1 511.634	1 653.350	1 556.094	0.001	596.02	-0.66
	1 603.248 5	1 511.634 3	1 653.350 0	1 556.094 1	0.000 1	599.80	-0.03
700	1 607.83	1 515.95	1 658.08	1 560.54	0.01	678.44	-3.08
	1 607.830	1 515.954	1 658.075	1 560.541	0.001	697.68	-0.33
	1 607.830 3	1 515.954 3	1 658.075 0	1 560.541 2	0.000 1	700.05	0.01
800	1 612.41	1 520.27	1 662.80	1 564.99	0.01	849.02	6.13
	1 612.412	1 520.274	1 662.800	1 564.988	0.001	799.34	-0.08
	1 612.412 1	1 520.274 3	1 662.800 0	1 564.988 2	0.000 1	799.12	-0.11
900	1 616.99	1 524.59	1 667.53	1 569.44	0.01	901.00	0.11
	1 616.994	1 524.594	1 667.525	1 569.435	0.001	901.00	0.11
	1 616.993 9	1 524.594 3	1 667.525 0	1 569.435 3	0.000 1	899.37	-0.07

查看所有表

定义绝对误差为误差的绝对值，由 表1 可统计不同步长的误差结果如 表2 所示。

表 2. 不同步长的误差统计表

Table 2. 不同步长的误差统计表

步长/nm

最大绝对

误差/(%)

最小绝对

误差/(%)

平均绝对

误差/(%)

0.01

44.41

0.11

13.21

0.001

1.47

0.08

0.81

0.000 1

0.39

0.01

0.15

查看所有表

λ

λ

λ_{n}

图 3. 计算应变和误差流程图

Fig. 3. Flowchart for calculating strain and error

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图 4. 长度为0.1 m的1 310 nm波长附近Bi-FLM干涉光谱

Fig. 4. Bi-FLM sensor interference spectrum near 1 310 nm when BF is 0.1 m

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表 3. 1 310 nm波长附近的计算应变和误差的结果

Table 3. 1 310 nm波长附近的计算应变和误差的结果

给定应变 $/ μ ε$	$λ'_{n} / n m$	$λ'_{n + 1} / n m$	$λ_{n} / n m$	$λ_{n + 1} / n m$	计算应变 $/ μ ε$	$误差 / (%)$
100	1 337.210 3	1 271.980 5	1 372.400 0	1 303.780 0	100.66	0.66
200	1 341.087 2	1 275.668 3	1 376.378 9	1 307.560 0	201.21	0.60
300	1 344.964 1	1 279.356 1	1 380.357 9	1 311.340 0	299.79	-0.07
400	1 348.841 0	1 283.043 9	1 384.336 8	1 315.120 0	400.33	0.08
500	1 352.717 9	1 286.731 7	1 388.315 8	1 318.900 0	498.92	-0.22
600	1 356.594 9	1 290.419 5	1 392.294 7	1 322.680 0	601.57	0.26
700	1 360.471 8	1 294.107 3	1 396.273 7	1 326.460 0	700.16	0.02
800	1 364.348 7	1 297.795 1	1 400.252 6	1 330.240 0	800.70	0.09
900	1 368.225 6	1 301.482 9	1 404.231 6	1 334.020 0	899.29	-0.08

查看所有表

2.2　讨论

θ + Δ θ = (2 n + 1) π

同理，欲求波峰波长也可令:

θ + Δ θ = \frac{2 π L_{0} B_{0}}{λ'_{n}} + \frac{2 π}{λ'_{n}} (B_{0} + k) (L' - L_{0}) = (2 n - 1) π

(19)

由(19)式可得:

λ'_{n} = \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{n - 0.5}

(20)

由(20)式可得:

λ'_{n + 1} - λ'_{n} = - \frac{L_{0} B_{0} + (B_{0} + k) (L' - L_{0})}{(n - 0.5) (n + 0.5)}

(21)

由(21)式可得:

L' = - \frac{(n + 0.5) (n - 0.5) (λ'_{n + 1} - λ'_{n}) - L_{0} k}{B_{0} + k}

(22)

由(9)式、(22)式可得:

n = \frac{(λ_{n + 1} - λ_{n}) - \sqrt[]{(λ_{n + 1} - λ_{n})^{2} + [(λ'_{n + 1} - λ'_{n}) - (λ_{n + 1} - λ_{n})] (λ'_{n + 1} - λ'_{n})}}{2 (λ'_{n + 1} - λ'_{n}) - 2 (λ_{n + 1} - λ_{n})}

(23)

θ + Δ θ = 2 n π

λ_{n} < λ'_{n}

由(15)式可得：

n + 1 = \frac{(λ_{n + 1} - λ_{n}) - \sqrt[]{(λ_{n + 1} - λ_{n})^{2} + [(λ'_{n + 1} - λ'_{n}) - (λ_{n + 1} - λ_{n})] (λ'_{n + 1} - λ'_{n})}}{2 (λ'_{n + 1} - λ'_{n}) - 2 (λ_{n + 1} - λ_{n})}

(24)

由(23)式可得：

n + 1 = \frac{2 (λ'_{n + 1} - λ'_{n}) - (λ_{n + 1} - λ_{n}) - \sqrt[]{(λ_{n + 1} - λ_{n})^{2} + (λ'_{n + 1} - λ'_{n})^{2} - (λ_{n + 1} - λ_{n}) (λ'_{n + 1} - λ'_{n})}}{2 (λ_{n + 1} - λ_{n}) - 2 (λ'_{n + 1} - λ'_{n})}

(25)

n + 1

L_{0} = 0.1 m

图 5. 长度为0.1 m的Bi-FLM相邻的3组不同波长组合图

Fig. 5. Bi-FLM sensor interference spectrum of three groups with adjacent different wavelengths when BF is 0.1 m

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λ_{n}

表 4. 相邻的3组不同波长组合计算应变和误差的结果

Table 4. 相邻的3组不同波长组合计算应变和误差的结果

给定应变 $/ μ ε$	波长1/nm	波长2 $/ n m$	波长3 $/ n m$	波长4 $/ n m$	计算应变 $/ μ ε$	$误差 / (%)$
100	1 448.644 4	1 490.034 3	1 533.858 8	1 580.339 4	100.40	0.40
	1 490.034 3	1 533.858 8	1 580.339 4	1 629.725	99.61	-0.39
	1 533.858 8	1 580.339 4	1 629.725	1 682.296 8	100.07	0.07
200	1 452.844 4	1 494.354 3	1 538.305 9	1 584.921 2	201.22	0.61
	1 494.354 3	1 538.305 9	1 584.921 2	1 634.45	199.87	-0.07
	1 538.305 9	1 584.921 2	1 634.45	1 687.174 2	199.59	-0.20
300	1 457.044 4	1 498.674 3	1 542.752 9	1 589.503	300.62	0.21
	1 498.674 3	1 542.752 9	1 589.503	1 639.175	298.93	-0.36
	1 542.752 9	1 589.503	1 639.175	1 692.0516	300.30	0.10
400	1 461.244 4	1 502.994 3	1 547.2	1 594.084 8	401.44	0.36
	1 502.994 3	1 547.2	1 594.084 8	1 643.9	399.17	-0.20
	1 547.2	1 594.084 8	1 643.9	1 696.929	401.44	0.36
500	1 465.444 4	1 507.314 3	551.647 1	1 598.666 7	500.96	0.19
	1 507.314 3	551.647 1	1 598.666 7	1 648.625	500.73	0.15
	1 551.647 1	1 598.666 7	1 648.625	1700	500.96	0.19
600	1 469.644 4	1 511.634 3	1 556.094 1	1 603.248 5	600.37	0.06
	1 511.634 3	1 556.094 1	1 603.248 5	1 653.35	599.80	-0.03
	1 556.094 1	1 603.248 5	1 653.35	1 706.683 9	600.37	0.06
700	1 473.844 4	1 515.954 3	1 560.541 2	1 607.830 3	701.19	0.17
	1 515.954 3	1 560.541 2	1 607.830 3	1 658.075	700.05	0.00
	1 560.541 2	1 607.830 3	1 658.075	1 711.561 3	701.19	0.17
800	1 478.044 4	1 520.274 3	1 564.988 2	1 612.412 1	800.59	0.07
	1 520.274 3	1 564.988 2	1 612.412 1	1 662.8	799.12	-0.11
	1 564.988 2	1 612.412 1	1 662.8	1 716.438 7	800.59	0.07
900	1 482.244 4	1 524.594 3	1 569.435 3	1 616.993 9	901.41	0.16
	1 524.594 3	1 569.435 3	1 616.993 9	1 667.525	899.376 2	-0.07
	1 569.435 3	1 616.993 9	1 667.525	1 721.316 1	901.411 6	0.16

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3 结论

研究结果表明：可以通过Bi⁃FLM传感器干涉光谱任意连续的2个相邻波谷波长、2个相邻波峰波长及其双折射光纤初始长度、初始双折射率和初始双折射应变系数计算双折射光纤所受应变大小。该方法只与波谷波长、波峰波长的相对位置相关，与波谷波长、波峰波长的绝对位置无关，故可以剔除初始相角的干扰。该方法只需找到干涉光谱的2个相邻波谷波长和2个相邻波峰波长，便可计算应变，无需任何人为判断因素，方便通过计算机编程实现在线测量。且该方法仅需1.5个周期的干涉光谱所蕴含的信息，方便实现双折射光纤长度较短的Bi⁃FLM传感器的在线测量。研究结果对Bi⁃FLM应变、振动等各类传感器实现计算机在线测量，提高测量精度具有指导意义。提出的测量方法虽仅需1.5个周期的干涉波形，但通过干涉光谱更少的信息计算应变是有待进一步研究的目标。

参考文献

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短双折射光纤环镜应变传感器在线测量方法研究下载： 514次

1 引言

1 理论分析

图 1. 双折射光纤环镜传感器原理图

Fig. 1. Principle schematic of Bi-FLM

2 结果与讨论

2.1　算法的验证

图 2. 长度为0.1 m的1 550 nm波长附近Bi-FLM干涉光谱

Fig. 2. Bi-FLM sensor interference spectrum near 1 550 nm when BF is 0.1 m

表 1. 1 550 nm波长附近的计算应变和误差的结果

Table 1. 1 550 nm波长附近的计算应变和误差的结果

表 2. 不同步长的误差统计表

Table 2. 不同步长的误差统计表

图 3. 计算应变和误差流程图

Fig. 3. Flowchart for calculating strain and error

图 4. 长度为0.1 m的1 310 nm波长附近Bi-FLM干涉光谱

Fig. 4. Bi-FLM sensor interference spectrum near 1 310 nm when BF is 0.1 m

表 3. 1 310 nm波长附近的计算应变和误差的结果

Table 3. 1 310 nm波长附近的计算应变和误差的结果

2.2　讨论

图 5. 长度为0.1 m的Bi-FLM相邻的3组不同波长组合图

Fig. 5. Bi-FLM sensor interference spectrum of three groups with adjacent different wavelengths when BF is 0.1 m

表 4. 相邻的3组不同波长组合计算应变和误差的结果

Table 4. 相邻的3组不同波长组合计算应变和误差的结果

3 结论

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短双折射光纤环镜应变传感器在线测量方法研究 下载： 514次

1 引 言

1 理论分析

图 1. 双折射光纤环镜传感器原理图

Fig. 1. Principle schematic of Bi-FLM

2 结果与讨论

2.1 算法的验证

图 2. 长度为0.1 m的1 550 nm波长附近Bi-FLM干涉光谱

Fig. 2. Bi-FLM sensor interference spectrum near 1 550 nm when BF is 0.1 m

表 1. 1 550 nm波长附近的计算应变和误差的结果

Table 1. 1 550 nm波长附近的计算应变和误差的结果

表 2. 不同步长的误差统计表

Table 2. 不同步长的误差统计表

图 3. 计算应变和误差流程图

Fig. 3. Flowchart for calculating strain and error

图 4. 长度为0.1 m的1 310 nm波长附近Bi-FLM干涉光谱

Fig. 4. Bi-FLM sensor interference spectrum near 1 310 nm when BF is 0.1 m

表 3. 1 310 nm波长附近的计算应变和误差的结果

Table 3. 1 310 nm波长附近的计算应变和误差的结果

2.2 讨 论

图 5. 长度为0.1 m的Bi-FLM相邻的3组不同波长组合图

Fig. 5. Bi-FLM sensor interference spectrum of three groups with adjacent different wavelengths when BF is 0.1 m

表 4. 相邻的3组不同波长组合计算应变和误差的结果

Table 4. 相邻的3组不同波长组合计算应变和误差的结果

3 结 论

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短双折射光纤环镜应变传感器在线测量方法研究下载： 514次

1 引言

2.1　算法的验证

2.2　讨论

3 结论