Abstract

A highly sensitive liquid-level sensor based on dual-wavelength single-longitudinal-mode fiber laser is proposed and demonstrated. The laser is formed by exploiting two parallel arranged phase-shift fiber Bragg gratings (ps-FBGs), acting as ultra-narrow bandwidth filters, into a double-ring resonators. By beating the dual-wavelength lasing output, a stable microwave signal with frequency stability better than 5 MHz is obtained. The generated beat frequency varies with the change of dual-wavelength spacing. Based on this characteristic, with one ps-FBG serving as the sensing element and the other one acting as the reference element, a highly sensitive liquid level sensor is realized by monitoring the beat frequency shift of the laser. The sensor head is directly bonded to a float which can transfer buoyancy into axial strain on the fiber without introducing other elastic elements. The experimental results show that an ultra-high liquid-level sensitivity of 2.12 × 107 MHz/m within the measurement range of 1.5 mm is achieved. The sensor presents multiple merits including ultra-high sensitivity, thermal insensitive, good reliability and stability.

© 2012 OSA

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    [CrossRef]

2012

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

2011

2010

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

2008

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

2007

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett.19(15), 1148–1150 (2007).
[CrossRef]

B. Yun, N. Chen, and Y. Cui, “Highly sensitive liquid-level sensor based on etched fiber Bragg grating,” IEEE Photon. Technol. Lett.19(21), 1747–1749 (2007).
[CrossRef]

2006

D. Bo, Z. Qida, L. Feng, G. Tuan, X. Lifang, L. Shuhong, and G. Hong, “Liquid-level sensor with a high-birefringence-fiber loop mirror,” Appl. Opt.45(30), 7767–7771 (2006).
[CrossRef] [PubMed]

X. Chen, Z. Deng, and J. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser,” IEEE Trans. Microw. Theory Tech.54(2), 804–809 (2006).
[CrossRef]

2005

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett.30(16), 2068–2070 (2005).
[CrossRef] [PubMed]

G. A. Campbell and R. Mutharasan, “Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever,” Sens. Actuators A Phys.122(2), 326–334 (2005).
[CrossRef]

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

2004

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

J. Liu, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photon. Technol. Lett.16(4), 1020–1022 (2004).
[CrossRef]

2003

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol.9(2), 57–79 (2003).
[CrossRef]

2001

1997

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

Antonio-Lopez, J. E.

Bo, D.

Campbell, G. A.

G. A. Campbell and R. Mutharasan, “Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever,” Sens. Actuators A Phys.122(2), 326–334 (2005).
[CrossRef]

Canales, I.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Chen, D.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

Chen, N.

B. Yun, N. Chen, and Y. Cui, “Highly sensitive liquid-level sensor based on etched fiber Bragg grating,” IEEE Photon. Technol. Lett.19(21), 1747–1749 (2007).
[CrossRef]

Chen, X.

X. Chen, Z. Deng, and J. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser,” IEEE Trans. Microw. Theory Tech.54(2), 804–809 (2006).
[CrossRef]

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett.30(16), 2068–2070 (2005).
[CrossRef] [PubMed]

Cui, Y.

B. Yun, N. Chen, and Y. Cui, “Highly sensitive liquid-level sensor based on etched fiber Bragg grating,” IEEE Photon. Technol. Lett.19(21), 1747–1749 (2007).
[CrossRef]

Culshaw, B.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Dai, Y.

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Demokan, M.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Deng, Z.

X. Chen, Z. Deng, and J. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser,” IEEE Trans. Microw. Theory Tech.54(2), 804–809 (2006).
[CrossRef]

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett.30(16), 2068–2070 (2005).
[CrossRef] [PubMed]

Dong, X.

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett.19(15), 1148–1150 (2007).
[CrossRef]

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

Dou, Q.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

Feng, L.

Fernandez-Vallejo, M.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Fu, H.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

Guo, T.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

He, S.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

He, Z.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

Ho, H.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Hong, G.

Huang, G.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

James, S. W.

Jin, W.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Khaliq, S.

Lee, B.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol.9(2), 57–79 (2003).
[CrossRef]

Li, X.

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Lifang, X.

LiKamWa, P.

Liu, D.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Q. Sun, J. Wang, D. Liu, and P. Shum, “Optical generation of microwave signal using FBG-based double-ring fiber laser assisted by saturable absorber,” Microw. Opt. Technol. Lett.53, 2478–2481 (2011).

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett.19(15), 1148–1150 (2007).
[CrossRef]

Liu, J.

J. Liu, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photon. Technol. Lett.16(4), 1020–1022 (2004).
[CrossRef]

Liu, Q.

Liu, W.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

Lopez-Amo, M.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Lopez-Higuer, J. M.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Luo, J.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

May-Arrioja, D. A.

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol.15(8), 1263–1276 (1997).
[CrossRef]

Mutharasan, R.

G. A. Campbell and R. Mutharasan, “Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever,” Sens. Actuators A Phys.122(2), 326–334 (2005).
[CrossRef]

Ngo, N. Q.

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett.19(15), 1148–1150 (2007).
[CrossRef]

Perez-Herrera, R. A.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Qida, Z.

Quintela, M. A.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
[CrossRef]

Sanchez-Mondragon, J. J.

Shuhong, L.

Shum, P.

Q. Sun, J. Wang, D. Liu, and P. Shum, “Optical generation of microwave signal using FBG-based double-ring fiber laser assisted by saturable absorber,” Microw. Opt. Technol. Lett.53, 2478–2481 (2011).

Stewart, G.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Sun, Q.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Q. Sun, J. Wang, D. Liu, and P. Shum, “Optical generation of microwave signal using FBG-based double-ring fiber laser assisted by saturable absorber,” Microw. Opt. Technol. Lett.53, 2478–2481 (2011).

Tatam, R. P.

Tjin, S. C.

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett.19(15), 1148–1150 (2007).
[CrossRef]

Tokunaga, T.

Tong, W.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Tuan, G.

Wang, J.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Q. Sun, J. Wang, D. Liu, and P. Shum, “Optical generation of microwave signal using FBG-based double-ring fiber laser assisted by saturable absorber,” Microw. Opt. Technol. Lett.53, 2478–2481 (2011).

Wei, Y.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

Wo, J.

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Xue, L.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

Yao, J.

X. Chen, Z. Deng, and J. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser,” IEEE Trans. Microw. Theory Tech.54(2), 804–809 (2006).
[CrossRef]

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett.30(16), 2068–2070 (2005).
[CrossRef] [PubMed]

J. Liu, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photon. Technol. Lett.16(4), 1020–1022 (2004).
[CrossRef]

Yeap, T. H.

J. Liu, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photon. Technol. Lett.16(4), 1020–1022 (2004).
[CrossRef]

Yun, B.

B. Yun, N. Chen, and Y. Cui, “Highly sensitive liquid-level sensor based on etched fiber Bragg grating,” IEEE Photon. Technol. Lett.19(21), 1747–1749 (2007).
[CrossRef]

Zhang, H.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

Zhang, M.

Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng.51(4), 044401 (2012).
[CrossRef]

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Zhang, Y.

Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun.232(1-6), 295–301 (2004).
[CrossRef]

Zhao, Q.

T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett.17(11), 2400–2402 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. B Lasers Opt.

Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt.106(2), 373–377 (2012).
[CrossRef]

Electron. Lett.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett.44(7), 459–461 (2008).
[CrossRef]

IEEE Photon. Technol. Lett.

M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett.22(6), 368–370 (2010).
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Figures (9)

Fig. 1
Fig. 1

The schematic diagram of the proposed double-ring EDFL.

Fig. 2
Fig. 2

The simulation results of the dual-wavelength lasing operation: (a) spectrum of individual uniform FBG, ps-FBGs, and ps-FBG1 + ps-FBG2; (b) spectrum of the coaction of the uniform FBG and the ps-FBGs (dual-wavelength lasing operation).

Fig. 3
Fig. 3

The schematic diagram of the sensing principle.

Fig. 4
Fig. 4

(a). Electrical spectrum of the beat signal observed from ESA, the insert shows the dual-wavelength lasing spectrum with wavelength spacing of 0.134 nm. (b). Scanning electrical spectrum of the beat signal over about half an hour with a time interval of 4 min.

Fig. 5
Fig. 5

Beat frequency shift vs. the change of temperature at different beat frequencies: (a) 10 GHz, (b) 20 GHz, (c) 30 GHz, (d) 40 GHz.

Fig. 6
Fig. 6

The experimental setup of liquid level detection.

Fig. 7
Fig. 7

The schematic diagram of the connecting vessel to adjust and calibrate the liquid level.

Fig. 8
Fig. 8

Beat frequency shift with the change of liquid level within the whole measurement range.

Fig. 9
Fig. 9

Beat frequency shift with the change of liquid level in bidirectional range.

Equations (6)

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Δν= ν 1 ν 2 = c λ 2 (Δ λ 1 Δ λ 2 )= c λ 2 δλ
δλ=0.78(ΔL/L)λ=0.78ελ
F float = F B +mg
F B =σ×S=εE×S
F float =ρg(Δh+ H 0 ) S 0
Δh=[ (mg+ES λΔν 0.78c )/ρg S 0 ] H 0

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