Abstract

A fiber pressure sensor with a collimator at the off-center position of a diaphragm is demonstrated. The detection mechanism is incident-angle sensitive rather than traditional working-distance sensitive. Due to the small beam divergence of the collimator, the control on working distance is less stringent, and high sensitivity can be realized because the coupling efficiency of the collimator is very sensitive to the incident angle decided by the off-center diaphragm reflection. Sensitivity of 1.11 and 0.16dB/KPa can be achieved with silicon diaphragm thicknesses of 100 and 150 μm, respectively. Moreover, the detection range can be continually shifted by changing the pressure in the sealed diaphragm cavity.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. Y. Zhao, C. Yu, and Y. Liao, “Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement,” Opt. Laser Technol. 36, 39–42 (2004).
    [CrossRef]
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    [CrossRef]
  19. M. T. Wlodarczyk, “High accuracy glow plug-integrated cylinder pressure sensor for closed loop engine control,” SAE Technical Paper 2006-01-0184 (2006).
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    [CrossRef]
  21. R. W. Gilsdorf and J. C. Palais, “Single-mode fiber coupling efficiency with graded-index rod lenses,” Appl. Opt. 33, 3440–3445 (1994).
    [CrossRef]
  22. M. D. Giovanni, Flat and Corrugated Diaphragm Design Handbook (Dekker, 1982).
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    [CrossRef]

2012

2011

2010

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

2009

2008

2007

S. H. Aref, H. Latifi, M. I. Zibaii, and M. Afshari, “Fiber optic Fabry–Perot pressure sensor with low sensitivity to temperature changes for downhole application,” Opt. Commun. 269, 322–330 (2007).
[CrossRef]

2006

2005

K. Totsu, Y. Haga, and M. Esashi, “Ultra-miniature fiber-optic pressure sensor using white light interferometry,” J. Micromech. Microeng. 15, 71–75 (2005).
[CrossRef]

E. Cibula and D. Donlagic, “Miniature fiber-optic pressure sensor with a polymer diaphragm,” Appl. Opt. 44, 2736–2744 (2005).
[CrossRef]

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

2004

Y. Zhao, C. Yu, and Y. Liao, “Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement,” Opt. Laser Technol. 36, 39–42 (2004).
[CrossRef]

S. T. Oh, W. T. Han, U. C. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG on the birefringence effect,” Opt. Express 12, 724–729 (2004).
[CrossRef]

2003

H. Zhang, S. Boussaad, and N. Tao, “High-performance differential surface plasmon resonance sensor using quadrant cell photodetector,” Rev. Sci. Instrum. 74, 150–153 (2003).
[CrossRef]

2001

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, and H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

1997

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

1996

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

1994

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

R. W. Gilsdorf and J. C. Palais, “Single-mode fiber coupling efficiency with graded-index rod lenses,” Appl. Opt. 33, 3440–3445 (1994).
[CrossRef]

1982

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Abeysinghe, D. C.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, and H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Afshari, M.

S. H. Aref, H. Latifi, M. I. Zibaii, and M. Afshari, “Fiber optic Fabry–Perot pressure sensor with low sensitivity to temperature changes for downhole application,” Opt. Commun. 269, 322–330 (2007).
[CrossRef]

Archambault, J.-L.

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

Aref, S. H.

S. H. Aref, H. Latifi, M. I. Zibaii, and M. Afshari, “Fiber optic Fabry–Perot pressure sensor with low sensitivity to temperature changes for downhole application,” Opt. Commun. 269, 322–330 (2007).
[CrossRef]

Atkins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Barton, J. S.

Boussaad, S.

H. Zhang, S. Boussaad, and N. Tao, “High-performance differential surface plasmon resonance sensor using quadrant cell photodetector,” Rev. Sci. Instrum. 74, 150–153 (2003).
[CrossRef]

Boyd, J. T.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, and H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Braune, T.

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Chan, C. C.

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

Chen, J.

Chen, L. H.

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

Chiang, K. S.

Chin, K. K.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Chung, Y.

Cibula, E.

Cole, J. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Dakin, J. P.

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

Dandridge, A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Dasgupta, S.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, and H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Donlagic, D.

Esashi, M.

K. Totsu, Y. Haga, and M. Esashi, “Ultra-miniature fiber-optic pressure sensor using white light interferometry,” J. Micromech. Microeng. 15, 71–75 (2005).
[CrossRef]

Fammer, K. R.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Gander, M. J.

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Gilsdorf, R. W.

Giovanni, M. D.

M. D. Giovanni, Flat and Corrugated Diaphragm Design Handbook (Dekker, 1982).

Goh, S. K.

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

Haga, Y.

K. Totsu, Y. Haga, and M. Esashi, “Ultra-miniature fiber-optic pressure sensor using white light interferometry,” J. Micromech. Microeng. 15, 71–75 (2005).
[CrossRef]

Han, W. T.

Huang, X.

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

Jackson, H. E.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, and H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Jones, J. D. C.

Kersey, A.

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Klotzbuecher, T.

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Latifi, H.

S. H. Aref, H. Latifi, M. I. Zibaii, and M. Afshari, “Fiber optic Fabry–Perot pressure sensor with low sensitivity to temperature changes for downhole application,” Opt. Commun. 269, 322–330 (2007).
[CrossRef]

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Lee, S. H.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Lenardic, B.

Li, B.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Li, C.

Liao, X.

Liao, Y.

Y. Zhao, C. Yu, and Y. Liao, “Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement,” Opt. Laser Technol. 36, 39–42 (2004).
[CrossRef]

Liu, W. J.

Lu, L.

Lu, W.

MacPherson, W. N.

Maffeo, M.

Meng, H.

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

Niezrecki, C.

Oh, S. T.

Ott, J.

Paek, U. C.

Palais, J. C.

Patrick, H.

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Pedrazzani, J.

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

Pevec, S.

Pinet, E.

Priest, R. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Ran, Z. L.

Rao, Y.

Y. Rao, “Recent progress in fiber-optic extrinstic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12, 227–237 (2006).
[CrossRef]

Rao, Y. J.

Rashleigh, S. C.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Reekie, L.

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

Ren, D.

Roman, H.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Russo, O.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Schmitz, F.

Shen, W.

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

Shi, X.

Sigel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microwave Theory Tech. 30, 472–511 (1982).
[CrossRef]

Sun, J.

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

Tao, N.

H. Zhang, S. Boussaad, and N. Tao, “High-performance differential surface plasmon resonance sensor using quadrant cell photodetector,” Rev. Sci. Instrum. 74, 150–153 (2003).
[CrossRef]

Tian, Y.

Totsu, K.

K. Totsu, Y. Haga, and M. Esashi, “Ultra-miniature fiber-optic pressure sensor using white light interferometry,” J. Micromech. Microeng. 15, 71–75 (2005).
[CrossRef]

Vengsarkar, A.

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

Wang, W.

Wang, X.

N. Wu, W. Wang, Y. Tian, X. Zou, M. Maffeo, C. Niezrecki, J. Chen, and X. Wang, “Low-cost rapid miniature optical pressure sensors for blast wave measurements,” Opt. Express 19, 10797–10804 (2011).
[CrossRef]

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Watson, S.

Williams, G.

H. Patrick, G. Williams, A. Kersey, J. Pedrazzani, and A. Vengsarkar, “Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination,” IEEE Photon. Technol. Lett. 8, 1223–1225 (1996).
[CrossRef]

Wlodarczyk, M. T.

M. T. Wlodarczyk, “High accuracy glow plug-integrated cylinder pressure sensor for closed loop engine control,” SAE Technical Paper 2006-01-0184 (2006).

Wu, N.

Wu, X.

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

Xiao, Z.

X. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. Russo, K. K. Chin, and K. R. Fammer, “An ultra-sensitive optical MEMS sensor for partial discharge detection,” J. Micromech. Microeng. 15, 521–527 (2005).
[CrossRef]

Xu, F.

Xu, M. G.

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

Yu, B.

Yu, C.

Y. Zhao, C. Yu, and Y. Liao, “Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement,” Opt. Laser Technol. 36, 39–42 (2004).
[CrossRef]

Yuan, W.

L. H. Chen, C. C. Chan, W. Yuan, S. K. Goh, and J. Sun, “High performance chitosan diaphragm-based fiber-optical acoustic sensor,” Sens. Actuators A 163, 42–47 (2010).
[CrossRef]

Zhang, G.

W. Shen, X. Wu, H. Meng, G. Zhang, and X. Huang, “Long distance fiber-optic displacement sensor based on fiber collimator,” Rev. Sci. Instrum. 81, 123104 (2010).
[CrossRef]

Zhang, H.

H. Zhang, S. Boussaad, and N. Tao, “High-performance differential surface plasmon resonance sensor using quadrant cell photodetector,” Rev. Sci. Instrum. 74, 150–153 (2003).
[CrossRef]

Zhao, Y.

Y. Zhao, C. Yu, and Y. Liao, “Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement,” Opt. Laser Technol. 36, 39–42 (2004).
[CrossRef]

Zibaii, M. I.

S. H. Aref, H. Latifi, M. I. Zibaii, and M. Afshari, “Fiber optic Fabry–Perot pressure sensor with low sensitivity to temperature changes for downhole application,” Opt. Commun. 269, 322–330 (2007).
[CrossRef]

Zou, X.

Appl. Opt.

Electron. Lett.

M. G. Xu, J.-L. Archambault, L. Reekie, and J. P. Dakin, “Discrimination between strain and temperature effects using dual-wavelength fiber grating sensors,” Electron. Lett. 30, 1085–1087 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic operating principle of (a) our fiber collimator sensor and (b) traditional FPI and fiber collimator sensor.

Fig. 2.
Fig. 2.

Analysis model of the sensor.

Fig. 3.
Fig. 3.

Theoretical results of the sensor with Si diaphragm thickness of 150 and 100 μm.

Fig. 4.
Fig. 4.

(a) Schematic diagram and (b) optical image of the sensor.

Fig. 5.
Fig. 5.

Experiment setup for sensor measurement (schematic diagram is shown as an inset).

Fig. 6.
Fig. 6.

Measurement results of the sensor with (a) 150 μm and (b) 100 μm thick Si diaphragm (the inset showing the curve in linear scale).

Fig. 7.
Fig. 7.

Temperature dependence response of the sensor with 150 μm thick Si diaphragm.

Fig. 8.
Fig. 8.

Tuning the detection range by changing the pressure inside the sealed cavity.

Equations (5)

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ΔL=(1ν2)(D/2)44.2Eh3ΔP,
θ=2arcsin(OCDR)=2arcsin(OCD×2ΔL(D/2)2+ΔL2),
ΔWD=((D/2)2+(ΔL)22ΔL)2OCD2((D/2)2+(ΔL)22ΔL)2(D/2)2,
ΔX=(WDΔWD)×tan(θ),
LOSS(dB)=4.3·(tanθn0·A·ω0)2+8.6·ln(1+12(2λ·(WDΔWD)πω12)2)+4.3·(ΔXω1)2,

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