Abstract

The general theory of a diaphragm fiber-optic sensor (DFOS) is proposed. We use a critical test to determine if a DFOS is based on Fabry–Perot interference or intensity modulation. By use of the critical test, this is the first design, to the best of our knowledge, of a purely Fabry–Perot DFOS, fabricated with microelectromechanical system technology, and characterized as an audible microphone and ultrasonic hydrophone with orders of improvement in signal-to-noise ratio.

© 2007 Optical Society of America

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References

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  1. A. Wang, Y. Liu, and B. Ward, "Prototype fiber-optic acoustic partial discharge sensor: lessons-learned documentation and field test," Tech. Rep. 1001768 (Electric Power Research Institute, 2002).
  2. B. Yu, D. W. Kim, J. Deng, H. Xiao, and A. Wang, "Fiber Fabry-Perot sensors for detection of partial discharges in power transformers," Appl. Opt. 42, 3241-3250 (2003), and references therein.
    [CrossRef] [PubMed]
  3. M. Yu and B. Balachandran, "Acoustic measurements using a fiber optic sensor system," J. Intell. Mater. Syst. Struct. 14, 409-414 (2003).
    [CrossRef]
  4. A. Saran "MEMS based Fabry-Perot pressure sensor and non-adhesive integration on optical fiber by anodic bonding," Ph.D. dissertation (University of Cincinnati, 2004).
  5. S. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. L. Russo, K. K. Chin, and K. R. Farmer, "An ultra-sensitive optical MEMS sensor for partial discharge detection," J. Micormech. Microeng. 15, 521-527 (2005).
    [CrossRef]
  6. J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, "A novel temperature-insensitive optical fiber pressure sensor for harsh environments," IEEE Photon. Technol. Lett. 17, 870-872 (2005).
    [CrossRef]
  7. Y. Zhu and A. Wang, "Miniature fiber-optic pressure sensor," IEEE Photon. Technol. Lett. 17, 447-449 (2005).
    [CrossRef]
  8. C. Fabry and A. Perot, "Théorie et applications d'une nouvelle méthode de Spectroscopie Interferentielle," Ann. Chim. Phys. 16, 115-144 (1899).
  9. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), p. 327.
  10. S. Timoshenko, Strength of Materials, Part 2, 3rd ed. (Van Nostrand, 1983), p. 97.
  11. M. di Giovanni, Flat and Corrugated Diaphragm Design Handbook (Marcel Dekker, 1982).
  12. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
    [CrossRef]
  13. A. Yariv, Optical Electronics, 4th ed. (Holt, Rinehart & Winston, 1991).
  14. D. Marcus, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1977).

2005 (3)

S. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. L. Russo, K. K. Chin, and K. R. Farmer, "An ultra-sensitive optical MEMS sensor for partial discharge detection," J. Micormech. Microeng. 15, 521-527 (2005).
[CrossRef]

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, "A novel temperature-insensitive optical fiber pressure sensor for harsh environments," IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Y. Zhu and A. Wang, "Miniature fiber-optic pressure sensor," IEEE Photon. Technol. Lett. 17, 447-449 (2005).
[CrossRef]

2003 (2)

1977 (1)

D. Marcus, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1977).

1899 (1)

C. Fabry and A. Perot, "Théorie et applications d'une nouvelle méthode de Spectroscopie Interferentielle," Ann. Chim. Phys. 16, 115-144 (1899).

Ann. Chim. Phys. (1)

C. Fabry and A. Perot, "Théorie et applications d'une nouvelle méthode de Spectroscopie Interferentielle," Ann. Chim. Phys. 16, 115-144 (1899).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Marcus, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703-718 (1977).

IEEE Photon. Technol. Lett. (2)

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, "A novel temperature-insensitive optical fiber pressure sensor for harsh environments," IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Y. Zhu and A. Wang, "Miniature fiber-optic pressure sensor," IEEE Photon. Technol. Lett. 17, 447-449 (2005).
[CrossRef]

J. Intell. Mater. Syst. Struct. (1)

M. Yu and B. Balachandran, "Acoustic measurements using a fiber optic sensor system," J. Intell. Mater. Syst. Struct. 14, 409-414 (2003).
[CrossRef]

J. Micormech. Microeng. (1)

S. Wang, B. Li, Z. Xiao, S. H. Lee, H. Roman, O. L. Russo, K. K. Chin, and K. R. Farmer, "An ultra-sensitive optical MEMS sensor for partial discharge detection," J. Micormech. Microeng. 15, 521-527 (2005).
[CrossRef]

Other (7)

A. Wang, Y. Liu, and B. Ward, "Prototype fiber-optic acoustic partial discharge sensor: lessons-learned documentation and field test," Tech. Rep. 1001768 (Electric Power Research Institute, 2002).

A. Saran "MEMS based Fabry-Perot pressure sensor and non-adhesive integration on optical fiber by anodic bonding," Ph.D. dissertation (University of Cincinnati, 2004).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980), p. 327.

S. Timoshenko, Strength of Materials, Part 2, 3rd ed. (Van Nostrand, 1983), p. 97.

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

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

A. Yariv, Optical Electronics, 4th ed. (Holt, Rinehart & Winston, 1991).

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Figures (8)

Fig. 1
Fig. 1

Principle of the DFOS.

Fig. 2
Fig. 2

Plane wave Fabry–Perot interferometric device with the incident beam tilted for convenience of illustration.

Fig. 3
Fig. 3

Gaussian beam emitted from fiber O′ coupled into fiber O with longitudinal, lateral, and angular mismatches of D, d, and θ.

Fig. 4
Fig. 4

Fiber coupling coefficients calculated from image sources.

Fig. 5
Fig. 5

DFOS with the design of the Q-point stabilized by microchannels.

Fig. 6
Fig. 6

(Color online) Optical microscope image of the fabricated Q-point stabilized DFOS showing an embossed center and microchannels.

Fig. 7
Fig. 7

(Color online) Static characterization of output optical intensity I ( out ) / I ( in ) as a function of pressure in comparison with the calculated curve from Eq. (10). Note that the contrast of the experimental result is not as strong as the calculated data because of the scattering and other noise-generating mechanisms.

Fig. 8
Fig. 8

(Color online) Comparison of the DFOS and the PZT as hydrophones: green (upper), PZT from the PAC; yellow (lower), DFOS of the NJIT and the PSEG; red (thin curve), FFT of the input signal peaked at 150   kHz .

Equations (35)

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E ( r ) = r + t t r e i 2 ϕ [ 1 + ( r r e i 2 ϕ ) + ( r r e i 2 ϕ ) 2 + ] ,
ϕ = ( 2 n π L / λ )
I ( o ) I ( i ) = E ( r ) E ( r ) * E ( i ) E ( i ) * = ( r + t t r e i ϕ 1 r r e i ϕ ) ( r + t t r e i ϕ 1 r r e i ϕ )
= 2 R a 2 R g   cos   ϕ 1 + R g 2 2 R g   cos   ϕ .
R g = | r r | ,
R a = r 2 + r 2 2 .
I ( o ) I ( i ) = 2 R 2 R cos ϕ 1 + R 2 2 R cos ϕ
I ( o ) I ( i ) F sin 2 ϕ 2 = F 2 ( 1 cos ϕ ) = F 2 [ 1 cos ( 4 π n λ L ) ] ,
F = 4 R ( 1 R ) 2 ,
Δ L = L L o = b 4 ( 1 ν 2 ) η E h 3 P ,
I ( o ) I ( i ) = 2 R a + 2 R g   sin ( π 2 P o P + θ o ) 1 + R g 2 + 2 R g 2   sin ( π 2 P o P + θ o ) ,
I ( o ) I ( i ) F 2 [ 1 + sin ( π 2 P o P + θ o ) ] ,
P o = η E h 3 λ 8 b 4 ( 1 ν 2 ) n ,
E x = ( 4 μ o / ε o P π n 2 w o 2 ) 1 / 2   exp ( r 2 w o 2 ) e i β z ,
H y = E x μ / ε = ( 4 n 2 ε o / μ o P π w o 2 ) 1 / 2   exp ( r 2 w o 2 ) e i β z ,
w o a = 0.65 + 1.619 V 3 / 2 + 2.879 V 6 .
E x = ( 4 μ o / ε o P π w 2 ) 1 / 2   exp ( r 2 w 2 ) e i k z e i k r 2 2 R ( z ) e i η ( z ) ,
w = w ( z ) = w o 1 + ( z z o ) 2 ,
R = R ( z ) = z ( 1 + z o 2 z 2 ) ,
η ( z ) = tan 1 z z o
z o = ( π w o 2 / λ )
θ o = lim z tan 1 w ( z ) z = tan 1 w o z o w o z o .
y = y ,
z = z   cos   θ + ( x d ) sin   θ + D ,
x = z   sin   θ + ( x d ) cos   θ .
T = [ 1 P 1 2   Re ( 0 E x * H y 2 π r d r ) ] 2 ,
E x = E x   cos   θ = cos   θ ( 4 μ o / ε o P π w 2 ) 1 / 2
× exp ( r 2 w 2 ) e i k D e i k r 2 2 R ( z ) e i η ( z ) ,
H y = E x μ o / ε o = ( 4 ε o / μ o P π w o 2 ) 1 / 2   exp ( r 2 w o 2 ) e i β z
r 2 = x 2 + y 2 , r 2 = x 2 + y 2
T = ( 2 w o w w o 2 + w 2 ) 2   exp ( 2 d 2 w o 2 + w 2 ) exp [ 2 ( π w o w θ ) 2 ( w o 2 + w 2 ) λ 2 ] ,
D m = 2 m L ,
θ m = 2 m α ,
d m = 2 m 2 α L .
E ( r ) = r + T ( 1 ) t t r e i 2 ϕ + T ( 2 ) t t r e i 2 ϕ ( r r e i 2 ϕ ) + T ( 3 ) t t r e i 2 ϕ ( r r e i 2 ϕ ) 2 + ,

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