Abstract

A multimode fiber sensor using the intensity inner product of speckle fields is presented. The sensitivity and the dynamic range of the displacement sensing are quantitatively analyzed. We show that the sensitivity of displacement can be in the submicrometer range. Experimental performances show that the results are consistent with the calculated results.

© 1993 Optical Society of America

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References

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  1. E. Udd, Fiber Optic Sensors (Wiley, New York, 1991).
  2. K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, R. O. Claus, “Fabry–Perot fiber-optic sensors in full-scale fatigue testing on a F-15 aircraft,” Appl. Opt. 31, 431–433 (1992).
    [CrossRef] [PubMed]
  3. K. D. Bennett, J. C. McKeeman, R. G. May, “Full field analysis of mode domain sensor signals for structure control,” in Fiber Optic Smart Structures and Skins, E. Udd, ed., Proc. Soc. Photo-Opt. Instrum. Eng.986, 85–89 (1988).
  4. E. G. Rawson, J. W. Goodman, R. E. Norton, “Frequency dependence of modal noise in multimode optical fibers,” J. Opt. Soc. Am. 70, 968–976 (1980).
    [CrossRef]
  5. J. W. Goodman, E. G. Rawson, “Statistics of modal noise in fibers: a case of constrained speckle,” Opt. Lett. 6, 324–326 (1981).
    [CrossRef] [PubMed]
  6. N. Takai, T. Asakura, “Statistical properties of laser speckles produced under illumination from a multimode optical fiber,” J. Opt. Soc. Am. A 2, 1281–1290 (1985).
    [CrossRef]
  7. N. Takai, “Spatial coherence properties of light from optical fibers,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 143–149 (1988).
  8. S. Wu, S. Yin, F. T. S. Yu, “Sensing with fiber specklegrams,” Appl. Opt. 30, 4468–4470 (1991).
    [CrossRef] [PubMed]
  9. S. Wu, S. Yin, S. Rajan, F. T. S. Yu, “Multichannel sensing with fiber specklegrams,” Appl. Opt. 31, 5975–5983 (1992).
    [CrossRef] [PubMed]
  10. A. Ogiwara, J. Ohtsubo, “Maximum dynamic range of clipped correlation of integrated laser speckle intensity,” J. Opt. Soc. Am. A 5, 403–405 (1988).
    [CrossRef]
  11. R. Barakat, “Clipped correlation functions of aperture integrated laser speckle,” Appl. Opt. 25, 3385–3388 (1986).
    [CrossRef]
  12. J. Churnside, “Speckle correlation measurements using clipped intensity signals,” Appl. Opt. 24, 2488–2490 (1985).
    [CrossRef] [PubMed]

1992 (2)

1991 (1)

1988 (1)

1986 (1)

R. Barakat, “Clipped correlation functions of aperture integrated laser speckle,” Appl. Opt. 25, 3385–3388 (1986).
[CrossRef]

1985 (2)

J. Churnside, “Speckle correlation measurements using clipped intensity signals,” Appl. Opt. 24, 2488–2490 (1985).
[CrossRef] [PubMed]

N. Takai, T. Asakura, “Statistical properties of laser speckles produced under illumination from a multimode optical fiber,” J. Opt. Soc. Am. A 2, 1281–1290 (1985).
[CrossRef]

1981 (1)

1980 (1)

Asakura, T.

N. Takai, T. Asakura, “Statistical properties of laser speckles produced under illumination from a multimode optical fiber,” J. Opt. Soc. Am. A 2, 1281–1290 (1985).
[CrossRef]

Barakat, R.

R. Barakat, “Clipped correlation functions of aperture integrated laser speckle,” Appl. Opt. 25, 3385–3388 (1986).
[CrossRef]

Bennett, K. D.

K. D. Bennett, J. C. McKeeman, R. G. May, “Full field analysis of mode domain sensor signals for structure control,” in Fiber Optic Smart Structures and Skins, E. Udd, ed., Proc. Soc. Photo-Opt. Instrum. Eng.986, 85–89 (1988).

Churnside, J.

Claus, R. O.

Goodman, J. W.

Gunther, M. F.

May, R. G.

K. D. Bennett, J. C. McKeeman, R. G. May, “Full field analysis of mode domain sensor signals for structure control,” in Fiber Optic Smart Structures and Skins, E. Udd, ed., Proc. Soc. Photo-Opt. Instrum. Eng.986, 85–89 (1988).

McKeeman, J. C.

K. D. Bennett, J. C. McKeeman, R. G. May, “Full field analysis of mode domain sensor signals for structure control,” in Fiber Optic Smart Structures and Skins, E. Udd, ed., Proc. Soc. Photo-Opt. Instrum. Eng.986, 85–89 (1988).

Murphy, K. A.

Norton, R. E.

Ogiwara, A.

Ohtsubo, J.

Rajan, S.

Rawson, E. G.

Takai, N.

N. Takai, T. Asakura, “Statistical properties of laser speckles produced under illumination from a multimode optical fiber,” J. Opt. Soc. Am. A 2, 1281–1290 (1985).
[CrossRef]

N. Takai, “Spatial coherence properties of light from optical fibers,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 143–149 (1988).

Udd, E.

E. Udd, Fiber Optic Sensors (Wiley, New York, 1991).

Vengsarkar, A. M.

Wu, S.

Yin, S.

Yu, F. T. S.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

A. Ogiwara, J. Ohtsubo, “Maximum dynamic range of clipped correlation of integrated laser speckle intensity,” J. Opt. Soc. Am. A 5, 403–405 (1988).
[CrossRef]

N. Takai, T. Asakura, “Statistical properties of laser speckles produced under illumination from a multimode optical fiber,” J. Opt. Soc. Am. A 2, 1281–1290 (1985).
[CrossRef]

Opt. Lett. (1)

Other (3)

K. D. Bennett, J. C. McKeeman, R. G. May, “Full field analysis of mode domain sensor signals for structure control,” in Fiber Optic Smart Structures and Skins, E. Udd, ed., Proc. Soc. Photo-Opt. Instrum. Eng.986, 85–89 (1988).

N. Takai, “Spatial coherence properties of light from optical fibers,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 143–149 (1988).

E. Udd, Fiber Optic Sensors (Wiley, New York, 1991).

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Figures (6)

Fig. 1
Fig. 1

Multimode fiber sensor for submicrometer displacement measurement. PZT, piezoelectric transducer.

Fig. 2
Fig. 2

Variation of the NIP as a function of phase deviation δ

Fig. 3
Fig. 3

(a) Relationship between the transverse displacement and the longitudinal elongation. (b) Microbending device.

Fig. 4
Fig. 4

NIPC as a function of displacement Δx for various thresholding levels.

Fig. 5
Fig. 5

(a) NIPC as a function of displacement Δx. (b) Enlarged NIPC as a function of displacement Δx.

Fig. 6
Fig. 6

Extended dynamic range by an autonomous processing technique.

Equations (27)

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A 0 ( x , y ) = m = 0 M a o m ( x , y ) exp { j [ ϕ o m ( x , y ) ] } ,
I 0 ( x , y ) = | A 0 ( x , y ) | 2 = m = 0 M n = 0 M a o m a o n exp [ j ( ϕ o m ϕ o n ) ] .
A ( x , y ) = m = 0 M [ a o m ( x , y ) + Δ a m ] exp { j [ ϕ o m ( x , y ) + Δ ϕ m ] } ,
I ( x , y ) = | A ( x , y ) | 2 = m = 0 M n = 0 M ( a o m + Δ a m ) ( a o n + Δ a n ) × exp [ j ( ϕ o m n + Δ ϕ m n ) ] ,
ϕ o m n = ϕ o m ϕ o n , Δ ϕ m n = Δ ϕ m Δ ϕ n .
I P = I 0 ( x , y ) I ( x , y ) d x d y = i = 0 M j = 0 M m = 0 M n = 0 M a o m a o m ( a o i + Δ a o i ) ( a o j + Δ a o j ) × exp [ j ( ϕ o m n + ϕ o i j + Δ ϕ i j ) ] d x d y ,
I P = i = 0 M j = 0 M B i j exp [ j ( Δ ϕ i j ) ] ,
B i j = m = 0 M n = 0 M a o m a o n ( a o i + Δ a o i ) ( a o j + Δ a o j ) × exp [ j ( ϕ o m n + ϕ o i j ) ] d x d y .
NIP = I 0 ( x , y ) I ( x , y ) d x d y [ I 0 2 ( x , y ) d x d y I 2 ( x , y ) d x d y ] 1 / 2 ,
0 < NIP 1 .
NIP = i = 0 M j = 0 M B i j exp [ j ( Δ ϕ i j ) ] ( i = 0 M j = 0 M B i j i = 0 M j = 0 M B i j ) 1 / 2 ,
B i j = m = 0 M n = 0 M a o m a o n a o i a o j exp [ j ( ϕ o m n + ϕ o i j ) ] d x d y ,
B i j = m = 0 N n = 0 M ( a o m + Δ a m ) × ( a o n + Δ a n ) ( a o i + Δ a i ) ( a o j + Δ a j ) × exp [ j ( ϕ o m n + ϕ o i j + Δ ϕ m n + Δ ϕ i j ) ] d x d y .
NIP = 1 ( M + 1 ) 2 i = 0 M j = 0 M exp [ j ( Δ ϕ i j ) ] ,
δ = Δ ϕ M 0 = Δ ϕ Μ Δ ϕ 0 ,
Δ ϕ i j = i j M δ ,
Δ ϕ k = 2 π λ C 0 η Δ L 1 cos θ k ,
Δ ϕ i j = 2 π λ C 0 η Δ L ( 1 cos θ i 1 cos θ j ) ,
δ = 2 π λ C 0 η Δ L ( 1 cos θ M 1 cos 0 ) < π ,
θ 0 = 0 , θ M = arcsin ( sin θ c η ) .
Δ x = Δ L 2 α sin 30 ° ,
0 . 05 μ m < Δ x < 4 . 5 μ m .
NIPC = g 0 ( x , y ) g ( x , y ) d x d y [ g 0 2 ( x , y ) d x d y g 2 ( x , y ) d x d y ] 1 / 2 ,
g 0 ( x , y ) = G [ I 0 ( x , y ) ] , g ( x , y ) = G [ I ( x , y ) ] ,
G [ f ( x , y ) ] = { [ d f ( x , y ) / d x ] 2 + [ d f ( x , y ) / d y ] 2 } 1 / 2 ,
G [ f ( x , y ) ] = | f ( x , y ) f ( x + 1 , y + 1 ) | + | f ( x + 1 , y ) f ( x , y + 1 ) | .
I ( x , y ) = { I ( x , y ) I ( x , y ) > T 0 I ( x , y ) < T ,

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