Abstract

We present a detailed theoretical and experimental study on the sensitivity enhancement for multimode fiber (MMF) speckle sensor. Using mode coupling theory, we derive an expression showing that the sensitivity of the MMF speckle sensor depends on the intensity profile of the MMF modes. Particularly, we use our theory to study the influence of the spatial filtering window on the sensitivity, and the experimental results have found a good agreement with the theory. Our results suggest that the sensitivity of an MMF speckle sensor can be greatly enhanced by adjusting the size and location of the spatial filtering window. An 80-fold improvement on sensitivity was achieved in our experiment, as compared with the conventional MMF speckle sensor with the filtering window placed at the center of the speckle field.

© 2016 Optical Society of America

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  8. M. Matsuura, R. Furukawa, Y. Matsumoto, A. Inoue, and Y. Koike, “Evaluation of modal noise in graded-index silica and plastic optical fiber links for radio over multimode fiber systems,” Opt. Express 22(6), 6562–6568 (2014).
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    [Crossref] [PubMed]
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    [Crossref]
  18. Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
    [Crossref] [PubMed]
  19. L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Common frequency suppression method for fiber specklegram perimeter sensors,” Proc. SPIE 9634, 96343R (2015).
  20. L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Fiber specklegram sensors sensitivities at high temperatures,” Proc. SPIE 9634, 96347J (2015).
    [Crossref]
  21. D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51(8), 1767–1783 (1972).
    [Crossref]
  22. C. P. Tsekrekos, R. W. Smink, B. P. de Hon, A. G. Tijhuis, and A. M. G. Koonen, “Near-field intensity pattern at the output of silica-based graded-index multimode fibers under selective excitation with a single-mode fiber,” Opt. Express 15(7), 3656–3664 (2007).
    [Crossref] [PubMed]
  23. B. Huang, N. K. Fontaine, R. Ryf, B. Guan, S. G. Leon-Saval, R. Shubochkin, Y. Sun, R. Lingle, and G. Li, “All-fiber mode-group-selective photonic lantern using graded-index multimode fibers,” Opt. Express 23(1), 224–234 (2015).
    [Crossref] [PubMed]
  24. W. Ha, S. Lee, Y. Jung, J. K. Kim, and K. Oh, “Acousto-optic control of speckle contrast in multimode fibers with a cylindrical piezoelectric transducer oscillating in the radial direction,” Opt. Express 17(20), 17536–17546 (2009).
    [Crossref] [PubMed]
  25. P. J. Kajenski, P. L. Fuhr, and D. R. Huston, “Mode coupling and phase modulation in vibrating waveguides,” J. Lightwave Technol. 10(9), 1297–1301 (1992).
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    [Crossref] [PubMed]
  29. S. Savović and A. Djordjevich, “Mode coupling in strained and unstrained step-index plastic optical fibers,” Appl. Opt. 45(26), 6775–6780 (2006).
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  30. S. Savovic, M. Kovacevic, J. Bajic, D. Stupar, A. Djordjevich, M. Zivanov, B. Drljaca, A. Simovic, and K. Oh, “Temperature dependence of mode coupling in low NA plastic optical fibers,” J. Lightwave Technol. 33(1), 89–94 (2015).
    [Crossref]
  31. D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
    [Crossref] [PubMed]
  32. J. Qiu, Y. Li, Q. Huang, Y. Wang, and P. Li, “Correcting speckle contrast at small speckle size to enhance signal to noise ratio for laser speckle contrast imaging,” Opt. Express 21(23), 28902–28913 (2013).
    [Crossref] [PubMed]
  33. A. Lev and B. Sfez, “Acousto-optical detection of hidden objects via speckle based imaging,” Opt. Express 23(20), 26460–26471 (2015).
    [Crossref] [PubMed]

2015 (7)

2014 (3)

2013 (4)

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

N. Gomez and J. Gomez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

J. Qiu, Y. Li, Q. Huang, Y. Wang, and P. Li, “Correcting speckle contrast at small speckle size to enhance signal to noise ratio for laser speckle contrast imaging,” Opt. Express 21(23), 28902–28913 (2013).
[Crossref] [PubMed]

2012 (1)

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

2010 (1)

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2007 (2)

2006 (2)

L. Su, K. S. Chiang, and C. Lu, “CO2-laser-induced long-period gratings in graded-index multimode fibers for sensor applications,” IEEE Photonics Technol. Lett. 18(1), 190–192 (2006).

S. Savović and A. Djordjevich, “Mode coupling in strained and unstrained step-index plastic optical fibers,” Appl. Opt. 45(26), 6775–6780 (2006).
[Crossref] [PubMed]

2005 (1)

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

1998 (1)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281(5379), 962–967 (1998).
[Crossref] [PubMed]

1996 (1)

1994 (1)

1993 (1)

1992 (1)

P. J. Kajenski, P. L. Fuhr, and D. R. Huston, “Mode coupling and phase modulation in vibrating waveguides,” J. Lightwave Technol. 10(9), 1297–1301 (1992).
[Crossref]

1989 (1)

1972 (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51(8), 1767–1783 (1972).
[Crossref]

Amitonova, L. V.

Bajic, J.

Balzhiev, P. E.

Bao, X.

Boas, D. A.

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

Bock, W. J.

Cai, H.

Chen, K.

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

Chen, L.

Cheng, F.

Chiang, K. S.

L. Su, K. S. Chiang, and C. Lu, “CO2-laser-induced long-period gratings in graded-index multimode fibers for sensor applications,” IEEE Photonics Technol. Lett. 18(1), 190–192 (2006).

Cigale, B.

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

Claus, R. O.

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

Cobo, A.

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

de Hon, B. P.

Djordjevich, A.

Dong, Y.

Ðonlagic, D.

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

Drljaca, B.

Dunn, A. K.

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

Eftimov, T. A.

Fang, Z.

Fontaine, N. K.

Fuhr, P. L.

P. J. Kajenski, P. L. Fuhr, and D. R. Huston, “Mode coupling and phase modulation in vibrating waveguides,” J. Lightwave Technol. 10(9), 1297–1301 (1992).
[Crossref]

W. B. Spillman, B. R. Kline, L. B. Maurice, and P. L. Fuhr, “Statistical-mode sensor for fiber optic vibration sensing uses,” Appl. Opt. 28(15), 3166–3176 (1989).
[Crossref] [PubMed]

Furukawa, R.

Gafsi, R.

Gao, R.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281(5379), 962–967 (1998).
[Crossref] [PubMed]

Garito, A. F.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281(5379), 962–967 (1998).
[Crossref] [PubMed]

Geng, J.

Gloge, D.

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51(8), 1767–1783 (1972).
[Crossref]

Gomez, J.

N. Gomez and J. Gomez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

Gomez, N.

N. Gomez and J. Gomez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

Gómez, J. A.

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

Guan, B.

Ha, W.

Huang, B.

Huang, Q.

Huston, D. R.

P. J. Kajenski, P. L. Fuhr, and D. R. Huston, “Mode coupling and phase modulation in vibrating waveguides,” J. Lightwave Technol. 10(9), 1297–1301 (1992).
[Crossref]

Inoue, A.

Jung, Y.

Kajenski, P. J.

P. J. Kajenski, P. L. Fuhr, and D. R. Huston, “Mode coupling and phase modulation in vibrating waveguides,” J. Lightwave Technol. 10(9), 1297–1301 (1992).
[Crossref]

Kim, J. K.

Kline, B. R.

Koike, Y.

Koonen, A. M. G.

Kovacevic, M.

Labarrvre, M.

Lecoy, P.

Lee, S.

Leon-Saval, S. G.

Lešnik, D.

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

Lev, A.

Li, G.

Li, J.

Li, P.

Li, Y.

Lingle, R.

Lomer, M.

L. Rodriguez-Cobo, M. Lomer, and J. M. Lopez-Higuera, “Fiber specklegram-multiplexed sensor,” J. Lightwave Technol. 33(12), 2591–2597 (2015).
[Crossref]

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Fiber specklegram sensors sensitivities at high temperatures,” Proc. SPIE 9634, 96347J (2015).
[Crossref]

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Common frequency suppression method for fiber specklegram perimeter sensors,” Proc. SPIE 9634, 96343R (2015).

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

Lopez-Higuera, J.

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Common frequency suppression method for fiber specklegram perimeter sensors,” Proc. SPIE 9634, 96343R (2015).

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Fiber specklegram sensors sensitivities at high temperatures,” Proc. SPIE 9634, 96347J (2015).
[Crossref]

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

Lopez-Higuera, J. M.

Lu, C.

L. Su, K. S. Chiang, and C. Lu, “CO2-laser-induced long-period gratings in graded-index multimode fibers for sensor applications,” IEEE Photonics Technol. Lett. 18(1), 190–192 (2006).

Lu, Z.

Malki, A.

Marin, E.

Matsumoto, Y.

Matsuura, M.

Maurice, L. B.

Meissner, K. E.

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

Meunier, J. P.

Michel, L.

Mosk, A. P.

Oh, K.

Pan, K.

Pinkse, P. W. H.

Plachkova, V. M.

Podbreznik, P.

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

Qiu, J.

Qu, R.

Rodriguez-Cobo, L.

L. Rodriguez-Cobo, M. Lomer, and J. M. Lopez-Higuera, “Fiber specklegram-multiplexed sensor,” J. Lightwave Technol. 33(12), 2591–2597 (2015).
[Crossref]

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Fiber specklegram sensors sensitivities at high temperatures,” Proc. SPIE 9634, 96347J (2015).
[Crossref]

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Common frequency suppression method for fiber specklegram perimeter sensors,” Proc. SPIE 9634, 96343R (2015).

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

Ryf, R.

Salazar, A.

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

Savovic, S.

Sfez, B.

Shubochkin, R.

Simovic, A.

Smink, R. W.

Spillman, W. B.

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

W. B. Spillman, B. R. Kline, L. B. Maurice, and P. L. Fuhr, “Statistical-mode sensor for fiber optic vibration sensing uses,” Appl. Opt. 28(15), 3166–3176 (1989).
[Crossref] [PubMed]

Stupar, D.

Su, L.

L. Su, K. S. Chiang, and C. Lu, “CO2-laser-induced long-period gratings in graded-index multimode fibers for sensor applications,” IEEE Photonics Technol. Lett. 18(1), 190–192 (2006).

Sun, Y.

Tijhuis, A. G.

Tsekrekos, C. P.

Uang, C. M.

Wang, J.

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281(5379), 962–967 (1998).
[Crossref] [PubMed]

Wang, Y.

Wen, M.

Xu, P.

Xu, X.

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

Yin, S.

Yu, F. T.

Zazula, D.

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

Zhang, H.

Zhelyazkova, K.

Zivanov, M.

Appl. Opt. (7)

Bell Syst. Tech. J. (1)

D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J. 51(8), 1767–1783 (1972).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. Su, K. S. Chiang, and C. Lu, “CO2-laser-induced long-period gratings in graded-index multimode fibers for sensor applications,” IEEE Photonics Technol. Lett. 18(1), 190–192 (2006).

J. Biomed. Opt. (2)

P. Podbreznik, D. Đonlagić, D. Lešnik, B. Cigale, and D. Zazula, “Cost-efficient speckle interferometry with plastic optical fiber for unobtrusive monitoring of human vital signs,” J. Biomed. Opt. 18(10), 107001 (2013).
[Crossref] [PubMed]

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

J. Lightwave Technol. (4)

Opt. Express (8)

L. V. Amitonova, A. P. Mosk, and P. W. H. Pinkse, “Rotational memory effect of a multimode fiber,” Opt. Express 23(16), 20569–20575 (2015).
[Crossref] [PubMed]

A. Lev and B. Sfez, “Acousto-optical detection of hidden objects via speckle based imaging,” Opt. Express 23(20), 26460–26471 (2015).
[Crossref] [PubMed]

B. Huang, N. K. Fontaine, R. Ryf, B. Guan, S. G. Leon-Saval, R. Shubochkin, Y. Sun, R. Lingle, and G. Li, “All-fiber mode-group-selective photonic lantern using graded-index multimode fibers,” Opt. Express 23(1), 224–234 (2015).
[Crossref] [PubMed]

Y. Dong, P. Xu, H. Zhang, Z. Lu, L. Chen, and X. Bao, “Characterization of evolution of mode coupling in a graded-index polymer optical fiber by using Brillouin optical time-domain analysis,” Opt. Express 22(22), 26510–26516 (2014).
[Crossref] [PubMed]

W. Ha, S. Lee, Y. Jung, J. K. Kim, and K. Oh, “Acousto-optic control of speckle contrast in multimode fibers with a cylindrical piezoelectric transducer oscillating in the radial direction,” Opt. Express 17(20), 17536–17546 (2009).
[Crossref] [PubMed]

J. Qiu, Y. Li, Q. Huang, Y. Wang, and P. Li, “Correcting speckle contrast at small speckle size to enhance signal to noise ratio for laser speckle contrast imaging,” Opt. Express 21(23), 28902–28913 (2013).
[Crossref] [PubMed]

M. Matsuura, R. Furukawa, Y. Matsumoto, A. Inoue, and Y. Koike, “Evaluation of modal noise in graded-index silica and plastic optical fiber links for radio over multimode fiber systems,” Opt. Express 22(6), 6562–6568 (2014).
[Crossref] [PubMed]

C. P. Tsekrekos, R. W. Smink, B. P. de Hon, A. G. Tijhuis, and A. M. G. Koonen, “Near-field intensity pattern at the output of silica-based graded-index multimode fibers under selective excitation with a single-mode fiber,” Opt. Express 15(7), 3656–3664 (2007).
[Crossref] [PubMed]

Opt. Lasers Eng. (2)

J. A. Gómez and A. Salazar, “Self-correlation fiber specklegram sensor using volume characteristics of speckle patterns,” Opt. Lasers Eng. 50(5), 812–815 (2012).
[Crossref]

N. Gomez and J. Gomez, “Effects of the speckle size on non-holographic fiber specklegram sensors,” Opt. Lasers Eng. 51(11), 1291–1295 (2013).
[Crossref]

Proc. SPIE (3)

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Common frequency suppression method for fiber specklegram perimeter sensors,” Proc. SPIE 9634, 96343R (2015).

L. Rodriguez-Cobo, M. Lomer, and J. Lopez-Higuera, “Fiber specklegram sensors sensitivities at high temperatures,” Proc. SPIE 9634, 96347J (2015).
[Crossref]

X. Xu, W. B. Spillman, R. O. Claus, K. E. Meissner, and K. Chen, “Spatially distributed sensor with dual processed outputs,” Proc. SPIE 5855, 58–61 (2005).
[Crossref]

Science (1)

A. F. Garito, J. Wang, and R. Gao, “Effects of random perturbations in plastic optical fibers,” Science 281(5379), 962–967 (1998).
[Crossref] [PubMed]

Sensor Actuat. A (1)

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Optical fiber strain sensor with extended dynamic range based on specklegrams,” Sensor Actuat. A 203, 341–345 (2013).

Other (3)

L. Rodriguez-Cobo, M. Lomer, A. Cobo, and J. Lopez-Higuera, “Radial processing scheme of speckle patterns for sensing applications,” in Advanced Photonics Congress 2013, OSA Technical Digest (Optical Society of America, 2013), paper JT3A.26.
[Crossref]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991), Chap.4.

J. W. Goodman, Speckle Phenomena in Optics:Theory and Applications (Roberts and Company Publishers, 2010), Chap.7.

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of the rings corresponding to cylindrical modes (principal mode group) in the image plane.
Fig. 2
Fig. 2 The normalized speckle intensity distributions (blue) and corresponding sensitivity curves (red) of the spatial filtering windows at different locations with window sizes of: a) 4 rings, and b) 12 rings. Each circle in the blue curve represents a spatial ring in the image plane.
Fig. 3
Fig. 3 The experimental setup to investigate the speckle field response to external perturbation.
Fig. 4
Fig. 4 One frame of the speckle field recorded by CCD. (a) the speckle field intensity distribution; (b) the same frame sectioned into 64 × 80 sub-images corresponding to spatial filtering windows of 16 × 16 pixels.
Fig. 5
Fig. 5 The total intensity of the selected speckle sections by different windows. (a) Background noise when the piezoelectric transducer was not activated; (b) the response when the 100Vpp 5Hz sine wave was applied to the piezoelectric transducer. Ipp represents the intensity level peak to peak, which determines the sensitivity.
Fig. 6
Fig. 6 Maps of Ipp and corresponding signal waveforms with the largest Ipp. The speckle field was sectioned into sub-images corresponding to the filtering window sizes of a)16 × 16, b)32 × 32, c)64 × 64, d)128 × 128, e) 256 × 256, and f) 1024 × 1280. The signal waveforms with the largest Ipp were given for, a) sub-image (32,35), b) sub-image (18,18), c) sub-image (9,9), d) sub-image (5,5), e) sub-image (3,3), and f) the whole image. For each sectioning window, the total intensities of 1000 frames were firstly calculated to obtain the waveforms and the Ipp values.
Fig. 7
Fig. 7 Intensity profile of pixels at 512th row and the sensitivity of corresponding windows of (a) 16 × 16 pixels, and (b) 256 × 256 pixels. The intensity profile is the blue curve. The green curve is the measured sensitivity (Ipp) of windows which covered the 512th row, obtained from the maps in Fig. 6(a) and Fig. 6(e). The red curve represents the calculated sensitivity based on the intensity profile using Eq. (10).
Fig. 8
Fig. 8 Schematic of the SMF-MMF misalignment-based speckle sensing system.
Fig. 9
Fig. 9 Sensitivity improvement using SMF-MMF misalignment.
Fig. 10
Fig. 10 Detected signal waveforms when the filtering SMF was misaligned to different positions with respect to the sensing MMF.

Equations (10)

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Δ P m = n = 1 & n m N d m n ( P n P m )
Δ P m = d m ( P m + 1 P m ) + d m 1 ( P m 1 P m )
P 1 ( t + Δ t ) = P 1 ( t ) + ( P 0 P 1 ) χ 01 ( P 1 P 2 ) χ 12
P 2 ( t + Δ t ) = P 2 ( t ) + ( P 1 P 2 ) χ 12 ( P 2 P 3 ) χ 23
P 3 ( t + Δ t ) = P 3 ( t ) + ( P 2 P 3 ) χ 23 ( P 3 P 4 ) χ 34
P 4 ( t + Δ t ) = P 4 ( t ) + ( P 3 P 4 ) χ 34 ( P 4 P 5 ) χ 45
P 5 ( t + Δ t ) = P 5 ( t ) + ( P 4 P 5 ) χ 45 ( P 5 P 6 ) χ 56
P 6 ( t + Δ t ) = P 6 ( t ) + ( P 5 P 6 ) χ 56 ( P 6 P 7 ) χ 67
P w i n d o w ( t + Δ t ) = α P 1 ( t + Δ t ) + i = 2 i = 5 P i ( t + Δ t ) + β P 6 ( t + Δ t ) = P w i n d o w ( t ) + α Δ 01 χ 01 + ( 1 α ) Δ 12 χ 12 ( 1 β ) Δ 56 χ 56 β Δ 67 χ 67
P w i n d o w ( t + Δ t ) = P w i n d o w ( t ) + ( α Δ 01 + ( 1 α ) Δ 12 ( 1 β ) Δ 56 β Δ 67 ) χ

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