Abstract

Focusing on the ultra-precision dimensional measurement of parts with micro-scale dimensions and high aspect ratios, a two-dimensional double fiber probe with a single fiber Bragg grating (DS-FBG probe) is investigated in detail in this paper. The theoretical analysis of the sensing principle is verified by spectrum simulations of the DS-FBG probe with a modified transfer matrix method using the strain distribution within the DS-FBG probe. The fabrication process and physical principle of the capillary-driven self-assembly of double fibers in the UV adhesive with a low viscosity are demonstrated. Experimental results indicate that resolutions of 30 nm in radial direction and 15 nm in axial direction can be achieved, and the short-term displacement drifts within 90 seconds are 28.0 nm in radial direction and 7.9 nm in axial direction, and the long-term displacement drifts within 1 hour are 61.3 nm in radial direction and 17.3 nm in axial direction. The repeatability of the probing system can reach 60 nm and the measurement result of a standard nozzle is 300.49 μm with a standard deviation of 20 nm.

© 2015 Optical Society of America

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References

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  1. G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
    [Crossref]
  2. M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
    [Crossref]
  3. J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).
  4. J. Tan, F. Wang, and J. Cui, “Fiber deflection probing method based on micro focal-length collimation,” Opt. Express 18(3), 2925–2933 (2010).
    [Crossref] [PubMed]
  5. E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
    [Crossref]
  6. J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
    [Crossref]
  7. J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
    [Crossref] [PubMed]
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  9. R. Ulrich, S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett. 5(6), 273–275 (1980).
    [Crossref] [PubMed]
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    [Crossref]
  11. M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
    [Crossref]
  12. Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
    [Crossref]
  13. M. Prabhugoud and K. Peters, “Modified transfer matrix formulation for Bragg grating strain sensors,” J. Lightwave Technol. 22(10), 2302–2309 (2004).
    [Crossref]
  14. J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
    [Crossref] [PubMed]
  15. P. Kralchevsky and K. Nagayama, “Particles at Fluid Interfaces and Membrane,” (Elsevier, 2001), pp. 469–499.
  16. J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
    [Crossref]

2015 (1)

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

2014 (1)

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

2013 (3)

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

2010 (1)

2009 (1)

E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
[Crossref]

2006 (1)

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

2004 (3)

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

M. Prabhugoud and K. Peters, “Modified transfer matrix formulation for Bragg grating strain sensors,” J. Lightwave Technol. 22(10), 2302–2309 (2004).
[Crossref]

2003 (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

1997 (1)

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

1980 (1)

Ahdad, F.

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

Balke, M.

E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
[Crossref]

Bico, J.

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

Boudaoud, A.

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

Bures, J.

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

Cui, J.

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

J. Tan, F. Wang, and J. Cui, “Fiber deflection probing method based on micro focal-length collimation,” Opt. Express 18(3), 2925–2933 (2010).
[Crossref] [PubMed]

Dai, G.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Danzebrink, H.-U.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Ding, G.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Doering, L.

E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
[Crossref]

Eickhoff, W.

Feng, K.

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

Gafsi, R.

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

He, M.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Hu, Y.

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

Huang, M.

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

Koenders, L.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Lecoy, P.

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

Li, J.

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

Li, L.

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

Li, Y.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Liu, R.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Lu, X.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Malki, A.

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

Moulin, L.

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

Peiner, E.

E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
[Crossref]

Peters, K.

Pohlenz, F.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Prabhugoud, M.

Qian, Y.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Rashleigh, S. C.

Roman, B.

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

Tan, J.

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

J. Tan, F. Wang, and J. Cui, “Fiber deflection probing method based on micro focal-length collimation,” Opt. Express 18(3), 2925–2933 (2010).
[Crossref] [PubMed]

Ulrich, R.

Wang, F.

Wang, H.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Wilkening, G.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Wu, J.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Xu, M.

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Yu, Y.-S.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Zhang, T.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Zhang, Y.

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

Zhang, Y. S.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Zhao, X.

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

Zhao, Z.-Y.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Zheng, W.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Zhuo, Z. C.

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. Cui, K. Feng, Y. Hu, J. Li, and J. Tan, “A twin fiber Bragg grating probe for the dimensional measurement of microholes,” IEEE Photonics Technol. Lett. 26(17), 1778–1781 (2014).
[Crossref]

Int. J. Solids Struct. (1)

M. Huang, “Stress effects on the performance of optical waveguides,” Int. J. Solids Struct. 40(7), 1615–1632 (2003).
[Crossref]

J. Lightwave Technol. (1)

Meas. Sci. Technol. (1)

G. Dai, F. Pohlenz, M. Xu, L. Koenders, H.-U. Danzebrink, and G. Wilkening, “Accurate and traceable measurement of nano- and microstructures,” Meas. Sci. Technol. 17(3), 545–552 (2006).
[Crossref]

Measurement (1)

J. Cui, K. Feng, Y. Zhang, and J. Tan, “Subpixel edge location method proposed to improve the performance of optical fiber spherical coupling probe during dimensional measurement of micro-cavities with high aspect ratio,” Measurement 47, 704–714 (2013).

Microelectron. Eng. (1)

E. Peiner, M. Balke, and L. Doering, “Form measurement inside fuel injector nozzle spray holes,” Microelectron. Eng. 86(4), 984–986 (2009).
[Crossref]

Microw. Opt. Technol. Lett. (1)

Y.-S. Yu, Z.-Y. Zhao, Z. C. Zhuo, W. Zheng, Y. Qian, and Y. S. Zhang, “Bend sensor using an embedded etched fiber Bragg grating,” Microw. Opt. Technol. Lett. 43(5), 414–417 (2004).
[Crossref]

Nature (1)

J. Bico, B. Roman, L. Moulin, and A. Boudaoud, “Adhesion: elastocapillary coalescence in wet hair,” Nature 432(7018), 690 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Sens. Actuator A-Phys. (3)

R. Gafsi, A. Malki, F. Ahdad, P. Lecoy, and J. Bures, “Static stress optical-fiber sensor,” Sens. Actuator A-Phys. 62(1), 501–505 (1997).
[Crossref]

M. He, R. Liu, Y. Li, H. Wang, X. Lu, G. Ding, J. Wu, T. Zhang, and X. Zhao, “Tactile probing system based on micro-fabricated capacitive sensor,” Sens. Actuator A-Phys. 194, 128–134 (2013).
[Crossref]

J. Cui, L. Li, J. Li, and J. Tan, “Fiber probe for micro-hole measurement based on detection of returning light energy,” Sens. Actuator A-Phys. 190, 13–18 (2013).
[Crossref]

Sensors (Basel) (1)

J. Cui, Y. Hu, K. Feng, J. Li, and J. Tan, “FBG interrogation method with high resolution and response speed based on a reflective-matched FBG scheme,” Sensors (Basel) 15(7), 16516–16535 (2015).
[Crossref] [PubMed]

Other (2)

F. P. Beer, E. R. Johnston, Jr., and J. T. DeWolf, Mechanics of Materials (McGraw-Hill, 1981), pp. 530–594.

P. Kralchevsky and K. Nagayama, “Particles at Fluid Interfaces and Membrane,” (Elsevier, 2001), pp. 469–499.

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Figures (13)

Fig. 1
Fig. 1 Schematic of the DS-FBG probe.
Fig. 2
Fig. 2 Schematic of the contact between the DS-FBG probe and part: (a) contact in radial direction and (b) contact in axial direction.
Fig. 3
Fig. 3 FEM simulation results of the fiber probes under a radial contact of 5 μm: (a) the common FBG probe under a contact in axis y, (b) the DS-FBG probe under a contact in axis y and (c) the DS-FBG probe under a contact in axis x.
Fig. 4
Fig. 4 FEM simulation results of the fiber probes under an axial contact of 1 μm: (a) the common FBG probe under a contact, and (b) the DS-FBG probe under a contact.
Fig. 5
Fig. 5 Simulation of DS-FBG probe under a radial displacement: (a) spectrum simulation results of the DS-FBG under a radial displacement of 5 μm, and (b) simulation of the reflected spectrum of the DS-FBG probe under a radial displacement from 0 μm to 5 μm.
Fig. 6
Fig. 6 Comparisons of the theory analysis and simulation of the DS-FBG probe under a radial displacement from 0 μm to 5 μm.
Fig. 7
Fig. 7 Fabrication of the DS-FBG probe: (a) fabrication process layout, and (b) photograph of the DS-FBG probe.
Fig. 8
Fig. 8 Experimental setup of the DS-FBG probing system: (a) schematic diagram of the probing system, (b) schematic diagram of the mechanical adjustment, (c) demodulation principle of the FBG interrogation system based on reflective-matched FBG, and (d) micro CMM developed by ourselves.
Fig. 9
Fig. 9 Schematic diagram of the rotation and tilt calibrations of the DS-FBG probe: (a) rotation calibration, and (b) tilt calibrations.
Fig. 10
Fig. 10 Experiments on the rotation and tilt calibrations of the DS-FBG probe: (a) rotation calibration around axis z, (b) title calibration around axis x, and (c) title calibration around axis y.
Fig. 11
Fig. 11 Experiments on the resolutions of the DS-FBG probe: (a) axial resolution, and (b) radial resolution.
Fig. 12
Fig. 12 Experiments on the stability of the DS-FBG probe: (a) short-term drift, and (b) long-term drift.
Fig. 13
Fig. 13 Experiments on the measurement performance of the DS-FBG probe: (a) repeatability, and (b) diameter measurement of a standard nozzle of 300 μm in norm diameter.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

σ z (z,y')= 3Ey' v r (Lz) L 3
v r = F L 3 3EI
[ 0 0 σ z ]=[ λ+2μ λ λ λ λ+2μ λ λ λ λ+2μ ][ ε x ε y ε z ]
{ ε x =v 3y' v r (Lz) L 3 ε y =v 3y' v r (Lz) L 3 ε z = 3y' v r (Lz) L 3
σ z (x,y')=-E v a L
v a = F a SE L
{ ε x =v v a L ε y =v v a L ε z = v a L
ΔΛ(x) Λ = ε z (z,y')
[ δ n x δ n y δ n z ]= n 3 2 [ p 11 p 12 p 12 p 12 p 11 p 12 p 12 p 12 p 11 ][ ε x ε y ε z ]
{ Λ'(z,y')=Λ[ 1 3y' v r (Ll) L 3 ][ 1+ 3y' v r L 3 3y' v r (Ll) u ] = Λ 0 +fu n z (z,y')={ 1+ n 2 2 [ p 12 V( p 11 + p 12 )][ 3y'(Ll) v r L 3 3y' v r L 3 u] }n =[1+ n 2 2 [ p 12 V( p 11 + p 12 )] 3y'(Ll) v r L 3 ]n n 2 2 [ p 12 V( p 11 + p 12 )] 3y' v r n L 3 u = n 0 +hu
λ B (u)=2 n z (z,y')Λ'(z,y') =2( n 0 +hu)( Λ 0 +fu) =2[ n 0 Λ 0 +(h Λ 0 +f n 0 )u+hf u 2 ] =2[ n 0 Λ 0 +(h Λ 0 +f n 0 )u]+O(u) =2[ n 0 Λ 0 +(h Λ 0 +f n 0 )u]+O(u) =2[ n 0 Λ 0 +ku]+O(u)
Δ λ Br λ Br = 2.367y'(Ll 1 2 l 0 ) L 3 v r
Δ λ Ba λ Ba = 0.789 L v a
| λ 1 λ 2 |= Δ λ 1 2 +Δ λ 2 2 8ln2

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