Abstract

A two-circle coaxial optical fiber bundle is a type of optical sensor which has been widely used in non-contact radial displacement measurement applications. This paper has focused on output characteristics of a two-circle coaxial optical fiber bundle used as a measurement unit in a probe designed to measure a three-dimensional tip clearance. First, a model that could calculate intensity point-by-point on each receiving fiber with a simplified algorithm of overlap area was established, an aperture angle compensation algorithm was then proposed to improve the performance of the model. In order to test the reliability of the model, an experiment was done with different three-dimensional displacement of the reflector. Comparison between experimental and simulation results indicates the model built in this article could better describe how three-dimensional displacement of reflector affects the output of the bundle than previous studies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
    [Crossref]
  2. J. W. H. Chivers, “A technique for the measurement of blade tip clearance in a gas turbine,” in Ph.D. thesis, (University of London, London, UK, 1989).
    [Crossref]
  3. A. G. Sheard and S. R. Turner, “Electromechanical measurement of turbomachinery blade tip-to-casing running clearance,” in Proceedings of the 37th American Society of Mechanical Engineers Gas Turbine and Aero-engine Congress, Cologne, Germany, V005T15A005(1992).
    [Crossref]
  4. S. J. Gill, M. D. Ingallinera, and A. G. Sheard, “Turbine tip clearance measurement system evaluation in an industrial gas turbine,”in Proceedings of the 42nd American Society of Mechanical Engineers Gas Turbine and Aero-engine Congress, Orlando, Florida, USA, V004T15A037 (1997).
    [Crossref]
  5. S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
    [Crossref]
  6. S. Heath and M. Imregun, “A survey of blade tip-timing measurement techniques for turbo machinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998).
    [Crossref]
  7. S. Heath, “A new technique for identifying synchronous resonances using tip-timing,” J. Eng. Gas Turbines Power 122(2), 219–225 (2000).
    [Crossref]
  8. J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).
  9. G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
    [Crossref]
  10. N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
    [Crossref]
  11. F. Teng, X. D. Zhang, and S. Y. Xie, “Research on Variation Mechanism of Three-dimensional Blade Tip Clearance of Aero-engine,” in Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence, 07734008 (2016).
    [Crossref]
  12. L. Büttner, T. Pfister, and J. Czarske, “Fiber-optic laser Doppler turbine tip clearance probe,” Opt. Lett. 31(9), 1217–1219 (2006).
    [Crossref] [PubMed]
  13. D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).
  14. I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
    [Crossref] [PubMed]
  15. I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
    [Crossref]
  16. B. H. Jia and X. D. Zhang, “An optical fiber blade tip clearance sensor for active clearance control applications,” Procedia Eng. 15, 984–988 (2011).
    [Crossref]
  17. B. H. Jia, “Research on optical fiber based measurement and active control technology of turbine tip clearance,” Ph.D. thesis, (Northwestern Polytechnical University, Xi’an, China, 2013).
  18. S. Y. Xie and X. D. Zhang, “Design and Modeling of Three-Dimensional Tip clearance Optical Probe Based on Two-circle coaxial optical fiber bundle,” Proceedings of IEEE International Conference on Sensors, 16582224(2016).
    [Crossref]
  19. R. O. Cook and C. W. Hamm, “Fiber optic lever displacement transducer,” Appl. Opt. 18(19), 3230–3241 (1979).
    [Crossref] [PubMed]
  20. H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
    [Crossref]
  21. L. Yang and X. D. Zhang, “Research on displacement sensor of two-circle coaxial reflective optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 29(2), 192–196 (2008).
  22. S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 37(1), 174–181 (2017).

2017 (2)

G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
[Crossref]

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 37(1), 174–181 (2017).

2015 (1)

2014 (1)

J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).

2013 (1)

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

2012 (1)

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

2011 (1)

B. H. Jia and X. D. Zhang, “An optical fiber blade tip clearance sensor for active clearance control applications,” Procedia Eng. 15, 984–988 (2011).
[Crossref]

2008 (1)

L. Yang and X. D. Zhang, “Research on displacement sensor of two-circle coaxial reflective optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 29(2), 192–196 (2008).

2007 (1)

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

2006 (1)

2000 (1)

S. Heath, “A new technique for identifying synchronous resonances using tip-timing,” J. Eng. Gas Turbines Power 122(2), 219–225 (2000).
[Crossref]

1998 (1)

S. Heath and M. Imregun, “A survey of blade tip-timing measurement techniques for turbo machinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998).
[Crossref]

1997 (2)

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
[Crossref]

1996 (1)

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

1979 (1)

Aldabaldetreku, G.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Battiato, G.

G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
[Crossref]

Beloki, J.

I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
[Crossref]

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Berganza, A.

Berruti, T. M.

G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
[Crossref]

Büttner, L.

Cao, H.

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

Chen, Y.

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

Cook, R. O.

Czarske, J.

Dimitriadis, G.

J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).

Duan, F. J.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

García, I.

I. García, J. Beloki, and A. Berganza, “Different configurations of a reflective intensity-modulated optical sensor to avoid modal noise in tip clearance measurements,” J. Lightwave Technol. 33(12), 2663–2669 (2015).
[Crossref]

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Garrido, J. G.

J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).

Guo, H. T.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Hamm, C. W.

Heath, S.

S. Heath, “A new technique for identifying synchronous resonances using tip-timing,” J. Eng. Gas Turbines Power 122(2), 219–225 (2000).
[Crossref]

S. Heath and M. Imregun, “A survey of blade tip-timing measurement techniques for turbo machinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998).
[Crossref]

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

Illarramendi, M. A.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Imregun, M.

S. Heath and M. Imregun, “A survey of blade tip-timing measurement techniques for turbo machinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998).
[Crossref]

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

Jia, B. H.

B. H. Jia and X. D. Zhang, “An optical fiber blade tip clearance sensor for active clearance control applications,” Procedia Eng. 15, 984–988 (2011).
[Crossref]

Jiménez, F.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Johann, E.

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

Li, Y.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Mozumdar, S.

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

Muller, D.

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

Pfister, T.

Rao, J. S.

N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
[Crossref]

Rigosi, G.

G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
[Crossref]

Sheard, A. G.

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

Sidhartc,

N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
[Crossref]

Vyas, N. S.

N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
[Crossref]

Wang, K.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Wright, J. R.

J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).

Xie, S. Y.

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 37(1), 174–181 (2017).

Yang, L.

L. Yang and X. D. Zhang, “Research on displacement sensor of two-circle coaxial reflective optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 29(2), 192–196 (2008).

Ye, D. C.

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Zhang, G.

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

Zhang, X. D.

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 37(1), 174–181 (2017).

B. H. Jia and X. D. Zhang, “An optical fiber blade tip clearance sensor for active clearance control applications,” Procedia Eng. 15, 984–988 (2011).
[Crossref]

L. Yang and X. D. Zhang, “Research on displacement sensor of two-circle coaxial reflective optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 29(2), 192–196 (2008).

Zhou, Z.

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

Zubia, J.

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Appl. Opt. (1)

Int. J. Mech. Sci. (1)

S. Heath and M. Imregun, “An improved single-parameter tip-timing method for turbo machinery blade vibration measurements using optical laser probes,” Int. J. Mech. Sci. 38(10), 1047–1058 (1996).
[Crossref]

Int. J. Rotating Mach. (1)

J. G. Garrido, G. Dimitriadis, and J. R. Wright, “A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances – part I: theoretical development,” Int. J. Rotating Mach. 2007(4), 981–1077 (2014).

J. Eng. Gas Turbines Power (3)

D. Muller, A. G. Sheard, S. Mozumdar, and E. Johann, “Capacitive measurement of compressor and turbine blade tip to Casing Running Clearance,” J. Eng. Gas Turbines Power 119(4), 877–884 (1997).
[Crossref]

S. Heath and M. Imregun, “A survey of blade tip-timing measurement techniques for turbo machinery vibration,” J. Eng. Gas Turbines Power 120(4), 784–791 (1998).
[Crossref]

S. Heath, “A new technique for identifying synchronous resonances using tip-timing,” J. Eng. Gas Turbines Power 122(2), 219–225 (2000).
[Crossref]

J. Lightwave Technol. (1)

Journal of Vibration, Measurement and Diagnosis (2)

L. Yang and X. D. Zhang, “Research on displacement sensor of two-circle coaxial reflective optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 29(2), 192–196 (2008).

S. Y. Xie and X. D. Zhang, “Research on three-dimensional output behavior of displacement sensor of two-circle coaxial optical fiber bundle,” Journal of Vibration, Measurement and Diagnosis 37(1), 174–181 (2017).

Mech. Res. Commun. (1)

G. Rigosi, G. Battiato, and T. M. Berruti, “Synchronous vibration parameters identification by tip timing measurements,” Mech. Res. Commun. 79, 7–14 (2017).
[Crossref]

Mechanism Mach. Theory (1)

N. S. Vyas, Sidhartc, and J. S. Rao, “Dynamic stress analysis and a fracture mechanics approach to life prediction of turbine blades,” Mechanism Mach. Theory 32(4), 511–527 (1997).
[Crossref]

Opt. Eng. (1)

D. C. Ye, F. J. Duan, H. T. Guo, Y. Li, and K. Wang, “Turbine blade tip clearance measurement using a skewed dual-beam fiber optic sensor,” Opt. Eng. 58(8), 1514–1522 (2012).

Opt. Lett. (1)

Procedia Eng. (1)

B. H. Jia and X. D. Zhang, “An optical fiber blade tip clearance sensor for active clearance control applications,” Procedia Eng. 15, 984–988 (2011).
[Crossref]

Sens. Actuators A Phys. (1)

H. Cao, Y. Chen, Z. Zhou, and G. Zhang, “Theoretical and experimental study on the optical fiber bundle displacement sensors,” Sens. Actuators A Phys. 136(2), 580–587 (2007).
[Crossref]

Sensors (Basel) (1)

I. García, J. Beloki, J. Zubia, G. Aldabaldetreku, M. A. Illarramendi, and F. Jiménez, “An optical fiber bundle sensor for tip clearance and tip timing measurements in a turbine rig,” Sensors (Basel) 13(6), 7385–7398 (2013).
[Crossref] [PubMed]

Other (6)

B. H. Jia, “Research on optical fiber based measurement and active control technology of turbine tip clearance,” Ph.D. thesis, (Northwestern Polytechnical University, Xi’an, China, 2013).

S. Y. Xie and X. D. Zhang, “Design and Modeling of Three-Dimensional Tip clearance Optical Probe Based on Two-circle coaxial optical fiber bundle,” Proceedings of IEEE International Conference on Sensors, 16582224(2016).
[Crossref]

F. Teng, X. D. Zhang, and S. Y. Xie, “Research on Variation Mechanism of Three-dimensional Blade Tip Clearance of Aero-engine,” in Proceedings of 13th International Conference on Ubiquitous Robots and Ambient Intelligence, 07734008 (2016).
[Crossref]

J. W. H. Chivers, “A technique for the measurement of blade tip clearance in a gas turbine,” in Ph.D. thesis, (University of London, London, UK, 1989).
[Crossref]

A. G. Sheard and S. R. Turner, “Electromechanical measurement of turbomachinery blade tip-to-casing running clearance,” in Proceedings of the 37th American Society of Mechanical Engineers Gas Turbine and Aero-engine Congress, Cologne, Germany, V005T15A005(1992).
[Crossref]

S. J. Gill, M. D. Ingallinera, and A. G. Sheard, “Turbine tip clearance measurement system evaluation in an industrial gas turbine,”in Proceedings of the 42nd American Society of Mechanical Engineers Gas Turbine and Aero-engine Congress, Orlando, Florida, USA, V004T15A037 (1997).
[Crossref]

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Figures (19)

Fig. 1
Fig. 1 Measurement principle of two-coaxial optical fiber bundle.
Fig. 2
Fig. 2 Three-dimensional tip clearance measurement probe.
Fig. 3
Fig. 3 Plane coordinate system of the bundle.
Fig. 4
Fig. 4 Space coordinates system of the bundle and reflector.
Fig. 5
Fig. 5 Space coordinates system including light beam and virtual plane.
Fig. 6
Fig. 6 Parameters on receiving fiber on the virtual plane.
Fig. 7
Fig. 7 Range of parameter disi with three overlapping situations between light beam and fiber.
Fig. 8
Fig. 8 Points divided in the fiber to calculate the intensity.
Fig. 9
Fig. 9 Sketch map of measurement principle with regard of NA.
Fig. 10
Fig. 10 Attenuation characteristics of constructed function.
Fig. 11
Fig. 11 Three-dimensional calibration table and the probe used in experiment.
Fig. 12
Fig. 12 Photo of light resource, preprocessing circuit and data acquisition unit.
Fig. 13
Fig. 13 Comparison between simulation and experiment results of output ratio.
Fig. 14
Fig. 14 Comparison between simulation and experiment results of intensity received by fibers.
Fig. 15
Fig. 15 Comparison results of output ratio with regard of NA.
Fig. 16
Fig. 16 Comparison results of receiving intensity with regard of NA.
Fig. 17
Fig. 17 Comparison results of intensity by inner circle under different ζ.
Fig. 18
Fig. 18 Comparison results of intensity by outer circle under different ζ.
Fig. 19
Fig. 19 Comparison results of output ratio under different ζ.

Tables (1)

Tables Icon

Table 1 Manufactured parameters of the bundle in the experiment

Equations (20)

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

M(h)= I out (h)/ I in (h)
M( h 0 , h 1 , h 2 )= I out ( h 0 , h 1 , h 2 )/ I in ( h 0 , h 1 , h 2 )
{ z 01 = z 0 +Ttanα z 02 = z 0 +Ttanβ
tanαx+tanβy+z z 0 =0
z v =2 z 0 1+tanαtan2α+tanβtan2β 1+ tan 2 α+ tan 2 β
tan2αx+tan2βy+z z v =0
M( z 0 ,α,β)= I out I in = i=7 12 s i I(r,z)ds i=1 6 s i I(r,z)ds
I(r,z)= K 0 I 0 π R 2 (z) exp[ r 2 / R 2 (z) ]
R(z)= a 0 (1+ζtan θ c z 3/2 )
M( z 0 ,α,β)= i=7 12 s i I(r,z)ds i=1 6 s i I(r,z)ds = i=7 12 S i I si i=1 6 S i I si
S i = σ i S
{ σ i =1 di s i <=0 σ i =1di s i /2 a 0 0<di s i <2 a 0 σ i =0 di s i >=2 a 0
M( z 0 ,α,β)= i=7 12 S i I si i=1 6 S i I si = i=7 12 σ i g si i=1 6 σ i g si
g(r,z)= 1 a 0 2 (1+ζtan θ c z 3/2 ) 2 exp{ r 2 /[ a 0 2 (1+ζtan θ c z 3/2 ) 2 ] }
g si = j=1 n L j g j j=1 n L j = j=1 n L j a 0 2 (1+ζtan θ c z j 3/2 ) 2 exp{ ( x j 2 + y j 2 )/[ a 0 2 (1+ζtan θ c z j 3/2 ) 2 ] } j=1 n y j
a j = a 0 T j
γ j =arccos( O j N j e | O j N j || e | )
f( γ j )={ 1 ( γ j υ) 0 ( γ j >υ)
f( γ je )= 1 [1+ ( γ je ./υ) 8 ]
g si =[ j=1 n L j g j ] f( γ je )/ j=1 n L j