Shape sensing using multi-core fiber optic cable and parametric curve solutions

doi:10.1364/OE.20.002967

Shape sensing using multi-core fiber optic cable and parametric curve solutions

Jason P. Moore and Matthew D. Rogge »View Author Affiliations

Optics Express, Vol. 20, Issue 3, pp. 2967-2973 (2012)
http://dx.doi.org/10.1364/OE.20.002967

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Abstract

The shape of a multi-core optical fiber is calculated by numerically solving a set of Frenet-Serret equations describing the path of the fiber in three dimensions. Included in the Frenet-Serret equations are curvature and bending direction functions derived from distributed fiber Bragg grating strain measurements in each core. The method offers advantages over prior art in that it determines complex three-dimensional fiber shape as a continuous parametric solution rather than an integrated series of discrete planar bends. Results and error analysis of the method using a tri-core optical fiber is presented. Maximum error expressed as a percentage of fiber length was found to be 7.2%.

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 2, 2011
Manuscript Accepted: January 18, 2012
Published: January 24, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Jason P. Moore and Matthew D. Rogge, "Shape sensing using multi-core fiber optic cable and parametric curve solutions," Opt. Express 20, 2967-2973 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-3-2967

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References

R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Elsevier, 2010).
M. J. Gander, W. N. MacPherson, R. McBride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multi-core fiber,” Electron. Lett.36(2), 120–121 (2000). [CrossRef]
G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett.28(6), 387–389 (2003). [CrossRef] [PubMed]
R. G. Duncan, M. E. Froggatt, S. T. Kreger, R. J. Seeley, D. K. Gifford, A. K. Sang, and M. S. Wolfe, “High-accuracy fiber-optic shape sensing,” Proc. SPIE6530, 65301S, 65301S-11 (2007). [CrossRef]
S. M. Klute, R. G. Duncan, R. S. Fielder, G. W. Butler, J. H. Mabe, A. K. Sang, R. J. Seeley, and M. T. Raum, “Fiber-optic shape sensing and distributed strain measurements on a morphing chevron,” in Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada, Jan. 9–12, 2006).
A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, 1993), Chap. 7.
J. Langer and D. A. Singer, “Lagrangian aspects of the Kirchhoff elastic rod,” SIAM Rev.38(4), 605–618 (1996). [CrossRef]
C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001), Chap. 14.
B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, “Use of 3000 Bragg grating strain sensors distributed on four eight-meter optical fibers during static load tests of a composite structure,” Proc. SPIE4332, 133–142 (2001). [CrossRef]

Electron. Lett.

M. J. Gander, W. N. MacPherson, R. McBride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multi-core fiber,” Electron. Lett.36(2), 120–121 (2000). [CrossRef]

Opt. Lett.

G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett.28(6), 387–389 (2003). [CrossRef] [PubMed]

Proc. SPIE

R. G. Duncan, M. E. Froggatt, S. T. Kreger, R. J. Seeley, D. K. Gifford, A. K. Sang, and M. S. Wolfe, “High-accuracy fiber-optic shape sensing,” Proc. SPIE6530, 65301S, 65301S-11 (2007). [CrossRef]
B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, “Use of 3000 Bragg grating strain sensors distributed on four eight-meter optical fibers during static load tests of a composite structure,” Proc. SPIE4332, 133–142 (2001). [CrossRef]

SIAM Rev.

J. Langer and D. A. Singer, “Lagrangian aspects of the Kirchhoff elastic rod,” SIAM Rev.38(4), 605–618 (1996). [CrossRef]

Other

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001), Chap. 14.
R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Elsevier, 2010).
S. M. Klute, R. G. Duncan, R. S. Fielder, G. W. Butler, J. H. Mabe, A. K. Sang, R. J. Seeley, and M. T. Raum, “Fiber-optic shape sensing and distributed strain measurements on a morphing chevron,” in Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada, Jan. 9–12, 2006).
A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, 1993), Chap. 7.

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[1] R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Elsevier, 2010).

[2] M. J. Gander, W. N. MacPherson, R. McBride, J. D. C. Jones, L. Zhang, I. Bennion, P. M. Blanchard, J. G. Burnett, and A. H. Greenaway, “Bend measurement using Bragg gratings in multi-core fiber,” Electron. Lett.36(2), 120–121 (2000). [CrossRef]

[3] G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett.28(6), 387–389 (2003). [CrossRef] [PubMed]

[4] R. G. Duncan, M. E. Froggatt, S. T. Kreger, R. J. Seeley, D. K. Gifford, A. K. Sang, and M. S. Wolfe, “High-accuracy fiber-optic shape sensing,” Proc. SPIE6530, 65301S, 65301S-11 (2007). [CrossRef]

[5] S. M. Klute, R. G. Duncan, R. S. Fielder, G. W. Butler, J. H. Mabe, A. K. Sang, R. J. Seeley, and M. T. Raum, “Fiber-optic shape sensing and distributed strain measurements on a morphing chevron,” in Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada, Jan. 9–12, 2006).

[6] A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, 1993), Chap. 7.

[7] J. Langer and D. A. Singer, “Lagrangian aspects of the Kirchhoff elastic rod,” SIAM Rev.38(4), 605–618 (1996). [CrossRef]

[8] C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001), Chap. 14.

[9] B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, “Use of 3000 Bragg grating strain sensors distributed on four eight-meter optical fibers during static load tests of a composite structure,” Proc. SPIE4332, 133–142 (2001). [CrossRef]

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Shape sensing using multi-core fiber optic cable and parametric curve solutions