Abstract

During vitreoretinal surgery, the surgeon manipulates retinal tissue with tool-to-tissue interaction forces below the human sensory threshold. A force sensor (FS) integrated with conventional surgical tools may significantly improve the surgery outcome by providing tactile feedback to the surgeon. We designed and built a surgical tool integrated with a miniature FS with an outer diameter smaller than 1 mm for vitreoretinal surgery based on low-coherence Fabry–Pérot (FP) interferometry. The force sensing elements are located at the tool tip which is in direct contact with tissue during surgery and the FP cavity length is interrogated by a fiber-optic common-path phase-sensitive optical coherence tomography (OCT) system. We have calibrated the FS's response to axial and lateral forces and conducted experiments to verify that our FS can simultaneously measure both axial and lateral force components.

© 2012 OSA

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References

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  1. P. K. Gupta, P. S. Jensen, and E. de Juan, “Surgical forces and tactile perception during retinal microsurgery,” in Proceedings of the Medical Image Computing and Computer-Assisted Intervention—MICCAI’99, Vol. 1679/1999 of Lecture Notes in Computer Science (Springer, 1999), pp. 1218–1225.
  2. M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser.5, 109–114 (1993).
  3. M. Kitagawa, D. Dokko, A. M. Okamura, B. T. Bethea, and D. D. Yuh., “Effect of sensory substitution on suture manipulation forces for surgical teleoperation, ” in Medicine Meets Virtual Reality 12, J. D. Westwood, R. S. Haluck, H. M. Hoffman, G. T. Mogel, R. Phillips, and R. A. Robb, eds. (IOS Press, 2004). pp. 157–163.
  4. T. Akinbiyi, C. E. Reiley, S. Saha, D. Burschka, C. J. Hasser, D. D. Yuh, and A. M. Okamura, “Dynamic augmented reality for sensory substitution in robot-assisted surgical systems,” in 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2006. EMBS '06 (IEEE, 2006), pp. 567–570.
  5. M. Balicki, A. Uneri, I. Iordachita, J. Handa, P. Gehlbach, and R. H. Taylor, “Micro-force sensing in robot assisted membrane peeling for vitreoretinal surgery,” in Medical Image Computing and Computer-Assisted Intervention—MICCAI 2010, Vol. 6363/2010 of Lecture Notes in Computer Science (Springer, 2010), pp. 303–310.
  6. A. Uneri and M. Balicki, J. Handa, P. Gehlbach, R. Taylor, and I. Iordachita, “New Steady-hand eye robot with microforce sensing for vitreoretinal surgery research,” in 2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), (IEEE, 2010), pp. 814–819.
  7. Z. Sun, M. Balicki, J. Kang, J. Handa, R. Taylor, and I. Iordachita, “Development and preliminary data of novel integrated optical microforce sensing tools for retinal microsurgery,” in IEEE International Conference on Robotics and Automation, 2009. ICRA '09 (IEEE, 2009), pp. 1897–1902.
  8. I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
    [CrossRef] [PubMed]
  9. K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
    [CrossRef]
  10. A. Menciassi, A. Eisinberg, G. Scalari, C. Anticoli, M. C. Carrozza, and P. Dario, “Force feedback-based microinstrument for measuring tissue properties and pulse in microsurgery,” in IEEE International Conference on Robotics and Automation, 2001 (IEEE, 2001), pp. 626–631.
  11. P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
    [CrossRef]
  12. P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature instrument tip force sensor for robot/human cooperative microsurgical manipulation with enhanced force feedback,” in Medical Image Computing and Computer-Assisted Intervention—MICCAI 2000, Vol. 1935/2000 of Lecture Notes in Computer Science (Springer, 2000), pp. 897–906.
  13. D. Jagtap and C. N. Riviere, “Applied force during vitreoretinal microsurgery with handheld instruments,” in 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2004. IEMBS '04 (IEEE, 2004), pp. 2771–2773.
  14. C. Yeh, Handbook of Fiber Optics: Theory and Applications (Academic, 1990), Chap. 11.
  15. P. Puangmali, H. Liu, K. Althoefer, and L. D. Seneviratne, “Optical fiber sensor for soft tissue investigation during minimally invasive surgery,” in IEEE International Conference on Robotics and Automation, 2008. ICRA 2008 (IEEE, 2008), pp. 2934–2939.
  16. S. Hirose and K. Yoneda, “Development of optical 6-axial force sensor and its signal calibration considering non-linear interference,” in 1990 IEEE International Conference on Robotics and Automation, 1990. Proceedings (IEEE, 1990), Vol. 1, pp. 46–53.
  17. H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A miniature MRI-compatible fiber-optic force sensor utilizing Fabry-Perot interferometer,” in Conference Proceedings of the Society for Experimental Mechanics Series2011, Volume 999999, Vol. 4 of MEMS and Nanotechnology (Springer, 2011), pp. 131–136.
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    [CrossRef] [PubMed]
  19. U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron.11, 11799–11805 (2005).
  20. J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
    [CrossRef]
  21. J. Zhang, B. Rao, L. Yu, and Z. Chen, “High-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Lett.34(21), 3442–3444 (2009).
    [CrossRef] [PubMed]
  22. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett.30(16), 2131–2133 (2005).
    [CrossRef] [PubMed]
  23. X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
    [CrossRef] [PubMed]
  24. M. Born and E. Wolf, Principles of Optics (Pergamon, 1964), Chap. 1.
  25. A. Pytel and J. Kiusalaas, Mechanics of Materials (Brooks/Cole, 2003), Chap. 6.
  26. R. D. Yates and D. J. Goodman, Probability and Stochastic Processes (Wiley, 2005), Chap. 5.

2010 (2)

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
[CrossRef] [PubMed]

2009 (2)

J. Zhang, B. Rao, L. Yu, and Z. Chen, “High-dynamic-range quantitative phase imaging with spectral domain phase microscopy,” Opt. Lett.34(21), 3442–3444 (2009).
[CrossRef] [PubMed]

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

2007 (1)

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

2005 (3)

2003 (1)

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

1993 (1)

M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser.5, 109–114 (1993).

Akkin, T.

Balicki, M.

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
[CrossRef] [PubMed]

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Berkelman, P. J.

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

Cense, B.

Chen, Z.

Cooper, K. L.

de Boer, J. F.

Fried, N. M.

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron.11, 11799–11805 (2005).

Gehlbach, P.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Han, J.-H.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

Handa, J.

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Iordachita, I.

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Jensen, P.

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

Joo, C.

Kang, J. U.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
[CrossRef] [PubMed]

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron.11, 11799–11805 (2005).

Kim, K.

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

Liu, X.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
[CrossRef] [PubMed]

Massimino, M. J.

M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser.5, 109–114 (1993).

Nelson, B.

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

Park, B. H.

Phee, S. J.

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Rao, B.

Sharma, U.

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron.11, 11799–11805 (2005).

Sheridan, T. B.

M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser.5, 109–114 (1993).

Shibru, H.

Song, C. G.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

Sun, Y.

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

Sun, Z.

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Taylor, R. H.

X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express18(23), 24331–24343 (2010).
[CrossRef] [PubMed]

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

Voyles, R.

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

Wang, A.

Whitcomb, L. L.

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

Yu, L.

Zhang, J.

Zhang, K.

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

Zhang, Y.

IEEE J. Quantum Electron. (1)

U. Sharma, N. M. Fried, and J. U. Kang, “All-fiber Fizeau optical coherence tomography: sensitivity optimization and system analysis,” IEEE J. Quantum Electron.11, 11799–11805 (2005).

IEEE J. Sel. Top. Quantum Electron. (1)

J. U. Kang, J.-H. Han, X. Liu, K. Zhang, C. G. Song, and P. Gehlbach, “Endoscopic functional Fourier domain common path optical coherence tomography for microsurgery,” IEEE J. Sel. Top. Quantum Electron.16(4), 781–792 (2010).
[CrossRef]

IEEE Sens. J. (1)

K. Kim, Y. Sun, R. Voyles, and B. Nelson, “Calibration of multi-axis MEMS force sensors using the shape-from-motion method,” IEEE Sens. J.7(3), 344–351 (2007).
[CrossRef]

IEEE Trans. Robot. Autom. (1)

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature microsurgical instrument tip force sensor for enhanced force feedback during robot-assisted manipulation,” IEEE Trans. Robot. Autom.19(5), 917–922 (2003).
[CrossRef]

IFAC Symp. Ser. (1)

M. J. Massimino and T. B. Sheridan, “Sensory substitution for force feedback in teleoperation,” IFAC Symp. Ser.5, 109–114 (1993).

Int. J. CARS (1)

I. Iordachita, Z. Sun, M. Balicki, J. U. Kang, S. J. Phee, J. Handa, P. Gehlbach, and R. H. Taylor, “A sub-millimetric, 0.25 mN resolution fully integrated fiber-optic force-sensing tool for retinal microsurgery,” Int. J. CARS4(4), 383–390 (2009).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Other (16)

P. J. Berkelman, L. L. Whitcomb, R. H. Taylor, and P. Jensen, “A miniature instrument tip force sensor for robot/human cooperative microsurgical manipulation with enhanced force feedback,” in Medical Image Computing and Computer-Assisted Intervention—MICCAI 2000, Vol. 1935/2000 of Lecture Notes in Computer Science (Springer, 2000), pp. 897–906.

D. Jagtap and C. N. Riviere, “Applied force during vitreoretinal microsurgery with handheld instruments,” in 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2004. IEMBS '04 (IEEE, 2004), pp. 2771–2773.

C. Yeh, Handbook of Fiber Optics: Theory and Applications (Academic, 1990), Chap. 11.

P. Puangmali, H. Liu, K. Althoefer, and L. D. Seneviratne, “Optical fiber sensor for soft tissue investigation during minimally invasive surgery,” in IEEE International Conference on Robotics and Automation, 2008. ICRA 2008 (IEEE, 2008), pp. 2934–2939.

S. Hirose and K. Yoneda, “Development of optical 6-axial force sensor and its signal calibration considering non-linear interference,” in 1990 IEEE International Conference on Robotics and Automation, 1990. Proceedings (IEEE, 1990), Vol. 1, pp. 46–53.

H. Su, M. Zervas, C. Furlong, and G. S. Fischer, “A miniature MRI-compatible fiber-optic force sensor utilizing Fabry-Perot interferometer,” in Conference Proceedings of the Society for Experimental Mechanics Series2011, Volume 999999, Vol. 4 of MEMS and Nanotechnology (Springer, 2011), pp. 131–136.

P. K. Gupta, P. S. Jensen, and E. de Juan, “Surgical forces and tactile perception during retinal microsurgery,” in Proceedings of the Medical Image Computing and Computer-Assisted Intervention—MICCAI’99, Vol. 1679/1999 of Lecture Notes in Computer Science (Springer, 1999), pp. 1218–1225.

A. Menciassi, A. Eisinberg, G. Scalari, C. Anticoli, M. C. Carrozza, and P. Dario, “Force feedback-based microinstrument for measuring tissue properties and pulse in microsurgery,” in IEEE International Conference on Robotics and Automation, 2001 (IEEE, 2001), pp. 626–631.

M. Kitagawa, D. Dokko, A. M. Okamura, B. T. Bethea, and D. D. Yuh., “Effect of sensory substitution on suture manipulation forces for surgical teleoperation, ” in Medicine Meets Virtual Reality 12, J. D. Westwood, R. S. Haluck, H. M. Hoffman, G. T. Mogel, R. Phillips, and R. A. Robb, eds. (IOS Press, 2004). pp. 157–163.

T. Akinbiyi, C. E. Reiley, S. Saha, D. Burschka, C. J. Hasser, D. D. Yuh, and A. M. Okamura, “Dynamic augmented reality for sensory substitution in robot-assisted surgical systems,” in 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2006. EMBS '06 (IEEE, 2006), pp. 567–570.

M. Balicki, A. Uneri, I. Iordachita, J. Handa, P. Gehlbach, and R. H. Taylor, “Micro-force sensing in robot assisted membrane peeling for vitreoretinal surgery,” in Medical Image Computing and Computer-Assisted Intervention—MICCAI 2010, Vol. 6363/2010 of Lecture Notes in Computer Science (Springer, 2010), pp. 303–310.

A. Uneri and M. Balicki, J. Handa, P. Gehlbach, R. Taylor, and I. Iordachita, “New Steady-hand eye robot with microforce sensing for vitreoretinal surgery research,” in 2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), (IEEE, 2010), pp. 814–819.

Z. Sun, M. Balicki, J. Kang, J. Handa, R. Taylor, and I. Iordachita, “Development and preliminary data of novel integrated optical microforce sensing tools for retinal microsurgery,” in IEEE International Conference on Robotics and Automation, 2009. ICRA '09 (IEEE, 2009), pp. 1897–1902.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964), Chap. 1.

A. Pytel and J. Kiusalaas, Mechanics of Materials (Brooks/Cole, 2003), Chap. 6.

R. D. Yates and D. J. Goodman, Probability and Stochastic Processes (Wiley, 2005), Chap. 5.

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Figures (7)

Fig. 1
Fig. 1

(a) System schematic of FPI FS; (b) detailed schematic of the system including FPI-FS and CP OCT interrogation; (c) cross section of tool shaft with fiber embedded; (d) CAD model for the Nitinol flexure; (e) CAD model of the FPI-FS probe without the tool handle; (f) CAD model of the FPI-FS probe with the tool handle; (g) photo of the tool pictured below a US quarter.

Fig. 2
Fig. 2

(a) Superposition of spectral interference signals from three FP cavities; (b) OCT signal with three coherence peaks corresponding to three FP cavities; (c) central part of the interference spectrum: with (red) and without (black) additional displacement δli; (d) complex OCT signals at the 1st, 2nd, and 3rd coherence peaks in the complex plane using polar coordinate system. Black symbols and red symbols represent OCT signals with and without additional displacement δli; (e) actual interferometric spectrum obtained from the FPI-FS; (f) amplitude of OCT signal obtained by Fourier transforming spectrum shown in Fig. 2(e).

Fig. 3
Fig. 3

(a) FS at neutral; (b) axial force changes the length of flexure and changes the FP cavity length; (c) lateral force leads flexure to bend and changes the FP cavity length; (d) diagram shows the calculation of cavity length induced by lateral force; (e) diagram shows the calculation of bi

Fig. 4
Fig. 4

(a) Photo of axial calibration setup; (b) schematic of axial calibration setup; (c) displacement versus axial force (first FP cavity); (d) displacement versus axial force (second FP cavity); (e) displacement versus axial force (third FP cavity).

Fig. 5
Fig. 5

(a) Photo of lateral calibration setup; (b) schematic of lateral calibration setup; (c)–(h) results from lateral calibration: (c)–(e) show displacements measured from three FP cavities at different θ with different lateral forces. Legends indicate number of testing weights applied to the sensor; (f)–(h) show displacements with different lateral loads when θ was 3π/2.

Fig. 6
Fig. 6

Fx, Fy and Fl extracted from displacements when θ took different values.

Fig. 7
Fig. 7

(a) Photo of 3D force measurement setup; (b) Schematic of 3D force measurement setup; (c) Measured and actual axial force; (d) Measured and actual lateral force; (e) Measured and actual axial force obtained by using the known load gravity as bias; (f) Measured and actual lateral force obtained by using the known load gravity as bias.

Equations (15)

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

L i = L i,0 +δ l i ( F ).
S( k )=η[ i=1 3 | E 1i ( k ) | 2 + i=1 3 | E 2i ( k ) | 2 + i=1 3 2Re( E 1i ( k ) E 2i * ( k ) ) ]
I OCT ( z )= F -1 [ S( k ) ]
I OCT ( z )= ηh( z ) i=1 3 [ | r a i | 2 + | r 2i a i | 2 ]               +η i=1 3 [ r r 2i * a i 2 h( z2 L i,0 ) e j2 k 0 δ l i ]               +η i=1 3 [ r * r 2i a i 2 h( z+2 L i,0 ) e j2 k 0 δ l i ]
2 k 0 δ l i = tan 1 { Im[ I OCT ( L i,0 ) ] Re[ I OCT ( L i,0 ) ] } N i π
δ l i = λ 0 4π tan 1 { Im[ I OCT ( L i,0 ) ] Re[ I OCT ( L i,0 ) ] } N i λ 0 4
δ l i ( F )= d i d i,0
b i = x i 2 + y i 2 cos( θ+ ε i )
δ l i = F z D A 0 E + x i 2 + y i 2 cos( θ+ε ) F l D 2 2EI     = D A 0 E F z + x i D 2 2EI F l cosθ y i D 2 2EI F l sinθ
δ l i = A ix F x + A iy F y + A iz F z
F l = F x 2 + F y 2
δl=AF
δl=[ d 1 d 01 d 2 d 02 d 3 d 03 ];A=[ A 1x   A 1y   A 1z A 2x   A 2y   A 2z A 3x   A 3y   A 3z ];F=[ F x F y F z ].
F= A 1 δl
F x =Gsinφcosθ; F y =Gsinφsinθ; F z =Gcosφ

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