Abstract

Multiactuated piezoelectric flextensional actuators (MAPFAs) is a fast-growing technology in development, with a wide range of applications in precision mechanics and nanotechnology. In turn, optical interferometry is an adequate technique to measure nano/micro-displacements and to characterize these MAPFAs. In this work, an efficient method for homodyne phase detection, based on a well-known Bessel functions recurrence relation, is developed, providing practical applications with a high dynamic range. Fading and electronic noise are taken into account in the analysis. An important advantage of the method is that, for each measurement, only a limited number of frequencies in the magnitude spectrum of the photodetected signal are used, without the need to know the phase spectrum. The dynamic range for phase demodulation is from 0.2 to 100πrad (or 10 nm to 16 μm for displacement, using 632.8 nm wavelength). The upper range can be easily expanded by adapting the electronic system to the signal characteristics. By using this interferometric technique, a new XY nanopositioner MAPFA prototype is tested in terms of linearity, displacement frequency response, and coupling rate.

© 2013 Optical Society of America

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2010 (3)

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

G. Heinzel, F. G. Cervanyes, A. F. G. Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express 18, 19076–19086 (2010).
[CrossRef]

2009 (3)

Y. Bitou, “High-accuracy displacement metrology and control using a dual Fabry–Perot cavity with an optical frequency comb generator,” Precis. Eng. 33, 187–193 (2009).
[CrossRef]

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Y. Tian, B. Shirinzadeh, and D. Zhang, “A flexure-based five-bar mechanism for micro/nano manipulation,” Sens. Actuators A 153, 96–104 (2009).
[CrossRef]

2008 (2)

S. Kang, J. La, H. Yoon, and K. Park, “A synthetic heterodyne interferometer for small amplitude of vibration measurement,” Rev. Sci. Instrum. 79, 053106 (2008).
[CrossRef]

M. M. Brundavanam, N. K. Viswanathan, and D. N. Rao, “Nanodisplacement measurement using spectral shifts in a white-light interferometer,” Appl. Opt. 47, 6334–6339 (2008).
[CrossRef]

2007 (2)

S. Devasia, E. Eleftheriou, and S. Moheimani, “A survey of control issues in nanopositioning,” IEEE Trans. Control Syst. Technol. 15, 802–823 (2007).
[CrossRef]

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Optimum placement of piezoelectric material in piezoactuator design,” Smart Mater. Struc. 16, 207–220 (2007).

2005 (4)

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Design of piezoelectric multi-actuated microtools using topology optimization,” Smart Mater. Struc. 14, 1431–1447 (2005).

S. Yokoyama, T. Yokoyama, and T. Araki, “High-speed subnanometre interferometry using an improved three-mode heterodyne interferometer,” Meas. Sci. Technol. 16, 1841–1847 (2005).
[CrossRef]

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
[CrossRef]

R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

2004 (1)

O. M. E. Rifai and K. Youcef-Toumi, “Trade-offs and performance limitations in mechatronic systems: a case study,” Ann. Rev. Cont. 28, 181–192 (2004).

2003 (1)

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

2001 (2)

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

1993 (1)

V. Sudarshanam and R. Claus, “Generic J1…J4 method of optical phase detection,” J. Mod. Opt. 40, 483–492 (1993).
[CrossRef]

1992 (1)

1991 (1)

1989 (1)

1982 (1)

1973 (1)

1967 (1)

H. A. Deferrari, R. A. Darby, and F. A. Andrews, “Vibrational displacement and mode-shape measurement by a laser interferometer,” J. Acoust. Soc. Am. 42, 982–990 (1967).
[CrossRef]

Alayli, Y.

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
[CrossRef]

Andrews, F. A.

H. A. Deferrari, R. A. Darby, and F. A. Andrews, “Vibrational displacement and mode-shape measurement by a laser interferometer,” J. Acoust. Soc. Am. 42, 982–990 (1967).
[CrossRef]

Araki, T.

S. Yokoyama, T. Yokoyama, and T. Araki, “High-speed subnanometre interferometry using an improved three-mode heterodyne interferometer,” Meas. Sci. Technol. 16, 1841–1847 (2005).
[CrossRef]

Barillot, F.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Bitou, Y.

Y. Bitou, “High-accuracy displacement metrology and control using a dual Fabry–Perot cavity with an optical frequency comb generator,” Precis. Eng. 33, 187–193 (2009).
[CrossRef]

Bouchilloux, P.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Brundavanam, M. M.

Campolo, D.

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Carbonari, R. C.

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Optimum placement of piezoelectric material in piezoactuator design,” Smart Mater. Struc. 16, 207–220 (2007).

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Design of piezoelectric multi-actuated microtools using topology optimization,” Smart Mater. Struc. 14, 1431–1447 (2005).

R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

Carrozza, M.

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Cervanyes, F. G.

Chassagne, L.

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
[CrossRef]

Chen, B.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

Chen, Z.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

Chetwynd, D. G.

S. T. Smith and D. G. Chetwynd, “Foundations of ultraprecision mechanism design,” in Developments in Nanotechnology (Gordon and Breach Science, 1992), Vol. 2, pp. 95–180.

Claeyssen, F.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Claus, R.

V. Sudarshanam and R. Claus, “Generic J1…J4 method of optical phase detection,” J. Mod. Opt. 40, 483–492 (1993).
[CrossRef]

Cuishaw, B.

Danzmann, K.

Darby, R. A.

H. A. Deferrari, R. A. Darby, and F. A. Andrews, “Vibrational displacement and mode-shape measurement by a laser interferometer,” J. Acoust. Soc. Am. 42, 982–990 (1967).
[CrossRef]

Dario, P.

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Deferrari, H. A.

H. A. Deferrari, R. A. Darby, and F. A. Andrews, “Vibrational displacement and mode-shape measurement by a laser interferometer,” J. Acoust. Soc. Am. 42, 982–990 (1967).
[CrossRef]

Devasia, S.

S. Devasia, E. Eleftheriou, and S. Moheimani, “A survey of control issues in nanopositioning,” IEEE Trans. Control Syst. Technol. 15, 802–823 (2007).
[CrossRef]

Eisinberg, A.

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Eleftheriou, E.

S. Devasia, E. Eleftheriou, and S. Moheimani, “A survey of control issues in nanopositioning,” IEEE Trans. Control Syst. Technol. 15, 802–823 (2007).
[CrossRef]

Fabbro, H.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Feng, Q.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

Feng, W.

Giallorenzi, T. G.

Guay, P.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Heinzel, G.

Howard, L. P.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Jin, W.

Juncar, P.

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
[CrossRef]

Kang, S.

S. Kang, J. La, H. Yoon, and K. Park, “A synthetic heterodyne interferometer for small amplitude of vibration measurement,” Rev. Sci. Instrum. 79, 053106 (2008).
[CrossRef]

Koo, K.

Kullmann, J.

La, J.

S. Kang, J. La, H. Yoon, and K. Park, “A synthetic heterodyne interferometer for small amplitude of vibration measurement,” Rev. Sci. Instrum. 79, 053106 (2008).
[CrossRef]

Le Letty, R.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Lhermet, N.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Li, M.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

Liang, J.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

Marin, A. F. G.

Menciassi, A.

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Micera, S.

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

Moheimani, S.

S. Devasia, E. Eleftheriou, and S. Moheimani, “A survey of control issues in nanopositioning,” IEEE Trans. Control Syst. Technol. 15, 802–823 (2007).
[CrossRef]

Nader, G.

R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

Nishiwaki, S.

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Optimum placement of piezoelectric material in piezoactuator design,” Smart Mater. Struc. 16, 207–220 (2007).

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Design of piezoelectric multi-actuated microtools using topology optimization,” Smart Mater. Struc. 14, 1431–1447 (2005).

R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

Park, K.

S. Kang, J. La, H. Yoon, and K. Park, “A synthetic heterodyne interferometer for small amplitude of vibration measurement,” Rev. Sci. Instrum. 79, 053106 (2008).
[CrossRef]

Pernick, B. J.

Pratt, J. R.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Rao, D. N.

Ren, J.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

Rifai, O. M. E.

O. M. E. Rifai and K. Youcef-Toumi, “Trade-offs and performance limitations in mechatronic systems: a case study,” Ann. Rev. Cont. 28, 181–192 (2004).

Sheem, S. K.

Shirinzadeh, B.

Y. Tian, B. Shirinzadeh, and D. Zhang, “A flexure-based five-bar mechanism for micro/nano manipulation,” Sens. Actuators A 153, 96–104 (2009).
[CrossRef]

Silva, E. C. N.

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Optimum placement of piezoelectric material in piezoactuator design,” Smart Mater. Struc. 16, 207–220 (2007).

R. C. Carbonari, E. C. N. Silva, and S. Nishiwaki, “Design of piezoelectric multi-actuated microtools using topology optimization,” Smart Mater. Struc. 14, 1431–1447 (2005).

R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

Smith, D. T.

D. T. Smith, J. R. Pratt, and L. P. Howard, “A fiber-optic interferometer with subpicometer resolution for dc and low-frequency displacement measurement,” Rev. Sci. Instrum. 80, 035105 (2009).
[CrossRef]

Smith, S. T.

S. T. Smith and D. G. Chetwynd, “Foundations of ultraprecision mechanism design,” in Developments in Nanotechnology (Gordon and Breach Science, 1992), Vol. 2, pp. 95–180.

Spillman, W. B. J.

E. Udd and W. B. J. Spillman, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2011).

Srinivasan, K.

Sudarshanam, V.

V. Sudarshanam and R. Claus, “Generic J1…J4 method of optical phase detection,” J. Mod. Opt. 40, 483–492 (1993).
[CrossRef]

Sudarshanam, V. S.

Tian, Y.

Y. Tian, B. Shirinzadeh, and D. Zhang, “A flexure-based five-bar mechanism for micro/nano manipulation,” Sens. Actuators A 153, 96–104 (2009).
[CrossRef]

Topcu, S.

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
[CrossRef]

Udd, E.

E. Udd and W. B. J. Spillman, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2011).

Uttamchandani, D.

Viswanathan, N. K.

Xie, F.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

Yokoyama, S.

S. Yokoyama, T. Yokoyama, and T. Araki, “High-speed subnanometre interferometry using an improved three-mode heterodyne interferometer,” Meas. Sci. Technol. 16, 1841–1847 (2005).
[CrossRef]

Yokoyama, T.

S. Yokoyama, T. Yokoyama, and T. Araki, “High-speed subnanometre interferometry using an improved three-mode heterodyne interferometer,” Meas. Sci. Technol. 16, 1841–1847 (2005).
[CrossRef]

Yoon, H.

S. Kang, J. La, H. Yoon, and K. Park, “A synthetic heterodyne interferometer for small amplitude of vibration measurement,” Rev. Sci. Instrum. 79, 053106 (2008).
[CrossRef]

Yorck, M.

F. Claeyssen, R. Le Letty, F. Barillot, N. Lhermet, H. Fabbro, P. Guay, M. Yorck, and P. Bouchilloux, “Mechanisms based on piezoactuators,” Proc. SPIE 4332, 225–233 (2001).

Youcef-Toumi, K.

O. M. E. Rifai and K. Youcef-Toumi, “Trade-offs and performance limitations in mechatronic systems: a case study,” Ann. Rev. Cont. 28, 181–192 (2004).

Yu, B.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

Yuan, L.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

Zhang, D.

Y. Tian, B. Shirinzadeh, and D. Zhang, “A flexure-based five-bar mechanism for micro/nano manipulation,” Sens. Actuators A 153, 96–104 (2009).
[CrossRef]

Zhang, L. M.

Zhen, S.

S. Zhen, B. Chen, L. Yuan, M. Li, J. Liang, and B. Yu, “A novel interferometric vibration measurement sensor with quadrature detection based on 1/8 waveplate,” Opt. Laser Technol. 42, 362–365 (2010).
[CrossRef]

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Appl. Opt. (5)

IEE Proc. Circuits Devices Syst. (1)

A. Eisinberg, A. Menciassi, S. Micera, D. Campolo, M. Carrozza, and P. Dario, “Pi force control of a microgripper for assembling biomedical microdevices,” IEE Proc. Circuits Devices Syst. 148, 348–352 (2001).
[CrossRef]

IEEE Trans. Control Syst. Technol. (1)

S. Devasia, E. Eleftheriou, and S. Moheimani, “A survey of control issues in nanopositioning,” IEEE Trans. Control Syst. Technol. 15, 802–823 (2007).
[CrossRef]

IEEE/ASME Trans. Mechatron. (1)

A. Menciassi, A. Eisinberg, M. Carrozza, and P. Dario, “Force sensing microinstrument for measuring tissue properties and pulse in microsurgery,” IEEE/ASME Trans. Mechatron. 8, 10–17 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

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S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, “Improving the accuracy of homodyne Michelson interferometers using polarisation state measurement techniques,” Opt. Commun. 247, 133–139 (2005).
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Opt. Express (1)

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F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42, 208–213 (2010).
[CrossRef]

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[CrossRef]

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Y. Bitou, “High-accuracy displacement metrology and control using a dual Fabry–Perot cavity with an optical frequency comb generator,” Precis. Eng. 33, 187–193 (2009).
[CrossRef]

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R. C. Carbonari, G. Nader, S. Nishiwaki, and E. C. N. Silva, “Experimental and numerical characterization of multi-actuated piezoelectric device designs using topology optimization,” in Proc. SPIE 5764, 472–481 (2005).

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Y. Tian, B. Shirinzadeh, and D. Zhang, “A flexure-based five-bar mechanism for micro/nano manipulation,” Sens. Actuators A 153, 96–104 (2009).
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

XY nanopositioner prototype.

Fig. 2.
Fig. 2.

Relation between x and x for the Pernick method with (a) n=2 and (b) n=3. The percent relative error Δx is also represented.

Fig. 3.
Fig. 3.

Bathtubs graph for the Pernick method using n=2.

Fig. 4.
Fig. 4.

Envelope of maxima |Vk(x)|/AF and three values of ϕ0(t): 0.3156π, 0.3634π, and π/2rad. The numbers above the peaks indicate the order of the harmonic with a larger magnitude in that interval.

Fig. 5.
Fig. 5.

Function that indicates which harmonic envelope of order k is larger for each pair of (x,ϕ0).

Fig. 6.
Fig. 6.

Information relative to dynamic range (gray strips), envelope of maxima (white strips), and large error (black strips) for each value of k (odd). (a) ϕ0(t) between π/2±0.3156πrad and between 3π/2±0.3156πrad. (b) ϕ0(t)=0.2641πrad. Ambiguity case k=1 is shown in yellow strip.

Fig. 7.
Fig. 7.

Information relative to dynamic range (gray strips), envelope of maxima (white strips), and large error (black strips) for each value of k (even). (a) ϕ0(t) between 0±0.1974πrad and between π±0.1974πrad. (b) ϕ0(t)=0.2641πrad. Ambiguity case k=2 is shown in yellow strip.

Fig. 8.
Fig. 8.

Bathtub graph for the n-CPM.

Fig. 9.
Fig. 9.

Simulation of the n-CPM showing the selection of the best values of n for some points.

Fig. 10.
Fig. 10.

XY nanopositioner generated movement linearity curves at the frequencies of 370 and 930 Hz.

Fig. 11.
Fig. 11.

XY nanopositioner coupled movement linearity curves at the frequencies of 290 and 910 Hz.

Fig. 12.
Fig. 12.

Generated and coupled XY nanopositioner displacement frequency response, in terms of modulation index- and displacement-to-applied voltage ratio.

Fig. 13.
Fig. 13.

Coupling rate Sxy as a function of frequency.

Tables (1)

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Table 1. Dynamic Range as a Function of na

Equations (7)

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

v(t)=A(12+F{Q2J0(x)Pi=1J2i1(x)sin[(2i1)(ωst+ϕs)]+Qi=1J2i(x)cos[2i(ωst+ϕs)]}),
V2i1(x)=AFPJ2i1(x)
V2i(x)=AFQJ2i(x),
x2=4n(n+1)(n+2)Jn+1(x)(n+2)Jn1(x)+2(n+1)Jn+1(x)+nJn+3(x),
(x)2=4n(n+1)(n+2)Vn+1(x)(n+2)Vn1(x)+2(n+1)Vn+1(x)+nVn+3(x),
V2i1(x)=AF[PJ2i1(x)+K/(2i1)m]
V2i(x)=AF[QJ2i(x)+K/(2i)m],

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