Abstract

A method named lateral scanning confocal microscopy (LtSCM) is proposed with the aim of determining the in-plane displacement of microstructures, especially of those moving components within microelectromechanical systems (MEMS) actuators and sensors, which feature high aspect ratio and limited geometrical size in one or two dimensions within the surface plane. The principle of the LtSCM is presented and theoretically analyzed, which indicates that the LtSCM has the potential to determine with high resolution the in-plane displacement, position, and even the geometrical size of the object. Furthermore, in the case of in-plane displacement measurement, the measurement resolution of the LtSCM should be insensitive to the dynamic performance of the movable microstructures, i.e., from quasi-static to ultrahigh speed. In a proof-of-principle experiment, the voltage-displacement response of an electrostatic comb-drive actuator has been obtained with nanometric resolution.

© 2007 Optical Society of America

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  1. P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).
  2. M. A. Haque and M. T. A. Saif, Exp. Mech. 43, 248 (2003).
    [CrossRef]
  3. Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
    [CrossRef]
  4. C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
    [CrossRef]
  5. N. B. Hubbard and L. L. Howell, J. Micromech. Microeng. 15, 1482 (2005).
    [CrossRef]
  6. S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
    [CrossRef]
  7. D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
    [CrossRef]
  8. C.-H. Lee and J. Wang, Opt. Commun. 135, 233 (1997).
    [CrossRef]

2005

N. B. Hubbard and L. L. Howell, J. Micromech. Microeng. 15, 1482 (2005).
[CrossRef]

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

2003

M. A. Haque and M. T. A. Saif, Exp. Mech. 43, 248 (2003).
[CrossRef]

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

2002

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

1997

C.-H. Lee and J. Wang, Opt. Commun. 135, 233 (1997).
[CrossRef]

1995

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Binggeli, M.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Brugger, J.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Chang, S.

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

de Rooij, N. F.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Enikov, E.

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

Fang, J.

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

Haque, M. A.

M. A. Haque and M. T. A. Saif, Exp. Mech. 43, 248 (2003).
[CrossRef]

Howell, L. L.

N. B. Hubbard and L. L. Howell, J. Micromech. Microeng. 15, 1482 (2005).
[CrossRef]

Hubbard, N. B.

N. B. Hubbard and L. L. Howell, J. Micromech. Microeng. 15, 1482 (2005).
[CrossRef]

Indermuhle, P.-F.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Jaecklin, V. P.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Jeon, J.-U.

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

Jeong, H.-M.

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

Kim, C.-H.

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

Kim, Y.-K.

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

Lee, C.-H.

C.-H. Lee and J. Wang, Opt. Commun. 135, 233 (1997).
[CrossRef]

Linder, C.

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

Nelson, B. J.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

Piybongkarn, D.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

Potasek, D. P.

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

Rajamani, R.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

Saif, M. T. A.

M. A. Haque and M. T. A. Saif, Exp. Mech. 43, 248 (2003).
[CrossRef]

Sezen, A. S.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

Sun, Y.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

Wang, C. S.

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

Wang, J.

C.-H. Lee and J. Wang, Opt. Commun. 135, 233 (1997).
[CrossRef]

Xiong, C. Y.

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

Exp. Mech.

M. A. Haque and M. T. A. Saif, Exp. Mech. 43, 248 (2003).
[CrossRef]

IEEE Trans. Control Syst. Technol.

D. Piybongkarn, Y. Sun, R. Rajamani, A. S. Sezen, and B. J. Nelson, IEEE Trans. Control Syst. Technol. 13, 138 (2005).
[CrossRef]

J. Microelectromech. Syst.

C.-H. Kim, H.-M. Jeong, J.-U. Jeon, and Y.-K. Kim, J. Microelectromech. Syst. 12, 470 (2003).
[CrossRef]

J. Micromech. Microeng.

N. B. Hubbard and L. L. Howell, J. Micromech. Microeng. 15, 1482 (2005).
[CrossRef]

Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, J. Micromech. Microeng. 12, 832 (2002).
[CrossRef]

Nanotechnology

S. Chang, C. S. Wang, C. Y. Xiong, and J. Fang, Nanotechnology 16, 344 (2005).
[CrossRef]

Opt. Commun.

C.-H. Lee and J. Wang, Opt. Commun. 135, 233 (1997).
[CrossRef]

Sens. Actuators, A

P.-F. Indermuhle, V. P. Jaecklin, J. Brugger, C. Linder, N. F. de Rooij, and M. Binggeli, Sens. Actuators, A 46-47, 562 (1995).

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Figures (6)

Fig. 1
Fig. 1

Principle of the lateral confocal microscopy.

Fig. 2
Fig. 2

Geometrical explanation to Eq. (7).

Fig. 3
Fig. 3

Typical intensity response for lateral confocal microscopy with square apertures, where max ( b , c ) < 2 λ ( f a ) .

Fig. 4
Fig. 4

Experimental setup of a lateral confocal microscope.

Fig. 5
Fig. 5

Lateral confocal response of the experimental setup.

Fig. 6
Fig. 6

Actual voltage-displacement response of the actuator under test obtained by the experimental lateral confocal microscope.

Equations (8)

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

U 1 ( x , y ) = F { t ( x , y ) } .
U 3 ( x , y ) = F { t ( x , y ) } o ( x , y ) d ( x , y ) ,
I = U 3 ( x , y ) d x d y 2 .
o ( x , y ) = rect ( x u c ) ,
U 3 ( x , y ) = a 2 sinc ( a x λ f ) sinc ( a y λ f ) rect ( x u c ) rect ( x b ) rect ( y b ) .
I ( u ) = a 4 C 2 ( b ) [ b 2 b 2 sinc ( a x λ f ) rect ( x u c ) d x ] 2 ,
f a λ > c 2 , b c .
I ( u ) = k u + I 0 ,

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