Abstract

The fabrication and characterization of an optically addressable deformable mirror for a spatial light modulator is described. Device operation utilizes an electrostatically driven pixellated aluminized polymeric membrane mirror supported above an optically controlled photoconductive GaAs substrate. A 5  μm thick grid of patterned photoresist supports the 2  μm thick aluminized Mylar membrane. A conductive ZnO layer is placed on the back side of the GaAs wafer. A standard Michelson interferometer is used to measure mirror deformation data as a function of illumination, applied voltage, and frequency. A simplified analysis of device operation is also presented.

© 2006 Optical Society of America

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  1. C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).
  2. C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).
  3. C. Warde and J. E. Hubbard, Jr., " Membrane-mirror-light-valve-based infrared scene projector," in Characterization and Propagation of Sources and Backgrounds, W.R.Watkins and D.Clement, eds., Proc. SPIE 2223, 544- 557 ( 1994).
  4. L. E. Somers, " The photoemitter membrane light modulator image transducer," in Advances in Electronics and Electron Physics, J. D. McGee, ed. (Academic, 1972), Vol. 33A, p. 493.
    [CrossRef]
  5. F. Reizman, " An optical spatial phase modulator array activated by optical signals," in Proceedings of the 1969 Electro-Optical Systems Design Conference (IEEE, 1969), pp. 225- 230.
  6. A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).
  7. D. R. Pape, " Optically addressed membrane spatial light modulator," Opt. Eng. 24, 107- 110 ( 1985).
  8. K. Preston, Jr., " An array optical spatial phase modulator," in Proceedings of the IEEE International Solid State Circuits Conference (Institute of Electrical and Electronics Engineers, 1968), p. 100.
  9. D. R. Pape and L. J. Hornbeck, " Characteristics of the deformable mirror device for optical information processing," Opt. Eng. 22, 675- 681 ( 1983).
  10. L. J. Hornbeck, Deformable-Mirror Spatial Light Modulators, Vol. ICR1150 of SPIE Critical Reviews (SPIE, 1989), pp. 86- 102.
  11. N. Clark, " A silicon eye using MEMS micromirrors," MRS Bull. 26(4), 320- 324 ( 2001).
  12. C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
    [CrossRef]
  13. J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).
  14. B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

2003 (1)

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

1986 (1)

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

1985 (1)

D. R. Pape, " Optically addressed membrane spatial light modulator," Opt. Eng. 24, 107- 110 ( 1985).

1983 (1)

D. R. Pape and L. J. Hornbeck, " Characteristics of the deformable mirror device for optical information processing," Opt. Eng. 22, 675- 681 ( 1983).

Clark, N.

N. Clark, " A silicon eye using MEMS micromirrors," MRS Bull. 26(4), 320- 324 ( 2001).

Drehman, A.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Ersen, A.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Fisher, A. D.

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

Fukuda, R. C.

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

Genetti, G.

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

Goodhue, W.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Haji-saeed, B.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

Hornbeck, L. J.

D. R. Pape and L. J. Hornbeck, " Characteristics of the deformable mirror device for optical information processing," Opt. Eng. 22, 675- 681 ( 1983).

L. J. Hornbeck, Deformable-Mirror Spatial Light Modulators, Vol. ICR1150 of SPIE Critical Reviews (SPIE, 1989), pp. 86- 102.

Hubbard, J.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Hubbard, J. E.

C. Warde and J. E. Hubbard, Jr., " Membrane-mirror-light-valve-based infrared scene projector," in Characterization and Propagation of Sources and Backgrounds, W.R.Watkins and D.Clement, eds., Proc. SPIE 2223, 544- 557 ( 1994).

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

Ieong, H.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Khoury, J.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

Kierstead, J.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Kolluru, R.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Lee, J. N.

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

Leon, R.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Lerman, L.

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

Ling, L. C.

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

Liu, A. Q.

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Loizides, W.

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

McCann, J.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Pape, D. R.

D. R. Pape, " Optically addressed membrane spatial light modulator," Opt. Eng. 24, 107- 110 ( 1985).

D. R. Pape and L. J. Hornbeck, " Characteristics of the deformable mirror device for optical information processing," Opt. Eng. 22, 675- 681 ( 1983).

Preston, K.

K. Preston, Jr., " An array optical spatial phase modulator," in Proceedings of the IEEE International Solid State Circuits Conference (Institute of Electrical and Electronics Engineers, 1968), p. 100.

Pyburn, D.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Quan, C.

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Reizman, F.

F. Reizman, " An optical spatial phase modulator array activated by optical signals," in Proceedings of the 1969 Electro-Optical Systems Design Conference (IEEE, 1969), pp. 225- 230.

Sengupta, S. K.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Shang, H. M.

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Shrauger, J. M. V.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Somers, L. E.

L. E. Somers, " The photoemitter membrane light modulator image transducer," in Advances in Electronics and Electron Physics, J. D. McGee, ed. (Academic, 1972), Vol. 33A, p. 493.
[CrossRef]

Tay, C. J.

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Testorf, M.

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Wang, S. H.

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Wang, X. -Y.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

Warde, C.

C. Warde and J. E. Hubbard, Jr., " Membrane-mirror-light-valve-based infrared scene projector," in Characterization and Propagation of Sources and Backgrounds, W.R.Watkins and D.Clement, eds., Proc. SPIE 2223, 544- 557 ( 1994).

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

Woods, C. L.

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

Opt. Eng. (4)

A. D. Fisher, L. C. Ling, J. N. Lee, and R. C. Fukuda, " Photoemitter membrane light modulator," Opt. Eng. 25, 261- 268 ( 1986).

D. R. Pape, " Optically addressed membrane spatial light modulator," Opt. Eng. 24, 107- 110 ( 1985).

D. R. Pape and L. J. Hornbeck, " Characteristics of the deformable mirror device for optical information processing," Opt. Eng. 22, 675- 681 ( 1983).

C. Quan, S. H. Wang, C. J. Tay, A. Q. Liu, and H. M. Shang, " Deformation measurement of a micro-rf capacitive switch membrane using laser interferometry," Opt. Eng. 42, 92- 97 ( 2003).
[CrossRef]

Other (10)

J. Khoury, C. L. Woods, B. Haji-Saeed, S. K. Sengupta, W. Goodhue, and J. Kierstead, " Theoretical modeling of the operational mechanism of a photoconductive MEMS spatial light modulator under ac and dc bias," in Optical Pattern Recognition XV, D.P.Casasent and T.-H.Chao, eds., Proc. SPIE 5437, 288- 292 ( 2004).

B. Haji-saeed, R. Kolluru, D. Pyburn, R. Leon, S. K. Sengupta, M. Testorf, W. Goodhue, J. Khoury, A. Drehman, C. L. Woods, and J. Kierstead, " Photoconductive optically driven deformable membrane under high frequency bias: fabrication, characterization, and modeling," submitted to Appl. Opt.

L. J. Hornbeck, Deformable-Mirror Spatial Light Modulators, Vol. ICR1150 of SPIE Critical Reviews (SPIE, 1989), pp. 86- 102.

N. Clark, " A silicon eye using MEMS micromirrors," MRS Bull. 26(4), 320- 324 ( 2001).

K. Preston, Jr., " An array optical spatial phase modulator," in Proceedings of the IEEE International Solid State Circuits Conference (Institute of Electrical and Electronics Engineers, 1968), p. 100.

C. Warde, J. McCann, J. M. V. Shrauger, H. Ieong, A. Ersen, X. -Y. Wang, and J. Hubbard, " Membrane mirror light modulator technology," in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I.Cindrich, S.Lee, and R.L.Sutherland, eds., Proc. SPIE 3951, 191- 199 (2000).

C. Warde, J. E. Hubbard, Jr., G. Genetti, L. Lerman, and W. Loizides, " Membrane mirror light valve for high-definition projection display," in Electroluminescent Materials, Devices, and Large-Screen Displays, E. M. Conwell, M. Stolka, and M. R. Miller, eds., Proc. SPIE 1910,270- 279 ( 1993).

C. Warde and J. E. Hubbard, Jr., " Membrane-mirror-light-valve-based infrared scene projector," in Characterization and Propagation of Sources and Backgrounds, W.R.Watkins and D.Clement, eds., Proc. SPIE 2223, 544- 557 ( 1994).

L. E. Somers, " The photoemitter membrane light modulator image transducer," in Advances in Electronics and Electron Physics, J. D. McGee, ed. (Academic, 1972), Vol. 33A, p. 493.
[CrossRef]

F. Reizman, " An optical spatial phase modulator array activated by optical signals," in Proceedings of the 1969 Electro-Optical Systems Design Conference (IEEE, 1969), pp. 225- 230.

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Figures (13)

Fig. 1
Fig. 1

Photoconductive optically controlled spatial light modulator.

Fig. 2
Fig. 2

Membrane driven by dc voltage before light illumination.

Fig. 3
Fig. 3

Membrane driven by dc voltage before light illumination.

Fig. 4
Fig. 4

A, Transmitivity of GaAs versus wavelength; B, absorption coefficient α versus wavelength for GaAs.

Fig. 5
Fig. 5

Experimental arrangement.

Fig. 6
Fig. 6

A, Fringe of a 7 mm circular pixel device before sawtoothed voltage is applied; B, same fringe after driving by sawtoothed voltage; C, Difference between A and B; A′, entire surface of 7   mm circular pixel device before sawtoothed voltage is applied; B′, the same fringes after driving by sawtoothed voltage; C′, difference between A′ and B′.

Fig. 7
Fig. 7

A, Fringes of a 7   mm circular pixel device after focusing by a lens and before lamp illumination on the back; B, the same fringes after lamp illumination; C, the difference between A and B; A′, fringes of a 7   mm circular pixel device before lamp illumination; B′, the same fringes after lamp illumination; C′, difference between A′ and B′.

Fig. 8
Fig. 8

A, Fringes of a 1   mm × 1   mm device before laser illumination on the back; B, the same fringes after laser illumination; C, the difference between A and B; A′, fringes of a 2   mm × 2   mm device before lamp illumination; B′, the same fringes after lamp illumination; C′, the difference between A′ and B′.

Fig. 9
Fig. 9

A, Fringes of a 1   mm × 1   mm device focused on one pixel by a lens and before laser illumination on the back; B, the same fringes after laser illumination; C, difference between A and B; A′, fringes of a 2   mm × 2   mm device focused on one pixel before lamp illumination; B′, the same fringes after lamp illumination; C′, difference between A′ and B′.

Fig. 10
Fig. 10

Deformation of membrane (1 mm × 1 mm device) versus voltage for frequencies A, f = 2   Hz;   B,   f = 3   Hz ; C , f = 4   Hz;   D,   f = 7   Hz;   and   E,   f = 10   Hz .

Fig. 11
Fig. 11

Deformation of a membrane (1 mm × 1 mm device) versus frequency for voltages A, 80; B, 70; C, 60; D, 50; E, 40; and F, 30 V.

Fig. 12
Fig. 12

The deformation of a membrane (2 mm × 2 mm device) versus voltage for frequencies A, 2; B, 2.5; and C, 3   Hz and versus frequency for voltages D, 22; E, 20; and F, 15 V.

Fig. 13
Fig. 13

Deformation of a membrane ( 7   mm circular pixel device) versus frequency for voltages A, 60 and B, 50   V ; and versus voltage for C, frequency 2 Hz.

Equations (9)

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

C 2 πε 0 r 1     2 s + πε 0 r 1     2 h 2 s 2 ,
h = ε 0 r 1     2 V 2 8 T s 2 ,
C = C 1 C 2 C 1 + C 2 ,
V 2 = C 1 V C 1 + C 2 .
V 2 C 1 V s C 1 s + πε 0 r 1     2 .
h = ε 0 r 1     2 C 1     2 V 2 8 T ( C 1 s + ε 0 r 1     2 π ) 2 .
h = ε 0 r 1     2 V 2 8 T s 2 .
Δ h = h h = ε 0 r 1     2 V 2 8 T s 2 [ C 1     2 ( C 1 + C 0 ) 2 1 ] ,
d = 1 1 + 2 nft ) 2 ,

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