Abstract

Optical profilometry is widely applied for measuring the morphology of objects by projecting predetermined patterns on them. In this technique, the compact size is one of the interesting issues for practical applications. The generation of pattern by the interference of coherent light sources has a potential to reduce the dimension of the illumination part. Moreover, this method can make fine patterns without projection optics, and the illumination part is free of restriction from the numerical aperture of the projection optics. In this paper, a phase-shifting profilometry is implemented by using a single liquid crystal (LC) cell. The LC phase modulator is designed to generate the interference patterns with several different spatial frequencies by changing selection of the spacing between the micro-pinholes. We manufactured the LC phase modulator and calibrated it by measuring the phase modulation amount depending on an applied voltage. Our optical profilometry using the single LC cell can generate multi-spatial frequency patterns as well as four steps of the phase-shifted patterns. This method can be implemented compactly, and the reconstructed depth profile is obtained without a phase-unwrapping algorithm.

© 2012 Optical Society of America

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References

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  1. M. Chang and C. S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
    [CrossRef]
  2. F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
    [CrossRef]
  3. C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
    [CrossRef]
  4. M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
    [CrossRef]
  5. M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
    [CrossRef]
  6. D. S. Metha, S. K. Dubey, M. M. Hossain, and C. Shakher, “Simple multifrequency and phase shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry,” Appl. Opt. 44, 7515–7521 (2005).
    [CrossRef]
  7. C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
    [CrossRef]
  8. T. C. Kraan, T. V. Bommel, and R. A. M. Hikmet, “Modeling liquid-crystal gradient-index lenses,” J. Opt. Soc. Am. A 24, 3467–3477 (2007).
    [CrossRef]
  9. D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
    [CrossRef]
  10. H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
    [CrossRef]
  11. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
    [CrossRef]
  12. K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
    [CrossRef]
  13. W. Su and H. Liu, “Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities,” Opt. Express 14, 9178–9187 (2006).
    [CrossRef]
  14. E. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express 17, 7818–7830 (2009).
    [CrossRef]
  15. E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D. W. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry,” Opt. Express 13, 1561–1569 (2005).
    [CrossRef]
  16. E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, B. G. Curcio, M. Muramatsu, and D. Soga, “Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers,” J. Opt. Soc. Am. A 22, 2872–2879 (2005).
    [CrossRef]
  17. M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
    [CrossRef]
  18. E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
    [CrossRef]
  19. J. Hahn, H. Kim, and B. Lee, “Optimization of the spatial light modulation with twisted nematic liquid crystals by a genetic algorithm,” Appl. Opt. 47, D87–D95 (2008).
    [CrossRef]

2010 (1)

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (2)

T. C. Kraan, T. V. Bommel, and R. A. M. Hikmet, “Modeling liquid-crystal gradient-index lenses,” J. Opt. Soc. Am. A 24, 3467–3477 (2007).
[CrossRef]

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

2006 (3)

W. Su and H. Liu, “Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities,” Opt. Express 14, 9178–9187 (2006).
[CrossRef]

M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

2005 (4)

2004 (2)

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Q. Mu, “Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision,” Opt. Express 12, 6403–6409 (2004).
[CrossRef]

K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
[CrossRef]

2002 (1)

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

2001 (1)

F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
[CrossRef]

2000 (2)

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

1993 (1)

M. Chang and C. S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

Barbosa, E. A.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, B. G. Curcio, M. Muramatsu, and D. Soga, “Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers,” J. Opt. Soc. Am. A 22, 2872–2879 (2005).
[CrossRef]

Bommel, T. V.

Burgarth, V.

K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
[CrossRef]

Cao, Z.

Chang, M.

M. Chang and C. S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

Chicharo, J. F.

Curcio, B. G.

Dubey, S. K.

Fan, Y. H.

H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
[CrossRef]

Feldkhum, D. L.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Filho, A. A. V.

Gesualdi, M. R. R.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, B. G. Curcio, M. Muramatsu, and D. Soga, “Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers,” J. Opt. Soc. Am. A 22, 2872–2879 (2005).
[CrossRef]

Hagen, K. M.

K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
[CrossRef]

Hahn, J.

Hikmet, R. A. M.

Ho, C. S.

M. Chang and C. S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

Hossain, M. M.

Hu, L.

Huang, H.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

Itoh, M.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

Jang, E.

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

Jung, U.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

Kang, S.-W.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

Karapinar, R.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

Kim, E.

Kim, H.

Kim, H.-R.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

Kim, J.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

Kraan, T. C.

Lalor, M. J.

F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
[CrossRef]

Lee, B.

Lee, S. D.

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

Li, D.

Li, E. B.

Lima, E. A.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

Lin, Y. H.

H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
[CrossRef]

Liu, H.

Liu, Y.

Lucchetta, D. E.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

Manni, A.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

Mermeistein, M. S.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Metha, D. S.

Mu, Q. Q.

Muramatsu, M.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, B. G. Curcio, M. Muramatsu, and D. Soga, “Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers,” J. Opt. Soc. Am. A 22, 2872–2879 (2005).
[CrossRef]

Park, C.-S.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

Park, K.-W.

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

Peng, X.

Ren, H.

H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
[CrossRef]

Shakher, C.

Shirley, L. G.

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Simoni, F.

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

Soga, D.

M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

E. A. Barbosa, A. A. V. Filho, M. R. R. Gesualdi, B. G. Curcio, M. Muramatsu, and D. Soga, “Single-exposure, photorefractive holographic surface contouring with multiwavelength diode lasers,” J. Opt. Soc. Am. A 22, 2872–2879 (2005).
[CrossRef]

Su, W.

Tsai, M.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

Wu, F.

F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
[CrossRef]

Wu, S. T.

H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
[CrossRef]

Xi, J.

Xuan, L.

Yao, J. Q.

Yatagai, T.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

Yu, C. J.

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

Zeid, A. A.

K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
[CrossRef]

Zhang, D. W.

Zhang, H.

F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulator using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86, 141110 (2005).
[CrossRef]

Exp. Mech. (1)

M. Chang and C. S. Ho, “Phase-measuring profilometry using sinusoidal grating,” Exp. Mech. 33, 117–122 (1993).
[CrossRef]

J. Appl. Phys. (1)

D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, “Phase-only modulation by nanosized polymer-dispersed liquid crystal,” J. Appl. Phys. 91, 6060–6065 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

K. M. Hagen, V. Burgarth, and A. A. Zeid, “Profilometry with a multi-wavelength diode laser interferometer,” Meas. Sci. Technol. 15, 741–746 (2004).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

C.-S. Park, K.-W. Park, U. Jung, J. Kim, S.-W. Kang, and H.-R. Kim, “Dynamic fringe pattern generation using an electrically tunable liquid crystal Fabry-Perot cell for a miniaturized optical 3-D surface scanning profilometer,” Mol. Cryst. Liq. Cryst. 526, 28–37 (2010).
[CrossRef]

C. J. Yu, E. Jang, H.-R. Kim, and S. D. Lee, “Design and fabrication of high-performance liquid crystal gratings,” Mol. Cryst. Liq. Cryst. 454, 765–778 (2006).
[CrossRef]

Opt. Commun. (1)

F. Wu, H. Zhang, and M. J. Lalor, “A novel design for fiber optic interferometric fringe projection phase-shifting 3-D profilometry,” Opt. Commun. 187, 347–357 (2001).
[CrossRef]

Opt. Eng. (3)

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Multiwavelength fringe scanning profilometry for wide gapped sample,” Opt. Eng. 39, 970–977 (2000).
[CrossRef]

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, “Enhanced multiwavelength holographic profilometry by laser mode selection,” Opt. Eng. 46, 075601 (2007).
[CrossRef]

M. S. Mermeistein, D. L. Feldkhum, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (1)

M. R. R. Gesualdi, D. Soga, and M. Muramatsu, “Real-Time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique,” Opt. Lasers Eng. 44, 56–67 (2006).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of the LC phase modulator for utilizing four-step phase shifting and multi-spatial frequencies with a single cell.

Fig. 2.
Fig. 2.

Structure of the LC director distribution depending on the patterned electrode on the backside glass substrate, (a) without and (b) with an applied voltage, which correspond to the voltage-variable OPL region ( OPL I ) and the fixed OPL region ( OPL II ), respectively.

Fig. 3.
Fig. 3.

Fabrication process of the backside glass substrate with the patterned ITO electrode and the micro-pinhole array by the patterned Al layer, which are prepared for phase shifting and multi-spatial frequency switching, respectively.

Fig. 4.
Fig. 4.

Experimental setup for measuring the phase modulation of the LC layer according to an applied voltage.

Fig. 5.
Fig. 5.

Fringe patterns generated by two micro-pinholes ( Δ g = 600 μm ), where the projected images are obtained at the relative phase modulation amounts of (a)  M phase = 0 , (b)  M phase = π / 2 , (c)  M phase = π , and (d)  M phase = 3 π / 2 .

Fig. 6.
Fig. 6.

(a) Relative phase modulation amounts of the LC phase modulator depending on Δ g of the micro-pinhole arrays according to the applied voltages; (b) voltage conditions required for the four-step phase modulations of the fringe patterns projected by two pinholes of Δ g = 600 μm among the pinhole array.

Fig. 7.
Fig. 7.

Geometric parameters of the optical profilometry.

Fig. 8.
Fig. 8.

Experimental setup of the optical profilometry system with the LC phase modulator.

Fig. 9.
Fig. 9.

(a) Object with the slanted surface and the fringe patterns projected on the object with various spatial frequencies by switching two micro-pinholes used for projection: (b)  Δ g = 200 μm , (c)  Δ g = 400 μm , (d)  Δ g = 600 μm , and (e)  Δ g = 800 μm .

Fig. 10.
Fig. 10.

3D depth profiles of the object shown in Fig. 9(a), which is reconstructed (a) with two spatial frequencies and (b) with multi-spatial frequencies.

Fig. 11.
Fig. 11.

(a) Front-view image of three spheres ( diameter = 40 mm ) used as the objects, which are arranged at different positions and depths; (b)–(e) the fringe patterns projected on the object with various spatial frequencies by using two micro-pinholes of Δ g = 200 , 400, 600, and 800 μm, respectively.

Fig. 12.
Fig. 12.

Reconstructed (a) 2D position profile and (b) 3D depth profile obtained from the fringe patterns projected on the object of Fig. 11(a).

Equations (16)

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

I int ( m ) = I int , 0 cos ( 2 π m p / Λ + M Phase ) ,
Λ = f λ / Δ g .
X ( k ) = m = 1 N I int , 0 cos ( 2 π m p / Λ + M Phase ) ω N ( m 1 ) ( k 1 ) ,
M Phase = angle [ X ( p N / Λ + 1 ) ] .
z POI z C = ( y POI y C ) cot ( ϕ C θ POI ) ,
z POI z M = ( y POI y M ) cot α .
z POI = ( y C y M ) ( z C z M ) tan α tan α + tan ( ϕ C θ POI ) + z C ,
y POI = ( z C z M ) ( y C y M ) cot α cot α + cot ( ϕ C θ POI ) + y C .
cos ( 2 π f n η ) = [ I n , 0 ( η ) I n , π ( η ) ] / 2 ,
sin ( 2 π f n η ) = [ I n , 3 π / 2 ( η ) I n , π / 2 ( η ) ] / 2 ,
f n = n f 1 .
H n ( η ) = cos ( 2 π f n η ) + j sin ( 2 π f n η ) .
W ( η ; s ) = real [ n exp ( j 2 π f n s ) H n ( η ) ] ,
α = α n f n s ,
R ( η ) = max { W ( η ; s ) } ,
P ( η ) = { s | W ( η ; s ) = R ( η ) } .

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