Abstract

We propose a novel axial nano-displacement measuring approach. Based on asymmetrical illumination, the axial drifts of the sample plane can be measured by detecting the position of the centroid of the focal spot. Both CCD and QD are used as the detector in the system and two data processing models are designed. With a relatively simple and applicable configuration, the proposed system can realize a wide measuring range of >4λand a high axial resolution of 2nm. Moreover, the presented approach is immune to the influence caused by the energy fluctuation of the laser source. Possessing these advantages, this measuring method has big potential to be applied in modern engineering and scientific researches.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).
  2. A. A. Michelson, “The relative motion of the Earth and the Luminiferous ether,” Am. J. Sci.22, 120–129 (1881).
  3. S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Precis. Eng.17(4), 258–265 (1995).
    [CrossRef]
  4. S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
    [CrossRef]
  5. T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
    [CrossRef]
  6. C. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun.215(1-3), 17–23 (2003).
    [CrossRef]
  7. S. Olyaee and M. Nejad, “Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system,” Optoelectronics, IET1(5), 211–220 (2007).
    [CrossRef]
  8. S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
    [CrossRef]
  9. K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE8082, 80823O (2011).
    [CrossRef]
  10. K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sensor Review31(4), 358–367 (2011).
    [CrossRef]
  11. M. Minsky, “Microscopy apparatus,” (U.S.P.Office (Ed.).US, 1961), p. 5.
  12. W. Q. Zhao, J. B. Tan, and L. R. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express12(21), 5013–5021 (2004).
    [CrossRef] [PubMed]
  13. D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
    [CrossRef]
  14. C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
    [CrossRef] [PubMed]
  15. Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
    [CrossRef]
  16. L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt.51(13), 2379–2387 (2012).
    [CrossRef] [PubMed]
  17. D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
    [CrossRef]
  18. B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 253, 358–379 (1959).
    [CrossRef]
  19. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
    [CrossRef]
  20. C. Altucci, R. Bruzzese, D. D'Antuoni, C. de Lisio, and S. Solimeno, “Harmonic generation in gases by use of Bessel-Gauss laser beams,” J. Opt. Soc. Am. B17(1), 34–42 (2000).
    [CrossRef]
  21. M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
    [CrossRef]
  22. X. Hao, C. F. Kuang, Y. H. Li, and X. Liu, “Continuous manipulation of doughnut focal spot in a large scale,” Opt. Express20(12), 12692–12698 (2012).
    [CrossRef] [PubMed]

2012 (5)

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
[CrossRef]

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt.51(13), 2379–2387 (2012).
[CrossRef] [PubMed]

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

X. Hao, C. F. Kuang, Y. H. Li, and X. Liu, “Continuous manipulation of doughnut focal spot in a large scale,” Opt. Express20(12), 12692–12698 (2012).
[CrossRef] [PubMed]

2011 (2)

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE8082, 80823O (2011).
[CrossRef]

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sensor Review31(4), 358–367 (2011).
[CrossRef]

2010 (1)

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

2007 (1)

S. Olyaee and M. Nejad, “Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system,” Optoelectronics, IET1(5), 211–220 (2007).
[CrossRef]

2006 (1)

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

2004 (1)

2003 (1)

C. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun.215(1-3), 17–23 (2003).
[CrossRef]

2002 (3)

T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
[CrossRef]

S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
[CrossRef]

2000 (1)

1999 (1)

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

1995 (1)

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Precis. Eng.17(4), 258–265 (1995).
[CrossRef]

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

1881 (1)

A. A. Michelson, “The relative motion of the Earth and the Luminiferous ether,” Am. J. Sci.22, 120–129 (1881).

Ali, M. Y.

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Altucci, C.

Borghi, R.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
[CrossRef]

Bruzzese, R.

Choi, H. S.

T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
[CrossRef]

Cosijns, S.

S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

D'Antuoni, D.

de Lisio, C.

Eom, T. B.

T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
[CrossRef]

Fujigaki, M.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Haitjema, H.

S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

Hao, X.

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

X. Hao, C. F. Kuang, Y. H. Li, and X. Liu, “Continuous manipulation of doughnut focal spot in a large scale,” Opt. Express20(12), 12692–12698 (2012).
[CrossRef] [PubMed]

Hao, X. A.

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Hosoe, S.

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Precis. Eng.17(4), 258–265 (1995).
[CrossRef]

Iwasaki, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Ku, Y. L.

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

Kuang, C. F.

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

X. Hao, C. F. Kuang, Y. H. Li, and X. Liu, “Continuous manipulation of doughnut focal spot in a large scale,” Opt. Express20(12), 12692–12698 (2012).
[CrossRef] [PubMed]

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt.51(13), 2379–2387 (2012).
[CrossRef] [PubMed]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
[CrossRef]

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Lee, S. K.

T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
[CrossRef]

Li, H. F.

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

Li, L.

Li, Y. H.

Liu, X.

X. Hao, C. F. Kuang, Y. H. Li, and X. Liu, “Continuous manipulation of doughnut focal spot in a large scale,” Opt. Express20(12), 12692–12698 (2012).
[CrossRef] [PubMed]

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt.51(13), 2379–2387 (2012).
[CrossRef] [PubMed]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
[CrossRef]

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Luo, D.

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
[CrossRef]

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

L. Li, C. F. Kuang, D. Luo, and X. Liu, “Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses,” Appl. Opt.51(13), 2379–2387 (2012).
[CrossRef] [PubMed]

Madanipour, K.

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE8082, 80823O (2011).
[CrossRef]

Matsumoto, H.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Matui, T.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

Michelson, A. A.

A. A. Michelson, “The relative motion of the Earth and the Luminiferous ether,” Am. J. Sci.22, 120–129 (1881).

Morimoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

Nejad, M.

S. Olyaee and M. Nejad, “Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system,” Optoelectronics, IET1(5), 211–220 (2007).
[CrossRef]

Ohnishi, J.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Olyaee, S.

S. Olyaee and M. Nejad, “Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system,” Optoelectronics, IET1(5), 211–220 (2007).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Porras, M. A.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
[CrossRef]

Qiu, L. R.

Ratnam, M.

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sensor Review31(4), 358–367 (2011).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 253, 358–379 (1959).
[CrossRef]

Santarsiero, M.

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
[CrossRef]

Schellekens, P.

S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

Seta, K.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Solimeno, S.

Suzuki, N.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Tan, J. B.

Tavassoly, M. T.

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE8082, 80823O (2011).
[CrossRef]

Wang, T. T.

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 253, 358–379 (1959).
[CrossRef]

Wu, C.

C. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun.215(1-3), 17–23 (2003).
[CrossRef]

Yamamoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

Yen, K.

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sensor Review31(4), 358–367 (2011).
[CrossRef]

Yokoyama, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Zhao, W. Q.

Am. J. Sci. (1)

A. A. Michelson, “The relative motion of the Earth and the Luminiferous ether,” Am. J. Sci.22, 120–129 (1881).

Appl. Opt. (1)

Exp. Mech. (1)

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech.21, 20–34 (2006).

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol.10(12), 1233–1239 (1999).
[CrossRef]

Opt. Commun. (3)

C. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry,” Opt. Commun.215(1-3), 17–23 (2003).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

M. A. Porras, R. Borghi, and M. Santarsiero, “Suppression of dispersive broadening of light pulses with Bessel-Gauss beams,” Opt. Commun.206(4-6), 235–241 (2002).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

D. Luo, C. F. Kuang, and X. Liu, “Fiber-based chromatic confocal microscope with Gaussian fitting method,” Opt. Laser Technol.44(4), 788–793 (2012).
[CrossRef]

Opt. Lasers Eng. (2)

Y. L. Ku, C. F. Kuang, D. Luo, T. T. Wang, and H. F. Li, “Differential internal multi-reflection method for nano-displacement measurement,” Opt. Lasers Eng.50(10), 1445–1449 (2012).
[CrossRef]

D. Luo, C. F. Kuang, X. Hao, and X. Liu, “High-precision laser alignment technique based on spiral phase plate,” Opt. Lasers Eng.50(7), 944–949 (2012).
[CrossRef]

Optoelectronics, IET (1)

S. Olyaee and M. Nejad, “Nonlinearity and frequency-path modelling of three-longitudinal-mode nanometric displacement measurement system,” Optoelectronics, IET1(5), 211–220 (2007).
[CrossRef]

Precis. Eng. (2)

S. Cosijns, H. Haitjema, and P. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Precis. Eng.17(4), 258–265 (1995).
[CrossRef]

Proc. SPIE (1)

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE8082, 80823O (2011).
[CrossRef]

Rev. Sci. Instrum. (2)

T. B. Eom, H. S. Choi, and S. K. Lee, “Frequency stabilization of an internal mirror He–Ne laser by digital control,” Rev. Sci. Instrum.73(1), 221–224 (2002).
[CrossRef]

C. F. Kuang, M. Y. Ali, X. A. Hao, T. T. Wang, and X. Liu, “Superresolution confocal technology for displacement measurements based on total internal reflection,” Rev. Sci. Instrum.81(10), 103702 (2010).
[CrossRef] [PubMed]

Sensor Review (1)

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sensor Review31(4), 358–367 (2011).
[CrossRef]

Other (2)

M. Minsky, “Microscopy apparatus,” (U.S.P.Office (Ed.).US, 1961), p. 5.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 253, 358–379 (1959).
[CrossRef]

Supplementary Material (1)

» Media 1: AVI (1220 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

The schematic optical diagram

Fig. 2
Fig. 2

(a) The diagram of the phase plate. (b) Intensity distribution of the beam wavefront after passing through the phase plate.

Fig. 3
Fig. 3

The beam intensity distribution on the sample plane when the sample plane is at different axial positions. (a) z = −1.6 λ. (b) z = −0.8 λ. (c) z = 0 λ. (d) z = 0.8 λ.(e) z = 1.6 λ .The calculation is taken out with an objective lens of NA = 1.4. (Media 1)

Fig. 4
Fig. 4

The simulated response curves in the CCD detecting mode (a) and QD detecting mode (b) under different polarization states: X direction linear (red), Y direction linear (green), circular (blue), radial (black) and azimuthal (brown). Inset: the magnified views of the regions indicated by black dashed boxes.

Fig. 5
Fig. 5

Curve fitting of the response curves. (a) CCD detecting mode. (b) QD detecting mode.

Fig. 6
Fig. 6

Large-scale experiment results. (a) The axial displacement of the sample plane in CCD detecting mode. (b) The axial displacement of the sample plane in QD detecting mode. (c) The waveform of D c when the sample plane moves as (a). (d) The waveform of D q when the sample plane moves as (b).

Fig. 7
Fig. 7

Resolution experiment results. (a) The axial displacement of the sample plane in determining the resolution of CCD detecting mode. (b) The axial displacement of the sample plane in determining the resolution of QD detecting mode. (c) The waveform of D c when the sample plane moves as (a). (d) The waveform of D q when the sample plane moves as (b).

Fig. 8
Fig. 8

Comparison of response curves of Gaussian beam (blue curve) and Bessel-Gauss beam (red curve) in CCD detecting mode (a) and QD detecting mode (b).

Fig. 9
Fig. 9

(a) Quarter-circle filter. (b) Comparison of response curves of semi-circle illumination (blue) and quarter-circle illumination (red) in CCD detecting mode. (c) Comparison of response curves of semi-circle illumination (blue) and quarter-circle illumination (red) in QD detecting mode.

Equations (6)

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

E(x',y',z)= e ikz iλz E(x,y)O(x,y) e ik 2z [ (x'x) 2 + (y'y) 2 ] dxdy
E(x,y)=A e [ ( x 2 + y 2 )/ a 2 ]
O(x,y)={ 1,<x<,<y<0 1,<x<,0y<
E( r 2 , φ 2 , z 2 )=iC Ω sin(θ) A 1 (θ,φ) A 2 (θ,φ)[ p x p y p z ] e ikn( z 2 cosθ+ r 2 sinθcos(φ φ 2 )) dθdφ
D c = i=1 N y ci P i i=1 N P i
D q = U 1 + U 2 U 3 U 4 U 1 + U 2 + U 3 + U 4

Metrics