Abstract

We propose a simple multifrequency spatial-carrier and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry (LSI). In this system a wedge-shaped plate lateral shearing interferometer is used and, owing to the presence of tilt, a finite number of fringes parallel to the direction of the shear appears; hence a significant spatial-carrier frequency is generated at the focus position. We further enhance the spatial-carrier frequency either by changing the wavelength of the laser light or by slight defocusing. A synthetic interferogram with low spatial-carrier frequency is obtained by use of laser light of two wavelengths simultaneously in the lateral shear interferometer. We obtain the phase-shifted fringe patterns from the same setup by simply moving the wedge plate in an in-plane parallel direction, using a linear translator. The fringe projection system was tested for measurement of the three-dimensional shape of a discontinuous object. The present system has many advantages; e.g., it is a common-path interferometry and hence is insensitive to external vibrations, is compact in size, and is relatively inexpensive.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  2. H. J. Tiziani, “Optical metrology of engineering surfaces-scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, 1997).
  3. M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
    [CrossRef]
  4. K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
    [CrossRef]
  5. J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
    [CrossRef]
  6. Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37, 1005–1010 (1998).
    [CrossRef]
  7. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase measuring profilometry of a 3-D diffuse object,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef]
  8. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  9. X. Su, W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [CrossRef]
  10. S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
    [CrossRef]
  11. C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
    [CrossRef]
  12. C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
    [CrossRef] [PubMed]
  13. P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [CrossRef]
  14. J.-L. Li, H.-J. Su, X.-Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
    [CrossRef] [PubMed]
  15. R. Windecker, M. Fliescher, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3376 (1997).
    [CrossRef]
  16. J. Zhong, Y. Zhang, “Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry,” Appl. Opt. 40, 492–500 (2001).
    [CrossRef]
  17. D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, 1992).
  18. R. S. Kasana, K. J. Rosenbruch, “Determination of the refractive index of a lens using the Murty shearing interferometer,” Appl. Opt. 22, 3526–3531 (1983).
    [CrossRef] [PubMed]
  19. T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
    [CrossRef]
  20. C. Shakher, S. Prakash, “Monitoring/measurement of vibrations using shearing interferometry and interfermetric grating,” Opt. Lasers Eng. 38, 269–277 (2002).
    [CrossRef]
  21. P. Singh, C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
    [CrossRef]
  22. P. Singh, M. S. Faridi, C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
    [CrossRef]
  23. D. W. Griffin, “Phase-shifting shearing interferometer,” Opt. Lett. 26, 140–141 (2001).
    [CrossRef]
  24. J. B. Song, Y. W. Lee, I. W. Lee, Y.-H. Lee, “Simple phase-shifting method in a wedge-plate lateral-shearing interferometer,” Appl. Opt. 43, 3989–3992 (2004).
    [CrossRef] [PubMed]
  25. H.-H. Lee, J.-H. You, S.-H. Park, “Phase-shifting lateral shearing interferometer with two pairs of wedge plates,” Opt. Lett. 28, 2243–2245 (2003).
    [CrossRef] [PubMed]
  26. E. Mihaylova, M. Whelan, V. Toal, “Simple phase shifting lateral shearing interferometer,” Opt. Lett. 29, 1264–1266 (2004).
    [CrossRef] [PubMed]
  27. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef] [PubMed]
  28. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  29. Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  30. G. Margheri, C. Giunti, S. Manhart, R. Maurer, “Double wavelength superheterodyne interferometer for absolute ranging with submillimeter resolution: results obtained with a demonstration model by use of rough and reflective targets,” Appl. Opt. 36, 6211–6216 (1997).
    [CrossRef]
  31. C. C. Williams, H. K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
    [CrossRef] [PubMed]
  32. H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferferometer,” Rev. Sci. Instrum. 53, 641–643 (1982).
    [CrossRef]
  33. R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
    [CrossRef]
  34. G. L. Bourdet, A. G. Orszag, “Absolute distance measurement by CO2 laser multiwavelength interferometry,” Appl. Opt. 18, 225–227 (1979).
    [CrossRef] [PubMed]
  35. P. de Groot, “Unusual techniques for absolute distance measurement,” Opt. Eng. 40, 28–32 (2001).
    [CrossRef]
  36. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  37. Y. Ishii, R. Onodera, “Two-wavelength laser diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
    [CrossRef] [PubMed]
  38. D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
    [CrossRef]
  39. D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
    [CrossRef]

2005

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

2004

2003

H.-H. Lee, J.-H. You, S.-H. Park, “Phase-shifting lateral shearing interferometer with two pairs of wedge plates,” Opt. Lett. 28, 2243–2245 (2003).
[CrossRef] [PubMed]

P. Singh, C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

2002

C. Shakher, S. Prakash, “Monitoring/measurement of vibrations using shearing interferometry and interfermetric grating,” Opt. Lasers Eng. 38, 269–277 (2002).
[CrossRef]

2001

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

X. Su, W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

J. Zhong, Y. Zhang, “Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry,” Appl. Opt. 40, 492–500 (2001).
[CrossRef]

D. W. Griffin, “Phase-shifting shearing interferometer,” Opt. Lett. 26, 140–141 (2001).
[CrossRef]

P. de Groot, “Unusual techniques for absolute distance measurement,” Opt. Eng. 40, 28–32 (2001).
[CrossRef]

2000

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1999

M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
[CrossRef]

1998

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37, 1005–1010 (1998).
[CrossRef]

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

1997

1995

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

1991

1989

1986

1985

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
[CrossRef]

1984

1983

1982

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[CrossRef]

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferferometer,” Rev. Sci. Instrum. 53, 641–643 (1982).
[CrossRef]

1979

1973

1971

Bourdet, G. L.

Brown, G. M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Case, S. K.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, W.

X. Su, W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Cheng, Y. Y.

Chiang, F.-P.

P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Choi, Y. B.

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37, 1005–1010 (1998).
[CrossRef]

Dandliker, R.

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

de Groot, P.

P. de Groot, “Unusual techniques for absolute distance measurement,” Opt. Eng. 40, 28–32 (2001).
[CrossRef]

Facchini, M.

M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
[CrossRef]

Faridi, M. S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

P. Singh, M. S. Faridi, C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Fleischer, M.

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

Fliescher, M.

R. Windecker, M. Fliescher, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3376 (1997).
[CrossRef]

Fujigaki, M.

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

Giunti, C.

Griffin, D. W.

Halioua, M.

He, X. Y.

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Huang, P. S.

P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Hug, K.

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

Ikeda, Y.

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

Ina, H.

Ishii, Y.

Iwata, K.

Jacquot, P.

M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
[CrossRef]

Jalkio, J. A.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
[CrossRef]

Kamiya, K.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Kang, X.

Kasana, R. S.

Kikuta, H.

Kim, R. C.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
[CrossRef]

Kim, S. W.

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37, 1005–1010 (1998).
[CrossRef]

Kobayashi, S.

Korner, K.

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

Lee, H.-H.

Lee, I. W.

Lee, Y. W.

Lee, Y.-H.

Lehmann, M.

M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
[CrossRef]

Li, J.-L.

Liu, H. C.

Manhart, S.

Margheri, G.

Matsumoto, H.

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferferometer,” Rev. Sci. Instrum. 53, 641–643 (1982).
[CrossRef]

Maurer, R.

Mehta, D. S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

Mihaylova, E.

Mirza, S.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

Miyashiro, H.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Morimoto, Y.

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

Nagata, R.

Nomura, T.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Okuda, S.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Onodera, R.

Orszag, A. G.

Park, S.-H.

Polhemus, C.

Politch, J.

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

Prakash, S.

C. Shakher, S. Prakash, “Monitoring/measurement of vibrations using shearing interferometry and interfermetric grating,” Opt. Lasers Eng. 38, 269–277 (2002).
[CrossRef]

Quan, C.

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Rosenbruch, K. J.

Shakher, C.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

P. Singh, M. S. Faridi, C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

P. Singh, C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

C. Shakher, S. Prakash, “Monitoring/measurement of vibrations using shearing interferometry and interfermetric grating,” Opt. Lasers Eng. 38, 269–277 (2002).
[CrossRef]

Shang, H. M.

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Singh, P.

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

P. Singh, M. S. Faridi, C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

P. Singh, C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

Song, J. B.

Song, M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Srinivasan, V.

Su, H.-J.

Su, X.

X. Su, W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Su, X.-Y.

Takeda, M.

Tashiro, H.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Tay, C. J.

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Tiziani, H. J.

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

R. Windecker, M. Fliescher, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3376 (1997).
[CrossRef]

H. J. Tiziani, “Optical metrology of engineering surfaces-scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, 1997).

Toal, V.

Wang, C. F.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Whelan, M.

Wickramasinghe, H. K.

Williams, C. C.

Windecker, R.

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

R. Windecker, M. Fliescher, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3376 (1997).
[CrossRef]

Wyant, J. C.

Yoneyana, S.

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

Yoshikawa, K.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

You, J.-H.

Zhang, C.

P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Zhang, Y.

Zhong, J.

Zimmermann, E.

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

Appl. Opt.

G. L. Bourdet, A. G. Orszag, “Absolute distance measurement by CO2 laser multiwavelength interferometry,” Appl. Opt. 18, 225–227 (1979).
[CrossRef] [PubMed]

R. S. Kasana, K. J. Rosenbruch, “Determination of the refractive index of a lens using the Murty shearing interferometer,” Appl. Opt. 22, 3526–3531 (1983).
[CrossRef] [PubMed]

V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase measuring profilometry of a 3-D diffuse object,” Appl. Opt. 23, 3105–3108 (1984).
[CrossRef]

Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef] [PubMed]

H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
[CrossRef] [PubMed]

J.-L. Li, H.-J. Su, X.-Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
[CrossRef] [PubMed]

G. Margheri, C. Giunti, S. Manhart, R. Maurer, “Double wavelength superheterodyne interferometer for absolute ranging with submillimeter resolution: results obtained with a demonstration model by use of rough and reflective targets,” Appl. Opt. 36, 6211–6216 (1997).
[CrossRef]

J. Zhong, Y. Zhang, “Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry,” Appl. Opt. 40, 492–500 (2001).
[CrossRef]

C. Quan, C. J. Tay, X. Kang, X. Y. He, H. M. Shang, “Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting,” Appl. Opt. 42, 2329–2335 (2003).
[CrossRef] [PubMed]

J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
[CrossRef] [PubMed]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

J. B. Song, Y. W. Lee, I. W. Lee, Y.-H. Lee, “Simple phase-shifting method in a wedge-plate lateral-shearing interferometer,” Appl. Opt. 43, 3989–3992 (2004).
[CrossRef] [PubMed]

Exp. Tech.

M. Lehmann, P. Jacquot, M. Facchini, “Shape measurement of large surfaces by fringe projection,” Exp. Tech. 23, 31–35 (1999).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase-shifting,” Opt. Commun. 189, 21–29 (2001).
[CrossRef]

Opt. Eng.

P. S. Huang, C. Zhang, F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

R. Windecker, M. Fliescher, H. J. Tiziani, “Three-dimensional topometry with stereo microscopes,” Opt. Eng. 36, 3372–3376 (1997).
[CrossRef]

K. Korner, R. Windecker, M. Fleischer, H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40, 1653–1660 (2001).
[CrossRef]

J. A. Jalkio, R. C. Kim, S. K. Case, “Three-dimensional inspection using multi-stripe structured light,” Opt. Eng. 24, 966–974 (1985).
[CrossRef]

Y. B. Choi, S. W. Kim, “Phase-shifting grating projection moiré topography,” Opt. Eng. 37, 1005–1010 (1998).
[CrossRef]

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

S. Yoneyana, Y. Morimoto, M. Fujigaki, Y. Ikeda, “Three-dimensional surface profile measurement of a moving object by a spatial-offset phase stepping method,” Opt. Eng. 42, 137–142 (2003).
[CrossRef]

R. Dandliker, K. Hug, J. Politch, E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34, 2407–2412 (1995).
[CrossRef]

P. de Groot, “Unusual techniques for absolute distance measurement,” Opt. Eng. 40, 28–32 (2001).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Two-wavelength lateral shearing interferometry,” Opt. Eng. 44, 85,603–85,609 (2005).
[CrossRef]

D. S. Mehta, P. Singh, M. S. Faridi, S. Mirza, C. Shakher, “Distance measurement with extended range using lateral shearing interferometry and Fourier transform fringe analysis,” Opt. Eng. 44, 63,602–63,611 (2005).
[CrossRef]

P. Singh, C. Shakher, “Measurement of the temperature of a gaseous flame using a shearing plate,” Opt. Eng. 42, 80–85 (2003).
[CrossRef]

P. Singh, M. S. Faridi, C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Opt. Lasers Eng.

C. Shakher, S. Prakash, “Monitoring/measurement of vibrations using shearing interferometry and interfermetric grating,” Opt. Lasers Eng. 38, 269–277 (2002).
[CrossRef]

X. Su, W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Opt. Lett.

Precis. Eng.

T. Nomura, K. Kamiya, H. Miyashiro, S. Okuda, H. Tashiro, K. Yoshikawa, “Shape measurements of mirror surfaces with lateral-shearing interferometer during machine running,” Precis. Eng. 22, 185–189 (1998).
[CrossRef]

Rev. Sci. Instrum.

H. Matsumoto, “Length measurement using infrared two-wavelength He–Xe laser interferferometer,” Rev. Sci. Instrum. 53, 641–643 (1982).
[CrossRef]

Other

D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, 1992).

H. J. Tiziani, “Optical metrology of engineering surfaces-scope and trends,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, 1997).

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 (5)

Fig. 1
Fig. 1

Schematic diagram illustrating a two-wavelength lateral shearing interferometer based on a wedged plate.

Fig. 2
Fig. 2

Shearing interferograms at focus positions corresponding to (a) λ1, (b) λ2, and (c) Λ. (d), (e), (f) Corresponding Fourier spectra.

Fig. 3
Fig. 3

Shearing interferograms at defocus positions corresponding to (a) λ1, (b) λ2, and (c) Λ. (d), (e), (f) Corresponding Fourier spectra.

Fig. 4
Fig. 4

Phase-shifted shearing interferograms: (a) 0°, (b) 90°, (c) 180°, (d) 270°, (e) 360°.

Fig. 5
Fig. 5

(a) Example of a shearing interferogram projected onto a discontinuous object. (b) Reconstructed 3-D shape of the object.

Equations (12)

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

Δ W ( x , y ) = W ( x , y ) W ( x S , y ) = E k y = n k λ k ,
Δ W ( x , y ) = W ( x , y ) W ( x S , y ) = 2 D x k S + E k y = n k λ k ,
γ k = tan 1 ( 2 D x k S E k ) .
Δ W ( x , y ) = W ( x , y ) W ( x S , y ) = E y = N Λ ,
( W x ) S = n k λ k ,
( W X ) S = N Λ .
ϕ 1 ( x , y ) = 2 π λ 1 OPD ,
ϕ 2 ( x , y ) = 2 π λ 2 OPD .
Φ ( x , y ) = ϕ 1 ( x , y ) ϕ 2 ( x , y ) = 2 π ( 1 λ 1 1 λ 2 ) OPD = 2 π Λ OPD .
S = h sin 2 θ ( n 2 sin 2 θ ) 1 / 2 ,
ϕ k ( ρ 0 ) = 2 π λ k OPD = 2 π λ k β ρ 0 cos θ = 4 π α ρ 0 ( n k 2 sin 2 θ ) 1 / 2 λ k ,
ρ 2 π = λ k 2 α ( n k 2 sin 2 θ ) 1 / 2 .

Metrics