Abstract

Phase measurement techniques using a single-shot carrier fringe pattern play an important role in optical science and technology and have been widely used for various applications. In this paper, we focus on the comparative study of two major fringe analysis techniques, the sampling moiré (SM) and the windowed Fourier transform (WFT). While SM converts a single-fringe pattern to multiple phase-shifted moiré fringe patterns to extract the phase information in the spatial domain, WFT obtains the phase information in the windowed Fourier domain; thus, the two methods look entirely different. We evaluate the phase extraction errors of SM and windowed Fourier ridges (WFRs) as a typical WFT method for both linear and nonlinear phases with/without noise against the reference Fourier transform (FT) technique. For the simulated fringe patterns with linear or nonlinear phase and different random noise level, all the methods have high phase extraction accuracies. For a real experiment with more complicated phase and discontinuities, SM and WFR, both local methods, yield quite similar results and outperform FT.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Windowed Fourier transform for fringe pattern analysis: theoretical analyses

Qian Kemao, Haixia Wang, and Wenjing Gao
Appl. Opt. 47(29) 5408-5419 (2008)

Advanced carrier squeezing interferometry: a technique to suppress gamma distortion in fringe projection profilometry

Ronggang Zhu, Bo Li, Rihong Zhu, Yong He, and Jianxin Li
Appl. Opt. 56(9) 2556-2562 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [Crossref]
  2. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
    [Crossref]
  3. L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
    [Crossref]
  4. M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
    [Crossref]
  5. Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high sensitivity and full field deformation measurement at micro/nano scales,” Appl. Opt. 55, 6858–6865 (2016).
    [Crossref]
  6. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [Crossref]
  7. J. Endo, J. Chen, D. Koboyashi, Y. Wada, and H. Fujita, “Transmission laser microscope using the phase-shifting techniques and its application to measurement of optical waveguides,” Appl. Opt. 41, 1308–1314 (2002).
    [Crossref]
  8. Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
    [Crossref]
  9. M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
    [Crossref]
  10. G. Rajshekhar and P. Rastogi, “Fringe analysis: premise and perspectives,” Opt. Lasers Eng. 50, iii–x (2012).
    [Crossref]
  11. J. Buytaert and J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40, 114–131 (2011).
    [Crossref]
  12. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  13. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [Crossref]
  14. S. Vanlanduit, J. Vanherzeele, P. Guillaume, B. Cauberghe, and P. Verboven, “Fourier fringe processing by use of an interpolated Fourier-transform technique,” Appl. Opt. 43, 5206–5213 (2004).
    [Crossref]
  15. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [Crossref]
  16. Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).
  17. C. Wang and F. Da, “Phase demodulation using adaptive windowed Fourier transform based on Hilbert–Huang transform,” Opt. Express 20, 18459–18477 (2012).
    [Crossref]
  18. L. Watkins, S. Tan, and T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
    [Crossref]
  19. J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993–4998 (2004).
    [Crossref]
  20. M. Gdeisat, D. Burton, and M. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
    [Crossref]
  21. L. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50, 1015–1022 (2012).
    [Crossref]
  22. G. Rajshekhar and P. Rastogi, “Fringe demodulation using the two-dimensional phase differencing operator,” Opt. Lett. 37, 4278–4280 (2012).
    [Crossref]
  23. G. Rajshekhar and P. Rastogi, “Multiple signal classification technique for phase estimation from a fringe pattern,” Appl. Opt. 51, 5869–5875 (2012).
    [Crossref]
  24. M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
    [Crossref]
  25. P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
    [Crossref]
  26. M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
    [Crossref]
  27. Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
    [Crossref]
  28. J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier,” Opt. Commun. 271, 59–64 (2007).
    [Crossref]
  29. H. Guo, Q. Yang, and M. Chen, “Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications,” Appl. Opt. 46, 1057–1065 (2007).
    [Crossref]
  30. A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity contrast determination,” Appl. Opt. 46, 4613–4624 (2007).
    [Crossref]
  31. J. Xu, Q. Xu, and H. Peng, “Spatial carrier phase-shifting algorithm based on least-squares iteration,” Appl. Opt. 47, 5446–5453 (2008).
    [Crossref]
  32. S. K. Debnath and Y. Park, “Real-time quantitative phase imaging with a spatial phase-shifting algorithm,” Opt. Lett. 36, 4677–4679 (2011).
    [Crossref]
  33. S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
    [Crossref]
  34. M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
    [Crossref]
  35. L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
    [Crossref]
  36. N. Agarwal and Q. Kemao, “Windowed Fourier ridges as a spatial carrier phase-shifting algorithm,” Opt. Eng. 56, 080501 (2017).
    [Crossref]
  37. S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling Moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51, 3214–3223 (2012).
    [Crossref]
  38. S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
    [Crossref]
  39. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [Crossref]
  40. P. S. Huang, Q. J. Hu, and F. P. Chiang, “Double three-step phase-shifting algorithm,” Appl. Opt. 41, 4503–4509 (2002).
    [Crossref]
  41. P. S. Huang, C. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [Crossref]
  42. S. Zhang, “High-resolution three-dimensional profilometry with binary phase-shifting methods,” Appl. Opt. 50, 1753–1757 (2011).
    [Crossref]
  43. S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
    [Crossref]
  44. Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
    [Crossref]
  45. Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
    [Crossref]
  46. Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
    [Crossref]
  47. S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
    [Crossref]
  48. P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42, 4954–4957 (2017).
    [Crossref]
  49. Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
    [Crossref]
  50. S. Ri and H. Tsuda, “Two-dimensional sampling Moiré method for fast and accurate phase analysis of single fringe pattern,” Proc. SPIE 8769, 876921 (2013).
    [Crossref]

2018 (3)

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

2017 (4)

N. Agarwal and Q. Kemao, “Windowed Fourier ridges as a spatial carrier phase-shifting algorithm,” Opt. Eng. 56, 080501 (2017).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
[Crossref]

P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42, 4954–4957 (2017).
[Crossref]

2016 (1)

2015 (1)

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

2013 (2)

S. Ri and H. Tsuda, “Two-dimensional sampling Moiré method for fast and accurate phase analysis of single fringe pattern,” Proc. SPIE 8769, 876921 (2013).
[Crossref]

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

2012 (8)

L. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50, 1015–1022 (2012).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

G. Rajshekhar and P. Rastogi, “Fringe analysis: premise and perspectives,” Opt. Lasers Eng. 50, iii–x (2012).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling Moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51, 3214–3223 (2012).
[Crossref]

C. Wang and F. Da, “Phase demodulation using adaptive windowed Fourier transform based on Hilbert–Huang transform,” Opt. Express 20, 18459–18477 (2012).
[Crossref]

G. Rajshekhar and P. Rastogi, “Multiple signal classification technique for phase estimation from a fringe pattern,” Appl. Opt. 51, 5869–5875 (2012).
[Crossref]

G. Rajshekhar and P. Rastogi, “Fringe demodulation using the two-dimensional phase differencing operator,” Opt. Lett. 37, 4278–4280 (2012).
[Crossref]

2011 (3)

2010 (4)

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[Crossref]

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

2009 (2)

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
[Crossref]

2008 (1)

2007 (3)

2006 (1)

2004 (2)

2003 (2)

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

M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
[Crossref]

2002 (2)

2001 (1)

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

1999 (1)

1997 (2)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[Crossref]

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

1995 (2)

P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
[Crossref]

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[Crossref]

1991 (1)

M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[Crossref]

1984 (1)

1983 (1)

1982 (1)

Abid, A.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

Agarwal, N.

N. Agarwal and Q. Kemao, “Windowed Fourier ridges as a spatial carrier phase-shifting algorithm,” Opt. Eng. 56, 080501 (2017).
[Crossref]

Arai, Y.

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

Asundi, A. K.

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[Crossref]

Asundi, K.

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

Barnes, T.

Bryanston-Cross, P. J.

P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
[Crossref]

Burton, D.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

M. Gdeisat, D. Burton, and M. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[Crossref]

Buytaert, J.

J. Buytaert and J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40, 114–131 (2011).
[Crossref]

Cauberghe, B.

Chan, P. H.

P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
[Crossref]

Chen, J.

Chen, M.

Chen, W.

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

Chiang, F. P.

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

P. S. Huang, Q. J. Hu, and F. P. Chiang, “Double three-step phase-shifting algorithm,” Appl. Opt. 41, 4503–4509 (2002).
[Crossref]

Cuevas, F. J.

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[Crossref]

Da, F.

Debnath, S. K.

Dirckx, J.

J. Buytaert and J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40, 114–131 (2011).
[Crossref]

Endo, J.

Ferrari, J. A.

J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier,” Opt. Commun. 271, 59–64 (2007).
[Crossref]

Frins, E. M.

J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier,” Opt. Commun. 271, 59–64 (2007).
[Crossref]

Fujigaki, M.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
[Crossref]

Fujita, H.

Gdeisat, M.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

M. Gdeisat, D. Burton, and M. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[Crossref]

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[Crossref]

Guillaume, P.

Guo, H.

Halioua, M.

Hamamoto, T.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Hu, Q. J.

Huang, L.

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

Huang, P. S.

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

P. S. Huang, Q. J. Hu, and F. P. Chiang, “Double three-step phase-shifting algorithm,” Appl. Opt. 41, 4503–4509 (2002).
[Crossref]

Hytch, M.

M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
[Crossref]

Ina, H.

Kemao, Q.

N. Agarwal and Q. Kemao, “Windowed Fourier ridges as a spatial carrier phase-shifting algorithm,” Opt. Eng. 56, 080501 (2017).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).

Kobayashi, D.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

Kobayashi, S.

Koboyashi, D.

Kodera, M.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Koyama, M.

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
[Crossref]

Kujawinska, M.

M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[Crossref]

Lalor, M.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

M. Gdeisat, D. Burton, and M. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[Crossref]

Lei, S.

Lilley, F.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

Liu, H. C.

Liu, Z.

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Miyahsita, N.

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Miyashita, N.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Moore, C.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

Morimoto, Y.

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
[Crossref]

Muramatsu, T.

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling Moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51, 3214–3223 (2012).
[Crossref]

Mutoh, K.

Nanbara, K.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

Ng, C. S.

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[Crossref]

Pan, B.

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

Park, Y.

Parker, S. C.

P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
[Crossref]

Patorski, K.

Peng, H.

Penisson, J.

M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
[Crossref]

Putaux, J.

M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
[Crossref]

Qudeisat, M.

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

Rajshekhar, G.

Rastogi, P.

G. Rajshekhar and P. Rastogi, “Fringe demodulation using the two-dimensional phase differencing operator,” Opt. Lett. 37, 4278–4280 (2012).
[Crossref]

G. Rajshekhar and P. Rastogi, “Multiple signal classification technique for phase estimation from a fringe pattern,” Appl. Opt. 51, 5869–5875 (2012).
[Crossref]

G. Rajshekhar and P. Rastogi, “Fringe analysis: premise and perspectives,” Opt. Lasers Eng. 50, iii–x (2012).
[Crossref]

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[Crossref]

Ri, S.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
[Crossref]

P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42, 4954–4957 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high sensitivity and full field deformation measurement at micro/nano scales,” Appl. Opt. 55, 6858–6865 (2016).
[Crossref]

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

S. Ri and H. Tsuda, “Two-dimensional sampling Moiré method for fast and accurate phase analysis of single fringe pattern,” Proc. SPIE 8769, 876921 (2013).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling Moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51, 3214–3223 (2012).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
[Crossref]

Saka, M.

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

Servin, M.

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[Crossref]

Shi, W.

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Shiraki, K.

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

Srinivasan, V.

Styk, A.

Su, X.

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

Sugiyama, T.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Suguro, K.

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Takeda, M.

Tan, S.

Tsuda, H.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
[Crossref]

P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42, 4954–4957 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high sensitivity and full field deformation measurement at micro/nano scales,” Appl. Opt. 55, 6858–6865 (2016).
[Crossref]

S. Ri and H. Tsuda, “Two-dimensional sampling Moiré method for fast and accurate phase analysis of single fringe pattern,” Proc. SPIE 8769, 876921 (2013).
[Crossref]

Tsuzaki, K.

Vanherzeele, J.

Vanlanduit, S.

Verboven, P.

Wada, Y.

Wang, C.

Wang, Q.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

P. Xia, Q. Wang, S. Ri, and H. Tsuda, “Calibrated phase-shifting digital holography based on a dual-camera system,” Opt. Lett. 42, 4954–4957 (2017).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25, 13465–13480 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high sensitivity and full field deformation measurement at micro/nano scales,” Appl. Opt. 55, 6858–6865 (2016).
[Crossref]

Watkins, L.

L. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50, 1015–1022 (2012).
[Crossref]

L. Watkins, S. Tan, and T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24, 905–907 (1999).
[Crossref]

Weng, J.

Wójciak, J.

M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[Crossref]

Xia, P.

Xie, H.

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Xu, J.

Xu, Q.

Yamada, T.

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

Yamaguchi, I.

Yang, Q.

Yokozeki, S.

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

Yoshioka, A.

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Zhang, C.

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

Zhang, Q.

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Zhang, S.

Zhang, T.

Zhong, J.

Appl. Opt. (14)

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high sensitivity and full field deformation measurement at micro/nano scales,” Appl. Opt. 55, 6858–6865 (2016).
[Crossref]

J. Endo, J. Chen, D. Koboyashi, Y. Wada, and H. Fujita, “Transmission laser microscope using the phase-shifting techniques and its application to measurement of optical waveguides,” Appl. Opt. 41, 1308–1314 (2002).
[Crossref]

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
[Crossref]

S. Vanlanduit, J. Vanherzeele, P. Guillaume, B. Cauberghe, and P. Verboven, “Fourier fringe processing by use of an interpolated Fourier-transform technique,” Appl. Opt. 43, 5206–5213 (2004).
[Crossref]

J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993–4998 (2004).
[Crossref]

M. Gdeisat, D. Burton, and M. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[Crossref]

G. Rajshekhar and P. Rastogi, “Multiple signal classification technique for phase estimation from a fringe pattern,” Appl. Opt. 51, 5869–5875 (2012).
[Crossref]

H. Guo, Q. Yang, and M. Chen, “Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications,” Appl. Opt. 46, 1057–1065 (2007).
[Crossref]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity contrast determination,” Appl. Opt. 46, 4613–4624 (2007).
[Crossref]

J. Xu, Q. Xu, and H. Peng, “Spatial carrier phase-shifting algorithm based on least-squares iteration,” Appl. Opt. 47, 5446–5453 (2008).
[Crossref]

S. Ri and T. Muramatsu, “Theoretical error analysis of the sampling Moiré method and phase compensation methodology for single-shot phase analysis,” Appl. Opt. 51, 3214–3223 (2012).
[Crossref]

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

P. S. Huang, Q. J. Hu, and F. P. Chiang, “Double three-step phase-shifting algorithm,” Appl. Opt. 41, 4503–4509 (2002).
[Crossref]

S. Zhang, “High-resolution three-dimensional profilometry with binary phase-shifting methods,” Appl. Opt. 50, 1753–1757 (2011).
[Crossref]

Exp. Mech. (3)

S. Ri, T. Muramatsu, M. Saka, K. Nanbara, and D. Kobayashi, “Accuracy of the sampling Moiré method and its application to deflection measurements of large-scale structures,” Exp. Mech. 52, 331–340 (2012).
[Crossref]

S. Ri, M. Saka, K. Nanbara, and D. Kobayashi, “Dynamics thermal deformation measurement of large-scale, high-temperature piping in thermal power plants utilizing the sampling Moiré method and grating magnets,” Exp. Mech. 53, 1635–1646 (2013).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50, 501–508 (2010).
[Crossref]

J. Mod. Opt. (2)

M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853–1862 (1995).
[Crossref]

Y. Arai, S. Yokozeki, K. Shiraki, and T. Yamada, “High precision two-dimensional spatial fringe analysis method,” J. Mod. Opt. 44, 739–751 (1997).
[Crossref]

J. Opt. (1)

J. Buytaert and J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt. 40, 114–131 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

M. Kodera, Q. Wang, S. Ri, H. Tsuda, A. Yoshioka, T. Sugiyama, T. Hamamoto, and N. Miyashita, “Characterization technique for detection of atom-size crystalline defects and strains using two-dimensional fast-Fourier-transform sampling Moiré method,” Jpn. J. Appl. Phys. 57, 04FC04 (2018).
[Crossref]

Nanotechnology (1)

Q. Wang, S. Ri, H. Tsuda, M. Kodera, K. Suguro, and N. Miyahsita, “Visualization and automatic detection of defect distribution in GaN atomic structure from sampling Moiré phase,” Nanotechnology 28, 455704 (2017).
[Crossref]

Nature (1)

M. Hytch, J. Putaux, and J. Penisson, “Measurement of the displacement field of dislocation to 0.03 Å by electron microscopy,” Nature 423, 270–273 (2003).
[Crossref]

Opt. Commun. (1)

J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier,” Opt. Commun. 271, 59–64 (2007).
[Crossref]

Opt. Eng. (2)

N. Agarwal and Q. Kemao, “Windowed Fourier ridges as a spatial carrier phase-shifting algorithm,” Opt. Eng. 56, 080501 (2017).
[Crossref]

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

Opt. Express (2)

Opt. Lasers Eng. (12)

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

G. Rajshekhar and P. Rastogi, “Fringe analysis: premise and perspectives,” Opt. Lasers Eng. 50, iii–x (2012).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[Crossref]

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50, 529–533 (2012).
[Crossref]

M. Gdeisat, A. Abid, D. Burton, M. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[Crossref]

P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343–354 (1995).
[Crossref]

L. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50, 1015–1022 (2012).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Lasers Eng. 107, 315–324 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Lasers Eng. 110, 155–162 (2018).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: a review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

Opt. Lett. (6)

Proc. SPIE (2)

M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[Crossref]

S. Ri and H. Tsuda, “Two-dimensional sampling Moiré method for fast and accurate phase analysis of single fringe pattern,” Proc. SPIE 8769, 876921 (2013).
[Crossref]

Other (1)

Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).

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 (11)

Fig. 1.
Fig. 1. Principles of 2D-FT, 1D-SM, and 1D-WFR. Both 1D-SM and 1D-WFR process a 2D fringe pattern row-by-row in this study.
Fig. 2.
Fig. 2. Simulated fringe pattern with 256    pixels × 256    pixels . (a) Linear phase in case of k = 0 , nonlinear phase in the case of (b)  k = 0.5 , (c)  k = 1.0 , and (d)  k = 2.0 , respectively. The yellow line in Fig. 2(c) indicates the 1D data to be examined in detail.
Fig. 3.
Fig. 3. Simulation result of noiseless for nonlinear phase in the case of P = 8.1 and T = 8 . The gray and light-pink zones indicate the phase error is less than 1% and 0.1% of 2 π , respectively.
Fig. 4.
Fig. 4. Simulation results of one section for (a) 2D-FT, 1D-SM (1-order) and (b) 1D-SM (3-order), 1D-WFR in the case of a nonlinear phase ( k = 1.0 ) without noise, as one example. The gray and light-pink zones indicate the phase error is less than 1% and 0.1% of 2 π , respectively.
Fig. 5.
Fig. 5. RMS phase error versus random noise obtained by different techniques for (a) linear phase and (b) nonlinear phase. The gray and light-pink zones indicate the phase error is less than 1% and 0.1% of 2 π , respectively.
Fig. 6.
Fig. 6. Phase error distributions obtained by three different techniques for a peaks phase with P = 8.1 and a nonlinearity k = 1.0 under a noise level of 1%. (a) 2D-FT, (b) 1D-SM (1-order), (c) 1D-SM (3-order), and (d) 1D-WFR, both in the case of T = 8    pixels .
Fig. 7.
Fig. 7. Experimental fringe image with an original size of 1600    pixels × 1200    pixels by fringe projection method; the target is a diffuse statue. Only nonshaded region on right-hand side with 400    pixels × 800    pixels is used for comparison of four techniques, including PSM, 2D-FT, 1D-SM (1-order/3-order), and 1D-WFR.
Fig. 8.
Fig. 8. Phase analysis results obtained by the eight-step PSM. (a) Fringe pattern, (b) phase, (c) amplitude, and (d) phase gradient distributions.
Fig. 9.
Fig. 9. Phase analysis results obtained by 2D-FT, 1D-SM (1-order/3-order), and 1D-WFR. (a) Fourier spectrum by 2D-FT and the first frequency component is used to calculate the phase distribution, moiré fringes by the 1D-SM in the case of (b) 1-order (linear) interpolation and (c) 3-order interpolation when the sampling pitch is 15 pixels, (d) ridge map by 1D-WFR to finding the optimal local frequency; (e)–(h) phase distributions by 2D-FT, 1D-SM (1-order), 1D-SM (3-order), and 1D-WFR, respectively.
Fig. 10.
Fig. 10. Experimental results of phase gradient obtained by (a) 2D-FT, (b) 1D-SM (1-order), (c) 1D-SM (3-order), (d) 1D-WFR; (e)–(h) phase differences in percentage between each spatial phase analysis method and temporal eight-step PS method. The yellow area indicated that the absolute phase difference exceeds 5%.
Fig. 11.
Fig. 11. Comparison of cross section AA of phase gradient for eight-step PSM, 1D-SM (3-order), and 1D-WFR.

Tables (1)

Tables Icon

Table 1. Comparison Result of the Computation Time for Three Methodsa

Equations (18)

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

f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ω c x + φ 0 ( x , y ) ] = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ] ,
f ( x ) = a ( x ) + b ( x ) cos [ ω c x + φ 0 ( x ) ] = a ( x ) + b ( x ) cos [ φ ( x ) ] .
ω c = 2 π f c = 2 π P .
f ( x , y ) = a ( x , y ) + 1 2 b ( x , y ) exp [ j φ ( x , y ) ] + 1 2 b ( x , y ) exp [ j φ ( x , y ) ] ,
f ^ ( x , y ) = F 1 ( BPF { F [ f ( x , y ) ] } ) 1 2 b ( x , y ) exp [ j φ ( x , y ) ] ,
φ F T ( x , y ) = tan 1 [ Im { f ^ ( x , y ) } Re { f ^ ( x , y ) } ] .
f m , t ( x ) = a m ( x ) + b m ( x ) cos [ 2 π ( 1 P 1 T ) x + φ 0 ( x ) + 2 π t T ] = a m ( x ) + b m ( x ) cos [ φ m ( x ) + 2 π t T ] , ( t = 0 , 1 , , T 1 ) ,
φ m ( x ) = tan 1 [ t = 0 T 1 f m , t ( x ) sin ( 2 π t T ) t = 0 T 1 f m , t ( x ) cos ( 2 π t T ) ] .
φ S M ( x ) = φ m ( x ) + 2 π x / T .
S f ( u ; ξ x ) = f ( x ) g ( x u ) exp [ j ξ x ( x u ) ] d x ,
g ( x ) = ( π σ x 2 ) 1 / 4 exp ( x 2 2 σ x 2 ) ,
ω ^ x = arg max ξ x | S f ( u ; ξ x ) | .
φ WFR ( x ) = tan 1 { Im { S f [ u ; ω ^ x ( u ) ] } Re { S f [ u ; ω ^ x ( u ) ] } } 1 2 tan 1 [ σ x 2 c ^ x x ( u ) ] ,
φ simu ( x , y ) = 2 π P x + k · peaks ( M ) ,
Δ φ ( x ) = φ method ( x ) φ simu ( x ) , method = [ FT , SM , WFR ] ,
f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ω c x + φ 0 ( x , y ) ] + n ( x , y ) ,
f n ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) + δ n ] , ( n = 0 , 1 , , N 1 ) ,
φ ( x , y ) x = 1 2 [ φ ( x + 1 , y ) φ ( x 1 , y ) ] .

Metrics