Abstract

Moiré technique is often used to measure surface morphology and deformation fields. CCD moiré is a special kind of moiré and is produced when a digital camera is used to capture periodic grid structures, like gratings. Different from the ordinary moiré setups with two gratings, however, CCD moiré requires only one grating. But the formation mechanism is not fully understood and also, a high-quality CCD moiré pattern is hard to achieve. In this paper, the formation mechanism of a CCD moiré pattern, based on the imaging principle of a digital camera, is analyzed and a way of simulating the pattern is proposed. A universal period formula is also proposed and the validity of the simulation and formula is verified by experiments. The proposed model is shown to be an efficient guide for obtaining high-quality CCD moiré patterns.

© 2014 Optical Society of America

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References

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  1. D. M. Meadows, W. O. Johnson, and J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9(4), 942–947 (1970).
    [Crossref] [PubMed]
  2. D. Post, B. Han, and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer, 1994).
  3. P. K. Rastogi and E. Hack, Optical Methods for Solid Mechanics: A Full-Field Approach (Wiley-VCH, 2012)
  4. W. N. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2007).
  5. J. A. Buytaert and J. J. Dirckx, “Moiré profilometry using liquid crystals for projection and demodulation,” Opt. Express 16(1), 179–193 (2008).
    [Crossref] [PubMed]
  6. X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
    [Crossref]
  7. C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
    [Crossref]
  8. T. Tu and W. B. Goh, “Moiré pattern from a CCD camera – are they annoying artifacts or can they be useful,” in Proceedings of International Conference on Computer Vision Theory and Applications (2009).
  9. R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
    [Crossref]
  10. T. Tu and W. B. Goh, Using CCD Moiré Pattern Analysis to Implement Pressure-Sensitive Touch Surfaces (Springer, 2009).

2010 (1)

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

2008 (1)

2004 (1)

C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
[Crossref]

2003 (1)

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

1970 (1)

Allen, J. B.

Buytaert, J. A.

Chang, R. S.

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

Dirckx, J. J.

Fu, Y.

C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
[Crossref]

Goh, W. B.

T. Tu and W. B. Goh, “Moiré pattern from a CCD camera – are they annoying artifacts or can they be useful,” in Proceedings of International Conference on Computer Vision Theory and Applications (2009).

Hou, Z.

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Johnson, W. O.

Kang, Y.

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Li, X.

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Lin, C. H.

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

Liu, H. C.

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

Meadows, D. M.

Qiu, W.

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Quan, C.

C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
[Crossref]

Sheu, J. Y.

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

Tay, C. J.

C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
[Crossref]

Tu, T.

T. Tu and W. B. Goh, “Moiré pattern from a CCD camera – are they annoying artifacts or can they be useful,” in Proceedings of International Conference on Computer Vision Theory and Applications (2009).

Xiao, X.

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Appl. Opt. (1)

Exp. Mech. (1)

X. Xiao, Y. Kang, Z. Hou, W. Qiu, X. Li, and X. Li, “Displacement and strain measurement by circular and radial gratings moire method,” Exp. Mech. 50(2), 239–244 (2010).
[Crossref]

Opt. Commun. (1)

C. Quan, Y. Fu, and C. J. Tay, “Determination of surface contour by temporal analysis of shadow moiré fringes,” Opt. Commun. 230(1–3), 23–33 (2004).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

R. S. Chang, J. Y. Sheu, C. H. Lin, and H. C. Liu, “Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform,” Opt. Laser Technol. 35(1), 43–47 (2003).
[Crossref]

Other (5)

T. Tu and W. B. Goh, Using CCD Moiré Pattern Analysis to Implement Pressure-Sensitive Touch Surfaces (Springer, 2009).

T. Tu and W. B. Goh, “Moiré pattern from a CCD camera – are they annoying artifacts or can they be useful,” in Proceedings of International Conference on Computer Vision Theory and Applications (2009).

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer, 1994).

P. K. Rastogi and E. Hack, Optical Methods for Solid Mechanics: A Full-Field Approach (Wiley-VCH, 2012)

W. N. Sharpe, Handbook of Experimental Solid Mechanics (Springer, 2007).

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Figures (9)

Fig. 1
Fig. 1 Formation of a CCD moiré pattern.
Fig. 2
Fig. 2 Principle of the CCD moiré pattern showing: (a) a line of CCD imaging units and, (b) one single imaging unit.
Fig. 3
Fig. 3 CCD moiré patterns formed under different conditions showing: (a) p/q = 0.33, (b) p/q = 1.10, (c) p/q = 1.94 and (d) the fitting data.
Fig. 4
Fig. 4 The period of moiré pattern from theory and simulation with n varying from 0 to 3.5.
Fig. 5
Fig. 5 A comparison between the results of the new formula and the simulation showing (a) a comparison when 0<n<4 and (b) a comparison when 0<n<1.
Fig. 6
Fig. 6 The curve of the gray level contrast Gr varies with n.
Fig. 7
Fig. 7 The experimental arrangement.
Fig. 8
Fig. 8 Captured CCD moiré patterns showing (a) n = 0.53, (b) n = 1.10 and (c) n = 2.18.
Fig. 9
Fig. 9 A comparison between experimental and theoretical results.

Equations (16)

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

q= d v + d i
G=CI b d v
T= p m q
T= p | pq |
T= p (1+m)qp
m= p s / p r
n= p q
T= n | n1 |
T= n mn+1
k | n1 = 1 | [n]n |
T | n1 = n | [n]n |
k | n<1 = 1 | n×[ 1 n ]1 |
T | n<1 = n | n×[ 1 n ]1 |
T={ n | n×[ 1 n ]1 | n<1 n | [n]n | n1
G r = G max G min
n= p s × ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 d

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