Abstract

The fringe patterns seen when using moiré instruments are similar to the patterns seen in traditional interferometry but differ in the spacing between consecutive fringes. In traditional interferometry, the spacing is constant and related to the wavelength of the source. In moiré fringe projection, the spacing (the effective wavelength) may not be constant over the field of view and the spacing depends on the system geometry. In these cases, using a constant effective wavelength over the field of view causes inaccurate surface height measurements. We examine the calibration process of the moiré fringe projection measurement, which takes this varying wavelength into account to produce a pixel-by-pixel wavelength map. The wavelength calibration procedure is to move the object in the out-of-plane direction a known distance until every pixel intensity value goes through at least one cycle. A sinusoidal function is then fit to the data to extract the effective wavelength pixel by pixel, yielding an effective wavelength map. A calibrated step height was used to validate the effective wavelength map with results within 1% of the nominal value of the step height. The error sources that contributed to the uncertainty in determining the height of the artifact are also investigated.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Creath and J. C. Wyant, "Moiré and fringe projection techniques," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 653-686.
  2. J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometers," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 501-598.
  3. C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
    [CrossRef]
  4. Y. Choi and S. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. 37, 1005-1010 (1998).
    [CrossRef]
  5. J. J. Dirckx and W. F. Decraemer, "Automatic calibration method for phase shift shadow moiré interferometry," Appl. Opt. 29, 1474-1476 (1990).
    [CrossRef] [PubMed]
  6. A. M. Samara, "Enhanced dynamic range fringe projection for micro-structure characterization," Ph.D. dissertation (University of North Carolina at Charlotte, 2005).
  7. A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).
  8. B. W. Bell, "Digital heterodyne topography," Ph.D. dissertation (University of Arizona, 1985).
  9. M. Idesawa, T. Yatagai, and T. Soma, "Scanning moiré method and automatic measurement of 3-D shapes," Appl. Opt. 16, 2152-2162 (1977).
    [CrossRef] [PubMed]
  10. D. S. Purcell, "Construction and error analysis of a moiré fringe projection system," M.S. thesis (University of North Carolina at Charlotte, 2005).
  11. R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3-D phase distribution," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. Novak, eds., Proc. SPIE 5856, 109-117 (2005).
    [CrossRef]
  12. K. J. Gasvik, Optical Metrology (Wiley, 2002), pp. 173-192.
    [CrossRef]
  13. Y. Arai and S. Yokozeki, "Improvement of measurement accuracy in shadow moiré by considering the influence of harmonics in the moiré profile," Appl. Opt. 38, 3503-3507 (1999).
    [CrossRef]

2005 (1)

R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3-D phase distribution," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. Novak, eds., Proc. SPIE 5856, 109-117 (2005).
[CrossRef]

2004 (1)

C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
[CrossRef]

1999 (1)

1998 (1)

Y. Choi and S. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. 37, 1005-1010 (1998).
[CrossRef]

1992 (1)

A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).

1990 (1)

1977 (1)

Arai, Y.

Bell, B. W.

B. W. Bell, "Digital heterodyne topography," Ph.D. dissertation (University of Arizona, 1985).

Bremand, F.

C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
[CrossRef]

Breque, C.

C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
[CrossRef]

Bruning, J. H.

J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometers," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 501-598.

Choi, Y.

Y. Choi and S. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. 37, 1005-1010 (1998).
[CrossRef]

Creath, K.

K. Creath and J. C. Wyant, "Moiré and fringe projection techniques," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 653-686.

Decraemer, W. F.

Dirckx, J. J.

Dupre, J.

C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
[CrossRef]

Fagg, A. H.

A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).

Gasvik, K. J.

K. J. Gasvik, Optical Metrology (Wiley, 2002), pp. 173-192.
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometers," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 501-598.

Hales, B. S.

A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).

Idesawa, M.

Kim, S.

Y. Choi and S. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. 37, 1005-1010 (1998).
[CrossRef]

Purcell, D. S.

D. S. Purcell, "Construction and error analysis of a moiré fringe projection system," M.S. thesis (University of North Carolina at Charlotte, 2005).

Samara, A. M.

A. M. Samara, "Enhanced dynamic range fringe projection for micro-structure characterization," Ph.D. dissertation (University of North Carolina at Charlotte, 2005).

Sitnik, R.

R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3-D phase distribution," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. Novak, eds., Proc. SPIE 5856, 109-117 (2005).
[CrossRef]

Soma, T.

Stahl, H. P.

A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).

Wyant, J. C.

K. Creath and J. C. Wyant, "Moiré and fringe projection techniques," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 653-686.

Yatagai, T.

Yokozeki, S.

Appl. Opt. (3)

Opt. Eng. (1)

Y. Choi and S. Kim, "Phase-shifting grating projection moiré topography," Opt. Eng. 37, 1005-1010 (1998).
[CrossRef]

Opt. Lasers Eng. (1)

C. Breque, J. Dupre, and F. Bremand, "Calibration of a system of projection moiré for relief measuring: biomedical applications," Opt. Lasers Eng. 41, 241-260 (2004).
[CrossRef]

Proc. SPIE (2)

A. H. Fagg, B. S. Hales, and H. P. Stahl, "Systematic errors of a projection moiré contouring system," in Surface Characterization and Testing IV, K. Creath and J. E. Greivenkamp, eds., Proc. SPIE 1776, 120-129 (1992).

R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3-D phase distribution," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. Novak, eds., Proc. SPIE 5856, 109-117 (2005).
[CrossRef]

Other (6)

K. J. Gasvik, Optical Metrology (Wiley, 2002), pp. 173-192.
[CrossRef]

B. W. Bell, "Digital heterodyne topography," Ph.D. dissertation (University of Arizona, 1985).

D. S. Purcell, "Construction and error analysis of a moiré fringe projection system," M.S. thesis (University of North Carolina at Charlotte, 2005).

A. M. Samara, "Enhanced dynamic range fringe projection for micro-structure characterization," Ph.D. dissertation (University of North Carolina at Charlotte, 2005).

K. Creath and J. C. Wyant, "Moiré and fringe projection techniques," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 653-686.

J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometers," in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 501-598.

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 (7)

Fig. 1
Fig. 1

Divergent fringe projection setup.

Fig. 2
Fig. 2

(Color online) Moiré fringe projection system.

Fig. 3
Fig. 3

Moiré pattern obtained for the calibration artifact.

Fig. 4
Fig. 4

Plot of intensity (gray value) versus objection position (mm) for a pixel (144, 176). The solid curve is the best-fit curve calculated by matlab.

Fig. 5
Fig. 5

Effective wavelength map for the moiré fringe projection system.

Fig. 6
Fig. 6

(a) Reference phase map of the mirror. (b) Phase map of the step height. (c) Corrected phase map of the step height.

Fig. 7
Fig. 7

(a) Experimental setup for rotational object misalignment. (b) Graph showing the change in step height measurement versus angle. The solid curve is a quadratic fit to the data. (c) Experimental setup for z displacement of the object. (d) Plot of change in step height measurement (mm) versus z displacement (mm). The solid curve is a quadratic fit to the data.

Tables (2)

Tables Icon

Table 1 Statistics for Effective Wavelength Map λ eff ( x , y )

Tables Icon

Table 2 Uncertainty Sources Associated with ψ and λeff

Equations (7)

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

I moire ( x ) = A { 1 + cos [ 2 π ϕ ( x ) + 2 π ψ ( x , z ) ] } ,
I moire ( x ) = A { 1 + cos [ 2 π ψ ( x , z ) ] } .
ψ moire ( x ) = z p x 0 cos θ 0 [ sin θ 0 + ( l k l p cos θ 0 ) x l p l k ] × ( 1 + x sin θ 0 l p ) 2 ,
ψ int ( x , y ) = 2 π z ( x , y ) λ ,
λ eff ( x ) = p x 0 cos θ 0 ( 1 + x sin θ 0 l p ) 2 [ sin θ 0 + ( l k l p cos θ 0 ) x l p l k ] .
z ( x , y ) = λ eq ( x , y ) 2 π ψ ( x , y ) .
y = b + A sin ( 2 π λ eq z + ξ ) ,

Metrics