Abstract

The technique of generating sinusoidal fringe patterns by defocusing squared binary structured ones has numerous merits for high-speed three-dimensional (3D) shape measurement. However, it is challenging for this method to realize a multifrequency phase-shifting (MFPS) algorithm because it is difficult to simultaneously generate high-quality sinusoidal fringe patterns with different periods. This paper proposes to realize an MFPS algorithm utilizing an optimal pulse width modulation (OPWM) technique that can selectively eliminate high-order harmonics of squared binary patterns. We successfully develop a 556 Hz system utilizing a three-frequency algorithm for simultaneously measuring multiple objects.

© 2011 Optical Society of America

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References

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  1. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
    [CrossRef]
  2. X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
    [CrossRef]
  3. S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34(20), 3080–3082 (2009).
    [CrossRef] [PubMed]
  4. S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
    [CrossRef]
  5. S. Zhang, “Flexible 3-D shape measurement using projector defocusing: extended measurement range,” Opt. Lett. 35(7), 931–933 (2010).
  6. Y. Wang and S. Zhang, “Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing,” Opt. Lett. 35(24), 4121–4123 (2010).
    [CrossRef] [PubMed]
  7. D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007).
    [CrossRef]
  8. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, 1998).
  9. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26(14), 2810–2816 (1987).
    [CrossRef] [PubMed]
  10. C. E. Towers, D. P. Towers, and J. D. Jones, “Optimum frequency selection in multifrequency interferometry,” Opt. Lett. 28(11), 887–889 (2003).
    [CrossRef] [PubMed]
  11. V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
    [CrossRef]
  12. S. Zhang, D. van der Weide, and J. Olvier, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010).
    [CrossRef] [PubMed]
  13. M. Schaffer, M. Grosse, and R. Kowarschik, “High-speed pattern projection for three-dimensional shape measurement using laser speckles,” Appl. Opt. 49(18), 3622–3629 (2010).
    [CrossRef] [PubMed]

2010 (6)

2009 (1)

2004 (1)

V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
[CrossRef]

2003 (1)

1992 (1)

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

1987 (1)

Agelidis, V. G.

V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
[CrossRef]

Bally, G. V.

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

Balouktsis, A.

V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
[CrossRef]

Balouktsis, I.

V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
[CrossRef]

Creath, K.

Gorthi, S.

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

Grosse, M.

Jones, J. D.

Kowarschik, R.

Lei, S.

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
[CrossRef]

S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34(20), 3080–3082 (2009).
[CrossRef] [PubMed]

Olvier, J.

Rastogi, P.

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

Schaffer, M.

Su, X.-Y.

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

Towers, C. E.

Towers, D. P.

van der Weide, D.

Vukicevic, D.

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

Wang, Y.

Zhang, S.

Zhou, W.-S.

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

Appl. Opt. (2)

IEEE Power Electron. Lett. (1)

V. G. Agelidis, A. Balouktsis, and I. Balouktsis, “On applying a minimization technique to the harmonic elimilation PWM control: the bipolar waveform,” IEEE Power Electron. Lett. 2, 41–44 (2004).
[CrossRef]

Opt. Commun. (1)

X.-Y. Su, W.-S. Zhou, G. V. Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94(13), 561–573 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (2)

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

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
[CrossRef]

Opt. Lett. (4)

Other (2)

D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007).
[CrossRef]

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, 1998).

Supplementary Material (2)

» Media 1: MOV (113 KB)     
» Media 2: MOV (1056 KB)     

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Figures (3)

Fig. 1
Fig. 1

Quarter-wave symmetric OPWM waveform.

Fig. 2
Fig. 2

(a) Photograph of the captured scene; (b) One fringe pattern (λ1 = 60 pixels); (c) One fringe pattern (λ2 = 90 pixels); (d) One fringe pattern(λ3 = 102 pixels); (e) Wrapped phase ϕ1; (f) Wrapped phase ϕ2; (g) Wrapped phase ϕ3; (h) Equivalent phase difference Δϕ12; (i) Equivalent phase difference Δϕ13; (j) Resultant phase Δϕ123.

Fig. 3
Fig. 3

(a) Averaged image of the object ( Media 1); (b) 3-D result ( Media 2).

Equations (11)

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

I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) .
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) / ( 2 I 2 I 1 I 3 ) ] ,
I ( x , y ) = ( I 1 + I 2 + I 3 ) / 3 .
Φ = [ C h ( x , y ) / λ ] 2 π .
Δ Φ 12 = Φ 1 Φ 2 = [ C h ( x , y ) / λ 12 eq ] 2 π .
Δ ϕ 12 = [ Φ 1 Φ 2 ] ( mod 2 π ) = [ ϕ 1 ϕ 2 ] ( mod 2 π ) .
Δ ϕ 13 = [ ϕ 1 ϕ 3 ] ( mod 2 π ) = { [ C h ( x , y ) / λ 13 eq ] 2 π } ( mod 2 π ) ,
Δ ϕ 123 = ( Δ ϕ 13 Δ ϕ 12 ) ( mod 2 π ) = { [ C h ( x , y ) / λ 123 eq ] 2 π } ( mod 2 π ) .
b k = 4 π θ = 0 π / 2 f ( θ ) sin ( k θ ) d θ .

Metrics