Abstract

Three-dimensional profilometry by sinusoidal fringe projection using phase-shifting algorithms is usually distorted by the nonlinear intensity response of commercial video projectors. To overcome this problem, several methods including sinusoidal pulse width modulation (SPWM) were proposed to generate sinusoidal fringe patterns with binary ones by defocusing the project to some certain extent. However, the residual errors are usually nonnegligible for highly accurate measurement fields, especially when the defocusing level is insufficient. In this work, we propose two novel methods to further improve the defocusing technique. We find that by properly optimizing SPWM patterns according to some criteria, and combining SPWM technique with four-step phase-shifting algorithm, the dominant undesired harmonics will have no impact on the phase obtained. We also propose a new sinusoidal fringe generation technique called tripolar SPWM, which can generate ideal sinusoidal fringe patterns with a very small degree of defocusing. Simulations and experiments are presented to verify the performance of these two proposed techniques.

© 2012 Optical Society of America

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References

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    [CrossRef]

2012 (2)

2011 (2)

2010 (7)

2009 (2)

2007 (2)

S. Zhang, and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

S. Zhang, and S. T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007).
[CrossRef]

2004 (2)

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-D shape measurement: color coupling and imbalance compensation,” Proc. SPIE 5265, 205–212 (2004).
[CrossRef]

R. Hofling and E. Ahl, “ALP: Universal DMD controller for metrology and testing,” Proc. SPIE 5289, 322–329 (2004).
[CrossRef]

2003 (1)

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

2000 (1)

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

1992 (1)

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

Ahl, E.

R. Hofling and E. Ahl, “ALP: Universal DMD controller for metrology and testing,” Proc. SPIE 5289, 322–329 (2004).
[CrossRef]

Alonso, J. R.

Asundil, A.

Ayubi, G. A.

Ayubi, J. A.

Brown, G. M.

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

Chen, F.

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

Chiang, F. P.

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-D shape measurement: color coupling and imbalance compensation,” Proc. SPIE 5265, 205–212 (2004).
[CrossRef]

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

Di Martino, J. M.

Ekstrand, L.

Fernandez, A.

Fernández, A.

Ferrari, J. A.

Flores, J. L.

Gorthi, S. S.

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

Hao, Q.

Hassebrook, L. G.

Hoang, T.

Hofling, R.

R. Hofling and E. Ahl, “ALP: Universal DMD controller for metrology and testing,” Proc. SPIE 5289, 322–329 (2004).
[CrossRef]

Huang, L.

Huang, P. S.

S. Zhang, and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-D shape measurement: color coupling and imbalance compensation,” Proc. SPIE 5265, 205–212 (2004).
[CrossRef]

Huang, P. S. S.

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

Kemao, Q.

Lau, D. L.

Lei, S. Y.

Liu, K.

Nguyen, D.

Pan, B.

Pan, J. H.

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-D shape measurement: color coupling and imbalance compensation,” Proc. SPIE 5265, 205–212 (2004).
[CrossRef]

Perciante, C. D.

Rastogi, P.

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

Song, M. M.

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

Su, X. Y.

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Laser Eng. 48, 191–204 (2010).
[CrossRef]

Su, X.-Y.

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

von Bally, G.

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

Vukicevic, D.

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

Wang, Y.

Wang, Y. C.

Wang, Y. J.

Wang, Z. Y.

Yau, S. T.

Zhang, C. P.

P. S. S. Huang, C. P. 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. C.

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Laser Eng. 48, 191–204 (2010).
[CrossRef]

Zhang, S.

Zhou, W.-S.

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

Appl. Opt. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

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

Opt. Eng. (3)

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

S. Zhang, and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

Opt. Laser Eng. (2)

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Laser Eng. 48, 191–204 (2010).
[CrossRef]

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

Opt. Lasers Eng. (1)

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

Opt. Lett. (7)

Proc. SPIE (2)

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed 3-D shape measurement: color coupling and imbalance compensation,” Proc. SPIE 5265, 205–212 (2004).
[CrossRef]

R. Hofling and E. Ahl, “ALP: Universal DMD controller for metrology and testing,” Proc. SPIE 5289, 322–329 (2004).
[CrossRef]

Other (1)

B. W. Williams, ed., Principles and Elements of Power Electronics (Barry W Williams, 2006).

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Figures (15)

Fig. 1.
Fig. 1.

Typical crossed-optical-axes profilometry arrangement.

Fig. 2.
Fig. 2.

Frequency spectrum of one cross section of the squared binary structured pattern.

Fig. 3.
Fig. 3.

SPWM waveform generation and harmonics distribution. (a) The sinusoidal and the modulation triangle waveforms with fc=10f0;(b) the resultant binary SPWM waveform; (c) frequency spectrum of (b).

Fig. 4.
Fig. 4.

Comparison between two ways to generate discrete SPWM pattern with fringe pitch of 80 pixels and fc=10f0. (a) The sinusoidal and the modulation triangle waveforms with low resolution; (b) the sinusoidal and the modulation triangle waveforms with high resolution; (c) the resultant SPWM pattern from (a); (d) the resultant SPWM pattern by down sampling the high resolution SPWM pattern obtained from (b).

Fig. 5.
Fig. 5.

Comparison among SPWM patterns (fringe pitch 80 pixels) with different modulation frequencies. Top row: The sinusoidal and the modulation triangle waveforms with (a) fc=6f0, (b) fc=12f0, and (c) fc=10f0. Middle row: (d)–(f) the resultant binary SPWM waveform from (a), (b), and (c). Bottom row: (g)–(i) frequency spectra of (d), (e), and (f).

Fig. 6.
Fig. 6.

Alleviating the aliasing effect by reducing the amplitude of the triangle carrier by 3%. (a) The sinusoidal and the modulation triangle waveforms with reduced amplitude; (b) the resultant binary SPWM waveform; (c) frequency spectrum of (b). Comparing with the frequency spectrum shown in Fig. 5(f), the improvement is obvious.

Fig. 7.
Fig. 7.

Two good examples of SPWM patterns generated using the proposed rules. (a) The binary SPWM waveform with fringe pitch of 60 pixels and fc=8f0; (b) frequency spectrum of (a); (c) the binary SPWM waveform with fringe pitch of 100 pixels and fc=12f0; (b) frequency spectrum of (c).

Fig. 8.
Fig. 8.

Tripolar SPWM wave form generation and harmonics distribution. (a) The sinusoidal and the two modulation triangle waveforms displaced by π(fc=10f0); (b),(c) the two binary SPWM waveforms obtained; (d) the resultant tripolar SPWM pattern; (e) frequency spectrum of (d).

Fig. 9.
Fig. 9.

A good example of tripolar SPWM pattern generated using the proposed optimization rules. (a) The tripolar SPWM waveform with fringe pitch of 80 pixels and fc=8f0; (b) frequency spectrum of (a).

Fig. 10.
Fig. 10.

Simulation results of SBM using three to five-step phase-shifting algorithms. (a) The original squared binary structured pattern; (b) the Gaussian smoothed version of (a); (c) frequency spectrum of (a); (d) frequency spectrum of (b); (e) the phase error of three-step algorithm (RMS: 0.1638 rad); (f) the phase error of four-step algorithm (RMS: 0.3250 rad); (g) the phase error of five-step algorithm (RMS: 0.0697 rad).

Fig. 11.
Fig. 11.

Simulation results of SPWM (fc=8f0) using three to five-step phase-shifting algorithms. (a) The original SPWM pattern; (b) the Gaussian smoothed version of (a); (c) frequency spectrum of (a); (d) frequency spectrum of (b); (e) the phase error of three-step algorithm (RMS: 0.2319 rad); (f) the phase error of four-step algorithm (RMS: 0.0436 rad); (g) the phase error of five-step algorithm (RMS: 0.1396 rad).

Fig. 12.
Fig. 12.

Simulation results of SPWM (fc=9f0) using three to five-step phase-shifting algorithms. (a) The original SPWM pattern; (b) the Gaussian smoothed version of (a); (c) frequency spectrum of (a); (d) frequency spectrum of (b); (e) the phase error of three-step algorithm (RMS: 0.1135 rad); (f) the phase error of four-step algorithm (RMS: 0.2306 rad); (g) the phase error of five-step algorithm (RMS: 0.1986 rad).

Fig. 13.
Fig. 13.

Simulation results of tripolar SPWM(fc=8f0) using three to five-step phase-shifting algorithms. (a) The original tripolar SPWM pattern; (b) the Gaussian smoothed version of (a) (filter size 8 pixels, standard deviation 1.5 pixels); (c) frequency spectrum of (a); (d) frequency spectrum of (b); (e) the phase error of three-step algorithm (RMS: 0.0488 rad); (f) the phase error of four-step algorithm (RMS: 0.0468 rad); (g) the phase error of five-step algorithm (RMS: 0.0389 rad).

Fig. 14.
Fig. 14.

3D measurement results of a plaster geometric model using different patterns (fringe pitch 60 pixels) with different phase-shifting algorithms when the projector is slightly defocused. The first row shows the tested object with SBM pattern (a), the 3D results of three-, four-, and five-step phase-shifting algorithms using SBM patterns (b)–(d). The second row shows the tested object with SPWM pattern (fc=8f0) (e), the 3-D results of three-, four-, and five-steps phase-shifting algorithms using SPWM patterns (fc=8f0) (f–h). The third row shows the tested object with SPWM pattern (fc=8f0) (i), the 3D results of three-, four-, and five-steps phase-shifting algorithms using SPWM patterns (fc=9f0) (j)–(l). The forth row shows the tested object with tripolar SPWM pattern (fc=8f0) (m), and the 3D results of three-, four-, and five-step phase-shifting algorithms using tripolar patterns (fc=8f0) (n-p).

Fig. 15.
Fig. 15.

3D shape measurement of a complex sculpture using the proposed techniques (fringe pitch 48 pixels). (a) One of SPWM pattern with fc=6f0; (b) the measured object with the slightly defocused SPWM pattern; (c) 3D result with the SPWM plus four-step phase-shifting method; (d) one of tripolar SPWM pattern with fc=7f0; (e) the measured object with the slightly defocused tripolar SPWM pattern; (f) 3D result with the tripolar SPWM plus three-step phase-shifting method.

Tables (1)

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Table 1. Sensitivity of Different Phase-Shifting Algorithms to Harmonics

Equations (10)

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I(x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)+2πfx],
h(x,y)=lϕAB/[2πdf+ϕAB],
p(x)=rect(2xT)*comb(xT),
P(fx)=Cj=+sinc(fx2f0)·δ(fxjf0),
h(x,y)=12πσ2exp(x2+y22σ2),
nfc±kf0.
In(x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)+2πn/N],
ϕ(x,y)=tan1n=1NIn(x,y)sin(2πn/N)n=1NIn(x,y)cos(2πn/N).
In(x,y)=A(x,y)+B(x,y)[cosϕ(x,y)+2πn/N]+k=2Bk(x,y){cosk[ϕ(x,y)+2πn/N]}.
2nfc±kf0,

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