Abstract

This paper presents a comparative study on three sinusoidal fringe pattern generation techniques with projector defocusing: the squared binary defocusing method (SBM), the sinusoidal pulse width modulation (SPWM) technique, and the optimal pulse width modulation (OPWM) technique. Because the phase error will directly affect the measurement accuracy, the comparisons are all performed in the phase domain. We found that the OPWM almost always performs the best, and SPWM outperforms SBM to a great extent, while these three methods generate similar results under certain conditions. We will briefly explain the principle of each technique, describe the optimization procedures for each technique, and finally compare their performances through simulations and experiments.

© 2012 Optical Society of America

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References

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2011

2010

2009

2007

2005

2004

H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43, 2906–2914 (2004).
[CrossRef]

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

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

2002

Agelidis, V. G.

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

Ajubi, G. A.

Asundi, A.

Ayubi, J. A.

Balouktsis, A.

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

Balouktsis, I.

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

Chen, M.

Chiang, F.-P.

Chiasson, J. N.

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

Dai, J.

Du, Z.

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

Ekstrand, L.

Ferrari, J. A.

Gorthi, S.

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

Guo, H.

Hao, Q.

Hassebrook, L. G.

He, H.

Huang, L.

Huang, P. S.

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

C. Zhang, P. S. Huang, and F.-P. Chiang, “Microscopic phase-shifting profilometry based on digital micromirror device technology,” Appl. Opt. 41, 5896–5904 (2002).
[CrossRef]

Kemao, Q.

Lau, D. L.

Lei, S.

Li, X.

Liu, K.

Martino, J. M. D.

Mckenzie, K. J.

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

Olvier, J.

Pan, B.

Rastogi, P.

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

Su, X.

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

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13, 3110–3116(2005).
[CrossRef]

Tolbert, L. M.

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

van der Weide, D.

Wang, Y.

Xu, Y.

Yau, S.-T.

Zhang, C.

Zhang, Q.

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

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13, 3110–3116(2005).
[CrossRef]

Zhang, S.

Appl. Opt.

IEEE Power Electron. Lett.

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

IEEE Trans. Power Electron.

J. N. Chiasson, L. M. Tolbert, K. J. Mckenzie, and Z. Du, “A complete solution to the harmonics elimination problem,” IEEE Trans. Power Electron. 19, 491–499 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

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

Opt. Express

Opt. Lasers Eng.

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

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

Opt. Lett.

Other

D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).

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Figures (14)

Fig. 1.
Fig. 1.

Influences of different defocusing degrees on the squared binary pattern. (a)–(e) show the patterns when the projector is nearly in focus to significantly defocused. (f)–(j) show the corresponding cross sections.

Fig. 2.
Fig. 2.

Modulate sinusoidal waveform with binary structured patterns. (a) The sinusoidal and the modulation waveforms. (b) The resultant binary waveform.

Fig. 3.
Fig. 3.

Quarter-wave symmetric OPWM waveform.

Fig. 4.
Fig. 4.

Example of three different patterns. (a) SBM pattern; (b) SPWM pattern; (c) OPWM pattern.

Fig. 5.
Fig. 5.

Influence of high-order harmonics on phase error. (a) Fringe pattern containing + 11th-order harmonics components. (b) Cross-section of (a). (c) Frequency spectrum of (b). (d) Phase error for signal in (b); (e)–(h) The corresponding results when the signal includes the fundamental, third, and ninth-order harmonics.

Fig. 6.
Fig. 6.

Influence of modulation frequency and fringe pitch on phase error with a nearly focused projector. (a) The square binary pattern after defocusing. (b) Phase error changes with modulation frequencies for different fringe pitches (P=36+6×n, n=1,2,10). (c) Phase error changes with the fringe pitches P (modulation period T=6 pixels).

Fig. 7.
Fig. 7.

Influence of modulation frequency and fringe pitch on phase error with a significantly defocused projector. (a) The square binary pattern after defocusing. (b) Phase error changes with modulation frequencies for different fringe pitches (P=36+6×n, n=1,2,10). (c) Phase error changes with the fringe pitches P (modulation period T=6 pixels).

Fig. 8.
Fig. 8.

OPWM optimization example. The first row shows a bad OPWM pattern, and the second row shows the good OPWM pattern. (a) One of the three phase-shifted OPWM patterns. (b) The frequency spectra before smoothing. (c) The frequency spectra after applying a smoothing filter. (d) The phase error. (e) One of the three phase-shifted OPWM patterns. (f) The frequency spectra before smoothing. (g) The frequency spectra after applying a smoothing filter. (h) The phase error.

Fig. 9.
Fig. 9.

Validation of the ideal sinusoidal fringe patterns utilized as reference. (a) The unwrapped phase map. (b) The actual phase error that will be coupled into the real measurement.

Fig. 10.
Fig. 10.

Experimental results on modulation frequency selections. The fringe pitches used here are 42, 60, 72, 90, 102, and 150 pixels. (a) The binary square pattern when the projector is nearly focused. (b) The cross section of (a). (c) The results when the projector is nearly focused; (d)–(f) show the corresponding results when the projector is significantly defocused.

Fig. 11.
Fig. 11.

OPWM optimization results. (a) The SBM pattern with 90 pixels per period. (b) OPWM pattern with third-order harmonics but without fifth- or seventh-order harmonics. (c) OPWM pattern with fifth- and seventh-order harmonics but without third-order harmonics. (d) Frequency spectra of the SBM pattern shown in (a). (e) Frequency spectra of the OPWM pattern in (b). (f) Frequency spectra of the OPWM pattern shown in (c).

Fig. 12.
Fig. 12.

Phase errors from the SBM pattern and different OPWM patterns.

Fig. 13.
Fig. 13.

Comparisons among SBM, SPWM, and OPWM under their respective optimal conditions. (a) The projector is nearly focused. (b) The projector is significantly defocused.

Fig. 14.
Fig. 14.

3D complex shape measurement under different amounts of defocusing. The first row shows the result when the projector is nearly focused, and the second row shows the results when the projector is significantly defocused. (a) Binary pattern when projector is nearly focused. (b) 3D result using SBM patterns. (c) 3D result using SPWM patterns. (d) 3D result using OPWM patterns. (e) Binary pattern when projector is more defocused. (f) 3D result using SBM patterns. (g) 3D result using SPWM patterns. (h) 3D result using OPWM patterns.

Equations (30)

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I1(x,y)=I(x,y)+I(x,y)cos(ϕ2π/3),
I2(x,y)=I(x,y)+I(x,y)cos(ϕ),
I3(x,y)=I(x,y)+I(x,y)cos(ϕ+2π/3),
ϕ(x,y)=tan1[3(I1I3)/(2I2I1I3)].
Sm(fc)={2fcx-2Nx[N/fc,(2N+1)/(2fc))-2fcx+2N+2x[(2N+1)/(2fc),(N+1)/fc),
Si(f0)=0.5+0.5cos(2πf0x).
Ib(x,y)={1Sm(fc)>Si(f0),0otherwise.
a0=12πθ=02πf(θ)dθ=0.5,
ak=1πθ=02πf(θ)cos(kθ)dθ,
bk=1πθ=02πf(θ)sin(kθ)dθ.
bk=4πθ=02πf(θ)sin(kθ)dθ.
bk=4π0α1sin(kθ)dθ+4πα2α3sin(kθ)dθ++4παnπ/2sin(kθ)dθ
=4kπ[1coskα1+coskα2coskα3++coskαn].
b1=1cos(α1)+cos(α2)cos(α3)+cos(α4)=π/4,
b5=1cos(5α1)+cos(5α2)cos(5α3)+cos(5α4)=0.0,
b7=1cos(7α1)+cos(7α2)cos(7α3)+cos(7α4)=0.0,
b11=1cos(11α1)+cos(11α2)cos(11α3)+cos(11α4)=0.0.
Δϕb(x,y)=[ϕb(x,y)ϕs(x,y)]mod2π,
Δϕp(x,y)=[ϕm(x,y)ϕs(x,y)]mod2π,
Δϕo(x,y)=[ϕo(x,y)ϕs(x,y)]mod2π.
y(x)={0x[(2n1)π,2nπ)1x[2nπ,(2n+1)π).
y(x)=0.5+k=02(2k+1)πsin[(2k+1)π].
I1h(x,y)=I(x,y)+I(x,y)cos(ϕ2π/3)+Ik(x,y)cos[(2k+1)(ϕ2π/3)],
I2h(x,y)=I(x,y)+I(x,y)cos(ϕ)+Ik(x,y)cos[(2k+1)ϕ],
I3h(x,y)=I(x,y)+I(x,y)cos(ϕ+2π/3)+Ik(x,y)cos[(2k+1)(ϕ+2π/3)],
ϕ(x,y)=tan1[3(I1hI3h)/(2I2hI1hI3h)]
=tan1[3(I1I3)/(2I2I1I3)].
Ik(x,y)=0.5+23πsin(f0x)+2(2k+1)πsin[(2k+1)f0x].
G(x,y)=12πσ2e(xx¯)2+(yy¯)22σ2.
G(x)=12πσe-(xx¯)22σ2.

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