Abstract

A novel approach is proposed to unwrap the phase maps of two fringe patterns in fringe pattern projection-based profilometry. In contrast to existing techniques, where spatial frequencies (i.e., the number of fringes on a pattern) of the two fringe patterns must be integers and coprime, the proposed method is applicable for any two fringe patterns with different fringe wavelengths (i.e., the number of pixels in a fringe) and thus provides more flexibility in the use of fringe patterns. Moreover, compared to the existing techniques, the proposed method is simpler in its implementation and has better antierror capability. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.

© 2014 Optical Society of America

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    [CrossRef]
  4. S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
    [CrossRef]
  17. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
    [CrossRef]
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2012 (1)

2011 (1)

2010 (1)

2009 (2)

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48, 105601 (2009).
[CrossRef]

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[CrossRef]

2007 (2)

2006 (2)

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

2005 (1)

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[CrossRef]

2004 (1)

2003 (2)

J. Li, L. G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20, 106–115 (2003).
[CrossRef]

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

1997 (3)

1994 (1)

1993 (1)

Chen, H. J.

Chen, W.

Cheng, W. Q.

Chiang, F.-P.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

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

Chicharo, J.

Ding, Y.

Fang, J.

Ghiglia, D. C.

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

Guan, C.

Hao, Q.

Hassebrook, L. G.

Huang, P. S.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

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

Huntley, J. M.

Jones, J. D. C.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[CrossRef]

Kinell, L.

Lau, D. L.

Li, J.

Li, J. L.

Li, X.

Liu, K.

Lv, D. J.

Pan, J.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

Pritt, M. D.

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

Saldner, H. O.

Su, H. J.

Su, X. Y.

Tan, Y.

Towers, C. E.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[CrossRef]

Towers, D. P.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[CrossRef]

Wang, S.

Wang, Y.

Xi, J.

Yau, S. T.

Yu, Y.

Zhang, C.

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

Zhang, J.

Zhang, S.

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48, 105601 (2009).
[CrossRef]

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[CrossRef]

S. Zhang, X. Li, and S. T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Zhao, H.

Appl. Opt. (6)

J. Opt. Soc. Am. A (2)

Opt. Eng. (4)

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48, 105601 (2009).
[CrossRef]

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

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multifrequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[CrossRef]

Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

Experiment results when λ1=23, λ2=47. (a) and (b) are the deformed fringe patterns, (c) and (d) are the wrapped phase maps, (e) and (f) are the recovered absolute phase maps of (c) and (d).

Fig. 2.
Fig. 2.

Experiment results when λ1=100, λ2=23. (a) and (b) are the deformed fringe patterns, (c) and (d) are the wrapped phase maps, (e) and (f) are the recovered absolute phase maps of (c) and (d).

Fig. 3.
Fig. 3.

Experiment results when λ1=100, λ2=52. (a) and (b) are the deformed fringe patterns, (c) and (d) are the wrapped phase maps, (e) and (f) are the recovered absolute phase maps of (c) and (d).

Tables (2)

Tables Icon

Table 1. Relationship of m2(y)λ2m1(y)λ1 and m1(y), m2(y) when λ1=23, λ2=47

Tables Icon

Table 2. Relationship of m2(y)λ2m1(y)λ1 and m1(y), m2(y) when λ1=52, λ2=100

Equations (25)

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{Φp1(yp)=Φc1(yc)Φp2(yp)=Φc2(yc),
{Φp1(yp)=(2π/λ1)ypΦp2(yp)=(2π/λ2)yp,yp[0,R).
{Φc1(yc)=2πm1(yc)+ϕc1(yc)Φc2(yc)=2πm2(yc)+ϕc2(yc),
0<ϕc1(yc),ϕc2(yc)<2π,
{(2π/λ1)yp=2πm1(yc)+ϕ1(yc)(2π/λ2)yp=2πm2(yc)+ϕ2(yc),yp[0,R).
λ1ϕ1(yc)λ2ϕ2(yc)2π=m2(yc)λ2m1(yc)λ1.
λ2<[λ1ϕ1(y)λ2ϕ2(y)]/2π<λ1
λ2<[m2(y)λ2m1(y)λ1]<λ1.
0m1(y)<R/λ1
0m2(y)<R/λ2.
m1(y)={0,0yp<λ11,λ1yp<2λ1[R/λ1]1,λ1([R/λ1]1)yp<λ1[R/λ1][R/λ1],λ1[R/λ1]yp<R
m2(y)={0,0yp<λ21,λ2yp<2λ2[R/λ2]1,λ2([R/λ2]1)yp<λ2[R/λ2][R/λ2],λ2[R/λ2]yp<R.
[λ2m2(ya)λ1m1(ya)][λ2m2(yb)λ1m1(yb)],foryayb.
Rλ1λ2.
[m2(ya)m2(yb)]/λ1=[m1(ya)m1(yb)]/λ2,foryayb.
[m2(ya)m2(yb)]=nλ1and[m1(ya)m1(yb)]=nλ2.
[kg2m2(ya)kg1m1(ya)][kg2m2(yb)kg1m1(yb)],foryayb
[g2m2(ya)g1m1(ya)][g2m2(yb)g1m1(yb)],foryayb.
N=N1+N21=[R/λ1]+[R/λ2]+1.
G=λ1+λ21[R/λ1]+[R/λ2]+1.
[λ1Δϕ1(y)λ2Δϕ2(y)]2π<λ1+λ22πΔϕmax<k2.
0Δϕmax<kπλ1+λ2.
λ1+λ2<kπΔϕmax.
0Δϕmax<πλ1+λ2=πR/f1+R/f2=πRf1f2f1+f2.
0Δϕmax<πRf1f2f1+f2πf1+f2.

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