Abstract

A novel phase-analysis method is proposed. To get the fringe order of a fringe image, the amplitude-modulation fringe pattern is carried out, which is combined with the phase-shift method. The primary phase value is obtained by a phase-shift algorithm, and the fringe-order information is encoded in the amplitude-modulation fringe pattern. Different from other methods, the amplitude-modulation fringe identifies the fringe order by the amplitude of the fringe pattern. In an amplitude-modulation fringe pattern, each fringe has its own amplitude; thus, the order information is integrated in one fringe pattern, and the absolute fringe phase can be calculated correctly and quickly with the amplitude-modulation fringe image. The detailed algorithm is given, and the error analysis of this method is also discussed. Experimental results are presented by a full-field shape measurement system where the data has been processed using the proposed algorithm.

© 2010 OSA

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References

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    [CrossRef]
  2. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  23. J. Li, G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20(1), 106–115 (2003).
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    [CrossRef]

2010

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

S. Y. Gai and F. P. Da, “A novel phase-shifting method based on strip marker,” Opt. Lasers Eng. 48(2), 205–211 (2010).
[CrossRef]

2008

X. Chen, J. Xi, and Y. Jin, “Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection,” Opt. Eng. 47(11), 113601–113611 (2008).
[CrossRef]

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

F. P. Da and S. Y. Gai, “Flexible three-dimensional measurement technique based on a digital light processing projector,” Appl. Opt. 47(3), 377–385 (2008).
[CrossRef] [PubMed]

M. Servin, M. Cywiak, D. Malacara-Hernandez, J. C. Estrada, and J. A. Quiroga, “Spatial carrier interferometry from M temporal phase shifted interferograms: squeezing interferometry,” Opt. Express 16(13), 9276–9283 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-13-9276 .
[CrossRef] [PubMed]

2007

S. Zhang, X. L. Li, and S. T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46(1), 50–57 (2007).
[CrossRef]

C. Yu and Q. J. Peng, “A correlation-based phase unwrapping method for Fourier-transform profilometry,” Opt. Eng. 45(6), 730–736 (2007).
[CrossRef]

2006

2004

C. Towers, D. Towers, and J. Jones, “Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry,” Opt. Express 12(6), 1136–1143 (2004).
[CrossRef] [PubMed]

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41(1), 57–71 (2004).
[CrossRef]

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–240 (2004).
[CrossRef]

2003

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

J. Li, G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20(1), 106–115 (2003).
[CrossRef]

2001

X. Y. Su and W. J. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

L. Kinell and M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40(14), 2297–2303 (2001).
[CrossRef]

1999

1997

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36(1), 277–280 (1997).
[CrossRef] [PubMed]

L. Di Stefano and F. Boland, “New phase extraction algorithm for phase profilometry,” Mach. Vis. Appl. 10(4), 188–200 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8(9), 986–992 (1997).
[CrossRef]

1994

1993

Blais, F.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–240 (2004).
[CrossRef]

Boland, F.

L. Di Stefano and F. Boland, “New phase extraction algorithm for phase profilometry,” Mach. Vis. Appl. 10(4), 188–200 (1997).
[CrossRef]

Busca, G.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

Carocci, M.

Chao, Y. J.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

Chen, M.

Chen, W.

Chen, W. J.

X. Y. Su and W. J. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

Chen, X.

X. Chen, J. Xi, and Y. Jin, “Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection,” Opt. Eng. 47(11), 113601–113611 (2008).
[CrossRef]

Chiang, F. P.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

Cywiak, M.

Da, F. P.

Di Stefano, L.

L. Di Stefano and F. Boland, “New phase extraction algorithm for phase profilometry,” Mach. Vis. Appl. 10(4), 188–200 (1997).
[CrossRef]

Estrada, J. C.

Fu, Q. L.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

Gai, S. Y.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

Guan, C.

Guo, H.

Hassebrook, G.

Hu, Q. Y.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

Huang, P. S.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

Huntley, J. M.

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8(9), 986–992 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
[CrossRef] [PubMed]

Iwata, K.

Jin, Y.

X. Chen, J. Xi, and Y. Jin, “Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection,” Opt. Eng. 47(11), 113601–113611 (2008).
[CrossRef]

Jones, J.

Kakunai, S.

Kinell, L.

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41(1), 57–71 (2004).
[CrossRef]

L. Kinell and M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40(14), 2297–2303 (2001).
[CrossRef]

Li, J.

Li, J. L.

Li, X. L.

Malacara-Hernandez, D.

McNeill, S. R.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

Peng, Q. J.

C. Yu and Q. J. Peng, “A correlation-based phase unwrapping method for Fourier-transform profilometry,” Opt. Eng. 45(6), 730–736 (2007).
[CrossRef]

Quiroga, J. A.

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

Rodella, R.

Sakamoto, T.

Saldner, H. O.

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8(9), 986–992 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
[CrossRef] [PubMed]

Sansoni, G.

Schreier, H. W.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

Servin, M.

Sjödahl, M.

Su, H. J.

Su, X. Y.

X. Y. Su and W. J. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36(1), 277–280 (1997).
[CrossRef] [PubMed]

Sutton, M. A.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

Tan, Y.

Towers, C.

Towers, D.

Xi, J.

X. Chen, J. Xi, and Y. Jin, “Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection,” Opt. Eng. 47(11), 113601–113611 (2008).
[CrossRef]

Yau, S. T.

Yu, C.

C. Yu and Q. J. Peng, “A correlation-based phase unwrapping method for Fourier-transform profilometry,” Opt. Eng. 45(6), 730–736 (2007).
[CrossRef]

Zappa, E.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

Zhang, S.

Zhao, H.

Zhao, W.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

Zheng, P.

Appl. Opt.

Exp. Mech.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, “Development and assessment of a single-image fringe projection method for dynamic applications,” Exp. Mech. 41(3), 205–217 (2001).
[CrossRef]

J. Electron. Imaging

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging 13(1), 231–240 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Mach. Vis. Appl.

L. Di Stefano and F. Boland, “New phase extraction algorithm for phase profilometry,” Mach. Vis. Appl. 10(4), 188–200 (1997).
[CrossRef]

Meas. Sci. Technol.

J. M. Huntley and H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8(9), 986–992 (1997).
[CrossRef]

Opt. Eng.

C. Yu and Q. J. Peng, “A correlation-based phase unwrapping method for Fourier-transform profilometry,” Opt. Eng. 45(6), 730–736 (2007).
[CrossRef]

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 487–493 (2003).
[CrossRef]

X. Chen, J. Xi, and Y. Jin, “Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection,” Opt. Eng. 47(11), 113601–113611 (2008).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

S. Y. Gai and F. P. Da, “A novel phase-shifting method based on strip marker,” Opt. Lasers Eng. 48(2), 205–211 (2010).
[CrossRef]

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41(1), 57–71 (2004).
[CrossRef]

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are,” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

X. Y. Su and W. J. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

Opt. Lett.

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Figures (15)

Fig. 1
Fig. 1

Amplitude-modulation fringe pattern.

Fig. 2
Fig. 2

Parameter λ.

Fig. 3
Fig. 3

Calculation result of λ.

Fig. 4
Fig. 4

Relationships in the reshape method.

Fig. 5
Fig. 5

Result of λ (reshaped).

Fig. 6
Fig. 6

System layout.

Fig. 7
Fig. 7

Fringe images of object 1.

Fig. 8
Fig. 8

Pixel gray of I^ and I1 .

Fig. 10
Fig. 10

Calculated λ(k) (reshaped).

Fig. 9
Fig. 9

Calculated λ(k) .

Fig. 11
Fig. 11

3D shape reconstruction result of object 1.

Fig. 12
Fig. 12

Experiment result of object 2.

Fig. 13
Fig. 13

Fringe image of object 3.

Fig. 14
Fig. 14

3D shape reconstruction result of object 3.

Fig. 15
Fig. 15

Error map of object 3.

Tables (1)

Tables Icon

Table 1 Experiment Results of Object 3 (Unit: mm)

Equations (24)

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

I(x,y)=a+bsin[θ(x,y)],
θ(x,y)=2k(x,y)π+φ(x,y),     0φ(x,y)<2π,
I^(x,y)={a+λ[k(x,y)]bsin[θ(x,y)],     0φ(x,y)<πa+bsin[θ(x,y)],             πφ(x,y)<2π ,
λ[k]=k/10,   k=1,2,...n,
λ[k]={0.1,0.2,...,n0.1},
I1(x,y)=a+bsin[θ(x,y)],
I2(x,y)=a+bsin[θ(x,y)+π/2],
I3(x,y)=a+bsin[θ(x,y)+π],
I4(x,y)=a+bsin[θ(x,y)+3π/2],
I1(x,y)I3(x,y)I2(x,y)I4(x,y)=sinθ(x,y)sin[θ(x,y)+π/2]=tanθ(x,y).
φ(x,y)=tan1[I1(x,y)I3(x,y)I2(x,y)I4(x,y)].
γ(x,y)=ba=2[I1(x,y)I2(x,y)]2+[I3(x,y)+I4(x,y)]2I1(x,y)+I2(x,y)+I3(x,y)+I4(x,y).
a=I1(x,y)+I2(x,y)+I3(x,y)+I4(x,y)4.
λ(x,y)=2[I^(x,y)a]I1(x,y)I3(x,y).
k(x,y)=10λ(x,y).
k(x01,y0)={k(x0,y0)1,     Δφ(x01,y0)>3π/2k(x0,y0),       Δφ(x01,y0)<π/2.
k(x0+1,y0)={k(x0,y0)+1,     Δφ(x0+1,y0)>3π/2k(x0,y0),       Δφ(x0+1,y0)<π/2.
I^(θ)={a+λ(θ)bsin(θ),       0φ(x,y)<πa+bsin(θ),           πφ(x,y)<2π,
dI^=bsin(θ)dλ+bλcosθdθ+bk=1n[δ(kπ)(λ|θ=kπ+λ|θ=kπ)],
dλ=1sin(θ)[1bdI^λcosθdθk=1n(δ(kπ)(λ|θ=kπ+λ|θ=kπ))].
θ(x,y)=kπ,I1(x,y)=I3(x,y).
{θ(x,y)(2kπ,2kπ+π),                   I1(x,y)>I3(x,y)θ(x,y)(2kπ+π,2kπ+2π),           I1(x,y)<I3(x,y).
{θ(x,y)(2kπ,2kπ+0.5π),               I2(x,y)I4(x,y)θ(x,y)(2kπ+0.5π,2kπ+π),           I2(x,y)<I4(x,y).
λ(x,y)={[λ(x+2,y)+λ(x+3,y)+λ(x+4,y)]/3,       I2(x,y)I4(x,y)[λ(x2,y)+λ(x3,y)+λ(x4,y)]/3,       I2(x,y)<I4(x,y).

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