Abstract

An algorithm based on the Fourier transform method without phase unwrapping is proposed to measure the 3D profile of objects. Phase unwrapping is essential and time consuming in conventional fringe projection techniques. To avoid this step, the method utilizes a color fringe pattern to substitute a gray-level fringe pattern. Intensity information can be used to extract the wrapped phase, while color information can be used to calculate the phase shift range. Combining the two parts, real phase value can be obtained without phase unwrapping. Experiments are conducted to verify the feasibility of this method.

© 2010 Optical Society of America

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References

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2008 (1)

2007 (2)

2006 (2)

S. Zhang and S.-T. Yau, Opt. Express 14, 2644 (2006).
[CrossRef] [PubMed]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, Opt. Commun. 266, 482 (2006).
[CrossRef]

2005 (1)

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

2003 (1)

2000 (1)

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

1983 (1)

Bingham, P. R.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Burton, D. R.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, Opt. Commun. 266, 482 (2006).
[CrossRef]

Cao, Y.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Chen, W.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

De Nicola, S.

Ferraro, P.

Finizio, A.

Gdeisat, M. A.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, Opt. Commun. 266, 482 (2006).
[CrossRef]

Ghiglia, D. C.

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

Grilli, S.

Lalor, M. J.

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, Opt. Commun. 266, 482 (2006).
[CrossRef]

Laporta, P.

Mann, C. J.

Miccio, L.

Motoh, K.

Osellame, R.

Paquit, V. C.

Paturzo, M.

Pritt, M. D.

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

Song, M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Su, H.

Su, X.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

Su, X.-y.

Takeda, M.

Tobin, K. W.

Volkov, V. V.

Xiang, L.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

Yau, S.-T.

Zhang, H.

Zhang, Q.

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

Zhang, S.

Zhu, Y.

Appl. Opt. (1)

Opt. Commun. (1)

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, Opt. Commun. 266, 482 (2006).
[CrossRef]

Opt. Eng. (1)

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

W. Chen, X. Su, Y. Cao, Q. Zhang, and L. Xiang, Opt. Lasers Eng. 43, 1267 (2005).
[CrossRef]

Opt. Lett. (2)

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Phase indeterminacy in FTP and (b) principle of CMFTP.

Fig. 2
Fig. 2

Calculation process of CMFTP.

Fig. 3
Fig. 3

Schematic experimental arrangement of fringe projection system.

Fig. 4
Fig. 4

(a) Gray deformed fringe pattern of the tested plate, (b) color-marking information, (c) phase map extracted by FTP and 2D phase-unwrapping algorithm, (d) phase map retrieved by CMFTP.

Equations (7)

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g ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + φ ( x , y ) ] ,
G ( f , v ) = Q ( f f 0 , v ) + Q * ( f + f 0 , v ) ,
g ̃ ( x , y ) = 1 2 b ( x , y ) exp [ i 2 π f 0 x + i φ ( x , y ) ] .
g ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + φ 0 ( x , y ) ] .
g ̃ 0 ( x , y ) = 1 2 b ( x , y ) exp [ i 2 π f 0 x + i φ 0 ( x , y ) ] ,
Δ φ ( x , y ) = arctan Im ( g ̃ ( x , y ) g ̃ 0 * ( x , y ) ) Re ( g ̃ ( x , y ) g ̃ 0 * ( x , y ) ) .
{ Δ φ ( x , y ) = arctan Im ( g ̃ ( x , y ) g ̃ 0 * ( x , y ) ) Re ( g ̃ ( x , y ) g ̃ 0 * ( x , y ) ) Δ φ ( x , y ) [ 2 n π , ( 2 n + 1 ) π ) } .

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