Abstract

A least-squares fitting technique for the carrier phase component in fringe projection profilometry is presented. The carrier phase distribution for an arbitrary measurement system can be perfectly described with a rational function, whose coefficients can be estimated by least-squares fitting to the measured reference phases, so that the restrictions and limitations in the existing techniques are eliminated.

© 2006 Optical Society of America

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Errata

Hongwei Guo, Mingyi Chen, and Peng Zheng, "Least-squares fitting of carrier phase distribution by using a rational function in fringe projection profilometry: erratum," Opt. Lett. 32, 487-487 (2007)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-32-5-487

References

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    [CrossRef]
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    [CrossRef]

2006 (3)

2005 (2)

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

L. Chen and C. Quan, Opt. Lett. 30, 2101 (2005).
[CrossRef] [PubMed]

2003 (2)

H. Guo and M. Chen, Opt. Eng. 42, 900 (2003).
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

1994 (1)

M. Pirga and M. Kujawinska, Measurement 13, 191 (1994).
[CrossRef]

1985 (1)

1983 (1)

Bi, H.

Chen, L.

Chen, M.

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

H. Guo and M. Chen, Opt. Eng. 42, 900 (2003).
[CrossRef]

García, V.

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

Guo, H.

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

H. Guo and M. Chen, Opt. Eng. 42, 900 (2003).
[CrossRef]

Halioua, Maurice

He, H.

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

Kujawinska, M.

M. Pirga and M. Kujawinska, Measurement 13, 191 (1994).
[CrossRef]

Liu, H. C.

Luna, E.

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

Mutoh, K.

Pirga, M.

M. Pirga and M. Kujawinska, Measurement 13, 191 (1994).
[CrossRef]

Quan, C.

Salas, L.

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

Salinas, J.

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

Servin, M.

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

Srinivasan, V.

Takeda, M.

Tay, C. J.

Wang, Z.

Yu, Y.

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

Appl. Opt. (2)

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

Measurement (1)

M. Pirga and M. Kujawinska, Measurement 13, 191 (1994).
[CrossRef]

Opt. Eng. (3)

L. Salas, E. Luna, J. Salinas, V. García, and M. Servin, Opt. Eng. 42, 3307 (2003).
[CrossRef]

H. Guo, H. He, Y. Yu, and M. Chen, Opt. Eng. 44, 033603 (2005).
[CrossRef]

H. Guo and M. Chen, Opt. Eng. 42, 900 (2003).
[CrossRef]

Opt. Lett. (3)

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Figures (2)

Fig. 1
Fig. 1

Geometry for fringe projection profilometry. (a) Positions and (b) orientations of the camera and projector, respectively, relative to the reference plane.

Fig. 2
Fig. 2

Experimental results. (a) Fringe pattern on the reference plane. (b) Phase map (in radians) reconstructed from (a). (c) Least-squares fitting result (in radians) of (b) using the rational function. (d) Residual (in radians) obtained by subtracting (c) from (b). (e) Deformed fringe pattern on the object. (f) Reconstructed 3D shape.

Equations (9)

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[ x E y E z E ] = [ κ ( i i o ) κ ( j j o ) 0 ] ,
[ x E y E z E ] = [ cos γ sin γ 0 sin γ cos γ 0 0 0 1 ] [ cos β 0 sin β 0 1 0 sin β 0 cos β ] [ 1 0 0 0 cos α sin α 0 sin α cos α ] [ x E y E 0 ] .
[ x D y D z D ] = [ ( x C z E x E z C ) ( z E z C ) ( y C z E y E z C ) ( z E z C ) 0 ] = [ ( b 1 x E + b 2 y E ) ( 1 + a 1 x E + a 2 y E ) ( b 3 x E + b 4 y E ) ( 1 + a 1 x E + a 2 y E ) 0 ] ,
ϕ ( i , j ) = ϕ D .
[ x D y D z D ] = [ 1 0 0 0 cos θ sin θ 0 sin θ cos θ ] [ cos ζ 0 sin ζ 0 1 0 sin ζ 0 cos ζ ] [ cos ξ sin ξ 0 sin ξ cos ξ 0 0 0 1 ] [ x D y D 0 ] .
[ x F y F z F ] = [ ( x P z D x D z P ) ( z D z P ) ( y P z D y D z P ) ( z D z P ) 0 ] = [ ( d 1 x D + d 2 y D ) ( 1 + c 1 x D + c 2 y D ) ( d 3 x D + d 4 y D ) ( 1 + c 1 x D + c 2 y D ) 0 ] ,
ϕ D = ϕ F = ϕ O + 2 π x F p ,
ϕ ( i , j ) = ( r + s i + t j ) ( 1 + u i + v j ) ,
r + s i + t j u ϕ ( i , j ) i v ϕ ( i , j ) j = ϕ ( i , j ) ,

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