Abstract

Fringe-projection profilometry is one of the most commonly used noncontact methods for acquiring the three- dimensional (3D) shape information of objects. In practice, the luminance nonlinearity caused by the gamma effect of a digital projector and a digital camera yields undesired fringe intensity changes, which substantially reduce the measurement accuracy. In this Letter, we present a robust and simple scheme to eliminate the intensity nonlinearity induced by the gamma effect by combining a universal phase-shifting algorithm with a gamma correction method. First, by using three-step and large-step phase-shifting techniques, the gamma value involved in the measurement system can be detected. Then, a gamma pre-encoding process is applied to the system for actual 3D shape measurements. With the proposed technique, high accuracy of measurement can be achieved with the conventional small-step phase-shifting algorithm. The validity of the technique is verified by experiments.

© 2010 Optical Society of America

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References

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2010 (1)

C. Quan, W. Chen, and C. Tay, Opt. Lasers Eng. 48, 235 (2010).
[CrossRef]

2009 (2)

2007 (2)

2005 (1)

2004 (2)

2003 (1)

P. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2003).
[CrossRef]

2001 (1)

H. Farid, IEEE Trans. Image Process. 10, 1428 (2001).
[CrossRef]

2000 (1)

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

1996 (1)

1985 (1)

Brohinsky, W.

Brown, G.

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

Chen, F.

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

Chen, M.

Chen, W.

C. Quan, W. Chen, and C. Tay, Opt. Lasers Eng. 48, 235 (2010).
[CrossRef]

Chiang, F.-P.

P. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2003).
[CrossRef]

Du, H.

Farid, H.

H. Farid, IEEE Trans. Image Process. 10, 1428 (2001).
[CrossRef]

Guo, H.

Han, B.

He, H.

Huang, L.

Huang, P.

P. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2003).
[CrossRef]

Jia, S.

Pan, B.

Qian, K.

Quan, C.

C. Quan, W. Chen, and C. Tay, Opt. Lasers Eng. 48, 235 (2010).
[CrossRef]

Song, M.

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

Stetson, K.

Surrel, Y.

Tay, C.

C. Quan, W. Chen, and C. Tay, Opt. Lasers Eng. 48, 235 (2010).
[CrossRef]

Wang, Z.

Weng, J.

Xiong, L.

Yau, S.

Zhang, C.

P. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2003).
[CrossRef]

Zhang, S.

Zhong, J.

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Figures (2)

Fig. 1
Fig. 1

Experimental results related to phase error and gamma detection: (a) phase error from multiple-step phase shifting without gamma pre-encoding, (b) linear relationship between γ and γ p , (c) phase error from three-step phase shifting with various pre-encoding gamma values, and (d) phase error of 300 pixels in an arbitrary line with different phase- shifting schemes.

Fig. 2
Fig. 2

Experimental results. From left to right and top to bottom: a captured fringe image, shape measurement results obtained by the three- and seven-step phase-shifting schemes without gamma correction, and the three-step phase- shifting scheme with proposed gamma correction method.

Equations (15)

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I t ( x , y ) = a ( x , y ) + j = 1 p b j ( x , y ) cos { j [ ϕ ( x , y ) + δ ] } ,
I i t = a + j = 1 p [ B j cos ( j δ i ) A j sin ( j δ i ) ] .
S = i = 1 p + 2 { a + j = 1 p [ B j cos ( j δ i ) A j sin ( j δ i ) ] I i } 2 .
i = 1 p + 2 cos ( δ i ) { a + j = 1 p [ B j cos ( j δ i ) A j sin ( j δ i ) ] I i } = 0.
[ i = 1 p + 2 cos 2 ( δ i ) ] B 1 i = 1 p + 2 cos ( δ i ) I i = 0.
B 1 = i = 1 p + 2 cos ( δ i ) I i i = 1 p + 2 cos 2 ( δ i ) .
A 1 = i = 1 p + 2 sin ( δ i ) I i i = 1 p + 2 sin 2 ( δ i ) .
ϕ = tan 1 A 1 B 1 = tan 1 i = 1 p + 2 sin ( δ i ) I i i = 1 p + 2 cos ( δ i ) I i .
I n = I 0 γ 0 ,
I 0 = I n γ p / γ 0 .
I 0 = c 1 I n c 0 γ p / γ 0 + γ b + c 2 = c 1 I n γ p / γ a + γ b + c 2 ,
ϕ = tan 1 { [ I 2 γ sin ( 2 π 3 ) + I 3 γ sin ( 4 π 3 ) ] I 1 γ + I 2 γ cos ( 2 π 3 ) + I 3 γ cos ( 4 π 3 ) } ,
γ = γ p / γ a + γ b .
tan 1 { [ I 2 γ sin ( 2 π 3 ) + I 3 γ sin ( 4 π 3 ) ] I 1 γ + I 2 γ cos ( 2 π 3 ) + I 3 γ cos ( 4 π 3 ) } ϕ c = 0 ,
γ a = γ p 1 γ p 2 γ 1 γ 2 , γ b = γ p 1 γ 2 γ 1 γ p 2 γ p 1 γ p 2 .

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