Abstract

The gamma effect of phase-measuring profilometry systems yields nonlinear errors, which will substantially reduce the 3D shape measurement accuracy. Here, a robust and flexible gamma correction method based on the probability distribution function (PDF) of the wrapped phase is presented. First, a series of PDF curves are generated from the simulated wrapped phase distributions with different gamma values. Second, an experimental PDF curve will be produced after obtaining the wrapped phase from the captured three-step phase-shift fringe images. Then, a correlation procedure will be used to find the most similar PDF curve from the simulated PDF curves, and the gamma value of the matched PDF curve is that of the current system. Note that the gamma value detected by this method will be smaller than the true value due to the defocusing effect of the projection system with a large aperture. Therefore, an improved PDF-based algorithm, which projects two sets of three-step phase-shifting sinusoidal fringe patterns with different pre-coded gamma values and produces two PDF curves, is also added. Then after one more correlation procedure, a more accurate systematic gamma value could be calculated. It does not need large-step phase-shift images and 2×3 fringe images are quite enough. The experimental results show that the technique is very fast, easy to use and quite accurate.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2015 (2)

2014 (2)

D. Zheng and F. Da, “Absolute phase retrieval for defocused fringe projection three-dimensional measurement,” Opt. Commun. 312, 302–311 (2014).
[Crossref]

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

2013 (1)

2011 (2)

2010 (7)

2009 (2)

2007 (2)

2004 (1)

2003 (1)

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement: an error analysis,” Proc. SPIE 5144, 372–380 (2003).
[Crossref]

2001 (1)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

1995 (1)

1992 (1)

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Asundi, A.

Baker, M. J.

M. J. Baker, J. Xi, and J. F. Chicharo, “Elimination of gamma non-linear luminance effects for digital video projection phase measuring profilometers,” in 4th IEEE International Symposium on Electronic Design, Test and Applications (IEEE, 2008), pp. 496–501.

Barnes, J. C.

Z. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Cai, Z.

Chen, M

Chicharo, J. F.

M. J. Baker, J. Xi, and J. F. Chicharo, “Elimination of gamma non-linear luminance effects for digital video projection phase measuring profilometers,” in 4th IEEE International Symposium on Electronic Design, Test and Applications (IEEE, 2008), pp. 496–501.

Da, F.

D. Zheng and F. Da, “Absolute phase retrieval for defocused fringe projection three-dimensional measurement,” Opt. Commun. 312, 302–311 (2014).
[Crossref]

Dai, J.

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50(17), 2572–2581 (2011).
[Crossref]

Ekstrand, L.

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe Projection Techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guo, H

Hao, Q.

Hassebrook, L.

He, D.

He, H

He, X. Y.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

Hoang, T.

Huang, L.

Huang, S.

Jiang, H.

Jin, H.

Kemao, Q.

Langoju, R.

Lau, D.

Lei, S.

Li, B.

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Li, Y.

Li, Z.

Liu, K.

Liu, X.

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Lohry, W.

Nguyen, D.

Nguyen, D. A.

Z. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Notni, G.

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement: an error analysis,” Proc. SPIE 5144, 372–380 (2003).
[Crossref]

Notni, G. H.

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement: an error analysis,” Proc. SPIE 5144, 372–380 (2003).
[Crossref]

Pan, B.

Patil, A.

Peng, X.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Qian, Y.

Quan, C.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

Ramani, S.

Rastogi, P.

Rathjen, C.

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Shang, H. M.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

Su, X. Y.

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Tay, C. J.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

von Bally, G.

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Vukicevic, D.

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Wang, C. F.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

Wang, H.

Wang, Y.

Wang, Z.

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
[Crossref]

Z. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Xi, J.

M. J. Baker, J. Xi, and J. F. Chicharo, “Elimination of gamma non-linear luminance effects for digital video projection phase measuring profilometers,” in 4th IEEE International Symposium on Electronic Design, Test and Applications (IEEE, 2008), pp. 496–501.

Xu, Y.

Yau, S. T.

Zhang, S.

Zhang, Z.

Zhao, C.

Zheng, D.

D. Zheng and F. Da, “Absolute phase retrieval for defocused fringe projection three-dimensional measurement,” Opt. Commun. 312, 302–311 (2014).
[Crossref]

Zhou, W.

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

Appl. Opt. (4)

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, “Shape measurement of small objects using LCD fringe projection with phase shifting,” Opt. Commun. 189(1-3), 21–29 (2001).
[Crossref]

X. Y. Su, W. Zhou, G. von Bally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–573 (1992).
[Crossref]

D. Zheng and F. Da, “Absolute phase retrieval for defocused fringe projection three-dimensional measurement,” Opt. Commun. 312, 302–311 (2014).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (3)

J. Dai, B. Li, and S. Zhang, “High-quality fringe pattern generation using binary pattern optimization through symmetry and periodicity,” Opt. Lasers Eng. 52, 195–200 (2014).
[Crossref]

Z. Wang, D. A. Nguyen, and J. C. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

S. Gorthi and P. Rastogi, “Fringe Projection Techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Opt. Lett. (6)

Pattern Recognit. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010).
[Crossref]

Proc. SPIE (1)

G. H. Notni and G. Notni, “Digital fringe projection in 3D shape measurement: an error analysis,” Proc. SPIE 5144, 372–380 (2003).
[Crossref]

Other (1)

M. J. Baker, J. Xi, and J. F. Chicharo, “Elimination of gamma non-linear luminance effects for digital video projection phase measuring profilometers,” in 4th IEEE International Symposium on Electronic Design, Test and Applications (IEEE, 2008), pp. 496–501.

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Figures (10)

Fig. 1.
Fig. 1. Camera image generation procedure.
Fig. 2.
Fig. 2. The fringe patterns projected with, (a) gamma = 1, (b) gamma = 2, (c) the phase errors, (d) the PDF curves with different gamma values.
Fig. 3.
Fig. 3. Architecture of the proposed method.
Fig. 4.
Fig. 4. The correlation curve of the PDFs vs. gamma value.
Fig. 5.
Fig. 5. Architecture of the proposed method with considering the defocusing effect and other factors.
Fig. 6.
Fig. 6. Gamma correction in the case of noise: (a) STD results corresponding to different levels of noise, (b) gamma detection results with 4% noise.
Fig. 7.
Fig. 7. Gamma detection results without considering defocusing and other factors: (a) the comparison of simulated and measured PDF curves, (b) the correlation curve.
Fig. 8.
Fig. 8. The residual phase errors compared with the ground truth.
Fig. 9.
Fig. 9. Gamma detection results with considering defocusing and other factors: (a) the comparison of simulated and measured PDF curves, (b) the phase errors.
Fig. 10.
Fig. 10. Measurement result of a gourd model: (a) captured fringe image, (b) phase error without correction, (c) the residual phase error after Thang’s gamma correction, (d) the result with our gamma correction, and (e) the cross sections of the phase errors.

Tables (2)

Tables Icon

Table 1. Quantitative Comparison of Measurement Results by Four Methods

Tables Icon

Table 2. Quantitative Comparison of Measurement Results by Two Methods

Equations (12)

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

I n ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + δ n ] ,
I n c = [ A c + B c cos ( ϕ + δ n ) ] γ  =  A  +  k = 1 B k cos [ k ( ϕ + δ n ) ] ,
ϕ = a r c tan ( n = 0 2 I n c sin δ n n = 0 2 I n c cos δ n ) = a r c tan ( B 1 sin ( ϕ ) B 2 sin ( 2 ϕ ) B 1 cos ( ϕ ) + B 2 cos ( 2 ϕ ) ) .
Δ ϕ = arctan { [ B 2 B 1 sin ( 3 ϕ ) ] / B 2 B 1 sin ( 3 ϕ ) ] [ 1 + B 2 B 1 cos ( 3 ϕ ) ] [ 1 + B 2 B 1 cos ( 3 ϕ ) ] } .
I n c = ( I n ) γ 0 ,
I n c = ( I n ) γ 0 / γ 0 γ p γ p = ( I n ) γ 0 .
I n c = C 1 ( I n ) γ a / γ a γ p γ p + γ b + C 2 ,
γ = γ a / γ a γ p γ p + γ b .
F ( m ) = P { 2 π m M π ϕ m < 2 π m + 1 M π } ,
R i = F F i F 2 F i 2 ,
{ γ 1 = γ a γ p 1 + γ b γ 2 = γ a γ p 2 + γ b ,
γ p = γ a 1 γ b .

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