Abstract

This paper presents a novel pixel-level resolution 3D profilometry technique that only needs binary phase-shifted structured patterns. This technique uses four sets of three phase-shifted binary patterns to achieve the phase error of less than 0.2%, and only requires two sets to reach similar quality if the projector is slightly defocused. Theoretical analysis, simulations, and experiments will be presented to verify the performance of the proposed technique.

© 2011 Optical Society of America

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References

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  1. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?,” Opt. Lasers Eng. 48, 133–140 (2010).
    [CrossRef]
  2. S. Lei and S. Zhang, “Flexible 3D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
    [CrossRef] [PubMed]
  3. X. Y. Su, W. S. 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]
  4. S. Zhang, D. van der Weide, and J. Olvier, “Superfast phase-shifting method for 3D shape measurement,” Opt. Express 18, 9684–9689 (2010).
    [CrossRef] [PubMed]
  5. Y. Gong and S. Zhang, “Ultrafast 3D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18, 19743–19754(2010).
    [CrossRef] [PubMed]
  6. D.Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).
    [CrossRef]
  7. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley,1998).
  8. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
    [CrossRef]
  9. I. I. Hirschman and D. V. Widder, The Convolution Transform (Princeton, 1955).

2010 (3)

2009 (1)

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

1992 (1)

X. Y. Su, W. S. 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]

Ghiglia, D. C.

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

Gong, Y.

Gorthi, S.

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

Hirschman, I. I.

I. I. Hirschman and D. V. Widder, The Convolution Transform (Princeton, 1955).

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

Lei, S.

Olvier, J.

Pritt, M. D.

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

Rastogi, P.

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

Su, X. Y.

X. Y. Su, W. S. 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]

van der Weide, D.

Von Bally, G.

X. Y. Su, W. S. 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. S. 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]

Widder, D. V.

I. I. Hirschman and D. V. Widder, The Convolution Transform (Princeton, 1955).

Zhang, S.

Zhou, W. S.

X. Y. Su, W. S. 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]

Opt. Commun. (1)

X. Y. Su, W. S. 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]

Opt. Eng. (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

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

Opt. Lett. (1)

Other (3)

I. I. Hirschman and D. V. Widder, The Convolution Transform (Princeton, 1955).

D.Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

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

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Figures (5)

Fig. 1
Fig. 1

Phase error caused by different harmonics. k is the integer used in Eq. (7).

Fig. 2
Fig. 2

Phase errors with using different phase-shifting methods under different degrees of defocusing. (a) Close to being an ideal square wave; (b) Phase errors for the SPS, DPS, and QPS methods are RMS 3.46%, 1.07%, and 0.10%, respectively; (c) Slightly blurred square wave; (d) Phase errors for the SPS, DPS, and QPS methods are RMS 1.61%, 0.11%, and 0.02%, respectively.

Fig. 3
Fig. 3

Phase errors with using different phase-shifting methods. (a) Fringe pattern is close to being in focus; (b) 320th row cross section; (c) Wrapped phase map; (d)–(f) Phase error maps for the SPS, DPS, and QPS methods, respectively; (g) Fringe pattern is slightly defocused; (h) 320th row cross section; (i) Wrapped phase map; (j)–(l) Phase error maps for the SPS, DPS, and QPS methods, respectively.

Fig. 4
Fig. 4

Phase errors with using different phase-shifting methods. (a) Cross sections of the phase error shown in the first row of Fig. 3. The phase errors are 2.67%, 0.46%, and 0.17% for the SPS, DPS, and QPS methods, respectively; (b) Cross sections of the phase error shown in the second row of Fig. 3. The phase errors are 1.48%, 0.21%, and 0.14% for the SPS, DPS, and QPS methods, respectively.

Fig. 5
Fig. 5

Experimental results with different binary phase-shifting methods. The top row shows the results when the projector is close to being in focus, and the bottom row shows the results when the projector is slightly defocused. (a) One of the binary fringe patterns; (b) 3D result with the SPS method; (c) 3D result with the DPS method; (d) 3D result with the QPS method; (e) One of the binary fringe patterns; (f) 3D result with the SPS method; (g) 3D result with the DPS method; (h) 3D result with the QPS method.

Equations (12)

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I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) .
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) / ( 2 I 2 I 1 I 3 ) ] .
Φ ( x , y ) = 2 π × k ( x , y ) .
y ( x ) = { 0 x [ ( 2 n 1 ) π , 2 n π ) 1 x [ 2 n π , ( 2 n + 1 ) π ) .
y ( x ) = 0.5 + k = 0 2 ( 2 k + 1 ) π sin [ ( 2 k + 1 ) x ] .
I 1 k ( x , y ) = I ( x , y ) + I ( x , y ) { cos ( ϕ 2 π / 3 ) + cos [ ( 2 k + 1 ) ( ϕ 2 π / 3 ) ] / ( 2 k + 1 ) } ,
I 2 k ( x , y ) = I ( x , y ) + I ( x , y ) { cos ( ϕ ) + cos [ ( 2 k + 1 ) ϕ ] / ( 2 k + 1 ) } ,
I 3 k ( x , y ) = I ( x , y ) + I ( x , y ) { cos ( ϕ + 2 π / 3 ) + cos [ ( 2 k + 1 ) ( ϕ + 2 π / 3 ) ] / ( 2 k + 1 ) } .
ϕ k ( x , y ) = tan 1 [ 3 ( I 1 k I 3 k ) / ( 2 I 2 k I 1 k I 3 k ) ] .
Δ Φ k ( x , y ) = Φ k ( x , y ) Φ ( x , y ) .

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