Abstract

The accuracy performance of fringe projection profilometry (FPP) depends on accurate phase-to-height (PTH) mapping and system calibration. The existing PTH mapping is derived based on the condition that the plane formed by axes of camera and projector is perpendicular to the reference plane, and measurement error occurs when the condition is not met. In this paper, a new geometric model for FPP is presented to lift the condition, resulting in a new PTH mapping relationship. The new model involves seven parameters, and a new system calibration method is proposed to determine their values. Experiments are conducted to verify the performance of the proposed technique, showing a noticeable improvement in the accuracy of 3D shape measurement.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. A. Asundi and Z. Wensen, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38(16), 3556–3561 (1999).
    [Crossref] [PubMed]
  6. M. J. Baker, J. T. Xi, and J. F. Chicharo, “Neural Network digital fringe calibration technique for structured light profilometers,” Appl. Opt. 46(8), 1233–1243 (2007).
    [Crossref] [PubMed]
  7. B. M. Chung and Y. C. Park, “Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection,” International Journal of Precision Engineering and Manufacturing 15(3), 407–413 (2014).
    [Crossref]
  8. Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
    [Crossref]
  9. H. Du and Z. Y. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32(16), 2438–2440 (2007).
    [Crossref] [PubMed]
  10. E. Zappa and G. Busca, “Fourier-transform profilometry calibration based on an exhaustive geometric model of the system,” Opt. Lasers 47(7-8), 754–767 (2009).
    [Crossref]
  11. E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
    [Crossref]
  12. L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
    [Crossref]
  13. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  14. S. Zhang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
    [Crossref]

2014 (2)

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53(16), 3415–3426 (2014).
[Crossref] [PubMed]

B. M. Chung and Y. C. Park, “Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection,” International Journal of Precision Engineering and Manufacturing 15(3), 407–413 (2014).
[Crossref]

2013 (1)

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

2012 (1)

2011 (1)

E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
[Crossref]

2009 (1)

E. Zappa and G. Busca, “Fourier-transform profilometry calibration based on an exhaustive geometric model of the system,” Opt. Lasers 47(7-8), 754–767 (2009).
[Crossref]

2007 (3)

2006 (1)

S. Zhang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

2003 (1)

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

2000 (1)

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

1999 (1)

1983 (1)

Asundi, A.

Baker, M. J.

Busca, G.

E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
[Crossref]

E. Zappa and G. Busca, “Fourier-transform profilometry calibration based on an exhaustive geometric model of the system,” Opt. Lasers 47(7-8), 754–767 (2009).
[Crossref]

Cao, Y. P.

Chen, C. M.

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

Chen, W. J.

Chen, Z.

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

Chiang, F. P.

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Chicharo, J. F.

Chung, B. M.

B. M. Chung and Y. C. Park, “Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection,” International Journal of Precision Engineering and Manufacturing 15(3), 407–413 (2014).
[Crossref]

Du, H.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Huang, P. S.

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Karpinsky, N.

Li, B.

Mao, X. F.

Mutoh, K.

Park, Y. C.

B. M. Chung and Y. C. Park, “Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection,” International Journal of Precision Engineering and Manufacturing 15(3), 407–413 (2014).
[Crossref]

Sala, P.

E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
[Crossref]

Song, L. M.

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

Su, X. Y.

Takeda, M.

Wang, Z. Y.

Wensen, Z.

Wu, Y. C.

Xi, J. T.

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

M. J. Baker, J. T. Xi, and J. F. Chicharo, “Neural Network digital fringe calibration technique for structured light profilometers,” Appl. Opt. 46(8), 1233–1243 (2007).
[Crossref] [PubMed]

Xiao, Y. S.

Yu, Y. G.

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

Zappa, E.

E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
[Crossref]

E. Zappa and G. Busca, “Fourier-transform profilometry calibration based on an exhaustive geometric model of the system,” Opt. Lasers 47(7-8), 754–767 (2009).
[Crossref]

Zhang, S.

Zhang, Z. Y.

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Appl. Opt. (6)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

International Journal of Precision Engineering and Manufacturing (1)

B. M. Chung and Y. C. Park, “Hybrid method for phase-height relationship in 3D shape measurement using fringe pattern projection,” International Journal of Precision Engineering and Manufacturing 15(3), 407–413 (2014).
[Crossref]

Opt. Eng. (2)

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

S. Zhang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Opt. Lasers (2)

E. Zappa and G. Busca, “Fourier-transform profilometry calibration based on an exhaustive geometric model of the system,” Opt. Lasers 47(7-8), 754–767 (2009).
[Crossref]

E. Zappa, G. Busca, and P. Sala, “Innovative calibration technique for fringe projection based 3D scanner,” Opt. Lasers 49(3), 331–340 (2011).
[Crossref]

Opt. Lett. (1)

Optoelectron. Lett. (1)

L. M. Song, C. M. Chen, Z. Chen, J. T. Xi, and Y. G. Yu, “Essential parameter calibration for the 3D scanner with only single camera and projector,” Optoelectron. Lett. 9(2), 143–147 (2013).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 The ideal geometric modal.
Fig. 2
Fig. 2 (a). An improved geometric model (b). Simplified geometric model.
Fig. 3
Fig. 3 Another improved geometric model in [3].
Fig. 4
Fig. 4 (a). Captured ideal fringes (b). Captured actual fringes.
Fig. 5
Fig. 5 The proposed geometric model for FPP.
Fig. 6
Fig. 6 Schematic illustration of systematic calibration.
Fig. 7
Fig. 7 System calibration equipment in our lab.
Fig. 8
Fig. 8 (a). image of calibration board on first position (b). that on second position (c). that on the third position.
Fig. 9
Fig. 9 (a) Reconstruction based on ideal geometric model (b) Reconstruction based on model in [3] (c) Reconstruction based on proposed model.

Tables (1)

Tables Icon

Table 1 Parameters of our Proposed PTH Mapping

Equations (32)

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h(x,y)= L C Δ φ DC ( x,y ) 2π f 0 dΔ φ DC ( x,y )
h( x,y )= Δ φ DC ( x,y ) L C ( L C + S 1 sin α 1 ) 2π f 0 L C r L C Δ φ DC ( x,y ) φ D ( x,y ) S 1 sin α 1
h(x,y)= Δ ϕ DC ( x,y ) L c cos θ 2 ( L c cos θ 2 + S 1 sin α 1 ) 2π f 0 L c ( rcos θ 2 + S 1 sin α 1 sin θ 2 ) ϕ D ( x,y ) S 1 sin α 1 ϕ DC ( x,y ) L c cos θ 2
K O p ¯ = O 1 O CT ¯ + E O CT ¯ = L C cos θ 0 cos θ 2 + S 1 sin a 1
tanδ= O 1 O CT ¯ AO ¯ + O O 1 ¯ and tanη= O P K ¯ KO ¯ CO ¯
AB ¯ = BD ¯ tanδ and BC ¯ = BD ¯ tanη
CA ¯ = BD ¯ ( 1 tanδ + 1 tanη )
h( x,y )= CA ¯ tanδtanη tanδ+tanη
h(x,y)= CA ¯ L c cos θ 0 cos θ 2 ( L c cos θ 0 cos θ 2 + S 1 sin α 1 ) L c cos θ 0 ( rcos θ 2 + S 1 sin α 1 sin θ 2 )+ AO ¯ S 1 sin α 1 + CA ¯ L c cos θ 0 cos θ 2
CA ¯ = Δ ϕ DC ( x,y ) 2π f 0 and AO ¯ = ϕ D ( x,y ) 2π f 0
h(x,y)= Δ ϕ DC ( x,y ) L c cos θ 0 cos θ 2 ( L c cos θ 0 cos θ 2 + S 1 sin α 1 ) 2π f 0 L c cos θ 0 ( rcos θ 2 + S 1 sin α 1 sin θ 2 ) ϕ D ( x,y ) S 1 sin α 1 Δ ϕ DC ( x,y ) L c cos θ 0 cos θ 2
s c [ u c v c 1 ] m ˜ c = [ α c γ c u c0 0 β c v c0 0 0 1 ] A c [ r 11 r 12 r 13 t 1 r 21 r 22 r 23 t 2 r 31 r 32 r 33 t 3 ] [ R c T c ] [ x y z 1 ] M ˜
s p [ u p v p 1 ] m ˜ p = [ α p γ p u p0 0 β p v p0 0 0 1 ] A p [ g 11 g 12 g 13 e 1 g 21 g 22 g 23 e 2 g 31 g 32 g 33 e 3 ] [ R p T p ] [ x y z 1 ] M ˜
I V l ( u p , v p )= I 1 + I 2 cos( 2π u p T V + l4 3 π ),l=1,2,...,6 and u p =0,1,2,..., M p
I H l ( u p , v p )= I 1 + I 2 cos( 2π v p T H + l4 3 π ),l=1,2,...,6 and v p =0,1,2,..., N p
I V n ( u c , v c )= I 1 + I 2 cos( ϕ V ( u c , v c )+ n4 3 π ),n=1,2,...,6 and u c =0,1,2,..., M c
I H n ( u c , v c )= I 1 + I 2 cos( ϕ H ( u c , v c )+ n4 3 π ),n=1,2,...,6 and v c =0,1,2,..., N c
ϕ V ( u c , v c )=arctan[ n=1 6 I V n ( u c , v c )sin( 2πn/6 ) n=1 6 I V n ( u c , v c )cos( 2πn/6 ) ] and ϕ H ( u c , v c )=arctan[ n=1 6 I H n ( u c , v c )sin( 2πn/6 ) n=1 6 I H n ( u c , v c )cos( 2πn/6 ) ]
Φ V ( u c , v c )= ϕ V ( u c , v c )+2π m V ( u c , v c )
Φ H ( u c , v c )= ϕ H ( u c , v c )+2π m H ( u c , v c )
u p = Φ V ( u c , v c ) 2π T V and v p = Φ H ( u c , v c ) 2π T H
[ x c y c z c ]= R c [ x wc y wc z wc ]+ T c
[ x p y p z p ]= R p [ x wp y wp z wp ]+ T p
[ x wc y wc z wc ]= R c 1 T c and [ x wp y wp z wp ]= R p 1 T p
S 1 = ( x wp x wc ) 2 + ( y wp y wc ) 2 + ( z wp z wc ) 2
α 1 =arcsin( | z wp z wc | S 1 )
r=| x wp x wc |
s c m ˜ c =H M ˜
M ˜ = s c H 1 m ˜ c
L c = ( x O x wc ) 2 + ( y O y wc ) 2 + z wc 2
θ 2 =arctan( | x O x wc | | z wc | )
θ 0 =arctan( | y O y wc | ( x O x wc ) 2 + z wc 2 )

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