Abstract

A new method of 3D measurement based on a digital light processing (DLP) projector is presented. The projection model of the DLP projector is analyzed, and the relationship between the fringe patterns of the DLP and the fringe strips projected into the 3D space is proposed. Then the 3D shape of the object can be obtained by this relationship. Meanwhile a calibration method for this model is presented. Using this calibration method, parameters of the model can be obtained by a calibration plate, and there is no requirement for the plate to move precisely. This new 3D shape measurement method does not require any restrictions as that in the classical methods. The camera and projector can be put in an arbitrary position, and it is unnecessary to arrange the system layout in parallel, vertical, or other stringent geometry conditions. The experiments show that this method is flexible and is easy to carry out. The system calibration can be finished quickly, and the system is applicable to many shape measurement tasks.

© 2008 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
    [CrossRef]
  2. Y. Hu, J. Xi, E. Li, J. Chicharo, and Z. Yang, "Three-dimensional profilometry based on shift estimation of projected fringe patterns," Appl. Opt. 45, 678-687 (2006).
    [CrossRef] [PubMed]
  3. W. Su, K. Shi, Z. Liu, B. Wang, K. Reichard, and S. Yin, "A large-depth-of-field projected fringe profilometry using supercontinuum light illumination," Opt. Express 13, 1025-1032 (2005).
    [CrossRef] [PubMed]
  4. T. Baumbach, W. Osten, C. Kopylow, and W. Jüptner, "Remote metrology by comparative digital holography," Appl. Opt. 45, 925-934 (2006).
    [CrossRef] [PubMed]
  5. D. Purcell, A. Davies, and F. Farahi, "Effective wavelength calibration for moiré fringe projection," Appl. Opt. 45, 8629-8635 (2006).
    [CrossRef] [PubMed]
  6. O. Duran, K. Althoefer, and L. D. Seneviratne, "State of the art in sensor technologies for sewer inspection," IEEE Sens. J. 2, 73-81 (2002).
    [CrossRef]
  7. L. Biancardi, G. Sansoni, and F. Docchio, "Adaptive whole-field optical profilometry: a study of the systematic errors," IEEE Trans. Instrum. Meas. 44, 36-41 (1999).
    [CrossRef]
  8. A. Tian, Z. Jiang, and Y. Huang, "A flexible new three-dimensional measurement technique by projected fringe pattern," Opt. Laser Technol. 38, 585-589 (2006).
    [CrossRef]
  9. Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
    [CrossRef]
  10. X. Su, W. Song, Y. Cao, and W. Chen, "Both phase-height mapping and coordinates calibration in PMP," Proc. SPIE 4829, 874-875 (2003).
  11. G. Sansoni, M. Carocci, and R. Rodella, "3D vision based on the combination of Gray code and phase shift light projection," Appl. Opt. 38, 6565-6573 (1999).
    [CrossRef]
  12. H. Guo, M. Chen, and P. Zheng, "Least-squares fitting of carrier phase distribution by using a rational function in fringe projection profilometry," Opt. Lett. 31, 3588-3590 (2006).
    [CrossRef] [PubMed]
  13. S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601 (2006).
    [CrossRef]
  14. R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3D-phase distribution," Proc. SPIE 5856, 109-117 (2005).
  15. T. Ha, Y. Takaya, T. Miyoshi, S. Ishizuka, and T. Suzuki, "High-precision on-machine 3D shape measurement using hypersurface calibration method," Proc. SPIE 5603, 40-50 (2004).
  16. G. Sansoni, T. Marco, and F. Docchio, "Fast 3D profilometer based upon the projection of a single fringe pattern and absolute calibration," Meas. Sci. Technol. 17, 1757-1766 (2006).
    [CrossRef]
  17. D. A. Forsyth and J. Ponce, Computer Vision: a Modern Approach (Pearson Education, 2003), pp. 38-45.

2006 (7)

2005 (1)

2003 (1)

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

2002 (1)

O. Duran, K. Althoefer, and L. D. Seneviratne, "State of the art in sensor technologies for sewer inspection," IEEE Sens. J. 2, 73-81 (2002).
[CrossRef]

2000 (1)

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

1999 (2)

G. Sansoni, M. Carocci, and R. Rodella, "3D vision based on the combination of Gray code and phase shift light projection," Appl. Opt. 38, 6565-6573 (1999).
[CrossRef]

L. Biancardi, G. Sansoni, and F. Docchio, "Adaptive whole-field optical profilometry: a study of the systematic errors," IEEE Trans. Instrum. Meas. 44, 36-41 (1999).
[CrossRef]

Appl. Opt. (4)

IEEE Sens. J. (1)

O. Duran, K. Althoefer, and L. D. Seneviratne, "State of the art in sensor technologies for sewer inspection," IEEE Sens. J. 2, 73-81 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

L. Biancardi, G. Sansoni, and F. Docchio, "Adaptive whole-field optical profilometry: a study of the systematic errors," IEEE Trans. Instrum. Meas. 44, 36-41 (1999).
[CrossRef]

Meas. Sci. Technol. (1)

G. Sansoni, T. Marco, and F. Docchio, "Fast 3D profilometer based upon the projection of a single fringe pattern and absolute calibration," Meas. Sci. Technol. 17, 1757-1766 (2006).
[CrossRef]

Opt. Eng. (3)

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

Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

A. Tian, Z. Jiang, and Y. Huang, "A flexible new three-dimensional measurement technique by projected fringe pattern," Opt. Laser Technol. 38, 585-589 (2006).
[CrossRef]

Opt. Lett. (1)

Other (4)

X. Su, W. Song, Y. Cao, and W. Chen, "Both phase-height mapping and coordinates calibration in PMP," Proc. SPIE 4829, 874-875 (2003).

R. Sitnik, "New method of structure light measurement system calibration based on adaptive and effective evaluation of 3D-phase distribution," Proc. SPIE 5856, 109-117 (2005).

T. Ha, Y. Takaya, T. Miyoshi, S. Ishizuka, and T. Suzuki, "High-precision on-machine 3D shape measurement using hypersurface calibration method," Proc. SPIE 5603, 40-50 (2004).

D. A. Forsyth and J. Ponce, Computer Vision: a Modern Approach (Pearson Education, 2003), pp. 38-45.

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Figures (11)

Fig. 1
Fig. 1

Diagram of the classical system layout.

Fig. 2
Fig. 2

Model of the projector.

Fig. 3
Fig. 3

Rectangular fringe.

Fig. 4
Fig. 4

Diagram of the new system layout.

Fig. 5
Fig. 5

Calibration plate.

Fig. 6
Fig. 6

Fringe pattern of calibration.

Fig. 7
Fig. 7

Measurement system.

Fig. 8
Fig. 8

(a) Two-dimensional image of connected spheres with a diameter of 50 mm, (b) obtained point clouds (top view), and (c) obtained point clouds (side view).

Fig. 9
Fig. 9

(a) Two-dimensional image of connected spheres with a diameter of 100 mm, (b) obtained point clouds (top view), and (c) obtained point clouds (side view).

Fig. 10
Fig. 10

(a) Obtained point clouds of a big sphere and (b) asphericity of a big sphere.

Fig. 11
Fig. 11

Measurement results of the head model. (a) 2D image (front view), (b) point clouds (front view), and (c) eye region of the point clouds.

Tables (2)

Tables Icon

Table 1 Matrix R , T , and G in Calibration

Tables Icon

Table 2 Experimental Results of the Connected Spheres

Equations (40)

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P P d 2 = B A B A + d 1 ,
X p Z p = u f p ,   Y p Z p = v f p ,
u = 1 μ x u 1 μ x v   cot   θ + u 0 ,
v = 1 μ y v sin 1 θ + v 0 ,
u = ( f p μ x X p f p μ x   cot   θ Y p + u 0 Z p ) / Z p ,
v = ( f p μ y sin 1 θ Y p + v 0 Z p ) / Z p .
g ( u , v ) = 255 , u = 6 i , 6 i + 1 , 6 i + 2 ,
i = 0 , 1 , 2 ,   …   ,
g ( u , v ) = 0 , u = 6 i + 3 , 6 i + 4 , 6 i + 5 ,
i = 0 , 1 , 2 ,   …   ,
α i u + β i v + γ i = 0 ,
α i f p μ x X p + ( β i f p μ y sin 1 θ α i f p μ x   cot   θ ) Y p + ( γ i + β i v 0 + α i u 0 ) Z p = 0 .
( X p Y p Z p ) = [ r c 11 r c 12 r c 13 r c 21 r c 22 r c 23 r c 31 r c 32 r c 33 ] ( X c Y c Z c ) + ( t c 1 t c 2 t c 3 ) ,
[ r c 11 r c 12 r c 13 r c 21 r c 22 r c 23 r c 31 r c 32 r c 33 ]
( w 11 w 12 w 13 w 14 w 31 w 32 w 33 w 34 ) × ( X c Y c Z c 1 u X c u Y c u Z c u ) T = 0 ,
( w 21 w 22 w 23 w 24 w 31 w 32 w 33 w 34 ) × ( X c Y c Z c 1 v X c v Y c v Z c v ) T = 0 ,
( α i β i γ i ) [ w 11 w 12 w 13 w 14 w 21 w 22 w 23 w 24 w 31 w 32 w 33 w 34 ] ( X c Y c Z c 1 ) T = 0 ,
w 11 = r c 11 r c 21   cot   θ μ x f p + r c 31 u 0 ,
w 21 = r c 21 f p μ y sin 1 θ + r c 31 v 0 , w 31 = r c 31 ,
w 12 = r c 12 r c 22   cot   θ μ x f p + r c 32 u 0 ,
w 22 = r c 22 f p μ y sin 1 θ + r c 32 v 0 , w 32 = r c 32 ,
w 13 = r c 13 r c 23   cot   θ μ x f p + r c 33 u 0 ,
w 23 = r c 23 f p μ y sin 1 θ + r c 33 v 0 , w 33 = r c 33 ,
w 14 = t 1 t 2   cot   θ μ x f p + t 3 u 0 ,
w 24 = t 2 f p μ y sin 1 θ + t 3 v 0 , w 34 = t 4 .
W = [ w 11 w 12 w 13 w 14 w 21 w 22 w 23 w 24 w 31 w 32 w 33 w 34 ] ,
ρ ( m n 1 ) = A c ( X c Y c Z c ) ,
m d = m + k 1 m ( m 2 + n 2 ) + k 2 m ( m 2 + n 2 ) 2 ,
n d = n + k 1 n ( m 2 + n 2 ) + k 2 n ( m 2 + n 2 ) 2 ,
A c = [ f m γ m 0 0 f n n 0 0 0 1 ] ,
( X c Y c Z c ) = ( R 0 T 0 ) ( a b 0 1 ) = ( r 1 r 2 r 3 T 0 ) ( a b 0 1 ) = ( r 1 r 2 T 0 ) ( a b 1 ) ,
r 1 2 = 1 , r 2 2 = 1 , r 1 · r 2 = 0 ,
ρ ( m n 1 ) = H ( a b 1 ) , H = A c ( r 1 r 2 T 0 ) ( a b 1 ) ,
G = H 1 = ( r 1 r 2 T 0 ) 1 A c 1 = [ g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 ] .
( a b 1 ) = ρ G ( m n 1 ) = 1 m g 7 + n g 8 + g 9 G ( m n 1 ) .
( X c Y c Z c ) = 1 m g 7 + n g 8 + g 9 A c 1 ( m n 1 ) .
[ m 1 n 1 1 0 0 0 a 1 m 1 a 1 n 1 a 1 0 0 0 m 1 n 1 1 b 1 m 1 b 1 n 1 b 1 m 2 n 2 1 0 0 0 a 2 m 2 a 2 n 2 a 2 0 0 0 m 2 n 2 1 b 2 m 2 b 2 n 2 b 2 m k n k 1 0 0 0 a k m k a k n k a k 0 0 0 m k n k 1 b k m k b k n k b k ] ( g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 ) = 0 ,
A c = [ 1478.461874 0.736461 381.584471 0.000000 1477.705745 293.381907 0.000000 0.000000 1.000000 ] ,
k 1 = 1.972249 10 8 , k 2 = 4.177390 10 1 4 .
[ 5.416565 0.083105 3.375657 741.472957 1.164168 5.881166 2.089277 543.165359 0.000711 0.000482 0.002001 1.000000 ] .

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