Abstract

We present three-dimensional profilometry based on triangulation in which a hexagonal pattern is projected on the object. To obtain an accurate result with a one-shot photographic image, the Fourier transform method and method of excess fraction are adopted. The three grating components of the hexagonal pattern are used. For compactness a new pattern projection scheme is introduced. The experimental results show that the constructed optical system works well for measuring the profile of a mannequin with a height resolution of ±1mm.

© 2008 Optical Society of America

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References

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  1. N. D'Apuzzo, “Overview of 3D surface digitization technologies in Europe,” Proc. SPIE 6056, 42-54 (2006).
  2. V. Srinivasan, H. C. Liu, and Maurice Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185-188 (1985).
    [CrossRef] [PubMed]
  3. M. Takeda and K. Mutoh, “Fourier-transform profilometry for the automatic measurement of 3D object shapes,” Appl. Opt. 22, 3977-3982 (1983).
    [CrossRef] [PubMed]
  4. J. Arines, “Least-squares modal estimation of wrapped phases: application to phase unwrapping,” Appl. Opt. 42, 3373-3378 (2003).
    [CrossRef] [PubMed]
  5. S. Kakunai, K. Iwata, S. Saitoh, and T.Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 133-138 (1992) (in Japanese).
  6. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36, 5347-5354 (1997).
    [CrossRef] [PubMed]
  7. A. Pfotner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667-673 (2003).
    [CrossRef]
  8. M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6, 449-454 (1999).
    [CrossRef]
  9. Y. Hao, Y. Zhao, and D. Li, “Multi-frequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38, 4106-4110 (1999).
    [CrossRef]
  10. K. Iwata, J. Zhang, and H. Kikuta, “Consideration of fractional fringe method on the basis of the least squares method,” Opt. Rev. 10, 202-205 (2003).
    [CrossRef]
  11. D. Crespo, J. Alonso, and E. Bernabeu, “Generalized grating imaging using an extended monochromatic light source,” J. Opt. Soc. Am. A 17, 1231-1240 (2000).
    [CrossRef]
  12. D. Crespo, J. Alonso, and E. Bernabeu, “Experimental measurements of generalized grating images,” Appl. Opt. 41, 1223-1228 (2002).
    [CrossRef] [PubMed]

2006

N. D'Apuzzo, “Overview of 3D surface digitization technologies in Europe,” Proc. SPIE 6056, 42-54 (2006).

2003

2002

2000

1999

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6, 449-454 (1999).
[CrossRef]

Y. Hao, Y. Zhao, and D. Li, “Multi-frequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38, 4106-4110 (1999).
[CrossRef]

1997

1992

S. Kakunai, K. Iwata, S. Saitoh, and T.Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 133-138 (1992) (in Japanese).

1985

1983

Appl. Opt.

J. Jpn. Soc. Precis. Eng.

S. Kakunai, K. Iwata, S. Saitoh, and T.Sakamoto, “Profile measurement by two-pitch grating projection,” J. Jpn. Soc. Precis. Eng. 58, 133-138 (1992) (in Japanese).

J. Opt. Soc. Am. A

Opt. Rev.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6, 449-454 (1999).
[CrossRef]

K. Iwata, J. Zhang, and H. Kikuta, “Consideration of fractional fringe method on the basis of the least squares method,” Opt. Rev. 10, 202-205 (2003).
[CrossRef]

Proc. SPIE

N. D'Apuzzo, “Overview of 3D surface digitization technologies in Europe,” Proc. SPIE 6056, 42-54 (2006).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the optical system.

Fig. 2
Fig. 2

Hexagonal grating.

Fig. 3
Fig. 3

Spectrum of the hexagonal grating.

Fig. 4
Fig. 4

Schematic of the whole optical system.

Fig. 5
Fig. 5

Hexagonal grating projected on a mannequin.

Fig. 6
Fig. 6

Measured result: (a) height distribution and (b) height along the line in (a).

Fig. 7
Fig. 7

Height distribution on a flat plate: (a) height determined with the individual gratings and (b) height determined by the excess fraction method.

Equations (25)

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I r ( x r , y r ) = A + B 1 cos [ 2 π ( x r p x 1 + y r p y 1 + ϕ 1 ) ] + B 2 cos [ 2 π ( x r p x 2 + y r p y 2 + ϕ 2 ) ] + B 3 cos [ 2 π ( x r p x 3 + y r p y 3 + ϕ 3 ) ] .
p x n = d | sin ( ξ ( n 3 ) π 3 ) | , p y n = d | cos ( ξ ( n 3 ) π 3 ) | , n = 1 , 2 , 3 ,
Δ x ( x r , y r ) = x q x r , Δ y ( x r , y r ) = y q y r .
I ( x r , y r ) = A ( x r , y r ) + B 1 ( x r , y r ) cos [ 2 π ( x r + Δ x p x 1 + y r + Δ y p y 1 + ϕ 1 ) ] + B 2 ( x r , y r ) cos [ 2 π ( x r + Δ x p x 2 + y r + Δ y p y 2 + ϕ 2 ) ] + B 3 ( x r , y r ) cos [ 2 π ( x r + Δ x p x 3 + y r + Δ y p y 3 + ϕ 3 ) ] .
Δ Φ n = Δ x p x n + Δ y p y n , n = 1 , 2 , 3.
x x r = z x z c z , x x q = z z s z ( x s x ) , y y r = z y z c z , y y q = z z s z ( y s y ) .
Δ x = x q x r = z x z c z z z s z ( x s x ) , Δ y = y q y = z y z c z z z s z ( y s y ) ,
x = z x r z c + x r , y = z y r z c + y r .
B n ( x r , y r ) exp [ 2 π i ( x r p x n + y r p y n + Δ Φ n + ϕ n ) ] , n = 1 , 2 , 3.
I n = B n ( x r , y r ) exp i [ 2 π ( Δ Φ n + ϕ n ) ] n = 1 , 2 , 3.
Δ Φ n = 1 2 π tan 1 Im ( I n ) Re ( I n ) ϕ n , n = 1 , 2 , 3.
R = 1 2 F .
R = d .
W / d < N / 3.
Δ Φ n = m n + ε n , n = 1 , 2 , 3 ,
Δ Φ n = z ( z c z ) ( z s z ) [ z c A n + z B n ] , n = 1 , 2 , 3 ,
A n = ( x r p x n + y r p y n ) z s z c ( x s x r p x n + y s y r p y n ) , n = 1 , 2 , 3 , B n = ( x s p x n + y s p y n ) + x r p x n ( z s z c 1 ) + y r p y n ( z s z c 1 ) , n = 1 , 2 , 3.
z z c = Δ Φ n ( 1 + z s / z c ) + A n D n 2 ( Δ Φ n B n ) , n = 1 , 2 , 3 ,
D n = ( Δ Φ n ( 1 + z s z c ) + A n ) 2 4 ( Δ Φ n B n ) Δ Φ n z s z c , n = 1 , 2 , 3.
z = n = 1 n = 3 w n z n 2 ,
w n = 1 / p n N , n = 1 , 2 , 3 ,
N = [ n = 1 n = 3 ( 1 p n ) 2 ] 1 / 2 .
V = n = 1 n = 3 ( w n ( z n z ) ) 2 .
L 10 = v d 1 d 2 λ , L 20 = L 10 d 2 d 1 d 2 , v :     integer .
d = d 1 d 2 d 1 d 2 .

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