Abstract

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object.

© 2007 Optical Society of America

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References

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  1. M. Takeda and K. Mutoh, "Fourier-transform profilometry for the automatic measurement of 3D object shapes," Appl. Opt. 22, 3977-3982 (1983).
    [CrossRef] [PubMed]
  2. J. Vanherzeele, P. Guillaume, and S. Vanlanduit, "Fourier fringe processing using a regressive Fourier-transform technique," Opt. Lasers Eng. 43, 645-658 (2005).
    [CrossRef]
  3. J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
    [CrossRef]
  4. D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
    [CrossRef]
  5. J. Zhong and J. Weng, "Phase retrieval of optical fringe patterns from the ridge of a wavelet transform," Opt. Lett. 30, 2560-2562 (2005).
    [CrossRef] [PubMed]
  6. X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
    [CrossRef]
  7. W.-S. Zhou and X.-Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
    [CrossRef]
  8. G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
    [CrossRef]
  9. K. J. Gåsvik, "Optical techniques," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993). pp. 23-71.
  10. T. Yatagai, "Intensity based analysis methods," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993) pp. 72-93.
  11. R.-H. Zheng, Y.-X. Wang, X.-R. Zhang, and Y.-L. Song, "Two-dimensional phase-measuring profilometry," Appl. Opt. 44, 954-958 (2005).
    [CrossRef] [PubMed]

2005

2004

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

2001

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

2000

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

1994

W.-S. Zhou and X.-Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

1990

J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

1983

Accardo, G.

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Ambrosini, D.

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Chen, W.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Ganotra, D.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

Gåsvik, K. J.

K. J. Gåsvik, "Optical techniques," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993). pp. 23-71.

Guattari, G.

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Guillaume, P.

J. Vanherzeele, P. Guillaume, and S. Vanlanduit, "Fourier fringe processing using a regressive Fourier-transform technique," Opt. Lasers Eng. 43, 645-658 (2005).
[CrossRef]

Guo, L.-R.

J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

Joseph, J.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

Li, J.

J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

Mutoh, K.

Paoletti, D.

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Sapia, C.

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Singh, K.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

Song, Y.-L.

Spagnolo, G. Schirripa

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

Su, X.

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

Su, X.-Y.

W.-S. Zhou and X.-Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

Takeda, M.

Vanherzeele, J.

J. Vanherzeele, P. Guillaume, and S. Vanlanduit, "Fourier fringe processing using a regressive Fourier-transform technique," Opt. Lasers Eng. 43, 645-658 (2005).
[CrossRef]

Vanlanduit, S.

J. Vanherzeele, P. Guillaume, and S. Vanlanduit, "Fourier fringe processing using a regressive Fourier-transform technique," Opt. Lasers Eng. 43, 645-658 (2005).
[CrossRef]

Wang, Y.-X.

Weng, J.

Yatagai, T.

T. Yatagai, "Intensity based analysis methods," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993) pp. 72-93.

Zhang, X.-R.

Zheng, R.-H.

Zhong, J.

Zhou, W.-S.

W.-S. Zhou and X.-Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

W.-S. Zhou and X.-Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

Opt. Eng.

J. Li, X.-Y. Su, and L.-R. Guo, "Improved Fourier-transform profilometry of the automatic measurement of three-dimensional object shapes," Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

Opt. Lasers Eng.

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

X. Su and W. Chen, "Fourier transform profilometry: a review," Opt. Lasers Eng. 35, 263-284 (2001).
[CrossRef]

G. Schirripa Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, "Contouring of artwork surface by fringe projection and FFT analysis," Opt. Lasers Eng. 33, 141-156 (2000).
[CrossRef]

J. Vanherzeele, P. Guillaume, and S. Vanlanduit, "Fourier fringe processing using a regressive Fourier-transform technique," Opt. Lasers Eng. 43, 645-658 (2005).
[CrossRef]

Opt. Lett.

Other

K. J. Gåsvik, "Optical techniques," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993). pp. 23-71.

T. Yatagai, "Intensity based analysis methods," in Interferograms Analysis, D. Robinson and G. T. Reid, eds. (IOP, 1993) pp. 72-93.

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Figures (8)

Fig. 1
Fig. 1

Geometrical sketch map.

Fig. 2
Fig. 2

Simulated object.

Fig. 3
Fig. 3

Deformed fringe distribution when α = 0 ° .

Fig. 4
Fig. 4

(a) Calculated height error when α 1 = 0 ° ; (b) calculated height error when α 1 = 10 ° ; (c) calculated height error when α 1 = 30 ° ; (d) calculated height error when α 1 = 50 ° ; (e) calculated height error when α 1 = 10 ° ; (f) height error distribution using the traditional method when α 1 = 50 ° .

Fig. 5
Fig. 5

Reference fringe.

Fig. 6
Fig. 6

Deformed fringe of a 3D object.

Fig. 7
Fig. 7

Correct height reconstruction.

Fig. 8
Fig. 8

Height reconstruction by the traditional method.

Tables (1)

Tables Icon

Table 1 Mean-Square Deviations and the Maximal Height Distribution Corresponding to Different Angles

Equations (122)

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I 1
I 20
I 1 O ¯
I 20 O 1 ¯
O 1
I 1 I 20 ¯
I 1 O ¯
I 20 O 1 ¯
D ( x , y )
C 1
I 1 A ¯
I 1 H ¯
I 20 O 1 ¯
I 1 H ¯
I 1 K ¯
I 2 O ¯
I 20
I 2
C 1
O A ¯
B D ¯
I 1 F ¯
I 2 O ¯
B D ¯
I 2 D ¯
I 1 F ¯
H G ¯
O O 1 ¯
O 1 I 20 ¯ = O I 2 ¯ = L
I 1 G ¯ = K O ¯ = r
I 1 I 20 ¯ = s
H I 1 I 20 = α 1
B C D = δ
B A D = γ
I 1 ( x , y ) = I 0 [ 1 + cos 2 π x f ( x ) ] ,
I 0
f ( x )
f ( x ) = f cos θ ( 1 2 x sin θ I 1 O ¯ ) ,
I 2 O ¯
Δ O I 1 G , I 1 O ¯ = r / sin θ
I 2 G ¯ = I 20 H ¯
I 1 ( x , y ) = I 0 { 1 + cos [ 2 π f x cos θ ( 1 2 x sin 2 θ r ) ] } ,
tan θ = r L + s sin α 1 .
I 2 ( x , y ) = I 0 { 1 + cos [ 2 π f x cos θ ×( 1 2 x sin 2 θ r ) ψ ( x , y ) ] } ,
ψ ( x , y )
h ( x , y )
ψ ( x , y ) = 2 π f C A ¯ cos θ ,
C A ¯
Δ A B D
Δ D I 1 F
Δ B C D
Δ D P F
C A ¯ B D ¯ = I 1 P ¯ D F ¯ = I 1 P ¯ L + s sin α 1 B D ¯ .
Δ P I 2 G
Δ O I 2 C
Δ B C D
P G ¯ I 2 G ¯ = r I 1 P ¯ s sin α 1 = O C ¯ L = B C ¯ B D ¯ = x L B D ¯ .
C A ¯ = B D ¯ L + s sin α 1 B D ¯ ( r x s sin α 1 L B D ¯ ) ,
ψ ( x , y ) = 2 π f cos θ B D ¯ L + s sin α 1 B D ¯ ( r x s sin α 1 L B D ¯ ) .
I 1 ( x , y ) = I 0 { 1 + cos [ 2 π f 0 x + ϕ 0 ( x , y ) ] } ,
I 2 ( x , y ) = I 0 { 1 + cos [ 2 π f 0 x + ϕ ( x , y ) ] } ,
f 0 = f cos θ
ϕ 0 ( x , y )
ϕ ( x , y )
I 1 ( x , y )
I 2 ( x , y )
ϕ 0 ( x , y )
ϕ ( x , y )
Δ ϕ ( x , y )
Δ ϕ ( x , y ) = ϕ ( x , y ) ϕ 0 ( x , y ) .
Δ A B D
Δ C B D
B D ¯ = C A ¯ cot γ cot δ ,
cot δ = O C ¯ / L = ϕ C / 2 π f 0 L
ϕ C
O A ¯ = ϕ A / 2 π f 0 = ϕ D / 2 π f 0
ϕ D
ϕ A
C A ¯ = | O A ¯ O C ¯ | = | ϕ D C / 2 π f 0 |
ϕ D C < 0
C A ¯ = ϕ D C 2 π f 0 .
Δ A K I 1
cot γ = r + O A ¯ L + s sin α 1 = 2 π f 0 r + ϕ D 2 π f 0 ( L + s sin α 1 ) .
cot δ = O C ¯ / L = ϕ C / 2 π f 0 L
B D ¯ = ϕ D C L ( L + s sin α 1 ) 2 π f 0 L r + L ϕ D C ϕ C s sin α 1 ,
α 1
f 0 = f cos θ
ϕ C
α 1 = 0
r = d
B D ¯ = L ϕ D C 2 π f 0 d + ϕ D C ,
α 1
I 20
h = 32.42   mm
α 1 = 0 °
512 × 512
r = 800
s = 400
L = 2000   mm
α 1 = 0 ° , 10 ° , 30 ° , 50 °
α 1 = 10 °
α 1 = 50 °
25.03   mm
31.73   mm
α 1 = 90 °
α 1 = 90 °
h = 32.5   mm
r = 360.0
s = 280.0   mm
α 1 = 17 °
L = 950.0   mm
T = 16
400 × 400
33.1   mm
27.4   mm
α = 0 °
α 1 = 0 °
α 1 = 10 °
α 1 = 30 °
α 1 = 50 °
α 1 = 10 °
α 1 = 50 °

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