Abstract

We present a method in which the 3D shape of an object can be measured and compared to the shape of the digital master of the object, e.g., the computer-aided design model. The measurement is done using a stereo camera system and a single projected fringe pattern. Because the digital master is available, i.e., the expected shape is known, only one projection and image recording is necessary; thus, the method becomes fast. The idea in this work is to find homologous points in the cameras, i.e., points corresponding to the same object point, using the object information. An algorithm to find the homologous points is presented and a method to calculate shape is described. Given the ambiguity due to the fact that the phase in the images is wrapped, there is a maximum deviation from the master that can be correctly detected. An analytical expression for this deviation is derived. Results from the shape measurement of an object both with and without deviations from the digital master are also presented. In these measurements, where the measurement volume is approximately 1dm3 and the fringe period on the object plane is about 1mm, the accuracy is ±40μm, and a deviation of max ±1.6mm can be correctly detected.

© 2010 Optical Society of America

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References

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  1. F. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
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  2. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [CrossRef]
  3. S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
    [CrossRef]
  4. W-H. Su, “Projected fringe profilometry using the area encoded algorithm for spatially isolated and dynamic objects,” Opt. Express 16, 2590–2596 (2008).
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    [CrossRef]
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    [CrossRef]
  8. X. Han and P. Huang, “Combined stereovision and phase shifting method: a new approach for 3-D shape measurement,” Proc. SPIE 7389, 73893C (2009).
    [CrossRef]
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    [CrossRef]
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2009 (2)

X. Han and P. Huang, “Combined stereovision and phase shifting method: a new approach for 3-D shape measurement,” Proc. SPIE 7389, 73893C (2009).
[CrossRef]

X. Han and P. Huang, “Combined stereovision and phase shifting method: use of a visibility-modulated fringe pattern,” Proc. SPIE 7389, 73893H (2009).
[CrossRef]

2008 (1)

2007 (1)

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

2006 (2)

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

A. Wiegmann, H. Wagner, and R. Kowarschik, “Human face measurement by projecting bandlimited random patterns,” Opt. Express 14, 7692–7698 (2006).
[CrossRef] [PubMed]

2003 (1)

2001 (2)

2000 (2)

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

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[CrossRef]

1999 (1)

P. Synnergren and M. Sjödahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31, 425–443 (1999).
[CrossRef]

1997 (1)

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

1995 (1)

1982 (1)

Bräuer-Burchardt, C.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Brown, G. M.

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

Chen, F. F.

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

Chen, W.

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

Guan, C.

Han, X.

X. Han and P. Huang, “Combined stereovision and phase shifting method: use of a visibility-modulated fringe pattern,” Proc. SPIE 7389, 73893H (2009).
[CrossRef]

X. Han and P. Huang, “Combined stereovision and phase shifting method: a new approach for 3-D shape measurement,” Proc. SPIE 7389, 73893C (2009).
[CrossRef]

Hassebrook, L.

Heinze, M.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Huang, P.

X. Han and P. Huang, “Combined stereovision and phase shifting method: a new approach for 3-D shape measurement,” Proc. SPIE 7389, 73893C (2009).
[CrossRef]

X. Han and P. Huang, “Combined stereovision and phase shifting method: use of a visibility-modulated fringe pattern,” Proc. SPIE 7389, 73893H (2009).
[CrossRef]

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Ina, H.

Jensen, K.

Kinell, L.

Kobayashi, S.

Kowarschik, R.

Kühmstedt, P.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Lau, D.

Munckelt, C.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Notni, G.

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

Prasad, A. K.

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[CrossRef]

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[CrossRef]

Sjödahl, M.

L. Kinell and M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297–2303 (2001).
[CrossRef]

P. Synnergren and M. Sjödahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31, 425–443 (1999).
[CrossRef]

Song, M.

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

Su, W-H.

Su, X.

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

Synnergren, P.

P. Synnergren and M. Sjödahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31, 425–443 (1999).
[CrossRef]

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

Takeda, M.

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[CrossRef]

Wagner, H.

Wiegmann, A.

Zhang, S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Eng. (4)

P. Synnergren, “Measurement of three-dimensional displacement fields and shape using electronic speckle photography,” Opt. Eng. 36, 2302–2310 (1997).
[CrossRef]

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

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (2)

P. Synnergren and M. Sjödahl, “A stereoscopic digital speckle photography system for 3-D displacement field measurements,” Opt. Lasers Eng. 31, 425–443 (1999).
[CrossRef]

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

Proc. SPIE (3)

P. Kühmstedt, C. Munckelt, M. Heinze, C. Bräuer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[CrossRef]

X. Han and P. Huang, “Combined stereovision and phase shifting method: a new approach for 3-D shape measurement,” Proc. SPIE 7389, 73893C (2009).
[CrossRef]

X. Han and P. Huang, “Combined stereovision and phase shifting method: use of a visibility-modulated fringe pattern,” Proc. SPIE 7389, 73893H (2009).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the camera system. The position vectors O 1 , O 2 , c 1 , and c 2 describe where the origins of the lens and detector coordinate systems are positioned. The point P in the world coordinate system is imaged to point P i on each detector.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

(a) Outline of the measurement object with three traces of depth 1, 2, and 3 mm milled off. (b) Outline of the digital master.

Fig. 4
Fig. 4

Captured fringe images from (a) the master camera and (b) the slave camera . The fringe period is approximately 1 mm in both images. (The images are cropped and contrast enhanced for clarity.)

Fig. 5
Fig. 5

Measurement results. As can be seen, the 2 mm trace is incorrectly detected. The black lines are cross sections that are used in Figs. 6, 7.

Fig. 6
Fig. 6

Cross sections of the measurement result compared with the cross sections of the digital master. The cross sections are taken at y = 35.5 , 26.9, 9.7, and 7.5 mm for (a)–(d), respectively.

Fig. 7
Fig. 7

Residuals between the cross sections of the measurement result and the cross sections of the real object. The cross sections are taken at y = 35.5 , 26.9, 9.7, and 7.5 mm for (a)–(d), respectively.

Equations (23)

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X i = ( x + O i x ) c i z O i z z c i x + Ω x i ( x , y , z , α ) = X ¯ i + Ω x i ( x , y , z , α ) ,
Y i = ( y + O i y ) c i z O i z z c i y + Ω y i ( x , y , z , α ) = Y ¯ i + Ω y i ( x , y , z , α ) ,
M = c i z / O i z
x ^ i = X i M = ( X ¯ i + Ω x i ) M ,
y ^ i = Y i M = ( Y ¯ i + Ω y i ) M .
x = 1 2 ( x ¯ 1 + x ¯ 2 z O 1 z ( x ¯ 1 + O 1 x ) z O 2 z ( x ¯ 2 + O 2 x ) ) ,
y = 1 2 ( y ¯ 1 + y ¯ 2 z O 1 z ( y ¯ 1 + O 1 y ) z O 2 z ( y ¯ 2 + O 2 y ) ) ,
z = 1 2 ( O 1 z ( x ¯ 1 x ¯ 2 ) x ¯ 1 + O 1 x O 1 z O 2 z [ x ¯ 2 + O 2 x ] O 2 z ( x ¯ 1 x ¯ 2 ) x ¯ 2 + O 2 x O 2 z O 1 z [ x ¯ 1 + O 1 x ] ) ,
x ¯ i = X ¯ i M = x ^ i Ω x i M ,
y ¯ i = Y ¯ i M = y ^ i Ω y i M
I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) + 2 π f 0 x ] = a ( x , y ) + c ( x , y ) e i 2 π f 0 x + c * ( x , y ) e i 2 π f 0 x
φ i ( x , y ) = tan 1 ( Im { c ( x , y ) } Re { c ( x , y ) } ) ,
Δ X = Δ φ λ d ( z ) 2 π ,
λ d ( z ) = λ ( z ) M ( z ) .
λ ( z ) = λ ( 0 ) ( O p z O p ) ,
M ( z ) = M ( 0 ) ( O z O z z ) .
λ d ( z ) = λ ( z ) M ( z ) = λ ( 0 ) M ( 0 ) ( O p z O p ) ( O z O z z ) .
λ d ( z ) = λ ( 0 ) M ( 0 ) .
e z = | O z O 1 x O 2 x λ ( 0 ) 2 π e φ | ,
e x = | λ ( 0 ) 2 π e φ | ,
min R , T k = 1 N ( d ( Rq k + T , p k ) ) ,
d ( q , p ) = min | φ 2 ( q ) φ 1 ( p ) | 2 ,
Δ z = ± λ d ( z ) ( O 2 z z ) 2 2 ( O 1 x O 2 x ) c 2 z + λ d ( z ) ( O 2 z z ) ,

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