Abstract

Three-dimensional (3D) surface shape measurement is a vital component in many industrial processes. The subject has developed significantly over recent years and a number of mainly noncontact techniques now exist for surface measurement, exhibiting varying levels of maturity. Within the larger group of 3D measurement techniques, one of the most promising approaches is provided by those methods that are based upon fringe analysis. Current techniques mainly focus on the measurement of small and medium-scale objects, while work on the measurement of larger objects is not so well developed. One potential solution for the measurement of large objects that has been proposed by various researchers is the concept of performing multipanel measurement and the system proposed here uses this basic approach, but in a flexible form of a single moveable sensor head that would be cost effective for measuring very large objects. Most practical surface measurement techniques require the inclusion of a calibration stage to ensure accurate measurements. In the case of fringe analysis techniques, phase-to-height calibration is required, which includes the use of phase-to-height models. Most existing models (both analytical and empirical) are intended to be used in a static measurement mode, which means that, typically, a single calibration is performed prior to multiple measurements being made using an unvarying system geometry. However, multipanel measurement strategies do not necessarily keep the measurement system geometry constant and thus require dynamic recalibration. To solve the problem of dynamic recalibration, we propose a class of models called hybrid models. These hybrid models inherit the basic form of analytical models, but their coefficients are obtained in an empirical manner. The paper also discusses issues associated with all phase-to-height models used in fringe analysis that have a quotient form, identifying points of uncertainty and regions of distortion as issues affecting accuracy in phase maps produced in this manner.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. B. A. Al-Rjoub, “Structured light optical non-contact measuring techniques: system analysis and modelling,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2007).
  17. D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
    [CrossRef]
  18. V. Hovorov, “A new method for the measurement of large objects using a moving sensor,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2008).

2007

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

2005

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A Pure Appl. Opt. 7, S368-S375 (2005).
[CrossRef]

2001

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

2000

F. Lilley, M. J. Lalor, and D. R. Burton, “A robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187-195 (2000).
[CrossRef]

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159-169 (2000).
[CrossRef]

1999

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to non-linear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524-1533 (1999).
[CrossRef]

A. Asundi and W. Zhou, “Mapping algorithm for 360 degprofilometry with time delayed integration imaging,” Opt. Eng. 38, 339-344 (1999).
[CrossRef]

1998

C. Reich, “Photogrammetrical matching of point clouds for 3D measurement of complex objects,” Proc. SPIE 3520, 100-110 (1998).
[CrossRef]

J. C. Wyant and J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691-698 (1998).
[CrossRef]

1995

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

1991

H. P. Stahl, “Review of phase-measuring interferometry,” Proc. SPIE 1332, 704-719 (1991).
[CrossRef]

1983

1982

1974

1966

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Accardo, G.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Al-Rjoub, B. A.

B. A. Al-Rjoub, “Structured light optical non-contact measuring techniques: system analysis and modelling,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2007).

Ambrosini, D.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Asundi, A.

A. Asundi and W. Zhou, “Mapping algorithm for 360 degprofilometry with time delayed integration imaging,” Opt. Eng. 38, 339-344 (1999).
[CrossRef]

Atkinson, J. T.

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

Brangaccio, D. J.

Bruning, J. H.

Burton, D. R.

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A Pure Appl. Opt. 7, S368-S375 (2005).
[CrossRef]

F. Lilley, M. J. Lalor, and D. R. Burton, “A robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187-195 (2000).
[CrossRef]

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to non-linear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524-1533 (1999).
[CrossRef]

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Chen, W.

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

Gallagher, J. E.

Goodall, A. J.

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

Guattari, G.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Herriott, D. R.

Hovorov, V.

V. Hovorov, “A new method for the measurement of large objects using a moving sensor,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2008).

Ina, H.

Karout, S. A.

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

Kobayashi, S.

Lalor, M. J.

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A Pure Appl. Opt. 7, S368-S375 (2005).
[CrossRef]

F. Lilley, M. J. Lalor, and D. R. Burton, “A robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187-195 (2000).
[CrossRef]

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to non-linear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524-1533 (1999).
[CrossRef]

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

Lilley, F.

F. Lilley, M. J. Lalor, and D. R. Burton, “A robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187-195 (2000).
[CrossRef]

Mutoh, K.

Notni, G.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159-169 (2000).
[CrossRef]

Paoletti, D.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Rajoub, B. A.

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A Pure Appl. Opt. 7, S368-S375 (2005).
[CrossRef]

Reich, C.

C. Reich, “Photogrammetrical matching of point clouds for 3D measurement of complex objects,” Proc. SPIE 3520, 100-110 (1998).
[CrossRef]

Rosenfeld, D. P.

Sapia, C.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Schmit, J.

J. C. Wyant and J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691-698 (1998).
[CrossRef]

Schreiber, W.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159-169 (2000).
[CrossRef]

Spagnolo, G. S.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

Stahl, H. P.

H. P. Stahl, “Review of phase-measuring interferometry,” Proc. SPIE 1332, 704-719 (1991).
[CrossRef]

Su, X.

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

Takeda, M.

White, A. D.

Wyant, J. C.

J. C. Wyant and J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691-698 (1998).
[CrossRef]

Zhang, H.

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to non-linear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524-1533 (1999).
[CrossRef]

Zhou, W.

A. Asundi and W. Zhou, “Mapping algorithm for 360 degprofilometry with time delayed integration imaging,” Opt. Eng. 38, 339-344 (1999).
[CrossRef]

Appl. Opt.

Int. J. Mach. Tools Manuf.

J. C. Wyant and J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691-698 (1998).
[CrossRef]

J. Opt. A Pure Appl. Opt.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A Pure Appl. Opt. 7, S368-S375 (2005).
[CrossRef]

B. A. Rajoub, D. R. Burton, M. J. Lalor, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Three-dimensional optical profilometry for artwork inspection,” J. Opt. A Pure Appl. Opt. 2, 353-361 (2000).
[CrossRef]

J. Opt. Soc. Am.

Metrologia

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Opt. Eng.

H. Zhang, M. J. Lalor, and D. R. Burton, “Robust, accurate seven-sample phase-shifting algorithm insensitive to non-linear phase-shift error and second-harmonic distortion: a comparative study,” Opt. Eng. 38, 1524-1533 (1999).
[CrossRef]

A. Asundi and W. Zhou, “Mapping algorithm for 360 degprofilometry with time delayed integration imaging,” Opt. Eng. 38, 339-344 (1999).
[CrossRef]

F. Lilley, M. J. Lalor, and D. R. Burton, “A robust fringe analysis system for human body shape measurement,” Opt. Eng. 39, 187-195 (2000).
[CrossRef]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159-169 (2000).
[CrossRef]

Opt. Lasers Eng.

D. R. Burton, A. J. Goodall, J. T. Atkinson, and M. J. Lalor, “The use of carrier frequency shifting for the elimination of phase discontinuities in fourier transform profilometry,” Opt. Lasers Eng. 23, 245-257 (1995).
[CrossRef]

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

Proc. SPIE

H. P. Stahl, “Review of phase-measuring interferometry,” Proc. SPIE 1332, 704-719 (1991).
[CrossRef]

C. Reich, “Photogrammetrical matching of point clouds for 3D measurement of complex objects,” Proc. SPIE 3520, 100-110 (1998).
[CrossRef]

Other

V. Hovorov, “A new method for the measurement of large objects using a moving sensor,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2008).

B. A. Al-Rjoub, “Structured light optical non-contact measuring techniques: system analysis and modelling,” Ph.D. dissertation (Liverpool John Moores University, U.K., 2007).

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Figures (6)

Fig. 1
Fig. 1

Point of uncertainty lying outside the sensor’s field of view.

Fig. 2
Fig. 2

Plot of the surface height measurement error Δ H calculated for 100 measured panels; where Δ H 0 = 0.05 H 0 , Δ φ 0 = 0.01 φ 0 .

Fig. 3
Fig. 3

Two-panel measurement of a cylinder. (a) and (b) Individual panel measurements, (c) panel stitching results without 3D correction, and (d) stitching results with 3D correction.

Fig. 4
Fig. 4

Three-panel measurement of a model aircraft wing. The three source fringe-pattern images of the partial wing sections are shown in (a), (b), and (c). (d) Registration of individual panels and (e) final assembled measurement after 3D correction.

Fig. 5
Fig. 5

Test object: decorative plaster wall plaque of a dancing woman holding a musical instrument.

Fig. 6
Fig. 6

Multipanel measurement results for the test object. Two example surfaces are shown, each made up of five measured panels. (a) and (b) 2D gray-scale representation of height values of the two samples. (c) and (d) 3D isoplot representations of both surfaces.

Tables (1)

Tables Icon

Table 1 Measurement Errors Derived Experimentally for the Different Phase-to-Height Models

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

h i = ( m n η 1 x z f + ( m 2 η 2 z f + η 1 x 0 z f + ( η 4 + η 2 y f η 1 x f ) z 0 + η 4 z f + η 2 v 0 z f ) m 2 ( m η 1 n x + m 2 η 2 y + ( ( η 2 z 0 η 2 y f η 1 x f + η 1 x 0 + η 2 y 0 η 3 z f ) n η 2 v 0 ) m 2 + ( u 0 z f z 0 + ( z f 2 η 1 z f ) u 0 ) n m ) ω x + ( z 0 z f z f 2 ) n m Φ + ( u 0 z 0 + ( z f η 1 ) u 0 ) n m ) ω x + ( z 0 z f ) n m Φ ,
h = A 1 x + A 2 + A 3 Φ A 4 x + A 5 y + A 6 + A 7 Φ ,
A 1 x + A 2 + A 3 Φ h A 4 x h A 5 y h A 6 h A 7 Φ = 0.
k 11 A 1 + k 21 A 2 + k 31 A 3 + k 41 A 4 + k 51 A 5 + k 61 A 6 + k 71 A 7 = 0 k 12 A 1 + k 22 A 2 + k 32 A 3 + k 42 A 4 + k 52 A 5 + k 62 A 6 + k 72 A 7 = 0 k 17 A 1 + k 27 A 2 + k 37 A 3 + k 47 A 4 + k 57 A 5 + k 67 A 6 + k 77 A 7 = 0 } .
A i = c A i * ,
h = c A 1 * + c A 2 * + c A 3 * Φ c A 4 * x + c A 5 * y + c A 6 * + c A 7 * Φ .
h = A 1 * + A 2 * + A 3 * Φ A 4 * x + A 5 * y + A 6 * + A 7 * Φ .
c = 1 A 6 .
A 1 x + A 2 + A 3 Φ h A 4 x h A 5 y h A 7 Φ = h .
A 1 x + A 2 + A 3 Φ h A 4 x h A 5 y h A 6 Φ = h .
h = A 1 x + A 2 + A 3 Φ A 4 x + A 5 y + 1 + A 6 Φ .
{ k 11 A 1 + k 21 A 2 + k 31 A 3 + k 41 A 4 + k 51 A 5 + k 61 A 6 = h 1 k 12 A 1 + k 22 A 2 + k 32 A 3 + k 42 A 4 + k 52 A 5 + k 62 A 6 = h 2 k 16 A 1 + k 26 A 2 + k 36 A 3 + k 46 A 4 + k 56 A 5 + k 66 A 6 = h 6 ,
A 4 x + A 5 y + 1 + A 6 Φ = 0.
A 4 x + A 5 y = 1 A 6 Φ .
h = A 1 x + A 2 + A 3 Φ 0 .
h = A 1 x + A 2 + A 3 Φ 0 .
h = A 1 x + A 2 + A 3 Φ 1 + A 6 Φ .
h = A 1 x + A 2 + A 3 Φ .
Δ H = ( Δ A H A ) 2 + ( Δ φ H φ ) 2 .
Δ H = ( Δ A φ ) 2 + ( Δ φ A ) 2 ,
A = H φ .
Δ A = ( Δ H A H ) 2 + ( Δ φ A φ ) 2 ,
Δ A = ( Δ H φ ) 2 + ( Δ φ H 2 ) 2
Δ A 0 = ( Δ H 0 φ 0 ) 2 + ( Δ φ 0 H 0 2 ) 2 .
Δ H 1 = ( Δ A 0 φ 0 ) 2 + ( Δ φ 0 A 0 ) 2 .
Δ A 1 = ( Δ H 1 φ 0 ) 2 + ( Δ φ 0 H 0 2 ) 2 .

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