Abstract

A technique to produce phase steps in a fringe projection system for shape measurement is presented. Phase steps are produced by introducing relative rotation between the object and the fringe projection probe (comprising a projector and camera) about the camera’s perspective center. Relative motion of the object in the camera image can be compensated, because it is independent of the distance of the object from the camera, whilst the phase of the projected fringes is stepped due to the motion of the projector with respect to the object. The technique was validated with a static fringe projection system by moving an object on a coordinate measuring machine (CMM). The alternative approach, of rotating a lightweight and robust CMM-mounted fringe projection probe, is discussed. An experimental accuracy of approximately 1.5% of the projected fringe pitch was achieved, limited by the standard phase-stepping algorithms used rather than by the accuracy of the phase steps produced by the new technique.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (1)

2003 (2)

J. Novak, “Five-step phase-shifting algorithms with unknown values of phase shift,” Optik (Stuttg.) 114(2), 63–68 (2003).
[CrossRef]

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

2002 (1)

1999 (2)

1997 (1)

1986 (1)

K. Creath, “Comparison of phase-measurement algorithms,” Proc. SPIE 680, 19–28 (1986).

1974 (1)

1967 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2(1), 13–23 (1966).
[CrossRef]

Barton, J. S.

Brangaccio, D. J.

Bruning, J. H.

Carocci, M.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2(1), 13–23 (1966).
[CrossRef]

Corini, S.

Creath, K.

K. Creath, “Comparison of phase-measurement algorithms,” Proc. SPIE 680, 19–28 (1986).

Docchio, F.

Gallagher, J. E.

Hand, D. P.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Herriott, D. R.

Jones, J. D. C.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, “Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement,” Appl. Opt. 41(16), 3348–3354 (2002).
[CrossRef] [PubMed]

Lazzari, S.

Lu, G.

Lui, H.

McBride, R.

Moore, A. J.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, “Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement,” Appl. Opt. 41(16), 3348–3354 (2002).
[CrossRef] [PubMed]

Novak, J.

J. Novak, “Five-step phase-shifting algorithms with unknown values of phase shift,” Optik (Stuttg.) 114(2), 63–68 (2003).
[CrossRef]

Reeves, M.

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Rodella, R.

Rosenfeld, D. P.

Sansoni, G.

Sparrow, E. M.

Torrance, K. E.

White, A. D.

Wu, S.

Yau, S.-T.

Yin, S.

Yu, F.T. S.U.

Zhang, S.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoelectrique et interferential du Bureau International des Poids et Mesures,” Metrologia 2(1), 13–23 (1966).
[CrossRef]

Opt. Eng. (1)

M. Reeves, A. J. Moore, D. P. Hand, and J. D. C. Jones, “Dynamic shape measurement system for laser materials processing,” Opt. Eng. 42(10), 2923–2929 (2003).
[CrossRef]

Optik (Stuttg.) (1)

J. Novak, “Five-step phase-shifting algorithms with unknown values of phase shift,” Optik (Stuttg.) 114(2), 63–68 (2003).
[CrossRef]

Proc. SPIE (1)

K. Creath, “Comparison of phase-measurement algorithms,” Proc. SPIE 680, 19–28 (1986).

Other (9)

J.-Y. Bouguet, “Camera calibration toolbox for Matlab”, http://www.vision.caltech.edu/bouguetj/calib_doc/index.html (accessed 5 February 2010).

3M, “3M MPro 110 Micro projector,” http://www.3mselect.co.uk/p-1783-3m-mpro-110-micro-projector-uk-model.aspx (accessed 5 February 2010).

D. M. Kranz, E. P. Rudd, D. Fishbaine, and C. E. Haugan, “Phase profilometry system with telecentric projector,” International Patent, Publication Number WO01/51887 (2001).

M. A. R. Cooper with S. Robson, “Theory of close-range photogrammetry,” in Close range photogrammetry and machine vision, K. B. Atkinson, ed., (Whittles Publishing, Caithness, UK, 2001).

J. G. Fryer, “Camera Calibration,” in Close range photogrammetry and machine vision, K. B. Atkinson, ed., (Whittles Publishing, Caithness, UK, 2001).

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of the 1997 Conference in Computer Vision and Pattern Recognition (CVPR ’97) (IEEE Computer Society, Washington, DC, 1997), pp. 1106–1112.

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D.W. Robinson and G.T. Reid, eds., 94–140 (Institute of Physics 1993).

H. Ragheb and E. R. Hancock, “Surface radiance: empirical data against model predictions,” in Proceedings of the 2004 International Conference on Image Processing (ICIP), (Institute of Electrical and Electronics Engineers, 2005), pp. 2689–2692.

N. J. Weston, Y. R. Huddart, A. J. Moore, and T. C. Featherstone, “Phase analysis measurement apparatus and method”, International patent pending WO2009 / 024757(A1) (2008).

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Figures (5)

Fig. 1
Fig. 1

Schematic of fringe projection system.

Fig. 2
Fig. 2

Error in the calculated probe tip image position after rotation about the perspective center of the camera at one plane in the measurement volume. Arrow lengths are scaled to make them visible: maximum arrow length 0.5 pixels.

Fig. 3
Fig. 3

Effect of phase stepping algorithm on the shape measurement errors for a plane surface. Graphs show a single line across the plane. Error for phase-stepped images recorded with rotation about the camera perspective center for (a) four frames (Carré’s algorithm, rms 3.1% of the projected fringe period for the entire plane) and (b) five frames (Novak’s algorithm, rms 1.6%). Error for standard phase-stepped images for (c) Novak’s algorithm (rms 1.5%) and (d) Bruning’s algorithm (rms 0.6%).

Fig. 4
Fig. 4

(a) Wrapped phase map for a free-form object using the new phase step technique and (b) calibrated height measurement along the line indicated. Inset shows a comparison to a standard phase step measurment.

Fig. 5
Fig. 5

Simulated errors from different error sources: (a) rms error from speckle noise; (b) mean error from linear variation in intensity between images; (c) mean error due to non-linear variation in phase step.

Equations (8)

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x _ p = c p Z P X _ P = [ x P y P c p ]
ϕ = 2 π c p p X P Z P .
ϕ = 2 π c p p X ^ _ P ( X _ X _ O P ) Z ^ _ P ( X _ X _ O P )
X _ R = X _ | X _ | ω V ^ _
Δ ϕ = 2 π c P p | X _ | ( X ^ _ P . V ^ _ X P Z P Z ^ _ P . V ^ _ Z P + | X _ | Z ^ _ P . V ^ _ ω ω )
Δ ϕ 2 π c P p Z P S ω cos α
Δ ϕ ' = 2 π c P p | X _ | ( X ^ _ P X P Z P Z ^ _ P ) . V ^ _ Z P ω ( 1 + | X _ | Z ^ _ P . V ^ _ Z P ω )
ε = p Z P 2 π c p Z ^ _ P . V ^ _ ( Z P X ^ _ P X P Z ^ _ P ) . V ^ _

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