Abstract

A three-dimensional (3-D) imaging system based on Gray-code projection is described; it is thought to be used as an integration to the already developed profilometer based on the projection of multifrequency gratings. The Gray-code method allows us to evaluate the 3-D profile of objects that present even marked discontinuities of the surface, thus increasing the flexibility of the measuring system as to the topology of the objects that can be measured. The basic aspects of Gray-code projection for 3-D imaging and profiling are discussed, with particular emphasis devoted to the study of the resolution of the method and to the analysis of the systematic errors. The results of this study allow us to determine the optimal setting of the parameters of the measurement and to develop a suitable calibration procedure. The procedures for implementing the Gray-code method are presented, and some interesting experimental results are reported. Calibration of the system reveals an accuracy of 0.2 mm, corresponding to 0.1% of the field of view.

© 1997 Optical Society of America

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References

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  1. W. Reichmann, “Fast object recording by means of structured light and photogrammetric techniques,” Proc. Int. Arch. Photogramm. Remote Sensing 30, 195–200 (1995.
  2. T. G. Stahs, F. M. Wahl, “Fast and versatile range data acquisition in a robot work cell,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, New York, 1990), pp.1169–1174.
  3. R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
    [Crossref] [PubMed]
  4. D. Poussart, D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989), Chap. 3.
  5. K. Leonhardt, U. Droste, H. J. Tiziani, “Microshape and rough-surface analysis by fringe projection,” Appl. Opt. 33, 7477–7488 (1994).
    [Crossref] [PubMed]
  6. G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
    [Crossref]
  7. S. Tang, Y. Y. Hung, “Fast profilometer for the automatic measurement of 3-D object shapes,” Appl. Opt. 29, 3012–3018 (1990).
    [Crossref] [PubMed]
  8. G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
    [Crossref]
  9. W. Osten, W. Nadeborn, P. Andrä, “General hierarchical approach in absolute phase measurement,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2860, 2–13 (1996).
    [Crossref]
  10. L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
    [Crossref]
  11. T. G. Stahs, F. M. Wahl, “Fast and robust range data acquisition in a low-cost environment,” in Close-Range Photogrammetry Meets Machine Vision, E. P. Baltsavias, A. Gruen, eds., Proc. SPIE1395, 496–503 (1990).
  12. W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).
  13. L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
    [Crossref]

1995 (3)

W. Reichmann, “Fast object recording by means of structured light and photogrammetric techniques,” Proc. Int. Arch. Photogramm. Remote Sensing 30, 195–200 (1995.

R. Windecker, H. J. Tiziani, “Topometry of technical and biological objects by fringe projection,” Appl. Opt. 34, 3644–3650 (1995).
[Crossref] [PubMed]

L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
[Crossref]

1994 (3)

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

K. Leonhardt, U. Droste, H. J. Tiziani, “Microshape and rough-surface analysis by fringe projection,” Appl. Opt. 33, 7477–7488 (1994).
[Crossref] [PubMed]

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

1993 (1)

W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).

1990 (1)

Andrä, P.

W. Osten, W. Nadeborn, P. Andrä, “General hierarchical approach in absolute phase measurement,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2860, 2–13 (1996).
[Crossref]

Biancardi, L.

L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
[Crossref]

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
[Crossref]

Carrato, S.

L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
[Crossref]

Docchio, F.

L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
[Crossref]

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

Droste, U.

Duwe, H. P.

W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).

Hung, Y. Y.

Krattenthaler, W.

W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).

Laurendeau, D.

D. Poussart, D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989), Chap. 3.

Leonhardt, K.

Mayer, K. J.

W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).

Minoni, U.

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

Nadeborn, W.

W. Osten, W. Nadeborn, P. Andrä, “General hierarchical approach in absolute phase measurement,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2860, 2–13 (1996).
[Crossref]

Osten, W.

W. Osten, W. Nadeborn, P. Andrä, “General hierarchical approach in absolute phase measurement,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2860, 2–13 (1996).
[Crossref]

Poussart, D.

D. Poussart, D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989), Chap. 3.

Ramponi, G.

L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
[Crossref]

Reichmann, W.

W. Reichmann, “Fast object recording by means of structured light and photogrammetric techniques,” Proc. Int. Arch. Photogramm. Remote Sensing 30, 195–200 (1995.

Sansoni, G.

L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
[Crossref]

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
[Crossref]

Stahs, T. G.

T. G. Stahs, F. M. Wahl, “Fast and robust range data acquisition in a low-cost environment,” in Close-Range Photogrammetry Meets Machine Vision, E. P. Baltsavias, A. Gruen, eds., Proc. SPIE1395, 496–503 (1990).

T. G. Stahs, F. M. Wahl, “Fast and versatile range data acquisition in a robot work cell,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, New York, 1990), pp.1169–1174.

Tang, S.

Tiziani, H. J.

Wahl, F. M.

T. G. Stahs, F. M. Wahl, “Fast and versatile range data acquisition in a robot work cell,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, New York, 1990), pp.1169–1174.

T. G. Stahs, F. M. Wahl, “Fast and robust range data acquisition in a low-cost environment,” in Close-Range Photogrammetry Meets Machine Vision, E. P. Baltsavias, A. Gruen, eds., Proc. SPIE1395, 496–503 (1990).

Windecker, R.

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (3)

G. Sansoni, L. Biancardi, U. Minoni, F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43, 558–566 (1994).
[Crossref]

L. Biancardi, G. Sansoni, F. Docchio, “Adaptive whole field optical profilometry: a study of the systematic errors,” IEEE Trans. Instrum. Meas. 44, 36–41 (1995).
[Crossref]

G. Sansoni, L. Biancardi, F. Docchio, U. Minoni, “Comparative analysis of low-pass filters for the demodulation of projected gratings in 3-D adaptive profilometry,” IEEE Trans. Instrum. Meas. 43, 50–55 (1994).
[Crossref]

Proc. Int. Arch. Photogramm. Remote Sensing (1)

W. Reichmann, “Fast object recording by means of structured light and photogrammetric techniques,” Proc. Int. Arch. Photogramm. Remote Sensing 30, 195–200 (1995.

Proc. Oesterr. Arbeitsgem. MustererKennung (1)

W. Krattenthaler, K. J. Mayer, H. P. Duwe, “3D- Surface measurement with coded light approach,” Proc. Oesterr. Arbeitsgem. MustererKennung 12, 103–114 (1993).

Other (5)

T. G. Stahs, F. M. Wahl, “Fast and versatile range data acquisition in a robot work cell,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, New York, 1990), pp.1169–1174.

D. Poussart, D. Laurendeau, “3-D sensing for industrial computer vision,” in Advances in Machine Vision, J. L. C. Sanz, ed. (Springer-Verlag, New York, 1989), Chap. 3.

W. Osten, W. Nadeborn, P. Andrä, “General hierarchical approach in absolute phase measurement,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. P. Jueptner, eds., Proc. SPIE2860, 2–13 (1996).
[Crossref]

L. Biancardi, S. Carrato, G. Ramponi, G. Sansoni, “Whole field optical profilometry: application of nonlinear processing algorithms to the enhancement of low-contrast images,” in Videometrico III, S. F. El-Hakim, ed., Proc. SPIE2350, 336–342 (1994).
[Crossref]

T. G. Stahs, F. M. Wahl, “Fast and robust range data acquisition in a low-cost environment,” in Close-Range Photogrammetry Meets Machine Vision, E. P. Baltsavias, A. Gruen, eds., Proc. SPIE1395, 496–503 (1990).

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Figures (18)

Fig. 1
Fig. 1

Optical geometry of the system.

Fig. 2
Fig. 2

Coding of the LP’s for n = 4 on the BPS in the absence (RBPS) and in the presence (OBPS) of an object.

Fig. 3
Fig. 3

System layout of the profilometer.

Fig. 4
Fig. 4

Example of the resolution of the measurement: (a) object under measurement, (b) plot of the profile along a single section.

Fig. 5
Fig. 5

Plot of the systematic error ∂z(x, y)/∂d as a function of z(x, y) and L for d = 592 mm.

Fig. 6
Fig. 6

Plot of the systematic error ∂z(x, y)/∂L as a function of z(x, y) and L for d = 592 mm.

Fig. 7
Fig. 7

Plot of the systematic error ∂z(x, y)/∂FW as a function of the shift Si, j for three settings of L and d that satisfy L/d = 0.84.

Fig. 8
Fig. 8

Plot of the systematic error ∂z(x, y)/∂FW as a function of z(x, y) and L for FW = 186.9 mm.

Fig. 9
Fig. 9

Comparison of the influence of inaccuracies ∂d, ∂L, and ∂FW on the height error ∂z(x, y) as functions of L for z(x, y) = 55 mm, d = 592 mm, and FW = 189 mm.

Fig. 10
Fig. 10

White-painted mechanical flange.

Fig. 11
Fig. 11

Image of the stripe pattern deformed by the mechanical flange.

Fig. 12
Fig. 12

3-D plot of the reconstructed profile of the flange.

Fig. 13
Fig. 13

Plot of a cross-sectional profile of the flange.

Fig. 14
Fig. 14

White-painted rack.

Fig. 15
Fig. 15

Plot of the reconstructed 3-D profile of the rack.

Fig. 16
Fig. 16

Objects used to evaluate the ability of the measurement procedures to adapt to surfaces differing in reflectivity.

Fig. 17
Fig. 17

3-D plot of the reconstructed profile of the blocks.

Fig. 18
Fig. 18

Comparison of the influence of inaccuracies ∂d, ∂L, and ∂FW on the height error ∂z(x, y) as functions of L for z(x, y) = 24.95 mm, d = 248 mm, and FW = 99.5 mm.

Tables (2)

Tables Icon

Table 1 Gray-Code Sequence for n = 4

Tables Icon

Table 2 Evaluation of Shifts Si, j and Sr(x, y) and Height z(x, y) Calculated at x = 107.4 mm along the Section of the Object in Fig. 4(b) for Three Values of the Estimate of FWe

Equations (12)

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

SRx, y=Si,jFWN.
AB¯CP¯=zx,yL-zx,y,
zx, y=LSRx, yd+SRx, y.
zmin=Lxmind+xmin.
zmin=Ldxmin=LdFWN.
FW=8.8Lf,
zx, yd=-LSRx, yYd+SRx, y2,
zx, yL=SRx, yd+SRx, y.
zx, yd=zx, y2-Lzx, yLd,
zx, yL=zx, yL.
zx, yFW=FWLSi,jFWNd+Si,jFWN=LdSi,jNd+FWN Si,j2.
zx, yFW=Lzx, yL+zx, yFWL+2zx, y2.

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