Abstract

An accurate system calibration method is presented in this paper to calibrate stereo deflectometry. A corresponding iterative optimization algorithm is also proposed to improve the system calibration accuracy. This merges CCD parameters and geometrical relation between CCDs and the LCD into one cost function. In this calibration technique, an optical flat acts as a reference mirror and simultaneously reflect sinusoidal fringe patterns into the two CCDs. The normal vector of the reference mirror is used as an intermediate variable to implement this iterative optimization algorithm until the root mean square of the reprojection errors converge to a minimum. The experiment demonstrates that this method can optimize all the calibration parameters and can effectively reduce reprojection error, which correspondingly improves the final reconstruction accuracy.

© 2015 Optical Society of America

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References

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  1. M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
    [Crossref]
  2. H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
    [Crossref]
  3. M. Beyerlein, N. Lindlein, and J. Schwider, “Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics,” Appl. Opt. 41(13), 2440–2447 (2002).
    [Crossref] [PubMed]
  4. M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
    [Crossref]
  5. G. Häusler, C. Faber, E. Olesch, and S. Ettl, “Deflectometry vs. Interferometry,” Proc. SPIE 8788, 1C–1–1C–11 (2013).
    [Crossref]
  6. E. Olesch, C. Faber, and G. Hausler, “Object reconstruction by deflectometry,” in Proceedings of DGao (2012).
  7. H. H. Rapp, Reconstruction of Specular Reflective Surfaces using Auto-Calibrating Deflectometry (KIT Scientific Publishing, 2012).
  8. S. Ettl, J. Kaminski, M. C. Knauer, and G. Häusler, “Shape reconstruction from gradient data,” Appl. Opt. 47(12), 2091–2097 (2008).
    [Crossref] [PubMed]
  9. C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 0R–1-0R–15 (2013).
  10. E. Olesch, C. Faber, and G. Häusler, “Deflectometric self-calibration for arbitrary specular surface,” in Proceedings of DGao (2011).
  11. J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Mirror-based extrinsic camera calibration,” in The Eighth Int. Workshop on the Algorithmic Foundations of Robotics, pp. 285-2992008.
  12. Y. L. Xiao, X. Su, and W. Chen, “Flexible geometrical calibration for fringe-reflection 3D measurement,” Opt. Lett. 37(4), 620–622 (2012).
    [Crossref] [PubMed]
  13. L. Huang, Q. Zhang, and A. Asundi, “Camera calibration with active phase target: improvement on feature detection and optimization,” Opt. Lett. 38(9), 1446–1448 (2013).
    [Crossref] [PubMed]
  14. Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of Seventh IEEE Conference on Computer and Vision (IEEE 1999), pp. 666–673.
    [Crossref]
  15. J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Camera to robot-body calibration using planar mirror reflections,” University of Minnesota, Dept. of Comp. Sci. & Eng., Tech. Rep. 2008–3001, July 2008.

2013 (1)

2012 (1)

2008 (1)

2005 (1)

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[Crossref]

2004 (1)

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

2002 (1)

2001 (1)

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Asundi, A.

Beyerlein, M.

Chen, W.

Ettl, S.

Hausler, G.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Häusler, G.

Hesch, J. A.

J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Mirror-based extrinsic camera calibration,” in The Eighth Int. Workshop on the Algorithmic Foundations of Robotics, pp. 285-2992008.

Hofbauer, U.

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Huang, L.

Kaminski, J.

S. Ettl, J. Kaminski, M. C. Knauer, and G. Häusler, “Shape reconstruction from gradient data,” Appl. Opt. 47(12), 2091–2097 (2008).
[Crossref] [PubMed]

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Knauer, M. C.

S. Ettl, J. Kaminski, M. C. Knauer, and G. Häusler, “Shape reconstruction from gradient data,” Appl. Opt. 47(12), 2091–2097 (2008).
[Crossref] [PubMed]

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Lindlein, N.

Mourikis, A. I.

J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Mirror-based extrinsic camera calibration,” in The Eighth Int. Workshop on the Algorithmic Foundations of Robotics, pp. 285-2992008.

Petz, M.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[Crossref]

Pruss, C.

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Reichelt, S.

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Rocktaeschel, M.

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Roumeliotis, S. I.

J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Mirror-based extrinsic camera calibration,” in The Eighth Int. Workshop on the Algorithmic Foundations of Robotics, pp. 285-2992008.

Schwider, J.

Su, X.

Tiziani, H. J.

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

Tutsch, R.

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[Crossref]

Xiao, Y. L.

Zhang, Q.

Appl. Opt. (2)

Opt. Lett. (2)

Proc. SPIE (3)

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

H. J. Tiziani, S. Reichelt, C. Pruss, M. Rocktaeschel, and U. Hofbauer, “Testing of aspheric surfaces,” Proc. SPIE 4440, 109–119 (2001).
[Crossref]

M. Petz and R. Tutsch, “Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces,” Proc. SPIE 5869, 58691D (2005).
[Crossref]

Other (8)

G. Häusler, C. Faber, E. Olesch, and S. Ettl, “Deflectometry vs. Interferometry,” Proc. SPIE 8788, 1C–1–1C–11 (2013).
[Crossref]

E. Olesch, C. Faber, and G. Hausler, “Object reconstruction by deflectometry,” in Proceedings of DGao (2012).

H. H. Rapp, Reconstruction of Specular Reflective Surfaces using Auto-Calibrating Deflectometry (KIT Scientific Publishing, 2012).

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 0R–1-0R–15 (2013).

E. Olesch, C. Faber, and G. Häusler, “Deflectometric self-calibration for arbitrary specular surface,” in Proceedings of DGao (2011).

J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Mirror-based extrinsic camera calibration,” in The Eighth Int. Workshop on the Algorithmic Foundations of Robotics, pp. 285-2992008.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of Seventh IEEE Conference on Computer and Vision (IEEE 1999), pp. 666–673.
[Crossref]

J. A. Hesch, A. I. Mourikis, and S. I. Roumeliotis, “Camera to robot-body calibration using planar mirror reflections,” University of Minnesota, Dept. of Comp. Sci. & Eng., Tech. Rep. 2008–3001, July 2008.

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Figures (10)

Fig. 1
Fig. 1 Projection model of stereo deflectometry
Fig. 2
Fig. 2 Calibration flowchart
Fig. 3
Fig. 3 (a) Stereo deflectometry system. (b) One captured fringe pattern by camera 1. (c) Same pattern captured by camera 2.
Fig. 4
Fig. 4 One unwrapped phase and its corresponding RMSE (root mean square error) in CCD 1. (a) Along x direction. (b) Along y direction
Fig. 5
Fig. 5 RMS of the reprojection errors. (a) On CCD 1 plane. (b) On CCD 2 plane
Fig. 6
Fig. 6 Reprojection errors before optimization. (a) On CCD 1 plane. (b) On CCD 2 plane
Fig. 7
Fig. 7 Reference mirror poses in the system
Fig. 8
Fig. 8 Calculated slope data and resulting error. (a) Slope data along x direction. (b) Slope data error along x direction. (c) Slope data along y direction. (d) Slope data error along y direction
Fig. 9
Fig. 9 (a) Reconstruction flat surface. (b) Resulting error. (c) Resulting error of one row
Fig. 10
Fig. 10 (a) Reconstructed concave surface. (b) Residual between reconstructed surface and fitted sphere

Equations (9)

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m = f ( p ' )
[ F C R V L C T V L C ] = min m f ( p ' )
a b s ( m f ( p ' ) ) > 3 × R M S ( m f ( p ' )
{ R V L C ( I 3 2 e 3 e 3 T ) = ( I 3 2 n C n C T ) R L C T V L C = ( I 3 2 n C n C T ) T L C + 2 d n C
[ F C * , n C , d , R L C * , T L C * ] = min m f ( p , F C , R V L C , T V L C )
a b s ( m f ( p , F C , R V L C , T V L C ) ) > 3 × R M S ( m f ( p , F C , R V L C , T V L C )
{ n L = ( R L C 1 1 n C 1 + R L C 2 1 n C 2 ) / 2 d p = ( ( d 1 n C 1 T T L C 1 ) + ( d 2 n C 2 T T L C 2 ) ) / 2
[ F C 1 * , F C 2 * , n L * , d p , * R L C 1 * , T L C 1 * , R L C 2 * , T L C 2 * ] = min ( m 1 , m 2 ) f *
{ n C = R L C * n L * , d = d p * + n C T T L C * , R V L C = ( I 3 2 n C n C T ) R L C * ( I 3 2 e 3 e 3 T ) 1 , T V L C = ( I 3 2 n C n C T ) T L C * + 2 d n C .

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