Abstract

The correspondence residuals due to the discrepancy between the reality and the shape model in use are analyzed for the modal phase measuring deflectometry. Slope residuals are calculated from these discrepancies between the modal estimation and practical acquisition. Since the shape mismatch mainly occurs locally, zonal integration methods which are good at dealing with local variations are used to reconstruct the height residual for compensation. Results of both simulation and experiment indicate the proposed height compensation method is effective, which can be used as a post-complement for the modal phase measuring deflectometry.

© 2017 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 (2004).
    [Crossref]
  2. J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43(10), 1305–1317 (2010).
    [Crossref]
  3. L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
    [Crossref] [PubMed]
  4. L. Huang, J. Xue, B. Gao, C. McPherson, J. Beverage, and M. Idir, “Modal phase measuring deflectometry,” Opt. Express 24(21), 24649–24664 (2016).
    [Crossref] [PubMed]
  5. W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
    [Crossref]
  6. G. Li, Y. Li, K. Liu, X. Ma, and H. Wang, “Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry,” J. Opt. Soc. Am. A 30(7), 1448–1459 (2013).
    [Crossref] [PubMed]
  7. L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  10. H. Ren, F. Gao, and X. Jiang, “Improvement of high-order least-squares integration method for stereo deflectometry,” Appl. Opt. 54(34), 10249–10255 (2015).
    [Crossref] [PubMed]
  11. L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
    [Crossref]

2016 (2)

2015 (2)

H. Ren, F. Gao, and X. Jiang, “Improvement of high-order least-squares integration method for stereo deflectometry,” Appl. Opt. 54(34), 10249–10255 (2015).
[Crossref] [PubMed]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

2014 (1)

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

2013 (1)

2012 (1)

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
[Crossref]

2011 (1)

2010 (1)

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43(10), 1305–1317 (2010).
[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 (2004).
[Crossref]

1980 (1)

Asundi, A.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Asundi, A. K.

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
[Crossref] [PubMed]

Balzer, J.

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43(10), 1305–1317 (2010).
[Crossref]

Bergmann, R. B.

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

Beverage, J.

Burke, J.

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

Gao, B.

Gao, F.

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 (2004).
[Crossref]

Huang, L.

L. Huang, J. Xue, B. Gao, C. McPherson, J. Beverage, and M. Idir, “Modal phase measuring deflectometry,” Opt. Express 24(21), 24649–24664 (2016).
[Crossref] [PubMed]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
[Crossref] [PubMed]

Huke, P.

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

Idir, M.

L. Huang, J. Xue, B. Gao, C. McPherson, J. Beverage, and M. Idir, “Modal phase measuring deflectometry,” Opt. Express 24(21), 24649–24664 (2016).
[Crossref] [PubMed]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Jiang, X.

Kaminski, J.

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

Kaznatcheev, K.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Knauer, M. C.

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

Li, G.

Li, W.

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

Li, Y.

Liu, K.

Ma, X.

McPherson, C.

Ng, C. S.

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
[Crossref] [PubMed]

Ren, H.

Southwell, W. H.

von Kopylow, C.

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

Wang, H.

Werling, S.

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43(10), 1305–1317 (2010).
[Crossref]

Xue, J.

Zhou, L.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Zuo, C.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Measurement (1)

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43(10), 1305–1317 (2010).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (2)

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

L. Huang, C. S. Ng, and A. K. Asundi, “Fast full-field out-of-plane deformation measurement using fringe reflectometry,” Opt. Lasers Eng. 50(4), 529–533 (2012).
[Crossref]

Proc. SPIE (2)

W. Li, P. Huke, J. Burke, C. von Kopylow, and R. B. Bergmann, “Measuring deformations with deflectometry,” Proc. SPIE 9203, 92030F (2014).
[Crossref]

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

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Figures (8)

Fig. 1
Fig. 1 A sketch of a general PMD illustrates a reversed ray tracing in deflectometry.
Fig. 2
Fig. 2 The x- and y-slope changes based on the rotations in right hand rule along y- and x-axes, respectively. (a) Rotation along y-axis with a positive angle gives a negative change to x-slope, and (b) rotation along x-axis with a positive angle offers a positive change to y-slope.
Fig. 3
Fig. 3 A PMD setup is simulated in world coordinates (a) to measure an SUT (b).
Fig. 4
Fig. 4 MPMD provides the model-based construction (a) which is the global shape of the SUT, correspondence residuals (b), and the vector map of the residuals caused by local shapes.
Fig. 5
Fig. 5 Slope residuals in x-(a) and y-directions (b) are calculated from the reprojection discrepancy and further integrated to obtain the height for compensation purpose (b).
Fig. 6
Fig. 6 Shape errors in MPMD (a) are reduced after height compensation (b) by using the proposed method. Shape reconstructed from updated slopes in Eq. (4) by using zonal reconstruction method directly (c).
Fig. 7
Fig. 7 Local defects are obvious in the SUT photo (a) as well as the captured vertical (b) and horizontal (c) fringe patterns. (d) is the reconstructed shape with MPMD, and (e) is the correspondence residual visualized as vectors.
Fig. 8
Fig. 8 The local height (c) is reconstructed from the residuals of x-slope (a) and y-slope (b), and then compensate to the MPMD reconstructed height as a final result (d).

Equations (7)

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

[ ω ^ , T ^ , c ^ ]=arg min ω,T,c n=1 N m ^ n ( ω,T,c ) m n 2 ,
r=m m ^ .
N ^ = m ^ X ^ m ^ X ^ P P ,
N= m X ^ m X ^ P P .
{ Δ s x =tan( arctan( s ^ x ) θ y ) s ^ x Δ s y =tan( arctan( s ^ y )+ θ x ) s ^ y ,
R=I+w+ w 2 1n n ^ v 2 ,
Δz= f zonal ( x ^ , y ^ ,Δ s x ,Δ s y ).

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