Abstract

In phase measuring deflectometry (PMD), a camera observes a sinusoidal fringe pattern via the surface of a specular object under test. Any slope variations of the surface lead to distortions of the observed pattern. Without height-angle ambiguity, carrier removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. However, in the usual measurement system, the carrier phase will be nonlinear due to the restrictions of system geometries. In this paper, based on the analytical carrier phase description in PMD, a carrier removal method is proposed to remove the nonlinear carrier phase. Both the theoretical analysis and the experiment results are presented. By comparison with reference-subtraction method and series-expansion method, this proposed method can achieve carrier removal process with only the measurement of one single object, as well as high accuracy and time-saving.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
    [CrossRef]
  2. L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express19(13), 12809–12814 (2011).
    [CrossRef] [PubMed]
  3. L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).
  4. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express18(9), 9684–9689 (2010).
    [CrossRef] [PubMed]
  5. A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt.37(23), 5416–5420 (1998).
    [CrossRef] [PubMed]
  6. H. W. Guo, M. Y. Chen, and P. Zheng, “Least-squares fitting of carrier phase distribution by using a rational function in fringe projection profilometry [corrected],” Opt. Lett.31(24), 3588–3590 (2006).
    [CrossRef] [PubMed]
  7. C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
    [CrossRef]
  8. Q. C. Zhang and Z. Y. Wu, “A carrier removal method in Fourier transform profilometry with Zernike polynomials,” Opt. Lasers Eng.51(3), 253–260 (2013).
    [CrossRef]
  9. L. J. Chen and C. J. Tay, “Carrier phase component removal: a generalized least-squares approach,” J. Opt. Soc. Am. A23(2), 435–443 (2006).
    [CrossRef] [PubMed]
  10. L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
    [CrossRef] [PubMed]

2013 (1)

Q. C. Zhang and Z. Y. Wu, “A carrier removal method in Fourier transform profilometry with Zernike polynomials,” Opt. Lasers Eng.51(3), 253–260 (2013).
[CrossRef]

2012 (2)

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

2011 (1)

2010 (1)

2007 (1)

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
[CrossRef]

2006 (2)

2004 (1)

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
[CrossRef]

1998 (1)

Asundi, A.

Asundi, A. K.

Chen, L. J.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
[CrossRef]

L. J. Chen and C. J. Tay, “Carrier phase component removal: a generalized least-squares approach,” J. Opt. Soc. Am. A23(2), 435–443 (2006).
[CrossRef] [PubMed]

Chen, M. Y.

Guo, H. W.

Häusler, G.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
[CrossRef]

Huang, L.

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
[CrossRef]

Kim, H.

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
[CrossRef]

Liu, Y.

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

Liu, Y. Z.

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

Ng, C. S.

Oliver, J.

Quan, C.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
[CrossRef]

Song, L.

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

Tay, C. J.

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
[CrossRef]

L. J. Chen and C. J. Tay, “Carrier phase component removal: a generalized least-squares approach,” J. Opt. Soc. Am. A23(2), 435–443 (2006).
[CrossRef] [PubMed]

Van Der Weide, D.

Wensen, Z.

Wu, Y. X.

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

Wu, Z. Y.

Q. C. Zhang and Z. Y. Wu, “A carrier removal method in Fourier transform profilometry with Zernike polynomials,” Opt. Lasers Eng.51(3), 253–260 (2013).
[CrossRef]

Yue, H. M.

L. Song, H. M. Yue, H. Kim, Y. X. Wu, Y. Liu, and Y. Z. Liu, “A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging,” Opt. Express20(22), 24505–24515 (2012).
[CrossRef] [PubMed]

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

Zhang, Q. C.

Q. C. Zhang and Z. Y. Wu, “A carrier removal method in Fourier transform profilometry with Zernike polynomials,” Opt. Lasers Eng.51(3), 253–260 (2013).
[CrossRef]

Zhang, S.

Zheng, P.

Appl. Opt. (1)

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

Journal of Optoelectronics·Laser (1)

L. Song, H. M. Yue, Y. X. Wu, Y. Liu, and Y. Z. Liu, “Fringe Reflection for Specular Object Measurement and Analysis on Variable Lateral Scales,” Journal of Optoelectronics·Laser23(11), 2154-2162 (2012).

Opt. Express (3)

Opt. Laser Technol. (1)

C. Quan, C. J. Tay, and L. J. Chen, “A study on carrier-removal techniques in fringe projection profilometry,” Opt. Laser Technol.39(6), 1155–1161 (2007).
[CrossRef]

Opt. Lasers Eng. (1)

Q. C. Zhang and Z. Y. Wu, “A carrier removal method in Fourier transform profilometry with Zernike polynomials,” Opt. Lasers Eng.51(3), 253–260 (2013).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. C. Knauer, J. Kaminski, and G. Häusler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE5457, 366–376 (2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic setup of the PMD.

Fig. 2
Fig. 2

Geometry of the PMD.

Fig. 3
Fig. 3

Data flow of the proposed method.

Fig. 4
Fig. 4

Computer simulation: (a) unwrapped phase distributions with x direction fringe patterns; (b) unwrapped phase distributions with y direction fringe patterns; (c) error distribution in x direction; (d) error distribution in y direction; (e) error of the reconstructed height.

Fig. 5
Fig. 5

Measurement setup of the experiment.

Fig. 6
Fig. 6

Carrier removal of a plane mirror with x direction fringe patterns: (a) fringe pattern with plane mirror; (b) unwrapped phase; (c) error distribution of the Eq. (8) in removing carrier phase; (d) error distribution of the Eq. (12) in removing carrier phase in x direction; (e) error distribution of the Eq. (13) in removing carrier phase in y direction; (f) reconstruction of the plane mirror.

Fig. 7
Fig. 7

reconstruction of a scratched mirror: (a) distorted fringe pattern; (b) reconstructing result by using proposed method; (c) a column(x = 4.0mm) of reconstructing results by using proposed method and 2-order series-expansion method separately ;(d) reconstruction result of reference subtraction method.

Tables (1)

Tables Icon

Table 1 RMSE and consuming time of the series-expansion method, the proposed new method and reference subtraction method

Equations (13)

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

I(x,y)=A( x,y )+B( x,y )cos[ 2π f 0 ( x,y )x+φ( x,y ) ].
g x = φ x φ rx 4π L y / P x .
g y = φ y φ ry 4π L y / P y .
φ rx ( x c )= 2π f 0 cosθ { ( x c cosγ X 0 + X f )[ ( X f x 0 )tanθ+ Z f + z 0 ] x c ( cosγtanθsinγ )+( X 0 X f )tanθ+ Z 0 Z f + X f x 0 }.
φ ry ( x c , y c )= 2π f 0 Z f ( fL ) y c f x c tanγ { { ( X f x 0 ) [ ( X f x 0 )tanθ+ Z f + z 0 ]( x c cosγ X 0 + X f ) ( cosγtanθsinγ ) x c +( X 0 X f )tanθ+ Z 0 Z f }tanθ+ Z 0 + Z f }.
φ rx ( x c )=a+ 1 b x c +c .
φ ry ( x c , y c )= y c ( 1 a x c 2 +b x c +c + 1 d x c +e ).
φ rx ( x c )=a+b x c +c x c 2 .
φ ry ( x c , y c ) = y c ( a+b x c +c x c 2 ).
φ rx ( x c )=25+ 10000 -0.3 x c +400 .
φ ry ( x c , y c )= y c -0.00005 x c 2 -0.005 x c +50 + y c -0.002 x c +20 .
φ rx ( x c )=a+b x c +c x c 2 +d y c .
φ ry ( x c , y c )= y c ( a+b x c +c x c 2 )+d x c +e.

Metrics