Abstract

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Tang, X. Y. Su, F. Wu, and Y. K. Liu, “A novel phase measuring deflectometry for aspheric mirror test,” Opt. Express 17, 19778–19784 (2009).
    [CrossRef]
  2. T. Yatagai, “Fringe scanning Ronchi test for aspherical surfaces,” Appl. Opt. 23, 3676–3679 (1984).
    [CrossRef]
  3. A. Cordero-Dávila, J. González-García, C. I. Robledo-Sánchez, and I. Leal-Cabrera, “Local and global surface errors evaluation using Ronchi test, without both approximation and integration,” Appl. Opt. 50, 4817–4823 (2011).
    [CrossRef]
  4. S. Lee and M. Guizar-Sicairos, “Validation of quantitative Ronchi test through numerical propagation,” Opt. Express 18, 18525–18531 (2010).
    [CrossRef]
  5. M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
    [CrossRef]
  6. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd. ed., D. Malacara, ed. (Wiley, 2007), pp. 317–360.
  7. D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt. 13, 1778–1780 (1974).
    [CrossRef]
  8. B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
    [CrossRef]
  9. D. Malacara, “Geometrical Ronchi test of aspherical mirrors,” Appl. Opt. 4, 1371–1374 (1965).
    [CrossRef]
  10. C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
    [CrossRef]
  11. Y. L. Xiao, X. Y. Su, and W. J. Chen, “Fringe inverse videogrammetry based on global pose estimation,” Appl. Opt. 50, 5630–5638 (2011).
    [CrossRef]
  12. J. Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  13. X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
    [CrossRef]
  14. X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48, 191–204(2010).
    [CrossRef]
  15. S. Zhang and S. Yau, “Three-dimensional data merging using Holoimage,” Opt. Eng. 47, 33608 (2008).
    [CrossRef]

2012 (1)

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

2011 (3)

2010 (2)

S. Lee and M. Guizar-Sicairos, “Validation of quantitative Ronchi test through numerical propagation,” Opt. Express 18, 18525–18531 (2010).
[CrossRef]

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48, 191–204(2010).
[CrossRef]

2009 (2)

Y. Tang, X. Y. Su, F. Wu, and Y. K. Liu, “A novel phase measuring deflectometry for aspheric mirror test,” Opt. Express 17, 19778–19784 (2009).
[CrossRef]

B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
[CrossRef]

2008 (1)

S. Zhang and S. Yau, “Three-dimensional data merging using Holoimage,” Opt. Eng. 47, 33608 (2008).
[CrossRef]

2004 (1)

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

1984 (1)

1974 (1)

1965 (1)

Casillas, F. J.

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Chen, W. J.

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

Y. L. Xiao, X. Y. Su, and W. J. Chen, “Fringe inverse videogrammetry based on global pose estimation,” Appl. Opt. 50, 5630–5638 (2011).
[CrossRef]

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Chiu-Zarate, R.

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Cordero-Dávila, A.

Cornejo, A.

Cornejo-Rodriguez, A.

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd. ed., D. Malacara, ed. (Wiley, 2007), pp. 317–360.

González-García, J.

Guizar-Sicairos, M.

Guo, C. F.

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

Leal-Cabrera, I.

Lee, S.

Lei, B. P.

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
[CrossRef]

Liu, Y. K.

Malacara, D.

Mora-González, M.

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Muñoz-Maciel, J.

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Peña-Lecona, F. G.

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Robledo-Sánchez, C. I.

Su, X. Y.

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

Y. L. Xiao, X. Y. Su, and W. J. Chen, “Fringe inverse videogrammetry based on global pose estimation,” Appl. Opt. 50, 5630–5638 (2011).
[CrossRef]

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48, 191–204(2010).
[CrossRef]

Y. Tang, X. Y. Su, F. Wu, and Y. K. Liu, “A novel phase measuring deflectometry for aspheric mirror test,” Opt. Express 17, 19778–19784 (2009).
[CrossRef]

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

Tang, Y.

Wu, F.

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
[CrossRef]

Y. Tang, X. Y. Su, F. Wu, and Y. K. Liu, “A novel phase measuring deflectometry for aspheric mirror test,” Opt. Express 17, 19778–19784 (2009).
[CrossRef]

Xiao, Y. L.

Yatagai, T.

Yau, S.

S. Zhang and S. Yau, “Three-dimensional data merging using Holoimage,” Opt. Eng. 47, 33608 (2008).
[CrossRef]

Zhang, Q. C.

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48, 191–204(2010).
[CrossRef]

Zhang, S.

S. Zhang and S. Yau, “Three-dimensional data merging using Holoimage,” Opt. Eng. 47, 33608 (2008).
[CrossRef]

Zhou, C. B.

B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
[CrossRef]

Appl. Opt. (5)

Opt. Eng. (1)

S. Zhang and S. Yau, “Three-dimensional data merging using Holoimage,” Opt. Eng. 47, 33608 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (3)

C. F. Guo, X. Y. Su, W. J. Chen, B. P. Lei, and F. Wu, “Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test,” Opt. Lasers Eng., 50, 165–169 (2012).
[CrossRef]

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48, 191–204(2010).
[CrossRef]

Proc. SPIE (2)

B. P. Lei, F. Wu, and C. B. Zhou, “Quantitative measurement of Φ140  mmF/2 parabolic surface with Ronchi grating test method,” Proc. SPIE 7283, 72832O (2009).
[CrossRef]

M. Mora-González, F. J. Casillas, J. Muñoz-Maciel, R. Chiu-Zarate, and F. G. Peña-Lecona, “The Ronchi test using a liquid crystal display as a phase grating,” Proc. SPIE 8082, 80823G (2011).
[CrossRef]

Other (2)

A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, 3rd. ed., D. Malacara, ed. (Wiley, 2007), pp. 317–360.

J. Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .

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 (11)

Fig. 1.
Fig. 1.

Structure of measurement setup.

Fig. 2.
Fig. 2.

Schematic of null grating design.

Fig. 3.
Fig. 3.

Schematic of measurement principle.

Fig. 4.
Fig. 4.

Tested surface in simulation.

Fig. 5.
Fig. 5.

Null sinusoidal gratings corresponding to the given (a) vertical fringes, (b) horizontal fringes on the ideal surface in simulation.

Fig. 6.
Fig. 6.

Errors of the reconstructed aspheric surface.

Fig. 7.
Fig. 7.

Null Ronchi grating.

Fig. 8.
Fig. 8.

Null sinusoidal gratings corresponding to the given (a) vertical fringes, (b) horizontal fringes on the ideal surface in experiment.

Fig. 9.
Fig. 9.

Captured fringe patterns: (a) vertical fringe pattern, (b) horizontal fringe pattern.

Fig. 10.
Fig. 10.

Measurement result using the three-coordinate measuring machine.

Fig. 11.
Fig. 11.

Differences between the results of the presented method and three-coordinate measuring machine.

Equations (15)

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

i=i2(|i||n|cosα)n,
In(x,y)=a1+a2cos[ϕ(x,y)],
[xcyczc]=R[xyz]+T.
ϕ=tan1[(I4I2)/(I1I3)].
Cr=(Cxx+Cyy)/r,
δb=ArCr.
tanβ=df(r)/dr,
tan(β+δβ)=d[f(r)+δf(r)]dr,
g(r)=δf(r)cosβ.
δtanβ=dg(r)cosβdr.
δβ=cosβdg(r)dr.
tanγ=(rLrb)/[Df(r)],
δγ=cos2γδbDf(r).
dg(r)dr=[Df(r)]δb2cosβ{(rCr)2+[Df(r)]2}.
F(r)=g(r)cosβ+f(r).

Metrics