OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 9 — Mar. 20, 2012
  • pp: 1276–1282

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

Chunfeng Guo, Xianyu Su, Wenjing Chen, Baiping Lei, and Fan Wu  »View Author Affiliations

Applied Optics, Vol. 51, Issue 9, pp. 1276-1282 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (862 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.1250) Optical design and fabrication : Aspherics
(220.4840) Optical design and fabrication : Testing

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 1, 2011
Revised Manuscript: January 10, 2012
Manuscript Accepted: January 13, 2012
Published: March 15, 2012

Chunfeng Guo, Xianyu Su, Wenjing Chen, Baiping Lei, and Fan Wu, "Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test," Appl. Opt. 51, 1276-1282 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited