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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 30 — Oct. 20, 2013
  • pp: 7311–7323

Method of misalignment aberrations removal in null test of cylindrical surface

Junzheng Peng, Dongbao Ge, Yingjie Yu, Kesheng Wang, and Mingyi Chen  »View Author Affiliations

Applied Optics, Vol. 52, Issue 30, pp. 7311-7323 (2013)

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The removal of misalignment aberrations is a key problem in the null test of cylindrical surfaces. Although the quadratic polynomial with two variables and the orthogonal Chebyshev polynomials have been used to separate the misalignment aberrations from the extracted phase data, there is no physical meaning corresponding to the polynomials coefficients. Additionally, the Runge phenomenon may occur when the high-order polynomials are employed. In this paper, all the possible aberrations caused by the adjustment errors were analyzed. Based on the first-order approximate principle, the mathematical models, which describe the relationship between the misalignment aberrations and the possible adjustment errors, were deduced. With these mathematical expressions, all the possible adjustment errors can be estimated by using the least-squares fitting algorithm, and then the genuine surface deviations can be obtained by subtracting the misalignment aberrations from the extracted phase data. Computer simulations and experiments have been conducted to demonstrate the validity and feasibility, which show more than 96% misalignment aberrations can be removed. Compared with the existing methods, the proposed model provides a feasible way to estimate adjustment errors with better accuracy.

© 2013 Optical Society of America

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(150.6910) Machine vision : Three-dimensional sensing
(120.6165) Instrumentation, measurement, and metrology : Speckle interferometry, metrology

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: May 22, 2013
Revised Manuscript: August 27, 2013
Manuscript Accepted: September 26, 2013
Published: October 16, 2013

Junzheng Peng, Dongbao Ge, Yingjie Yu, Kesheng Wang, and Mingyi Chen, "Method of misalignment aberrations removal in null test of cylindrical surface," Appl. Opt. 52, 7311-7323 (2013)

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  1. J. M. Geary, “Testing cylindrical lenses,” Opt. Eng. 26, 261219 (1987). [CrossRef]
  2. J. M. Geary, “Overview of cylindrical optics testing using a fiber optic reference,” Proc. SPIE 2536, 68–74 (1995). [CrossRef]
  3. J. Wyant and V. Bennett, “Using computer generated holograms to test aspheric wavefronts,” Appl. Opt. 11, 2833–2839 (1972). [CrossRef]
  4. S. Reichelt, C. Pruß, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002). [CrossRef]
  5. S. Reichelt, C. Pruss, and H. J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt. 42, 4468–4479 (2003). [CrossRef]
  6. P. Tam, K. Gross, and J. Bogan, “Interferometric testing of cylinder optics using computer generated hologram (CGH),” Proc. SPIE 3134, 162–166 (1997). [CrossRef]
  7. J. Schwider, N. Lindlein, R. Schreiner, and J. Lamprecht, “Grazing-incidence test for cylindrical microlenses with high numerical aperture,” J. Opt. A 4, S10–S16 (2002). [CrossRef]
  8. J. Lamprecht, N. Lindlein, and J. Schwider, “Null test measurement of high-numerical-aperture cylindrical microlenses in transmitted light,” Proc. SPIE 5180, 253–260 (2004). [CrossRef]
  9. K. Mantel, N. Lindlein, and J. Schwider, “Simultaneous characterization of the quality and orientation of cylindrical lens surfaces,” Appl. Opt. 44, 2970–2977 (2005). [CrossRef]
  10. K. Mantel, J. Lamprecht, N. Lindlein, and J. Schwider, “Absolute calibration in grazing incidence interferometry via rotational averaging,” Appl. Opt. 45, 3740–3745 (2006). [CrossRef]
  11. P. Reardon, F. Liu, and J. Geary, “Schmidt-like corrector plate for cylindrical optics,” Opt. Eng. 49, 053002 (2010). [CrossRef]
  12. J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. Eng. Des. 33, 105–125 (1998). [CrossRef]
  13. G. Kang, J. Xie, and Y. Liu, “New design techniques and alignment methods for CGH-null testing of aspheric surface,” Proc. SPIE 6624, 66240K (2008). [CrossRef]
  14. http://diffraction.com/cylinder.php .
  15. K. Khalsa, Metropro Reference Guide (Zygo Corporation, 2006).
  16. F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials,” Opt. Eng. 50, 043609 (2011). [CrossRef]
  17. F. Liu, B. M. Robinson, P. J. Reardon, and J. M. Geary, “Separating misalignment from misfigure in interferograms on cylindrical optics,” Opt. Express 21, 8856–8864 (2013). [CrossRef]
  18. B. M. Robinson and P. J. Reardon, “First-order perturbations of reflective surfaces and their effects in interferometric testing of mirrors,” J. Mod. Opt. 52, 2625–2636 (2005). [CrossRef]
  19. T. Dresel, N. Lindlein, and J. Schwider, “Empirical strategy for detection and removal of misalignment aberrations in interferometry,” Optik 112, 304–308 (2001). [CrossRef]
  20. D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Misalignment aberrations calibration in testing of high-numerical-aperture spherical surfaces,” Appl. Opt. 50, 2024–2031 (2011). [CrossRef]
  21. “Encoding and fabrication report: CGH cylinder null h45f15c,” (Diffraction International, 5810 Baker Road, Suite 225 Minnetonka, Minnesota 55345-5982, USA, 2012).

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