OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 27 — Sep. 20, 2006
  • pp: 6954–6964

Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction

M. Ares and S. Royo  »View Author Affiliations

Applied Optics, Vol. 45, Issue 27, pp. 6954-6964 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (3050 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We analyze an alternative to classical Zernike fitting based on the cubic B-spline model, and compare the strengths and weaknesses of each representation over a set of different wavefronts that cover a wide range of shape complexity. The results obtained show that a Zernike low-degree polynomial expansion or a cubic B-spline with a low number of breakpoints are the best choices for fitting simple wavefronts, whereas the cubic B-spline approach performs much better when more complex wavefronts are involved. The effect of noise level in the fit quality for the different wavefronts is also studied.

© 2006 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing

Original Manuscript: March 8, 2006
Manuscript Accepted: May 3, 2006

Virtual Issues
Vol. 1, Iss. 10 Virtual Journal for Biomedical Optics

M. Ares and S. Royo, "Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction," Appl. Opt. 45, 6954-6964 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. R. Rammage, D. R. Neal, and R. J. Copland, "Application of Shack-Hartmann wavefront sensing technology to transmissive optic metrology," in Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, A. Duparré and B. Singh, eds., Proc. SPIE 4779, 161-172 (2002). [CrossRef]
  2. W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980).
  3. K. W. Farmer, "Scattered data interpolation by C quintic splines using energy minimization," M. A. thesis (University of Georgia, 1997).
  4. G. Vdovin and P. M. Sarro, "Flexible mirror micromachined in silicon," Appl. Opt. 34, 2968-2972 (1995).
  5. P. M. Prieto, E. J. Fernández, S. Manzanera, and P. Artal, "Adaptive optics with a programmable phase modulator: applications in the human eye," Opt. Express 12, 4059-4071 (2004). [CrossRef]
  6. L. Seifert, J. Liesener, and H. J. Tiziani, "The adaptive Shack-Hartmann sensor," Opt. Commun. 216, 313-319 (2003). [CrossRef]
  7. X. Liu and Y. Gao, "B-spline based wavefront reconstruction for lateral shearing interferometric measurement of engineering surfaces," Advances in Abrasive Technology V (Trans Tech Publications, 2003), Vol. 238-239, pp. 169-174.
  8. L. Seifert, H. J. Tiziani, and W. Osten, "Wavefront reconstruction with the adaptive Shack-Hartmann sensor," Opt. Commun. 245, 255-269 (2005). [CrossRef]
  9. D. Malacara and S. L. DeVore, "Interferogram evaluation and wavefront fitting," in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, 1992).
  10. C. de Boor, A Practical Guide to Splines, revised edition (Springer-Verlag, 2001).
  11. J. Arasa, S. Royo, and N. Tomás, "Simple method for improving the sampling in profile measurements by use of the Ronchi test," Appl. Opt. 39, 4529-4534 (2000).
  12. S. Royo, J. Arasa, and C. Pizarro, "Profilometry of toroidal surfaces with an improved Ronchi test," Appl. Opt. 39, 5721-5731 (2000).
  13. C. L. Lawson and R. J. Hanson, Solving Least Square Problems (Prentice Hall, 1974).
  14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1997).

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