OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 8 — Aug. 1, 2009
  • pp: 1839–1846

Bilinear wavefront transformation

Keith Dillon  »View Author Affiliations


JOSA A, Vol. 26, Issue 8, pp. 1839-1846 (2009)
http://dx.doi.org/10.1364/JOSAA.26.001839


View Full Text Article

Enhanced HTML    Acrobat PDF (122 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Truncated expansions such as Zernike polynomials provide a powerful approach for describing wavefront data. However, many simple calculations with data in this form can require significant computational effort. Important examples include recentering, renormalizing, and translating the wavefront data. This paper describes a technique whereby these operations and many others can be performed with a simple matrix approach using monomials. The technique may be applied to other expansions by reordering the data and applying transformations. The key is the use of the vectorization operator to convert data between vector and matrix descriptions. With this conversion, one-dimensional polynomial techniques may be employed to perform separable operations. Examples are also given for differentiation and integration of wavefronts.

© 2009 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: January 8, 2009
Revised Manuscript: May 4, 2009
Manuscript Accepted: June 16, 2009
Published: July 29, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Keith Dillon, "Bilinear wavefront transformation," J. Opt. Soc. Am. A 26, 1839-1846 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-8-1839


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Z80.28-2004 Methods for reporting optical aberrations of eyes (American National Standards Institute, 2004).
  2. R. R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207-211 (1976). [CrossRef]
  3. A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on an ideal method to correct the eye's higher-order aberrations,” J. Opt. Soc. Am. A 18, 1003-1015 (2001). [CrossRef]
  4. J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937-1945 (2002). [CrossRef]
  5. C. E. Campbell, “Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed,” J. Opt. Soc. Am. A 20, 209-217 (2003). [CrossRef]
  6. G.-M. Dai, “Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula,” J. Opt. Soc. Am. A 23, 539-543 (2006). [CrossRef]
  7. A. J. E. M. Janssen and P. Dirksen, “Concise formula for the Zernike coefficients of scaled pupils,” J. Microlith. Microfab. Microsyst. Letters 5, 030501 (2006). [CrossRef]
  8. H. Shu, L. Luo, G. Han, and J.-L. Coatrieux, “General method to derive the relationship between two sets of Zernike coefficients corresponding to different aperture sizes,” J. Opt. Soc. Am. A 23, 1960-1966 (2006). [CrossRef]
  9. S. Bara, J. Arines, J. Ares, and P. Prado, “Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils,” J. Opt. Soc. Am. A 23, 2061-2066 (2006). [CrossRef]
  10. G.-M. Dai, Wavefront Optics for Vision Correction (SPIE Press, 2008). [CrossRef]
  11. L. Lundström and P. Unsbo, “Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils,” J. Opt. Soc. Am. A 24, 569-577 (2007). [CrossRef]
  12. R. R. Kreuger, R. A. Applegate, and S. M. McRae, Wavefront Customized Visual Correction: The Quest for Super-vision II (Slack, 2004).
  13. G.-M. Dai, “Wavefront expansion basis functions and their relationships,” J. Opt. Soc. Am. A 23, 1657-1668 (2006). [CrossRef]
  14. C.-H. Teh, “On image analysis by the methods of moments,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 496-513 (1988). [CrossRef]
  15. S. Roman, Advanced Linear Algebra, 3rd ed. (Springer, 2008).
  16. W.-H. Steeb, Matrix Calculus and Kronecker Product with Applications and C++ Programs (World Scientific, 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