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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


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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

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