Bilinear wavefront transformation
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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