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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 4 — Feb. 15, 2006
  • pp: 501–503

Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation

Guang-ming Dai  »View Author Affiliations


Optics Letters, Vol. 31, Issue 4, pp. 501-503 (2006)
http://dx.doi.org/10.1364/OL.31.000501


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Abstract

The set of Fourier series is discussed following some discussion of Zernike polynomials. Fourier transforms of Zernike polynomials are derived that allow for relating Fourier series expansion coefficients to Zernike polynomial expansion coefficients. With iterative Fourier reconstruction, Zernike representations of wavefront aberrations can easily be obtained from wavefront derivative measurements.

© 2006 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
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: September 6, 2005
Revised Manuscript: October 15, 2005
Manuscript Accepted: October 17, 2005

Virtual Issues
Vol. 1, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Guang-ming Dai, "Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation," Opt. Lett. 31, 501-503 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-4-501


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References

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  8. Equation in Ref. has an extra multiplication factor of 1/pi.
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