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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 4 — Apr. 12, 2006

Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula

Guang-ming Dai  »View Author Affiliations


JOSA A, Vol. 23, Issue 3, pp. 539-543 (2006)
http://dx.doi.org/10.1364/JOSAA.23.000539


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Abstract

In a recent paper [ J. Opt. Soc. Am. A 19, 1937 (2002) ] a recursive analytical formula was derived to calculate a set of new Zernike polynomial expansion coefficients from an original set when the size of the aperture is reduced. In the current paper I describe a more intuitive derivation of a simpler, nonrecursive formula, which is used to calculate the instantaneous refractive power.

© 2006 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: August 12, 2005
Revised Manuscript: August 26, 2005
Manuscript Accepted: August 31, 2005

Virtual Issues
Vol. 1, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Guang-ming Dai, "Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula," J. Opt. Soc. Am. A 23, 539-543 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-23-3-539


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References

  1. J. Liang, B. Grimm, S. Goelz, and J. Bille, 'Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,' J. Opt. Soc. Am. A 11, 1949-1957 (1994). [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1965).
  3. R. J. Noll, 'Zernike polynomials and atmospheric turbulence,' J. Opt. Soc. Am. 66, 203-211 (1976). [CrossRef]
  4. G.-m. Dai, 'Modal compensation of atmospheric turbulence with the use of Zernike polynomials and Karhunen-Loève functions,' J. Opt. Soc. Am. A 12, 2182-2193 (1995). [CrossRef]
  5. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, 'Standards for reporting the optical aberrations of eyes,' in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 232-244.
  6. K. A. Goldberg and K. Geary, 'Wave-front measurement errors from restricted concentric subdomains,' J. Opt. Soc. Am. A 18, 2146-2152 (2001). [CrossRef]
  7. J. Schwiegerling, 'Scaling Zernike expansion coefficients to different pupil sizes,' J. Opt. Soc. Am. A 19, 1937-1945 (2002). [CrossRef]
  8. 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]
  9. The last term in Eq. (A8) of Ref. should read ×r1∣m∣+2i/r2∣m∣+2i.
  10. G.-m. Dai, 'Optical surface optimization for the correction of presbyopia,' Appl. Opt. (to be published).
  11. G. Conforti, 'Zernike aberration coefficients from Seidel and higher-order power-series coefficients,' Opt. Lett. 8, 390-391 (1983). [CrossRef]
  12. M. Koomen, R. Tousey, and R. Scolnik, 'The spherical aberration of the eye,' J. Opt. Soc. Am. 39, 370-376 (1949). [CrossRef] [PubMed]

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