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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 28 — Oct. 1, 2010
  • pp: 5374–5377

Zernike coefficients of a scaled pupil

Virendra N. Mahajan  »View Author Affiliations

Applied Optics, Vol. 49, Issue 28, pp. 5374-5377 (2010)

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By expressing a scaled Zernike radial polynomial as a linear combination of the unscaled radial polynomials, we give a simple derivation for determining the Zernike coefficients of an aberration function of a scaled pupil in terms of their values for a corresponding unscaled pupil.

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.0110) Imaging systems : Imaging systems
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1010) Optical design and fabrication : Aberrations (global)

ToC Category:
Optical Design and Fabrication

Original Manuscript: July 28, 2010
Revised Manuscript: August 8, 2010
Manuscript Accepted: August 9, 2010
Published: September 24, 2010

Virtual Issues
Vol. 5, Iss. 14 Virtual Journal for Biomedical Optics

Virendra N. Mahajan, "Zernike coefficients of a scaled pupil," Appl. Opt. 49, 5374-5377 (2010)

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  1. J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937–1945(2002). [CrossRef]
  2. 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]
  3. G.-m. Dai, “Scaling Zernike expansion coefficients to smaller pupil sizes: a simpler formula,” J. Opt. Soc. Am. A 23, 539–547 (2006). [CrossRef]
  4. 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]
  5. A. J. E. M. Janssen and P. Dirksen, “Concise formula for the Zernike coefficients of scaled pupils,” J. Microlith., Microfab., Microsyst. 5, 030501 (2006). [CrossRef]
  6. J. A. Diaz, J. Fernandez-Dorado, C. Pizarro, and J. Arasa, “Zernike coefficients for concentric, circular pupils: an equivalent expression,” J. Mod. Opt. 56, 131 (2009). [CrossRef]
  7. V. N. Mahajan, Optical Imaging and Aberrations, Part II: Wave Diffraction Optics (SPIE Press, 2004), second printing.
  8. G.-m. Dai and V. N. Mahajan, “Zernike annular polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 24, 139–155 (2007). [CrossRef]
  9. V. N. Mahajan, “Zernike polynomials and wavefront fitting,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), pp. 498–546. [CrossRef]

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