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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2642–2646

Aberrations and spherocylindrical powers within subapertures of freeform surfaces

Thomas Raasch  »View Author Affiliations

JOSA A, Vol. 28, Issue 12, pp. 2642-2646 (2011)

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A method is described for the derivation of refractive properties and aberration structure of subapertures of freeform surfaces. Surface shapes are described in terms of Zernike polynomials. The method utilizes matrices to transform between Zernike and Taylor coefficients. Expression as a Taylor series facilitates the translation and size rescaling of subapertures of the surface. An example operation using a progressive addition lens surface illustrates the method.

© 2011 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.1005) Geometric optics : Aberration expansions
(080.4225) Geometric optics : Nonspherical lens design

Original Manuscript: September 22, 2011
Revised Manuscript: October 4, 2011
Manuscript Accepted: October 6, 2011
Published: November 25, 2011

Thomas Raasch, "Aberrations and spherocylindrical powers within subapertures of freeform surfaces," J. Opt. Soc. Am. A 28, 2642-2646 (2011)

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  1. 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]
  2. G. M. Dai, “Wavefront expansion basis functions and their relationships,” J. Opt. Soc. Am. A 23, 1657–1668 (2006). [CrossRef]
  3. G. M. Dai, “Wavefront expansion basis functions and their relationships: errata,” J. Opt. Soc. Am. A 23, 2970–2971 (2006). [CrossRef]
  4. K. A. Goldberg and K. Geary, “Wave-front measurement errors from restricted concentric subdomains,” J. Opt. Soc. Am. A 18, 2146–2152 (2001). [CrossRef]
  5. J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937–1945 (2002). [CrossRef]
  6. S. Bara, J. Arines, J. Ares, and P. Prado, “Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils,” J. Opt. Soc. Am. A 23, 2061–2066(2006). [CrossRef]
  7. S. Comastri, K. Bastida, A. Bianchetti, L. Perez, G. Perez, and G. Martin, “Zernike aberrations when pupil varies: selection rules, missing modes and graphical method to identify modes,” J. Opt. A 11, 085302 (2009). [CrossRef]
  8. L. Lundstrom and P. Unsbo, “Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils,” J. Opt. Soc. Am. A 24, 569–577 (2007). [CrossRef]
  9. A. Guirao, D. R. Williams, and I. G. Cox, “Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations,” J. Opt. Soc. Am. A 18, 1003–1015 (2001). [CrossRef]
  10. R. Blendowske, E. A. Villegas, and P. Artal, “An analytical model describing aberrations in the progression corridor of progressive addition lenses,” Optom. Vision Sci. 83, 666–671 (2006). [CrossRef]
  11. C. Fowler, “Recent trends in progressive power lenses,” Ophthalmic Physiol. Opt. 18, 234–237 (1998). [CrossRef] [PubMed]
  12. A. Guirao and D. R. Williams, “A method to predict refractive errors from wave aberration data,” Optom. Vision Sci. 80, 36–42 (2003). [CrossRef]
  13. E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vision Sci. 80, 106–114 (2003). [CrossRef]
  14. C. Zhou, W. Wang, K. Yang, X. Chai, and Q. Ren, “Measurement and comparison of the optical performance of an ophthalmic lens based on a Hartmann–Shack wavefront sensor in real viewing conditions,” Appl. Opt. 47, 6434–6441 (2008). [CrossRef] [PubMed]
  15. T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Optom. Vision Sci. 88, E217–226 (2011). [CrossRef]
  16. P. R. Riera, G. S. Pankretz, and D. M. Topa, “Efficient computation with special functions like the circle polynomials of Zernike,” in Optical Design and Analysis Software II, R.C.Juergens, ed. (SPIE, 2002), pp. 130–144.
  17. E. J. Sarver and M. T. Hall, “Fast evaluation of equal-spaced Zernike polynomial expansion samples,” J. Refract. Surg. 26, 61–65 (2010). [CrossRef] [PubMed]
  18. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, S652–660 (2002). [PubMed]
  19. American National Standards Institute, “Methods for reporting optical aberrations of eyes,” ANSI Z80.28-2004 (ANSI, 2004).
  20. L. W. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978). [PubMed]

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