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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2442–2458

Derivation of the propagation equations for higher order aberrations of local wavefronts

Gregor Esser, Wolfgang Becken, Werner Müller, Peter Baumbach, Josep Arasa, and Dietmar Uttenweiler  »View Author Affiliations


JOSA A, Vol. 28, Issue 12, pp. 2442-2458 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002442


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Abstract

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analytical propagation equations for HOA do not exist. Since HOA play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the propagation equations of power and astigmatism to the case of HOA (e.g., coma and spheri cal aberration). This is achieved by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the aberrations of a propagated wavefront directly from the aberrations of the original wavefront containing both low-order and high-order aberrations.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2720) Geometric optics : Mathematical methods (general)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(080.1005) Geometric optics : Aberration expansions
(080.1753) Geometric optics : Computation methods
(080.7343) Geometric optics : Wave dressing of rays

History
Original Manuscript: June 17, 2011
Revised Manuscript: September 23, 2011
Manuscript Accepted: September 23, 2011
Published: November 10, 2011

Citation
Gregor Esser, Wolfgang Becken, Werner Müller, Peter Baumbach, Josep Arasa, and Dietmar Uttenweiler, "Derivation of the propagation equations for higher order aberrations of local wavefronts," J. Opt. Soc. Am. A 28, 2442-2458 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-12-2442


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References

  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980), pp. 109–232.
  2. V. Mahajan, Optical Imaging and Aberrations: Part I. Ray Geometrical Optics (SPIE, 1998), pp. 91–361.
  3. G. Esser, W. Becken, W. Müller, P. Baumbach, J. Arasa, and D. Uttenweiler, “Derivation of the refractive equations for higher order aberrations of local wavefronts by oblique incidence,” J. Opt. Soc. Am. A 27, 218–237 (2010). [CrossRef]
  4. W. Becken, A. Seidemann, H. Altheimer, G. Esser, and D. Uttenweiler, “Spectacle lenses in sports: optimization of the imaging properties based on physiological aspects,” Z. Med. Phys. 17, 56–66 (2007). [CrossRef] [PubMed]
  5. W. Harris, “Wavefronts and their propagation in astigmatic systems,” Optom. Vis. Sci. 73, 606–612 (1996). [CrossRef] [PubMed]
  6. E. Acosta and R. Blendowske, “Paraxial propagation of astigmatic wavefronts in optical systems by an augmented stepalong method for vergences,” Optom. Vis. Sci. 82, 923–32 (2005). [CrossRef] [PubMed]
  7. E. Acosta and R. Blendowske, “Paraxial optics of astigmatic systems: relations between the wavefront and the ray picture approaches,” Optom. Vis. Sci. 84, E72 (2007). [CrossRef]
  8. H. Diepes and R. Blendowske, Optik und Technik der Brille (Optische Fachveröffentlichung GmbH, 2002), pp. 477–486.
  9. L. Thibos, “Propagation of astigmatic wavefronts using power vectors,” S. Afr. Optom. 62, 111–113 (2003).
  10. K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry; the comatic aberrations,” J. Opt. Soc. Am. A 27, 1490–1504 (2010). [CrossRef]
  11. K. P. Thompson, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26, 1503–1517(2009). [CrossRef]
  12. J. Arasa and J. Alda, “Real ray tracing,” in Encyclopedia of Optical Engineering (Marcel Dekker, 2004), doi:101081EEOE120027488. [CrossRef]
  13. J. Alda and J. Arasa, “Paraxial ray tracing,” in Encyclopedia of Optical Engineering (Marcel Dekker, 2004), doi:101081EEOE120009643. [CrossRef]
  14. G. Dai, Wavefront Optics for Vision Correction (SPIE, 2008), pp. 129–255. [CrossRef]
  15. K. Dillon, “Bilinear wavefront transformation,” J. Opt. Soc. Am. A 26, 1839–1846 (2009). [CrossRef]
  16. J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937–1945 (2002). [CrossRef]
  17. C. 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]
  18. G. Dai, “Scaling Zernike expansions coefficients to smaller pupil sizes: a simpler formula,” J. Opt. Soc. Am. 23, 539–543 (2006). [CrossRef]
  19. H. Shu, L. Luo, and G. Han, “General method to derive the relationship between two sets of Zernike coefficients corresponding to different aperture sizes,” J. Opt. Soc. Am. 23, 1960–1968(2006). [CrossRef]
  20. S. Bara, J. Arines, J. Ares, and P. Prado, “Direct transformation of Zernike eye aberration coefficients between scaled, rotated and/or displace pupils,” J. Opt. Soc. Am. 23, 2061–2066 (2006). [CrossRef]
  21. L. Lundström and P. Unsbo, “Transformation of Zernike coefficients: scaled, translated and rotated wavefronts with circular and elliptical pupils,” J. Opt. Soc. Am. 24, 569–577 (2007). [CrossRef]
  22. A. Guirao, D. Williams, and I. Cox, “Effect of the rotation and translation on the expected benefit of an ideal method to correct the eye’s high-order aberrations,” J. Opt. Soc. Am. A 18, 1003–1015 (2001). [CrossRef]
  23. G. Dai, C. Campbell, L. Chen, H. Zhao, and D. Chernyak, “Wavefront propagation from one plane to another with the use of Zernike polynomials and Taylor monomials,” Appl. Opt. 48, 477–488 (2009). [CrossRef] [PubMed]
  24. W. Harris, “Power vectors versus power matrices, and the mathematical nature of dioptric power,” Optom. Vis. Sci. 84, 1060–1063 (2007). [CrossRef] [PubMed]
  25. W. Harris, “Dioptric power: its nature and its representation in three- and four-dimensional space,” Optom. Vis. Sci. 74, 349–366 (1997). [CrossRef] [PubMed]
  26. L. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74, 367–375(1997). [CrossRef] [PubMed]
  27. G. M. Dai, “Wavefront expansion basis functions and their relationships,” J. Opt. Soc. Am. A 23, 1657–1666 (2006). [CrossRef]
  28. G.-M. Dai, “Wavefront expansion basis functions and their relationships: errata,” J. Opt. Soc. Am. A 23, 2970–2971 (2006). [CrossRef]

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