OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 5 — May. 1, 2001
  • pp: 1003–1015

Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations

Antonio Guirao, David R. Williams, and Ian G. Cox  »View Author Affiliations

JOSA A, Vol. 18, Issue 5, pp. 1003-1015 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (385 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An ideal correcting method, such as a customized contact lens, laser refractive surgery, or adaptive optics, that corrects higher-order aberrations as well as defocus and astigmatism could improve vision. The benefit achieved with this ideal method will be limited by decentration. To estimate the significance of this potential limitation we studied the effect on image quality expected when an ideal correcting method translates or rotates with respect to the eye’s pupil. Actual wave aberrations were obtained from ten human eyes for a 7.3-mm pupil with a Shack–Hartmann sensor. We computed the residual aberrations that appear as a result of translation or rotation of an otherwise ideal correction. The model is valid for adaptive optics, contact lenses, and phase plates, but it constitutes only a first approximation to the laser refractive surgery case where tissue removal occurs. Calculations suggest that the typical decentrations will reduce only slightly the optical benefits expected from an ideal correcting method. For typical decentrations the ideal correcting method offers a benefit in modulation 2–4 times higher (1.5–2 times in white light) than with a standard correction of defocus and astigmatism. We obtained analytical expressions that show the impact of translation and rotation on individual Zernike terms. These calculations also reveal which aberrations are most beneficial to correct. We provided practical rules to implement a selective correction depending on the amount of decentration. An experimental study was performed with an aberrated artificial eye corrected with an adaptive optics system, validating the theoretical predictions. The results in a keratoconic subject, also corrected with adaptive optics, showed that important benefits are obtained despite decentrations in highly aberrated eyes.

© 2001 Optical Society of America

OCIS Codes
(220.1000) Optical design and fabrication : Aberration compensation
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(330.5370) Vision, color, and visual optics : Physiological optics
(330.7310) Vision, color, and visual optics : Vision

Original Manuscript: June 16, 2000
Revised Manuscript: November 13, 2000
Manuscript Accepted: November 14, 2000
Published: May 1, 2001

Antonio Guirao, David R. Williams, and Ian 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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. N. Charman, “The retinal image in the human eye,” in Progress in Retinal Research, N. Osborne, G. Chader, eds. (Pergamon, Oxford, 1983), Vol. 2, Chap. 1.
  2. H. von Helmholtz, Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1896).
  3. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophysics 7, 766–795 (1962).
  4. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186, 558–578 (1966). [PubMed]
  5. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977). [CrossRef] [PubMed]
  6. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberra-tions of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984). [CrossRef] [PubMed]
  7. J. Santamarı́a, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987). [CrossRef]
  8. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Shack–Hartmann wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994). [CrossRef]
  9. P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995). [CrossRef]
  10. J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997). [CrossRef]
  11. R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997). [CrossRef]
  12. P. Mierdel, H. E. Krinke, W. Wiegand, M. Kaemmerer, T. Seiler, “A measuring device for the assessment of monochromatic aberrations in human eyes,” Ophthalmologe 94, 441–445 (1997). [CrossRef] [PubMed]
  13. I. Iglesias, M. E. Berrio, P. Artal, “Estimates of the ocular-wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998). [CrossRef]
  14. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wavefront aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998). [CrossRef]
  15. P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994). [CrossRef]
  16. A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, P. Artal, “Average optical performance of the human eye as a function of age in a normal population,” Invest. Ophthalmol. Visual Sci. 40, 203–213 (1999).
  17. R. A. Applegate, H. C. Howland, J. Buettner, A. J. Cottingham, R. P. Sharp, R. W. Yee, “Radial keratotomy (RK), corneal aberrations and visual performance,” Invest. Ophthalmol. Visual Sci. 36, 36–42 (1995).
  18. J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997). [CrossRef]
  19. T. Oshika, S. D. Klyce, R. A. Applegate, H. C. Howland, M. A. El Danasoury, “Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis,” Am. J. Ophthalmol. 127, 1–7 (1999). [CrossRef] [PubMed]
  20. P. M. Prieto, F. Vargas-Martin, S. Goelz, P. Artal, “Analysis of the performance of the Shack–Hartmann sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000). [CrossRef]
  21. J. Porter, I. G. Cox, A. Guirao, R. J. Potvin, M. A. Lagana, D. R. Williams, “A compact description of the eye’s aberrations in a large population,” Invest. Ophthalmol. Visual Sci. 41, S428 (2000).
  22. R. Navarro, E. Moreno-Barriuso, S. Bara, T. Mancebo, “Phase plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000). [CrossRef]
  23. S. M. MacRae, J. Schwiegerling, R. Snyder, “Customized corneal ablation and super vision,” J. Refract. Surgery 16, S230–S235 (2000).
  24. M. Mrochen, M. Kaemmerer, T. Seiler, “Wavefront-guided laser in situ keratomileusis: early results in three eyes,” J. Refract. Surgery 16, 116–121 (2000).
  25. J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997). [CrossRef]
  26. G. Y. Yoon, D. R. Williams, “Visual benefit of correcting the higher-order monochromatic aberrations and longitudinal chromatic aberration in the eye,” in Vision Science and Its Applications, 2000 OSA Technical Digest Series (Optical Society of America, Washington D.C., 2000) pp. PD5-1–PD5-4.
  27. A. Tomlinson, W. H. Ridder, R. Watanabe, “Blink-induced variations in visual performance with toric soft contact lenses,” Optom. Vision Sci. 71, 545–549 (1994). [CrossRef]
  28. R. B. Mandell, Contact Lens Practice, 4th ed. (Charles C. Thomas, Springfield, Ill., 1988).
  29. J. Schwiegerling, R. W. Snyder, “Eye movement during laser in situ keratomileusis,” J. Cataract Refractive Surgery 26, 345–351 (2000). [CrossRef]
  30. A. Tomlinson, “Succeeding with toric soft lenses,” Rev. Optom. 120, 71–80 (1983).
  31. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980). [CrossRef] [PubMed]
  32. C-J. Kim, R. R. Shannon, “Catalog of Zernike polynomials,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, San Diego, Calif., 1987), Vol. X, Chap. 4.
  33. This rms corresponds to a Strehl ratio lower than 0.05. This means that after a conventional correction of defocus and astigmatism, the optical quality is still poor in comparison with the diffraction limit.
  34. V. N. Mahajan, Optical Imaging and Aberrations (SPIE Press, Bellingham, Wash., 1998).
  35. S. Bará, T. Mancebo, E. Moreno-Barriuso, “Positioning tolerances for phase plates compensating aberrations of the human eye,” Appl. Opt. 39, 3413–3420 (2000). [CrossRef]
  36. The matrix elements were obtained by transforming the Zernike polynomials with a change of coordinates. The same result can be reached evaluating the function at displaced coordinates by means of a Taylor expansion: Zn±m(x-Δx, y-Δy)=∑k=0∞ (-1)kk! Δx ∂∂x+Δy ∂∂yk[Zn±m(x, y)].Thus the matrix [T] can be constructed by taking the first, second, etc., derivatives of the Zernike polynomials. [For the first derivatives, see R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976)]. [CrossRef]
  37. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  38. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990). [CrossRef] [PubMed]
  39. S. Marcos, S. A. Burns, E. Moreno-Barriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999). [CrossRef]
  40. D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985). [CrossRef] [PubMed]
  41. The exact factor depending on rotation in rule (R3) is 2[1-exp(m2σr2/2)], and approximately, 4 sin2(mσr/2), or m2σr2.
  42. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  43. P. Erickson, M. Robboy, “Performance characteristics of a hydrophilic concentric bifocal contact lens,” Am. J. Optom. Physiol. Opt. 62, 702–708 (1985). [CrossRef] [PubMed]
  44. D. R. Williams, J. Liang, D. T. Miller, A. Roorda, “Wavefront sensing and compensation for the human eye,” in Adaptive Optics Engineering Handbook, R. K. Tyson, ed. (Marcel Dekker, New York, 2000), Chap. 10.
  45. N. Chateau, J. de Brabander, F. Bouchard, H. Molenaar, “Infrared pupillometry in presbyopes fitted with soft contact lenses,” Optom. Vision Sci. 73, 733–741 (1996). [CrossRef]
  46. N. López-Gil, E. Villegas, A. Benito, E. Berrio, N. Chateau, P. Artal, “Are the aberrations introduced by soft contact lenses in the eye predictable?” Invest. Ophthalmol. Visual Sci. 41, S426 (2000).
  47. A. J. Taylor, S. D. R. Wilson, “Centration mechanism of soft contact lenses,” Optom. Vision Sci. 73, 215–221 (1996). [CrossRef]
  48. S. A. Little, A. S. Bruce, “Hydrogel (Acuvue) lens movement is influenced by the postlens tear film,” Optom. Vision Sci. 71, 364–370 (1994). [CrossRef]
  49. H. Hofer, P. Artal, B. Singer, J. L. Aragon, D. R. Williams, “Dynamics of the eye’s wave aberration,” J. Opt. Soc. Am. A 18, 497–506 (2000). [CrossRef]
  50. D. R. Williams, “Aliasing in foveal human vision,” Vision Res. 25, 195–205 (1985). [CrossRef]
  51. Liang et al. (see Ref. 25) found that aberrations beyond sixth order remained uncorrected after correction with adaptive optics and that the lower orders up to fourth order were significantly reduced. Although an explanation of this result is that the deformable mirror (37 actuators) could not correct those higher orders, a complementary reason may be that the effect of small decentration of observers makes ineffective a correction beyond the fourth-order.
  52. N. López-Gil, H. C. Howland, B. Howland, N. Charman, R. Applegate, “Generation of third-order spherical and coma aberration using radially symmetric fourth-order lenses,” J. Opt. Soc. Am. A 15, 2563–2571 (1998). [CrossRef]
  53. L. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978). [PubMed]
  54. N. Chateau, A. Blanchard, D. Baude, “Influence of myopia and aging on the optimal spherical aberration of soft contact lenses,” J. Opt. Soc. Am. A 15, 2589–2596 (1998). [CrossRef]
  55. P. Artal, A. Guirao, E. Villegas, C. González, N. Chateau, E. Berrio, “Image quality in eyes with spherical aberration induced by soft contact lenses,” Vision Science and Its Applications, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 232–235.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited