OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 12 — Dec. 1, 2002
  • pp: 2329–2348

Statistical variation of aberration structure and image quality in a normal population of healthy eyes

Larry N. Thibos, Xin Hong, Arthur Bradley, and Xu Cheng  »View Author Affiliations


JOSA A, Vol. 19, Issue 12, pp. 2329-2348 (2002)
http://dx.doi.org/10.1364/JOSAA.19.002329


View Full Text Article

Enhanced HTML    Acrobat PDF (1076 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A Shack–Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

© 2002 Optical Society of America

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(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

History
Original Manuscript: July 20, 2001
Revised Manuscript: June 10, 2002
Manuscript Accepted: June 10, 2002
Published: December 1, 2002

Citation
Larry N. Thibos, Xin Hong, Arthur Bradley, and Xu Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-12-2329


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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]
  2. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984). [CrossRef] [PubMed]
  3. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).
  4. M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990). [CrossRef] [PubMed]
  5. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998). [CrossRef]
  6. I. Iglesias, 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]
  7. 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).
  8. J. Liang, B. Grimm, S. Goelz, J. Bille, “Objective measurement of the wave aberrations of the human eye using a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994). [CrossRef]
  9. 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]
  10. T. O. Salmon, L. N. Thibos, A. Bradley, “Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor,” J. Opt. Soc. Am. A 15, 2457–2465 (1998). [CrossRef]
  11. J. Porter, A. Guirao, I. G. Cox, D. R. Williams, “The human eye’s monochromatic aberrations in a large population,” J. Opt. Soc. Am. A 18, 1793–1803 (2001). [CrossRef]
  12. L. N. Thibos, X. Hong, “Clinical applications of the Shack–Hartmann aberrometer,” Optom. Vision Sci. 76, 817–825 (1999). [CrossRef]
  13. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications, Vol. 35 of Trends in Optics and Photonics Series, V. Lakshminarayanan, ed. (Optical Society of America, Washington, D.C., 2000), pp. 232–244.
  14. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).
  15. X. Hong, L. N. Thibos, K. M. Haggerty, “Shack–Hartmann data analysis software for MATLAB” (2000), http://research.opt.indiana.edu .
  16. The array of spots formed in a Shack–Hartmann aberrometer provides only a crude estimate of pupil center and pupil diameter because the spots are displaced by the eye’s aberrations. A more accurate estimate may be obtained from the locations of the lenslets that produced the spots.
  17. L. N. Thibos, W. Wheeler, D. G. Horner, “Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error,” Optom. Vision Sci. 74, 367–375 (1997). [CrossRef]
  18. A. Marechal, “Etude des effets combinés de la diffraction et des aberrations géométriques sur l’image d’un point lumineux,” Rev. d’Optique 26, 257–277 (1947).
  19. J. E. Jackson, A User’s Guide To Principal Components (Wiley, New York, 1991).
  20. A. J. Thomasian, The Structure of Probability Theory with Applications (McGraw-Hill, New York, 1969).
  21. One implication of this result is that the mean magnitudes of Gaussian aberration coefficients are virtually ensured to be statistical significant. A t-test of the null hypothesis that the mean magnitude is zero would be rejected if the observed mean were more than twice the standard error of the mean. Since standard error=standarddeviation/n,rejection is ensured for n>2π-4=2.3.Thus a population of three or more individuals is enough to cause rejection of the null hypothesis for Gaussian variables.
  22. Critical pupil diameter should not be confused with optimum pupil diameter, defined as that pupil size which maximizes image quality. The latter is more difficult to quantify satisfactorily because of the lack of a universally accepted metric of image quality.
  23. P. A. Howarth, A. Bradley, “The longitudinal chromatic aberration of the human eye, and its correction,” Vision Res. 26, 361–366 (1986). [CrossRef] [PubMed]
  24. L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992). [CrossRef] [PubMed]
  25. W. N. Charman, “Wavefront aberrations of the eye: a review,” Optom. Vision Sci. 68, 574–583 (1991). [CrossRef]
  26. J. S. McLellan, S. Marcos, S. A. Burns, “Agerelated changes in monochromatic wave aberrations of the human eye,” Invest. Ophthalmol. Visual Sci. 42, 1390–1395 (2001).
  27. F. W. Campbell, “The depth-of-field of the human eye,” Opt. Acta 4, 157–164 (1957). [CrossRef]
  28. D. A. Atchison, W. N. Charman, R. L. Woods, “Subjective depth-of-focus of the eye,” Optom. Vision Sci. 74, 511–520 (1997). [CrossRef]
  29. J. Tucker, W. N. Charman, “The depth-of-focus of the human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975). [CrossRef] [PubMed]
  30. X. Zhang, M. Ye, A. Bradley, L. Thibos, “Apodization by the Stiles–Crawford effect moderates the visual impact of retinal image defocus,” J. Opt. Soc. Am. A 16, 812–820 (1999). [CrossRef]
  31. L. N. Thibos, A. Bradley, “Modeling the refractive and neuro-sensor systems of the eye,” in Visual Instrumentation: Optical Design and Engineering Principles, P. Mouroulis, ed. (McGraw-Hill, New York, 1999), pp. 101–159.
  32. R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993). [CrossRef] [PubMed]
  33. D. A. Atchison, A. Joblin, G. Smith, “Influence of Stiles–Crawford effect apodization on spatial visual performance,” J. Opt. Soc. Am. A 15, 2545–2551 (1998). [CrossRef]
  34. S. Marcos, E. Moreno, R. Navarro, “The depth-of-field of the human eye from objective and subjective measurements,” Vision Res. 39, 2039–2049 (1999). [CrossRef] [PubMed]
  35. S. Marcos, S. A. Burns, “On the symmetry between eyes of wavefront aberration and cone directionality,” Vision Res. 40, 2437–2447 (2000). [CrossRef] [PubMed]
  36. M. Koomen, R. Tousey, R. Scolnik, “The spherical aberration of the eye,” J. Opt. Soc. Am. 39, 370–376 (1949). [CrossRef] [PubMed]
  37. M. Koomen, R. Scolnik, R. Tousey, “A study of night myopia,” J. Opt. Soc. Am. 41, 80–90 (1951). [CrossRef]
  38. W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).
  39. J. A. Van Loo, J. M. Enoch, “The scotopic Stiles–Crawford effect,” Vision Res. 13, 1005–1009 (1975). [CrossRef]
  40. Readers unfamiliar with Zernike analysis should beware of the confusing, dual-usage of terms such as “spherical aberration” and “defocus.” The difference between classical Seidel usage and the more modern Zernike usage is analogous to the difference between the spherical power in a conventional prescription of refractive error and the mean spherical equivalent used in power vector notation. If one extracts the mean spherical equivalent from a conventional prescription, the remainder is an orthogonal component called “Jackson crossed cylinder” to avoid confusion with the term “cylinder” used in conventional prescriptions. Similarly, if one extracts mean sphere from Seidel spherical aberration the result is Zernike spherical aberration. Unfortunately, authors sometimes fail to explicitly state which definition they have in mind when using common names for aberrations. Thus readers must rely on context to resolve the ambiguity.
  41. P. Mouroulis, “Aberration and image quality representation for visual optical systems,” in Visual Instrumentation: Optical Design and Engineering Principles, P. Mouroulis, ed. (McGraw-Hill, New York, 1999), pp. 27–68.
  42. V. N. Mahajan, “Uniform versus Gaussian beams: a comparison of the effects of diffraction, abscuration, and aberrations,” J. Opt. Soc. Am. A 3, 470–485 (1986). [CrossRef]
  43. The same argument in a more familiar context would arise in a statistical analysis of the Fourier coefficients obtained from physiological responses to square-wave stimulation. Fourier expansion of a square wave yields a strict relationship between the amplitudes of the various harmonic components. Therefore, a quasi-square-wave-response waveform should still show evidence of a predictable correlation between Fourier coefficients.
  44. S. M. MacRae, R. R. Krueger, R. A. Applegate, Customized Corneal Ablation: The Quest for Super Vision (Slack, Thorofare, N.J., 2001).
  45. L. N. Piotrowski, F. W. Campbell, “A demonstration of the visual importance and flexibility of spatial-frequency amplitude and phase,” Perception 11, 337–346 (1982). [CrossRef] [PubMed]
  46. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  47. M. C. Rynders, B. A. Lidkea, W. J. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle psi in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995). [CrossRef]

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.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited