Abstract

We present a population study of peripheral wavefront aberrations in large off-axis angles in terms of Zernike coefficients. A laboratory Hartmann–Shack sensor was used to assess the aberrations in 0°, 20°, and 30° in the nasal visual field of 43 normal eyes. The elliptical pupil meant that the quantification could be done in different ways. The three approaches used were (1) over a circular aperture encircling the pupil, (2) over a stretched version of the elliptical pupil, and (3) over a circular aperture within the pupil (MATLAB conversion code given). Astigmatism (c22) increased quadratically and coma (c31) linearly with the horizontal viewing angle, whereas spherical aberration (c40) decreased slightly toward the periphery. There was no correlation between defocus and angle, although some trends were found when the subjects were divided into groups depending on refractive error. When comparing results of different studies it has to be kept in mind that the coefficients differ depending on how the elliptical pupil is taken into consideration.

© 2009 Optical Society of America

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References

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    [CrossRef]
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2009 (1)

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vision 9, 17 (2009).
[CrossRef]

2008 (3)

2007 (3)

2006 (3)

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 034026 (2006).
[CrossRef]

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

T. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32, 2064-2074 (2006).
[CrossRef]

2005 (3)

L. Lundström, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef] [PubMed]

L. Lundström, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298-306 (2005).
[CrossRef]

W. N. Charman, “Aberrations and myopia,” Ophthalmic Physiol. Opt. 25, 285-301 (2005).
[CrossRef] [PubMed]

2004 (1)

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

2003 (1)

L. Wang and D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896-1903 (2003).
[CrossRef]

2002 (4)

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. 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).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

J. Schwiegerling, “Scaling Zernike expansion coefficients to different pupil sizes,” J. Opt. Soc. Am. A 19, 1937-1945 (2002).
[CrossRef]

2001 (1)

1999 (1)

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207-217 (1999).
[CrossRef] [PubMed]

1998 (1)

1994 (1)

1993 (1)

1981 (1)

J. A. M. Jennings and W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445-455 (1981).
[CrossRef] [PubMed]

1978 (1)

J. A. M. Jennings and W. N. Charman, “Optical image quality in the peripheral retina,” Am. J. Optom. Physiol. Opt. 55, 582-590 (1978).
[PubMed]

Applegate, R. A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

Artal, P.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vision 9, 17 (2009).
[CrossRef]

L. Lundström, S. Manzanera, P. M. Prieto, D. B. Ayala, N. Gorceix, J. Gustafsson, P. Unsbo, and P. Artal, “Effect of optical correction and remaining aberrations on peripheral resolution acuity in the human eye,” Opt. Express 15, 12654-12661 (2007).
[CrossRef] [PubMed]

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207-217 (1999).
[CrossRef] [PubMed]

R. Navarro, P. Artal, and D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201-212 (1993).
[CrossRef] [PubMed]

Ashman, R.

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Atchison, D. A.

A. Mathur, D. A. Atchison, and D. H. Scott, “Ocular aberrations in the peripheral visual field,” Opt. Lett. 33, 863-865 (2008).
[CrossRef] [PubMed]

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 034026 (2006).
[CrossRef]

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Ayala, D. B.

Barnett, J. K.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Benito, A.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

Bille, J. F.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 5.

Bradley, A.

Castejón-Mochón, J. F.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

Charman, W. N.

W. N. Charman, “Aberrations and myopia,” Ophthalmic Physiol. Opt. 25, 285-301 (2005).
[CrossRef] [PubMed]

J. A. M. Jennings and W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445-455 (1981).
[CrossRef] [PubMed]

J. A. M. Jennings and W. N. Charman, “Optical image quality in the peripheral retina,” Am. J. Optom. Physiol. Opt. 55, 582-590 (1978).
[PubMed]

Cheng, H.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Cheng, X.

Cox, I. G.

Dainty, C.

Dorronsoro, C.

Goelz, S.

Goncharov, A. V.

Gorceix, N.

Grimm, B.

Guirao, A.

J. Porter, A. Guirao, I. G. Cox, and D. R. Williams, “Monochromatic aberrations of the human eye in a large population,” J. Opt. Soc. Am. A 18, 1793-1803 (2001).
[CrossRef]

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207-217 (1999).
[CrossRef] [PubMed]

Gustafsson, J.

L. Lundström, S. Manzanera, P. M. Prieto, D. B. Ayala, N. Gorceix, J. Gustafsson, P. Unsbo, and P. Artal, “Effect of optical correction and remaining aberrations on peripheral resolution acuity in the human eye,” Opt. Express 15, 12654-12661 (2007).
[CrossRef] [PubMed]

L. Lundström, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef] [PubMed]

L. Lundström, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298-306 (2005).
[CrossRef]

Hong, X.

Huynh, M. A.

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Jennings, J. A. M.

J. A. M. Jennings and W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445-455 (1981).
[CrossRef] [PubMed]

J. A. M. Jennings and W. N. Charman, “Optical image quality in the peripheral retina,” Am. J. Optom. Physiol. Opt. 55, 582-590 (1978).
[PubMed]

Kasthurirangan, S.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Koch, D. D.

L. Wang and D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896-1903 (2003).
[CrossRef]

Liang, J.

López-Gil, N.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

Lucas, S. D.

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Lundström, L.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vision 9, 17 (2009).
[CrossRef]

L. Lundström 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]

L. Lundström, S. Manzanera, P. M. Prieto, D. B. Ayala, N. Gorceix, J. Gustafsson, P. Unsbo, and P. Artal, “Effect of optical correction and remaining aberrations on peripheral resolution acuity in the human eye,” Opt. Express 15, 12654-12661 (2007).
[CrossRef] [PubMed]

L. Lundström, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef] [PubMed]

L. Lundström, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298-306 (2005).
[CrossRef]

Manzanera, S.

Marsack, J. D.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Mathur, A.

Mira-Agudelo, A.

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vision 9, 17 (2009).
[CrossRef]

Moreno, E.

Navarro, R.

Ngo, P. Q.

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Nowakowski, M.

O"Dwyer, V. M.

Porter, J.

Prieto, P. M.

Roorda, A.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Salmon, T.

T. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32, 2064-2074 (2006).
[CrossRef]

Schilt, D. W.

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

Schwiegerling, J.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

Scott, D. H.

Sheehan, M. T.

Svensson, I.

L. Lundström, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298-306 (2005).
[CrossRef]

Thibos, L.

Thibos, L. N.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

L. N. Thibos, X. Hong, A. Bradley, and X. 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).
[CrossRef]

Toal, V.

Unsbo, P.

van de Pol, C.

T. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32, 2064-2074 (2006).
[CrossRef]

Vilupuru, A. S.

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Wang, L.

L. Wang and D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896-1903 (2003).
[CrossRef]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

Wei, X.

Williams, D. R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 5.

Am. J. Optom. Physiol. Opt. (1)

J. A. M. Jennings and W. N. Charman, “Optical image quality in the peripheral retina,” Am. J. Optom. Physiol. Opt. 55, 582-590 (1978).
[PubMed]

J. Biomed. Opt. (2)

D. A. Atchison, “Higher order aberrations across the horizontal visual field,” J. Biomed. Opt. 11, 034026 (2006).
[CrossRef]

L. Lundström, P. Unsbo, and J. Gustafsson, “Off-axis wave front measurements for optical correction in eccentric viewing,” J. Biomed. Opt. 10, 034002 (2005).
[CrossRef] [PubMed]

J. Cataract Refractive Surg. (2)

T. Salmon and C. van de Pol, “Normal-eye Zernike coefficients and root-mean-square wavefront errors,” J. Cataract Refractive Surg. 32, 2064-2074 (2006).
[CrossRef]

L. Wang and D. D. Koch, “Ocular higher-order aberrations in individuals screened for refractive surgery,” J. Cataract Refractive Surg. 29, 1896-1903 (2003).
[CrossRef]

J. Opt. Soc. Am. A (7)

J. Refract. Surg. (1)

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” J. Refract. Surg. 18, 652-660 (2002).

J. Vision (2)

L. Lundström, A. Mira-Agudelo, and P. Artal, “Peripheral optical errors and their change with accommodation differ between emmetropic and myopic eyes,” J. Vision 9, 17 (2009).
[CrossRef]

H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vision 4, 272-280 (2004).
[CrossRef]

Ophthalmic Physiol. Opt. (1)

W. N. Charman, “Aberrations and myopia,” Ophthalmic Physiol. Opt. 25, 285-301 (2005).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Optom. Vision Sci. (2)

D. A. Atchison, S. D. Lucas, R. Ashman, M. A. Huynh, D. W. Schilt, and P. Q. Ngo, “Refraction and aberration across the horizontal central 10 degrees of the visual field,” Optom. Vision Sci. 83, 213-21 (2006).
[CrossRef]

L. Lundström, J. Gustafsson, I. Svensson, and P. Unsbo, “Assessment of objective and subjective eccentric refraction,” Optom. Vision Sci. 82, 298-306 (2005).
[CrossRef]

Vision Res. (3)

A. Guirao and P. Artal, “Off-axis monochromatic aberrations estimated from double pass measurements in the human eye,” Vision Res. 39, 207-217 (1999).
[CrossRef] [PubMed]

J. A. M. Jennings and W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445-455 (1981).
[CrossRef] [PubMed]

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistics in a normal young population,” Vision Res. 42, 1611-1617 (2002).
[CrossRef] [PubMed]

Other (2)

American National Standards Institute, “Methods for reporting optical aberrations of eyes,” ANSI Z80.28-2004 (2004).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 5.

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Figures (4)

Fig. 1
Fig. 1

A wavefront with spherical aberration and an elliptical pupil is converted into a circular aperture in three alternative ways: the leftmost image (Org) shows the original wavefront as it emerges from the eye; the second image (LC) presents the version that also contains extrapolated wavefront data; the third image (SE) is the alternative in which the original wavefront is stretched out into a circle; and the last image (SC) presents the version describing a circular subpart of the original wavefront.

Fig. 2
Fig. 2

Signed third- and fourth-order Zernike coefficients for a 4 mm circular subpupil (SC) in the three measured angles. The rectangular bars are the mean values, and the error bars show the standard deviation over the population.

Fig. 3
Fig. 3

Variation with angle for horizontal astigmatism ( c 2 2 , squares) and coma ( c 3 1 , diamonds) for two circular pupil sizes: 5 mm (LC, solid curves) and 4 mm (SC, dashed curves). The averages of the two signed Zernike coefficients are plotted in micrometers for the horizontal off-axis angles of 0°, 20°, and 30°. The curves are best-fit curves: c 2 2 follows a quadratic trend, for LC 0.0012 × θ 2 off - axis + 0.022 × θ off - axis and for SC 0.0008 × θ 2 off - axis + 0.013 × θ off - axis , whereas c 3 1 has a more linear behavior, for LC 0.016 μ m deg and for SC 0.0085 μ m deg .

Fig. 4
Fig. 4

Effect on the PSF if the Zernike representations are used incorrectly. The figures show pure spherical aberration for an elliptical pupil; on the upper row the off-angle is 30°, and on the lower row the angle is 50°. The leftmost column shows the true PSFs, the middle column illustrates the effect of using the LC representation without removing the extrapolated part of the wavefront, and in the rightmost column the SE representation is used without taking the stretched coordinate system into consideration.

Tables (3)

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Table 1 Population Statistics of the 43 Subjects in the Study (Mean Value ± Standard Deviation)

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Table 2 Variation with Off-Axis Angle (0°, 20°, and 30°) for the Absolute Values of Zernike Coefficients over the Population for Three Different Pupil Shapes a

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Table 3 Correlation with Off-Axis Angle for Each Signed Zernike Coefficient in μ m over a 5 mm Circular Aperture (LC) and a 4 mm Circular Aperture (SC) a

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