Abstract

The geometrical center of the pupil has often been used as the reference axis in ocular wave-front aberration measurement. However, the geometrical center of the pupil may shift when the pupil size changes under different conditions. In particular, for subjective methods, defining the center of the pupil precisely during the actual measurement is not always practical. Furthermore, the geometrical center of the pupil may not define the chief ray of the ocular optics because of the Stiles–Crawford apodization effect, which has a peak location that often deviates from the geometrical center of the pupil. We present the coefficient transformation table of the Taylor polynomial up to the sixth order with respect to reference axis shift. We illustrate the effect of wave-front aberration change with reference axis shift with experimental data. This type of wave-front aberration change could be a true measurement error if there is an error in defining the reference axis. We also propose using the coaxially sighted corneal reflex as a better reference axis in aberration measurement.

© 1998 Optical Society of America

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References

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  1. W. N. Charman, “Optics of the human eye,” in Visual Optics and Instrumentation (CRC, Boca Raton, Fla., 1991).
  2. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).
  3. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 11, 1508–1518 (1977).
    [CrossRef]
  4. 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]
  5. D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
    [CrossRef] [PubMed]
  6. M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
    [CrossRef]
  7. G. Walsh, “The effect of mydriasis on pupillary centration of the human eye,” Ophthalmic Physiol. Opt. 8, 178–182 (1988).
    [CrossRef]
  8. J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 280–309.
  9. H. Uozato, D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103, 264–275 (1987).
    [PubMed]
  10. M. Pande, J. S. Hillman, “Optical zone centration in keratorefractive surgery,” Ophthalmology 100, 1230–1237 (1993).
    [CrossRef] [PubMed]
  11. R. A. Applegate, H. C. Howland, “Noninvasive measurement of corneal topography,” IEEE Eng. Med. Biol. Mag. 42, 30–42 (1995).
    [CrossRef]
  12. A. G. Bennet, R. B. Rabbetts, Clinical Visual Optics, (Butterworth, Toronto, 1984).
  13. A. Ivanoff, “About the spherical aberration of the eye,” J. Opt. Soc. Am. 46, 901–904 (1956).
    [CrossRef] [PubMed]
  14. C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [CrossRef]
  15. C. Cui, The Misalignment of Ocular Components and Ocular Monochromatic Aberrations, Ph.D. dissertation (University of Waterloo, Waterloo, Ontario, Canada, 1998).
  16. 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]
  17. J. Gorrand, F. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
    [CrossRef] [PubMed]

1995 (3)

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

R. A. Applegate, H. C. Howland, “Noninvasive measurement of corneal topography,” IEEE Eng. Med. Biol. Mag. 42, 30–42 (1995).
[CrossRef]

J. Gorrand, F. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

1993 (2)

1992 (1)

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
[CrossRef]

1990 (1)

C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

1988 (1)

G. Walsh, “The effect of mydriasis on pupillary centration of the human eye,” Ophthalmic Physiol. Opt. 8, 178–182 (1988).
[CrossRef]

1987 (1)

H. Uozato, D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103, 264–275 (1987).
[PubMed]

1984 (1)

1977 (1)

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 11, 1508–1518 (1977).
[CrossRef]

1961 (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

1956 (1)

Applegate, R. A.

Atchison, D. A.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Bennet, A. G.

A. G. Bennet, R. B. Rabbetts, Clinical Visual Optics, (Butterworth, Toronto, 1984).

Campbell, C. W. M.

C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Campbell, M. C. W.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
[CrossRef]

Charman, W. N.

Christensen, J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Collins, M. J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Cui, C.

C. Cui, The Misalignment of Ocular Components and Ocular Monochromatic Aberrations, Ph.D. dissertation (University of Waterloo, Waterloo, Ontario, Canada, 1998).

Delori, F.

J. Gorrand, F. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

Enoch, J. M.

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 280–309.

Gorrand, J.

J. Gorrand, F. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

Guyton, D. L.

H. Uozato, D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103, 264–275 (1987).
[PubMed]

Harrison, E. M.

C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Hillman, J. S.

M. Pande, J. S. Hillman, “Optical zone centration in keratorefractive surgery,” Ophthalmology 100, 1230–1237 (1993).
[CrossRef] [PubMed]

Howland, B.

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 11, 1508–1518 (1977).
[CrossRef]

Howland, H. C.

R. A. Applegate, H. C. Howland, “Noninvasive measurement of corneal topography,” IEEE Eng. Med. Biol. Mag. 42, 30–42 (1995).
[CrossRef]

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]

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 11, 1508–1518 (1977).
[CrossRef]

Ivanoff, A.

Lakshminarayanan, V.

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]

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 280–309.

Pande, M.

M. Pande, J. S. Hillman, “Optical zone centration in keratorefractive surgery,” Ophthalmology 100, 1230–1237 (1993).
[CrossRef] [PubMed]

Rabbetts, R. B.

A. G. Bennet, R. B. Rabbetts, Clinical Visual Optics, (Butterworth, Toronto, 1984).

Simonet, P.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
[CrossRef]

C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

Uozato, H.

H. Uozato, D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103, 264–275 (1987).
[PubMed]

Walsh, G.

Waterworth, M. D.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Wildsoet, C. F.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Wilson, M. A.

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
[CrossRef]

Am. J. Ophthalmol. (1)

H. Uozato, D. L. Guyton, “Centering corneal surgical procedures,” Am. J. Ophthalmol. 103, 264–275 (1987).
[PubMed]

Biofizika (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

IEEE Eng. Med. Biol. Mag. (1)

R. A. Applegate, H. C. Howland, “Noninvasive measurement of corneal topography,” IEEE Eng. Med. Biol. Mag. 42, 30–42 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

A. Ivanoff, “About the spherical aberration of the eye,” J. Opt. Soc. Am. 46, 901–904 (1956).
[CrossRef] [PubMed]

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 11, 1508–1518 (1977).
[CrossRef]

J. Opt. Soc. Am. A (2)

Ophthalmic Physiol. Opt. (1)

G. Walsh, “The effect of mydriasis on pupillary centration of the human eye,” Ophthalmic Physiol. Opt. 8, 178–182 (1988).
[CrossRef]

Ophthalmology (1)

M. Pande, J. S. Hillman, “Optical zone centration in keratorefractive surgery,” Ophthalmology 100, 1230–1237 (1993).
[CrossRef] [PubMed]

Optom. Vision Sci. (1)

M. A. Wilson, M. C. W. Campbell, P. Simonet, “Change of pupil centration with change of illumination and pupil size,” Optom. Vision Sci. 69, 129–136 (1992).
[CrossRef]

Vision Res. (3)

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

J. Gorrand, F. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

C. W. M. Campbell, E. M. Harrison, P. Simonet, “Psychological measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Other (4)

C. Cui, The Misalignment of Ocular Components and Ocular Monochromatic Aberrations, Ph.D. dissertation (University of Waterloo, Waterloo, Ontario, Canada, 1998).

A. G. Bennet, R. B. Rabbetts, Clinical Visual Optics, (Butterworth, Toronto, 1984).

W. N. Charman, “Optics of the human eye,” in Visual Optics and Instrumentation (CRC, Boca Raton, Fla., 1991).

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed. (Macmillan, London, 1991), pp. 280–309.

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Figures (13)

Fig. 1
Fig. 1

Stiles–Crawford apodization effect and the effective center of the pupil.

Fig. 2
Fig. 2

Principal points of a Gullstrand–Emsley eye model (relaxed). P and P are the first and the secondary principal points of the model eye, respectively; N and N are the first and the secondary nodal points of the model eye, respectively. The distance between the center of curvature of the anterior surface of the cornea and the first nodal point N is 0.74 mm.

Fig. 3
Fig. 3

2D Maxwellian-view ocular wave-front aberration measurement system. PS’s light sources; MCF, color filter wheel; BS’s, beam splitters; M’s flat mirrors; PH, pinhole; MS’s, motorized optical stages; L’s, lens; MD, motion control driver; LS, light shutter; NF, neutral-density wheel wedge; DG’s, ground glasses; T’s, cross targets; CS, center of rotation of the camera mount system; LED, three infrared light-emitting diodes; CC, video CCD camera; JC, motion-controlling joystick; S, subject; HS, head mount system; VS, video screen; and COM, host computer. The solid lines represent the optical axis of the system; the dashed lines represent the controlling linkages.

Fig. 4
Fig. 4

Picture of the pupil showing the typical relationship between the GCP and the CSCR.

Fig. 5
Fig. 5

(a) Contour plot and (b) three-dimensional (3D) plot of the wave-front aberration of subject 1.

Fig. 6
Fig. 6

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 2.

Fig. 7
Fig. 7

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 3.

Fig. 8
Fig. 8

Plots of data for subject 4 measured in session 1. (a) is the contour plot with the contour interval of 1 λ; (b) is the 3D wave-front aberration plot (in μm) with positive aberrations going into the eye. In the pupil coordinate system, positive denotes the temporal side in the horizontal meridian and the superior section in the vertical meridian.

Fig. 9
Fig. 9

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 4 measured in session 2.

Fig. 10
Fig. 10

Contour plot and (b) 3D plot of the wave-front aberration of subject 1, measured with the pupil center as the reference.

Fig. 11
Fig. 11

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 2, with the pupil center as the reference.

Fig. 12
Fig. 12

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 3, with the pupil center as the reference.

Fig. 13
Fig. 13

(a) Contour plot and (b) 3D plot of the wave-front aberration of subject 1, with the pupil center as the reference.

Tables (2)

Tables Icon

Table 1 New Coefficients of the Taylor Polynomial up to the Sixth Order after a Reference Shift from (0, 0) to (Δx, Δy)

Tables Icon

Table 2 Pupil Decentrations from the CSCR of the Left Eyes of Three Subjects

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

W(x, y)=i=1IaiZi(x, y),
W(x, y)=i=1IaiZi(x+Δx, y+Δy).
W(x, y)=i=1Ibi(Δx, Δy)Zi(x, y),

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