Abstract

Local wavefront distortion by the total refractive system of the eye is measured by a variant of the Scheiner principle at some thirty loci of 1 mm diameter. At each locus we find the normal to the wavefront that could form a point focus. A simple visual display is used to review the data, and a steepest descents fit of the wavefronts with a power series enables comparison with more traditional measures of refractive error.

© 1992 Optical Society of America

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References

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  1. D. L. Guyton, “Automated Clinical Refraction” in Clinical Ophthalmology” T. D. Duane, ed. (Harper & Rowe, Hagerstown, Md., 1978), Vol. 1, Chap. 67, p.1.
  2. A. Ivanoff, “About the spherical aberration of the eye,” J. Opt. Soc. Am. 46, 901–903 (1953); A. Ivanoff, “Les aberrations de l’oeil,” Rev. Opt. (Paris) 26, 145–171 (1947); Ann. Opt. Ocul. 2, 97–104 (1953); M. J. Koomen, R. Skolnik, R. Tousey, “Spherical abberation of the eye and the choice of axis,” J. Opt. Soc. Am. 46, 903–904 (1956); A. Smirnov, “Measurement of the wave aberration of the human eye,” Biophysics 6, 766–795 (1962). G. Westheimer, “Spherical aberration of the eye,” Opt. Acta 2, 151–152 (1955).
    [CrossRef] [PubMed]
  3. S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).
  4. A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 28: 804–808 (1989).
    [CrossRef] [PubMed]
  5. R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]
  6. L. N. Thibos, “Optical limitations of the Maxwellian view interferometer,” Appl. Opt. 29, 1411–1419 (1990).
    [CrossRef] [PubMed]
  7. Fourward Technologies, Suite 140, 9932 Prospect Avenue, Santee, Calif. 92071.

1990 (1)

1989 (1)

1988 (1)

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

1983 (1)

S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).

1953 (1)

Adams, C.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Applegate, R. A.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Bille, J. F.

Braren, B.

S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).

Dreher, A. W.

Guyton, D. L.

D. L. Guyton, “Automated Clinical Refraction” in Clinical Ophthalmology” T. D. Duane, ed. (Harper & Rowe, Hagerstown, Md., 1978), Vol. 1, Chap. 67, p.1.

Howland, H. C.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Ivanoff, A.

Johnson, C. A.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Mannis, M. J.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Srinivasan, R.

S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).

Thibos, L. N.

Trokel, S. L.

S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).

Weinreb, R. N.

Zadnik, K.

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

Am. J. Ophthal. (1)

S. L. Trokel, R. Srinivasan, B. Braren, “Excimer laser surgery of the cornea,” Am. J. Ophthal. 97, 710–715 (1983); K. P. Thompson, K. D. Hanna, G. O. Waring, “Emerging technologies for refractive surgery: laser adjustable synthetic epikeratoplasty,” Rev. Corneal Surg. 5, 46–48 (1989).

Appl. Opt. (2)

Invest. Ophthalmol. Vis. Sci. (1)

R. A. Applegate, C. A. Johnson, H. C. Howland, M. J. Mannis, K. Zadnik, C. Adams, “Optical aberrations of the eye following radial keratotomy—initial results,” Invest. Ophthalmol. Vis. Sci. 29: 280 (1988); W. Charman, “Diffraction and the precision of measurement of corneal and other small radii,” Am. J. Optom. Arch. Am. Acad. Optom. 49, 672–680 (1972); W. Charman, G. Walsh, “Variations in the local refractive correction of the eye across its entrance pupil,” Optom. Vision Sci. 66, 34–40 (1989); B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1975). H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations of best focus for small artificial pupils,” Vision Res. 29, 979–983 (1989); 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); G. Walsh, W. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthal. Phys. Opt. 5, 23–31 (1985); G. Walsh, W. 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]

J. Opt. Soc. Am. (1)

Other (2)

Fourward Technologies, Suite 140, 9932 Prospect Avenue, Santee, Calif. 92071.

D. L. Guyton, “Automated Clinical Refraction” in Clinical Ophthalmology” T. D. Duane, ed. (Harper & Rowe, Hagerstown, Md., 1978), Vol. 1, Chap. 67, p.1.

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Figures (11)

Fig. 1
Fig. 1

Scheiner’s demonstration that refractive error results in two images of a distant star.

Fig. 2
Fig. 2

The two images can be made to coincide by changing the angle of the test beam at the cornea.

Fig. 3
Fig. 3

Only a slight (predictable) position error results from considering the cornea a plane.

Fig. 4
Fig. 4

The angles measured are u and v. Those used in calculations are γ and ϕ for the vector display, or α, β and γ for the wavefront fitting.

Fig. 5
Fig. 5

The instrument layout, described in the text.

Fig. 6
Fig. 6

A demonstration of the way the gimballed mirror changes the direction of the beam at the cornea, without changing its position. This figure has a different scale in the vertical and horizontal directions.

Fig. 7
Fig. 7

The appearance of the alignicator, on and off axis.

Fig. 8
Fig. 8

The vector display of data from a myopic and astigmatic eye.

Fig. 9
Fig. 9

The central data in vector display from a nearly emmetropic eye. The locations are shown closer than the actual separation of Fig. 8.

Fig. 10
Fig. 10

The wavefront from a quartic fit to eye HD, exhibiting over 7 diopters of myopia and nearly 3 diopters of astigmatism in the opposite sense.

Fig. 11
Fig. 11

The same wavefront as that of Fig. 11, with the sphere (myopia) and cylinder removed. This remnant is the part not correctable by spectacles.

Tables (2)

Tables Icon

Table I Correction Parameter’s Sphere, Cylinder, and Angle for BD as a Function of the Selected Fit Diametera

Tables Icon

Table II Repeated Measurements Over 3 Pupil Diameters for 4 Eyes

Equations (11)

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F ( x , y , z ) = 0.
F ( x , y , z ) = z - m = 0 Q n = 0 m C m , n x m - n y n .
n ( x , y ) = F / F ,
F = i [ - C 1 , 0 - C 2 , 1 y - 2 C 2 , 0 x ] + j [ - C 1 , 1 - C 2 , 1 x - 2 C 2 , 2 y ] + k ,
n ( x , y ) = i [ - C 2 , 1 y - C 2 , 0 x - 2 C 2 , 0 x ] + j [ - C 2 , 1 - 2 C 2 , 2 y ] + k ,
n ( x , y ) = i cos α + j cos β + k cos γ .
n m ( x , y ) = i sin u + sin v cos u + k cos v cos u .
n m ( x , y ) i u ( x , y ) + j v ( x , y ) = k ,
tan 2 Θ = C 2 , 1 / ( C 2 , 0 - C 2 , 2 ) ,
1 / R c = 2 C 2 , 1 / sin 2 Θ ,
1 / R s = - ( 2 C 2 , 0 + 2 C 2 , 2 + 1 / 2 R c ) ,

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