Abstract

We replicated results of the theoretical accuracy of the Howland crossed-cylinder aberroscope for measuring the monochromatic aberration of the human eye [J. Opt. Soc. Am. A 15, 24771998]. Two simple modifications to the previous mathematical analysis techniques, namely, the use of a new method for estimating the size of the unaberrated retinal grid element length and the correction of the aberroscope grid spacing size for magnification differences introduced during predistortion, almost completely eliminate the errors introduced into 4th-order wave-front-aberration coefficients for a centered predistorted aberroscope grid over a large range of back vertex distances. The use of the crossed cylinders in the aberroscope introduces only small amounts of wave-front aberration to the measurements of the schematic eye. Wave-front aberrations above the 4th order in a Taylor polynomial expression can introduce errors that vary as a function of pupil area. Results produced by orthogonal polynomial analysis confirm the least-squares analysis results. We believe that the Howland crossed-cylinder aberroscope can be used in its objective form to make accurate measurements of at least the 4th-order components of the wave-front aberration of the human eye. We note that care must be exercised both in the use of the equipment and in the analysis of the results to ensure that accuracy is maintained.

© 1999 Optical Society of America

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References

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  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. B. Howland, H. C. Howland, “Subjective measurement of high order aberrations of the eye,” Science 193, 580–582 (1976).
    [CrossRef] [PubMed]
  3. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of the monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  4. G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthalmic Physiol. Opt. 5, 23–31 (1985).
    [CrossRef] [PubMed]
  5. M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
    [CrossRef] [PubMed]
  6. D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
    [CrossRef] [PubMed]
  7. G. Walsh, M. J. Cox, “A new computerised video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
    [CrossRef] [PubMed]
  8. G. Smith, R. A. Applegate, H. C. Howland, “Assessment of the accuracy of the crossed-cylinder aberroscope technique,” J. Opt. Soc. Am. A 15, 2477–2487 (1998).
    [CrossRef]
  9. G. Smith, R. A. Applegate, H. C. Howland, “The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations,” Ophthalmic Physiol. Opt. 16, 222–229 (1996).
    [CrossRef] [PubMed]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.
  11. M. J. Cox, G. Walsh, “Reliability and validity studies of a new computer-assisted crossed-cylinder aberroscope,” Optom. Vision Sci. 74, 570–580 (1997).
    [CrossRef]

1998

1997

M. J. Cox, G. Walsh, “Reliability and validity studies of a new computer-assisted crossed-cylinder aberroscope,” Optom. Vision Sci. 74, 570–580 (1997).
[CrossRef]

1996

G. Smith, R. A. Applegate, H. C. Howland, “The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations,” Ophthalmic Physiol. Opt. 16, 222–229 (1996).
[CrossRef] [PubMed]

1995

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

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

G. Walsh, M. J. Cox, “A new computerised video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

1985

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthalmic Physiol. Opt. 5, 23–31 (1985).
[CrossRef] [PubMed]

1984

1977

1976

B. Howland, H. C. Howland, “Subjective measurement of high order aberrations of the eye,” Science 193, 580–582 (1976).
[CrossRef] [PubMed]

Applegate, R. A.

G. Smith, R. A. Applegate, H. C. Howland, “Assessment of the accuracy of the crossed-cylinder aberroscope technique,” J. Opt. Soc. Am. A 15, 2477–2487 (1998).
[CrossRef]

G. Smith, R. A. Applegate, H. C. Howland, “The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations,” Ophthalmic Physiol. Opt. 16, 222–229 (1996).
[CrossRef] [PubMed]

Atchison, D. A.

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

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

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 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 function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

Cox, M. J.

M. J. Cox, G. Walsh, “Reliability and validity studies of a new computer-assisted crossed-cylinder aberroscope,” Optom. Vision Sci. 74, 570–580 (1997).
[CrossRef]

G. Walsh, M. J. Cox, “A new computerised video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.

Howland, B.

Howland, H. C.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.

Smith, G.

G. Smith, R. A. Applegate, H. C. Howland, “Assessment of the accuracy of the crossed-cylinder aberroscope technique,” J. Opt. Soc. Am. A 15, 2477–2487 (1998).
[CrossRef]

G. Smith, R. A. Applegate, H. C. Howland, “The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations,” Ophthalmic Physiol. Opt. 16, 222–229 (1996).
[CrossRef] [PubMed]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.

Walsh, G.

M. J. Cox, G. Walsh, “Reliability and validity studies of a new computer-assisted crossed-cylinder aberroscope,” Optom. Vision Sci. 74, 570–580 (1997).
[CrossRef]

G. Walsh, M. J. Cox, “A new computerised video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthalmic Physiol. Opt. 5, 23–31 (1985).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of the monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

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 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 function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthalmic Physiol. Opt.

G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthalmic Physiol. Opt. 5, 23–31 (1985).
[CrossRef] [PubMed]

G. Smith, R. A. Applegate, H. C. Howland, “The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations,” Ophthalmic Physiol. Opt. 16, 222–229 (1996).
[CrossRef] [PubMed]

G. Walsh, M. J. Cox, “A new computerised video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

Optom. Vision Sci.

M. J. Cox, G. Walsh, “Reliability and validity studies of a new computer-assisted crossed-cylinder aberroscope,” Optom. Vision Sci. 74, 570–580 (1997).
[CrossRef]

Science

B. Howland, H. C. Howland, “Subjective measurement of high order aberrations of the eye,” Science 193, 580–582 (1976).
[CrossRef] [PubMed]

Vision Res.

M. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
[CrossRef] [PubMed]

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

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 43–49.

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Figures (15)

Fig. 1
Fig. 1

Predistorted crossed-cylinder aberroscope grid as imaged on the retina. The horizontal and vertical offsets that combine to produce the measured retinal grid element length by using Smith’s original method9 are shown.

Fig. 2
Fig. 2

Expected (dashed line) and measured (solid curves) values of wave-front-aberration coefficients w3 and w5 for a rotationally symmetric schematic eye measured with a crossed-cylinder aberroscope and use of predistorted (squares) and undistorted (circles) aberroscope grids, as a function of vertex distance. Measurements were made with the original least-squares technique of Smith and colleagues.9

Fig. 3
Fig. 3

Same as Fig. 2 but for wave-front-aberration coefficient w4.

Fig. 4
Fig. 4

Same as Fig. 2 but for wave-front-aberration coefficients w10 and w14.

Fig. 5
Fig. 5

Same as Fig. 2 but for wave-front-aberration coefficients w11 and w13.

Fig. 6
Fig. 6

Same as Fig. 2 but for wave-front-aberration coefficient w12.

Fig. 7
Fig. 7

Expected (dashed line) and measured (solid curves) retinal grid size length for a rotationally symmetric schematic eye measured with a crossed-cylinder aberroscope and use of predistorted (squares) and undistorted (circles) aberroscope grids, as a function of vertex distance. Measurements were made with the original least-squares technique of Smith and colleagues.9

Fig. 8
Fig. 8

Expected (dashed line) and measured (solid curve) values of wave-front-aberration coefficients w3 and w5 for a rotationally symmetric schematic eye measured with a crossed-cylinder aberroscope, as a function of vertex distance. A predistorted aberroscope grid with a corrected least-squares analysis technique (squares) and an orthogonal polynomial analysis technique (circles) was used.

Fig. 9
Fig. 9

Same as Fig. 8 but for wave-front-aberration coefficient w4.

Fig. 10
Fig. 10

Same as Fig. 8 but for wave-front-aberration coefficients w10 and w14.

Fig. 11
Fig. 11

Same as Fig. 8 but for wave-front-aberration coefficients w11 and w13.

Fig. 12
Fig. 12

Same as Fig. 8 but for wave-front-aberration coefficient w12.

Fig. 13
Fig. 13

Expected (dashed line) and measured values (solid curve with squares) of wave-front-aberration coefficients w10 and w14 for a rotationally symmetric schematic eye measured with a crossed-cylinder aberroscope but with the crossed cylinder removed. A predistorted aberroscope grid suitable for the vertex distance indicated was used together with a least-squares analysis technique.

Fig. 14
Fig. 14

Same as Fig. 13 but for wave-front-aberration coefficients w11 and w13.

Fig. 15
Fig. 15

Same as Fig. 13 but for wave-front-aberration coefficient w12.

Tables (1)

Tables Icon

Table 1 Results of Fitting, with Selected Coefficients, a One-Dimensional Taylor Polynomial to the Transverse Aberrations along a Radius of a Rotationally Symmetric Schematic Eye over a Range of Ray Heights from the Optical Axis

Equations (16)

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

W(X, Y)=w1X+w2Y+w3X2+w4XY+w5Y2+w6X3+w7X2Y+w8XY2+w9Y3+w10X4+w11X3Y+w12X2Y2+w13XY3+w14Y4,
W(Y)=W2,0Y2+W4,0Y4.
Xp=Xg+hKFcYg,
Yp=Yg+hKFcXg.
Xg=Xp-hFcYg,
Yg=Yp-hFcXg.
Xg=Xp-hFcYp+h2Fc2Xg,
Yg=Yp-hFcXp+h2Fc2Yg.
Xg=Xp-hFcYp1-h2Fc2,
Yg=Yp-hFcXp1-h2Fc2.
Xg1-Xg2=Xp1-hFcYp1-Xp2+hFcYp21-h2Fc2.
Yp1=Yp2.
ΔXg=ΔXp1-h2Fc2.
ΔYg=ΔYp1-h2Fc2.
Xr=FcFs Yg,
Yr=FcFs Xg,

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