Abstract

Simulations of the optics of the Howland crossed-cylinder aberroscope technique show that errors in alignment, data collection, and analysis can lead to unexpected asymmetries of the determined aberrations in a rotationally symmetric system. In particular, coma can be incorrectly indicated. The magnitude of the error in aberration measurement depends on the magnitude of the alignment, data collection, and alignment errors. These findings indicate that the tolerances for setting up the technique and data collection should be analyzed thoroughly before quantitative significance is given to the determined aberration coefficients.

© 1998 Optical Society of America

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References

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  1. B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1976).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  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. 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. J. Collins, C. F. Wildsoet, D. A. Atchison, “Monochromatic aberrations and myopia,” Vision Res. 35, 1157–1163 (1995).
    [CrossRef] [PubMed]
  7. G. Walsh, M. J. Cox, “A new computerized video-aberroscope for the determination of the aberrations of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1985).
    [CrossRef]
  8. 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]
  9. Please contact George Smith by e-mail at G.Smith@optometry.unimelb.edu.au for copies of the programs referred to in this paper.
  10. G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, 1997), pp. 636, 677, and 681.
  11. R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
    [PubMed]
  12. C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).
  13. This does not necessarily mean that the coma error is greater than the spherical aberration. The coma coefficient gives the error at the edge of a 1-mm-radius pupil. If the pupil radius is ρ, the level of coma error at the edge of the pupil is the value of the coma coefficient multiplied by ρ3, while the level of spherical aberration is the value of the spherical aberration coefficient multiplied by ρ4.

1998

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

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

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]

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

1985

G. Walsh, M. J. Cox, “A new computerized video-aberroscope for the determination of the aberrations of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1985).
[CrossRef]

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.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[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]

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

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]

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

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, 1997), pp. 636, 677, and 681.

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]

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

Cottingham, A. J.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Cox, M. J.

G. Walsh, M. J. Cox, “A new computerized video-aberroscope for the determination of the aberrations of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1985).
[CrossRef]

Howland, B.

Howland, H. C.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[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, 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. 67, 1508–1518 (1977).
[CrossRef] [PubMed]

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

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

Klyce, S. D.

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

Marti´nez, C. E.

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

McDonald, M. B.

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

Medina, J. P.

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

Sharp, R. P.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

Smith, G.

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. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, 1997), pp. 636, 677, and 681.

Walsh, G.

G. Walsh, M. J. Cox, “A new computerized video-aberroscope for the determination of the aberrations of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1985).
[CrossRef]

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 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 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]

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

Yee, R. W.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Refract. Surg.

R. A. Applegate, H. C. Howland, R. P. Sharp, A. J. Cottingham, R. W. Yee, “Corneal aberrations, visual performance and refractive surgery,” J. Refract. Surg. 14, 397–407 (1998).
[PubMed]

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. Walsh, M. J. Cox, “A new computerized video-aberroscope for the determination of the aberrations of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1985).
[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]

Science

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

Vision Res.

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]

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

Other

C. E. Martı́nez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, H. C. Howland, “Effect of pupil dilation on corneal optical aberrations after photorefractive keratectomy,” Arch. Opththalmol. (Chicago) (to be published).

This does not necessarily mean that the coma error is greater than the spherical aberration. The coma coefficient gives the error at the edge of a 1-mm-radius pupil. If the pupil radius is ρ, the level of coma error at the edge of the pupil is the value of the coma coefficient multiplied by ρ3, while the level of spherical aberration is the value of the spherical aberration coefficient multiplied by ρ4.

Please contact George Smith by e-mail at G.Smith@optometry.unimelb.edu.au for copies of the programs referred to in this paper.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, 1997), pp. 636, 677, and 681.

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Figures (3)

Fig. 1
Fig. 1

Sample of an aberrated retinal grid pattern generated by trace.pas.

Fig. 2
Fig. 2

Effect of vertex distance on the expected values (crossed-cylinder–eye system) of aberration coefficients for undistorted and predistorted grids. The vertex distance is measured to the front vertex of the eye and not to the entrance pupil, which is 3.0 mm farther inside the eye. (a) W3 and W5, (b) W4, (c) W10 and W14, (d) W11 and W13, (e) W12.

Fig. 3
Fig. 3

Estimates of the “unaberrated” grid side length, which are used to calculate the aberrations.

Tables (8)

Tables Icon

Table 1 Important Symbols Used in Equations

Tables Icon

Table 2 Modified Le Grand Schematic Eye (59.940 D) with a 5-D Crossed Cylinder (in mm)

Tables Icon

Table 3 Wave and Transverse Aberrations at Different Ray Heights from fap.pas, for the Eye Data Given in Table 2

Tables Icon

Table 4 Values of the Coefficients of Eqs. (4)

Tables Icon

Table 5 Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Setupa

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Table 6 Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa

Tables Icon

Table 7 Effect of Uncertainty on Reading the Grid Points, Assuming That the Uncertainty on Each Grid Point Is Defined by a Uniform Probability Distribution with Extreme Values Being 1/10 the Width of a Grid Elementa

Tables Icon

Table 8 Comparison of the Expected and Centered Crossed-Cylinder Aberration Coefficient Values and Actual Values for Various Sources of Error in the Data Collection and Analysisa

Equations (32)

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+higher-orderterms,
δξ-1FeW(X, Y)X,δη-1FeW(X, Y)Y,
-δξFe=W1+2W3X+W4Y+3W6X2+2W7XY+W8Y2+4W10X3+3W11X2Y+2W12XY2+W13Y3,
-δηFe=W2+W4X+2W5Y+W7X2+2W8XY+3W9Y2+W11X3+2W12X2Y+3W13XY2+4W14Y3.
W(Y)=W4,0Y4+higher-orderterms
(W6,0Y6+W8,0Y8+).
-δηFe=dW(Y)/dY=4W4,0Y3+higher-orderterms
(6W6,0Y5+8W8,0Y7+).
W10=W14=0.5W12=W4,0.
W11=W13=0.
W10=W14=0.024701 µm/mm4,
W12=0.048142 µm/mm4.
W3=W4=W5=W6=W7=W8=W9=0.
X=K(Fc/Fe)Yg,
Y=K(Fc/Fe)Xg,
X=Xg+dKFcYg,
Y=Yg+dKFcXg,
Xg=(dKFcY-X)[(dKFc)2-1],
Yg=(dKFcX-Y)[(dKFc)2-1].
X=KFcFe(dKFcX-Y)[(dKFc)2-1],
Y=KFcFe(dKFcY-X)[(dKFc)2-1].
KFcFe(dKFcX-Y)[(dKFc)2-1]=-1FeX[W3X2+W4XY+W5Y2],
KFcFe(dKFcY-X)[(dKFc)2-1]=-1FeY[W3X2+W4XY+W5Y2].
W4=-KFc[1-(dKFc)2],
W3=W5=d(KFc)22[1-(dKFc)2].
W10X4+W11X3(Y-Y0)+W12X2(Y-Y0)2+W13X(Y-Y0)3+W14(Y-Y0)4.
-W11Y0X3,-W122Y0X2Y,-W133Y0XY2,-W144Y0Y3,
W6X3,W7X2Y,W8XY2,W9Y3,
W6=-W11Y0,W7=-W122Y0,
W8=-W133Y0,W9=-W144Y0.
ΔW3=ΔW5=δF2=F2δl2n.
ΔW3=ΔW50.0013446δl,

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