Abstract

We have extended the method of Alvarez [J. Am. Optom. Assoc. 49, 24 (1978)] to generate a variable magnitude of third-order spherical and/or coma aberration by using a combination of fourth-order plates with a magnification system. The technique, based on the crossed-cylinder aberroscope, is used to measure the wave-front aberration generated by the plates. The method has been applied to correct the third-order spherical aberration generated by an artificial eye as well as the coma produced by a progressive addition ophthalmic lens. The simplicity of the method and its relatively low cost make it attractive for partial correction of the aberrations of the eye.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. L. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978).
    [PubMed]
  14. R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Ophthalmol. Soc. UK 27, 94–99 (1925–1926).
  15. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley-Interscience, New York, 1991).
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    [CrossRef] [PubMed]
  17. B. Howland, “Use of crossed cylinder lens in photographic lens evaluation,” Appl. Opt. 7, 1587–1599 (1968).
    [CrossRef] [PubMed]
  18. B. Bourdoncle, J. P. Chauveau, J. L. Mercier, “Traps in displaying optical performances of a progressive-addition lens,” Appl. Opt. 31, 3586–3593 (1992).
    [CrossRef] [PubMed]
  19. B. Howland, H. C. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1976).
    [CrossRef] [PubMed]
  20. G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, UK, 1997).

1998 (1)

1997 (3)

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

M. J. Collins, A. S. Goode, D. A. Atchison, “Accommodation and spherical aberration,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S1013 (1997).

1994 (1)

1992 (1)

1991 (1)

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vision Sci. 68, 608–616 (1991).
[CrossRef]

1987 (1)

1984 (1)

1978 (2)

L. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978).
[PubMed]

H. D. Crane, C. M. Steele, “Accurate three-dimensional eyetracker,” Appl. Opt. 17, 691–705 (1978).
[CrossRef] [PubMed]

1977 (1)

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

1976 (1)

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

1975 (1)

1968 (1)

1960 (1)

Aggarwala, K.

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Alvarez, L.

L. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978).
[PubMed]

Artal, P.

Atchison, D. A.

M. J. Collins, A. S. Goode, D. A. Atchison, “Accommodation and spherical aberration,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S1013 (1997).

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, UK, 1997).

Bescós, J.

Bille, J. F.

Bourdoncle, B.

Bradley, A.

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vision Sci. 68, 608–616 (1991).
[CrossRef]

Buchroeder, R. A.

Charman, W. N.

Chauveau, J. P.

Collins, M. J.

M. J. Collins, A. S. Goode, D. A. Atchison, “Accommodation and spherical aberration,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S1013 (1997).

Crane, H. D.

Fridge, D. L.

Goelz, S.

Goode, A. S.

M. J. Collins, A. S. Goode, D. A. Atchison, “Accommodation and spherical aberration,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S1013 (1997).

Grimm, B.

Hooker, R. B.

Howland, B.

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

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

B. Howland, “Use of crossed cylinder lens in photographic lens evaluation,” Appl. Opt. 7, 1587–1599 (1968).
[CrossRef] [PubMed]

Howland, H. C.

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. A 67, 1508–1518 (1977).
[CrossRef]

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

Katz, M.

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Kingslake, R.

R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Ophthalmol. Soc. UK 27, 94–99 (1925–1926).

Kruger, P. B.

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Liang, J.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley-Interscience, New York, 1991).

Mathews, S.

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Mercier, J. L.

Miller, D. T.

Nowbotsing, S.

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Prieto, P. M.

Santamari´a, J.

Smith, G.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, UK, 1997).

Steele, C. M.

Thibos, L. N.

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vision Sci. 68, 608–616 (1991).
[CrossRef]

Vargas-Marti´n, F.

Walsh, G.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986).

Williams, D. R.

Zhang, X.

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vision Sci. 68, 608–616 (1991).
[CrossRef]

Appl. Opt. (4)

Invest. Ophthalmol. Visual Sci. Suppl. (1)

M. J. Collins, A. S. Goode, D. A. Atchison, “Accommodation and spherical aberration,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S1013 (1997).

J. Am. Optom. Assoc. (1)

L. Alvarez, “Development of variable-focus lenses and a new refractor,” J. Am. Optom. Assoc. 49, 24–29 (1978).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Optom. Vision Sci. (1)

A. Bradley, X. Zhang, L. N. Thibos, “Achromatizing the human eye,” Optom. Vision Sci. 68, 608–616 (1991).
[CrossRef]

Science (1)

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

Trans. Ophthalmol. Soc. UK (1)

R. Kingslake, “The interferometer patterns due to the primary aberrations,” Trans. Ophthalmol. Soc. UK 27, 94–99 (1925–1926).

Vision Res. (1)

P. B. Kruger, S. Mathews, M. Katz, K. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Other (3)

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1986).

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley-Interscience, New York, 1991).

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, Cambridge, UK, 1997).

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Figures (11)

Fig. 1
Fig. 1

Schematic views of the generation of a variable amount of third-order spherical and coma aberrations by use of a magnification system between two plates that are displaced with respect to the optical axis. The wave front generated by the first plate is magnified and projected onto the second plate.

Fig. 2
Fig. 2

Schematic view of the setup. L, He–Ne laser (632.8 nm); NF, neutral-density filter; SF, spatial filter (consisting of a microscope objective and a pinhole); CO, collimator; M, mirror; S, iris stop; A, aberroscope; P1 and P2, plates; C, CCD camera.

Fig. 3
Fig. 3

Grid image recorded with a crossed-cylinder aberroscope of a negative third-order spherical aberration generated by a plate of K=-0.260×10-4. The PSF generated by the aberration is represented in the upper right-hand corner of the image.

Fig. 4
Fig. 4

Grid image recorded with a crossed-cylinder aberroscope of a negative horizontal (along the X axis) coma aberration generated by a combination of two plates with K1=-K2=-0.260×10-4 separated by a distance of 1 mm. The PSF generated by the aberration is represented in the upper right-hand corner of the image.

Fig. 5
Fig. 5

Schematic view of the setup used to measure and correct the spherical aberration of an artificial eye. L, He–Ne laser (632.8 nm); NF, neutral-density filter; SF, spatial filter; CO, collimator; M, mirror; S, iris stop; A, aberroscope; MS, magnification system (M=1); BS, beam splitter; P, plate; TL, trial lens; PS, positioners; LT, light trapper; C, CCD camera.

Fig. 6
Fig. 6

Aberroscopic images recorded on an artificial eye (a) before and (b) after correction of the third-order spherical aberration by use of a plate with K=-0.260×10-4.

Fig. 7
Fig. 7

Reconstruction of the wave-front error with the third- and fourth-order Taylor coefficients (GO) obtained from the aberroscopic images of Fig. 5(a) before and (b) after correction of the third- and fourth-order spherical aberration.

Fig. 8
Fig. 8

Aberroscopic image of a progressive lens (OD, 0 D; ADD, +2 D). The field represented is 19.7 mm and is centered in the midpoint between far and near vision (see Fig. 9). The image recorded has been rotated and flipped for clarity. Note the orthogonality of the grid in the upper portion and the distortion (owing to defocus, astigmatism, and coma) in the lower portion.

Fig. 9
Fig. 9

Precise location on the progressive lens (OD, 0 D; ADD, +2 D) of the zones analyzed by the aberroscopic technique. The gray circle corresponds to the zone presented in Fig. 8. The black circle corresponds to the zones presented in Figs. 10(a) and 10(c). The small and large open circles represent the centers for far and near vision, respectively.

Fig. 10
Fig. 10

Aberroscopic images recorded for a progressive ophthalmic lens (a) before correction of the third-order coma aberration, (b) with correction generated by the plates, and (c) after correction.

Fig. 11
Fig. 11

Reconstruction of the wave-front error (a) before and (b) after correction of third-order coma aberration by use of the third- and fourth-order Taylor coefficients obtained from the aberroscopic images of Figs. 10(a) and 10(c), respectively.

Tables (1)

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Table 1 Measurements and Calculations of Third-Order Spherical and Coma Aberrations of Wave Platesa

Equations (13)

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W(x, y)=1000(n-1){K1[x4+(y+h1)4+2x2(y+h1)2]+K2[x4+(y+h2)4+2x2(y+h2)2]},
W(x, y)=1000(n-1){[K1+K2](x2+y2)2+[4(K1h1+K2h2)]y(x2+y2)+[2(K1h12+K2h22)](x2+3y2)+[4(K1h13+K2h23)]y+(h14+h24)},
W(x, y)=z0+z2y+z4(2x2+2y2-1)+z5(y2-x2)+z8(3x2y+3y3-2y)+z12(6x4+6y4+12x2y2-6x2-6y2+1),
z0=A[(K1h14+K2h24)+2(K1h12+K2h22)r2+1/3(K1+K2)r4](piston),z2=4A[2/3(K1h1+K2h2)r3+(K1h13+K2h23)r](tilt),z4=A[2(K1h12+K2h22)r2+1/2(K1+K2)r4](defocus),z5=2A(K1h12+K2h22)r2(astigmatism),z8=(4A/3)(K1h1+K2h2)r3(third-order coma),z12=(A/6)(K1+K2)r4(third-order spherical),
K1/K2=-(h2/h1)2,
z12=A/6K1(r/M)4.
G=I=-3G+I4,H=J=-3J+H4,
h=r40.
h=r(120)1/4.
W(x, y)=1000(n-1){[(1/M4)K1+K2](x2+y2)2+[(4/M3)K1h1+K2h2]y(x2+y2)+[(2/M2)K1h12+K2h22](x2+3y2)+[(4/M)K1h13+K2h23]y+[(M4)h14+h24]}.
M=(h1/h2)(-K1/K2)1/2.
M=AK16S+AK11/4,h1=3CM34AK1(1+M2),
h2=-3CM24AK1(1+M2).

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