Abstract

Toroidal, spherocylindrical, ellipsoidal, and combined surfaces were used to correct astigmatism in aspheric spectacle lenses, and the differences among the proposed techniques were compared. Four astigmatic spectacle lenses were designed with the same optical parameters. A freeform measuring machine was used to evaluate posterior surfaces of aspheric spectacle lenses, and spherical and cylindrical power maps were generated and compared. The measured data were analyzed via commercial software. The toroidal lens helped to extend the clear vision range around the lens, and the ellipsoidal and spherocylindrical surfaces resulted in a more accurate centering of the lens around the optical axis of the eye, avoided astigmatism, and provided better visual perception.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
  3. V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
    [Crossref]
  4. T.W. Raasch, “Spherocylindrical refractive errors and visual acuity,” Optom. Vis. Sci. 72(4), 272–275 (1995).
    [Crossref]
  5. S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
    [Crossref]
  6. R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
    [Crossref]
  7. S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
    [Crossref]
  8. A. D. Atchison and M. Ankit, “Visual acuity with astigmatic blur,” Optom. Vis. Sci. 88(7), E798–E805 (2011).
    [Crossref]
  9. O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
    [Crossref]
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    [Crossref]
  11. J.P. Foley and C. Campbell, “An optical device with variable astigmatic power,” Optom. Vis. Sci. 76(9), 664–667 (1999).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  25. D. Meister, J. E. Sheedy, and O. D. Sheedy, “Introduction to ophthalmic optics,” SOLA Optical USA, (2000).
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    [Crossref]
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    [Crossref]

2014 (2)

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
[Crossref]

2013 (2)

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

2011 (2)

A. D. Atchison and M. Ankit, “Visual acuity with astigmatic blur,” Optom. Vis. Sci. 88(7), E798–E805 (2011).
[Crossref]

O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
[Crossref]

2010 (1)

2007 (4)

Z. Zalevsky, S. Ben Yaish, O. Yehezkel, and M. Belkin, “Thin spectacles for myopia, presbyopia and astigmatism insensitive vision,” Opt. Express 15(17), 10790–10803 (2007).
[Crossref]

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

S.A. Read, M.J. Collins, and L.G. Carney, “A review of astigmatism and its possible genesis,” Clin. Exp. Optometry 90(1), 5–19 (2007).
[Crossref]

G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007).
[Crossref]

2006 (1)

R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
[Crossref]

2003 (1)

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

1999 (1)

J.P. Foley and C. Campbell, “An optical device with variable astigmatic power,” Optom. Vis. Sci. 76(9), 664–667 (1999).
[Crossref]

1997 (1)

C. Novis, “Astigmatism and the toric intraocular lens and other vertex distance effects,” Surv. Ophthalmol. 42(3), 268–270 (1997).
[Crossref]

1995 (2)

T.W. Raasch, “Spherocylindrical refractive errors and visual acuity,” Optom. Vis. Sci. 72(4), 272–275 (1995).
[Crossref]

D. Malacara-Doblado, D. Malacara-Hernandez, and J. L. Garcia-Marquez, “Toroidal surfaces compared with spherocylindrical surfaces,” Proc. SPIE 2576, 232–235 (1995).
[Crossref]

1992 (2)

W. Rosenblum, D. O’Leary, and W. Blaker, “Computerized Moiré analysis of progressive addition lenses,” Optom. Vis. Sci. 69(12), 936–940 (1992).
[Crossref]

A. D. Atchison, “Spectacle lens design: a review,” Appl. Opt. 31(19), 3579–3585 (1992).
[Crossref]

1989 (1)

C. W. Fowler, “Assessment of toroidal surfaces by the measurement of curvature in three fixed meridians,” Oph. Phys. Optics 9(1), 79–80 (1989).
[Crossref]

Ankit, M.

A. D. Atchison and M. Ankit, “Visual acuity with astigmatic blur,” Optom. Vis. Sci. 88(7), E798–E805 (2011).
[Crossref]

Arne, O.

O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
[Crossref]

Artal, P.

P. Artal, Handbook of Visual Optics, Volume One (Taylor and Francis, 2017).

Atchison, A. D.

A. D. Atchison and M. Ankit, “Visual acuity with astigmatic blur,” Optom. Vis. Sci. 88(7), E798–E805 (2011).
[Crossref]

A. D. Atchison, “Spectacle lens design: a review,” Appl. Opt. 31(19), 3579–3585 (1992).
[Crossref]

Beheregaray, S.

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

Belkin, M.

Ben Yaish, S.

Benjamin, W. C.

H. Jonathan, M. James, and W. C. Benjamin, “Multi-axis lens design for astigmatism,” US9046698 (2015-6-2).

Blaker, W.

W. Rosenblum, D. O’Leary, and W. Blaker, “Computerized Moiré analysis of progressive addition lenses,” Optom. Vis. Sci. 69(12), 936–940 (1992).
[Crossref]

Campbell, C.

J.P. Foley and C. Campbell, “An optical device with variable astigmatic power,” Optom. Vis. Sci. 76(9), 664–667 (1999).
[Crossref]

Carney, L.G.

S.A. Read, M.J. Collins, and L.G. Carney, “A review of astigmatism and its possible genesis,” Clin. Exp. Optometry 90(1), 5–19 (2007).
[Crossref]

Collins, M. J.

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
[Crossref]

Collins, M.J.

S.A. Read, M.J. Collins, and L.G. Carney, “A review of astigmatism and its possible genesis,” Clin. Exp. Optometry 90(1), 5–19 (2007).
[Crossref]

de Gracia, P.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Denis, J.

B. Dominique, C. Pierre, J. Denis, and T. Jean, “Optical lens for correcting astigmatism,” US5016977 (1991-5-21).

Dominique, B.

B. Dominique, C. Pierre, J. Denis, and T. Jean, “Optical lens for correcting astigmatism,” US5016977 (1991-5-21).

Dorronsoro, C.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Evans, C.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Fang, F. Z.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Foley, J.P.

J.P. Foley and C. Campbell, “An optical device with variable astigmatic power,” Optom. Vis. Sci. 76(9), 664–667 (1999).
[Crossref]

Forbes, G. W.

Fowler, C. W.

C. W. Fowler, “Assessment of toroidal surfaces by the measurement of curvature in three fixed meridians,” Oph. Phys. Optics 9(1), 79–80 (1989).
[Crossref]

Frank, S.

O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
[Crossref]

Furlan, W. D.

R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
[Crossref]

Garcia-Marquez, J. L.

D. Malacara-Doblado, D. Malacara-Hernandez, and J. L. Garcia-Marquez, “Toroidal surfaces compared with spherocylindrical surfaces,” Proc. SPIE 2576, 232–235 (1995).
[Crossref]

Geeta, D.

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

Gerhard, F.

F. Gerhard and L. Hans, “Spectacle lens having astigmatic power,” US4613217 (1986-9-23).

Greynolds, A. W.

A. W. Greynolds, “Battle of the Biconics: Comparison and Application of Various Anamorphic Optical Surfaces,” in Imaging and Applied Optics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), FT2B.1.

Hans, L.

F. Gerhard and L. Hans, “Spectacle lens having astigmatic power,” US4613217 (1986-9-23).

Hernández, M.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Hiraoka, T.

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

Howard, S.

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

James, M.

H. Jonathan, M. James, and W. C. Benjamin, “Multi-axis lens design for astigmatism,” US9046698 (2015-6-2).

Jean, T.

B. Dominique, C. Pierre, J. Denis, and T. Jean, “Optical lens for correcting astigmatism,” US5016977 (1991-5-21).

Jonathan, H.

H. Jonathan, M. James, and W. C. Benjamin, “Multi-axis lens design for astigmatism,” US9046698 (2015-6-2).

Juan, T.

O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
[Crossref]

Landgrave, J.

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

Laura, R.

R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
[Crossref]

Laure, E. G.

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

Malacara, Z.

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

Malacara-Doblado, D.

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

D. Malacara-Doblado, D. Malacara-Hernandez, and J. L. Garcia-Marquez, “Toroidal surfaces compared with spherocylindrical surfaces,” Proc. SPIE 2576, 232–235 (1995).
[Crossref]

Malacara-Hernandez, D.

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

D. Malacara-Doblado, D. Malacara-Hernandez, and J. L. Garcia-Marquez, “Toroidal surfaces compared with spherocylindrical surfaces,” Proc. SPIE 2576, 232–235 (1995).
[Crossref]

Marcos, S.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Maria, V.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Marin, G.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Marta, T.

R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
[Crossref]

Meister, D.

D. Meister, J. E. Sheedy, and O. D. Sheedy, “Introduction to ophthalmic optics,” SOLA Optical USA, (2000).

Micah, R.

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

Novis, C.

C. Novis, “Astigmatism and the toric intraocular lens and other vertex distance effects,” Surv. Ophthalmol. 42(3), 268–270 (1997).
[Crossref]

O’Leary, D.

W. Rosenblum, D. O’Leary, and W. Blaker, “Computerized Moiré analysis of progressive addition lenses,” Optom. Vis. Sci. 69(12), 936–940 (1992).
[Crossref]

Oshika, T.

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

Pierre, C.

B. Dominique, C. Pierre, J. Denis, and T. Jean, “Optical lens for correcting astigmatism,” US5016977 (1991-5-21).

Raasch, T.W.

T.W. Raasch, “Spherocylindrical refractive errors and visual acuity,” Optom. Vis. Sci. 72(4), 272–275 (1995).
[Crossref]

Read, S. A.

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
[Crossref]

Read, S.A.

S.A. Read, M.J. Collins, and L.G. Carney, “A review of astigmatism and its possible genesis,” Clin. Exp. Optometry 90(1), 5–19 (2007).
[Crossref]

Rosenblum, W.

W. Rosenblum, D. O’Leary, and W. Blaker, “Computerized Moiré analysis of progressive addition lenses,” Optom. Vis. Sci. 69(12), 936–940 (1992).
[Crossref]

Sawides, L.

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

Sheedy, J. E.

D. Meister, J. E. Sheedy, and O. D. Sheedy, “Introduction to ophthalmic optics,” SOLA Optical USA, (2000).

Sheedy, O. D.

D. Meister, J. E. Sheedy, and O. D. Sheedy, “Introduction to ophthalmic optics,” SOLA Optical USA, (2000).

Vincent, S. J.

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
[Crossref]

Weckenmann, A.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

William, F.

F. William, “Corneal contact lens having inner ellipsoidal surface,” US3227507 (1966-1-4).

Yamamoto, T.

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

Yehezkel, O.

Zaetta, D. M.

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

Zalevsky, Z.

Zhang, G. X.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Zhang, X. D.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Am. J. Ophthalmol. (1)

S. Howard, R. Micah, D. Geeta, E. G. Laure, and D. M. Zaetta, “Myopic astigmatism and presbyopia trial,” Am. J. Ophthalmol. 135(5), 628–632 (2003).
[Crossref]

Appl. Opt. (1)

CIRP Ann. (1)

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Clin. Exp. Optometry (1)

S.A. Read, M.J. Collins, and L.G. Carney, “A review of astigmatism and its possible genesis,” Clin. Exp. Optometry 90(1), 5–19 (2007).
[Crossref]

Jpn. J. Ophthalmol. (1)

T. Yamamoto, T. Hiraoka, S. Beheregaray, and T. Oshika, “Influence of simple myopic against-the-rule and with-the-rule astigmatism on visual acuity in eyes with monofocal intraocular lenses,” Jpn. J. Ophthalmol. 58(5), 409–414 (2014).
[Crossref]

Oph. Phys. Optics (2)

S. A. Read, S. J. Vincent, and M. J. Collins, “The visual and functional impacts of astigmatism and its clinical management,” Oph. Phys. Optics 34(3), 267–294 (2014).
[Crossref]

C. W. Fowler, “Assessment of toroidal surfaces by the measurement of curvature in three fixed meridians,” Oph. Phys. Optics 9(1), 79–80 (1989).
[Crossref]

Opt. Eng. (1)

Z. Malacara, D. Malacara-Doblado, D. Malacara-Hernandez, and J. Landgrave, “Astigmatic optical surfaces, characteristics, testing, and differences between them,” Opt. Eng. 46(12), 123001 (2007).
[Crossref]

Opt. Express (3)

Optom. Vis. Sci. (7)

W. Rosenblum, D. O’Leary, and W. Blaker, “Computerized Moiré analysis of progressive addition lenses,” Optom. Vis. Sci. 69(12), 936–940 (1992).
[Crossref]

R. Laura, T. Marta, and W. D. Furlan, “Visual acuity in simple myopic astigmatism: influence of cylinder axis,” Optom. Vis. Sci. 83(5), 311–315 (2006).
[Crossref]

J.P. Foley and C. Campbell, “An optical device with variable astigmatic power,” Optom. Vis. Sci. 76(9), 664–667 (1999).
[Crossref]

V. Maria, P. de Gracia, C. Dorronsoro, L. Sawides, G. Marin, M. Hernández, and S. Marcos, “Astigmatism impact on visual performance: meridional and adaptational effects,” Optom. Vis. Sci. 90(12), 1430–1442 (2013).
[Crossref]

T.W. Raasch, “Spherocylindrical refractive errors and visual acuity,” Optom. Vis. Sci. 72(4), 272–275 (1995).
[Crossref]

A. D. Atchison and M. Ankit, “Visual acuity with astigmatic blur,” Optom. Vis. Sci. 88(7), E798–E805 (2011).
[Crossref]

O. Arne, T. Juan, and S. Frank, “Visual acuity with simulated and real astigmatic defocus,” Optom. Vis. Sci. 88(5), 562–569 (2011).
[Crossref]

Proc. SPIE (1)

D. Malacara-Doblado, D. Malacara-Hernandez, and J. L. Garcia-Marquez, “Toroidal surfaces compared with spherocylindrical surfaces,” Proc. SPIE 2576, 232–235 (1995).
[Crossref]

Surv. Ophthalmol. (1)

C. Novis, “Astigmatism and the toric intraocular lens and other vertex distance effects,” Surv. Ophthalmol. 42(3), 268–270 (1997).
[Crossref]

Other (7)

A. W. Greynolds, “Battle of the Biconics: Comparison and Application of Various Anamorphic Optical Surfaces,” in Imaging and Applied Optics 2015, OSA Technical Digest (online) (Optical Society of America, 2015), FT2B.1.

D. Meister, J. E. Sheedy, and O. D. Sheedy, “Introduction to ophthalmic optics,” SOLA Optical USA, (2000).

B. Dominique, C. Pierre, J. Denis, and T. Jean, “Optical lens for correcting astigmatism,” US5016977 (1991-5-21).

H. Jonathan, M. James, and W. C. Benjamin, “Multi-axis lens design for astigmatism,” US9046698 (2015-6-2).

F. Gerhard and L. Hans, “Spectacle lens having astigmatic power,” US4613217 (1986-9-23).

P. Artal, Handbook of Visual Optics, Volume One (Taylor and Francis, 2017).

F. William, “Corneal contact lens having inner ellipsoidal surface,” US3227507 (1966-1-4).

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Figures (15)

Fig. 1.
Fig. 1. Coordinate system.
Fig. 2.
Fig. 2. Rotation of the cylindrical lens.
Fig. 3.
Fig. 3. Simulation of sphere (left) and cylinder (right) for a toroidal surface. Sph: spherical power; Add: additional power; Cyl: cylindrical power; Axis: the axis of astigmatism.
Fig. 4.
Fig. 4. Simulation of sphere (left) and cylinder (right) for a spherocylindrical surface.
Fig. 5.
Fig. 5. Simulation of sphere (left) and cylinder (right) for an ellipsoidal surface.
Fig. 6.
Fig. 6. Simulation of sphere (left) and cylinder (right) for a combined surface.
Fig. 7.
Fig. 7. Four different astigmatic lenses: 1. toroidal surface, 2. spherocylindrical surface, 3. ellipsoidal surface, and 4. combined surface.
Fig. 8.
Fig. 8. Mean power measurements of sphere (left) and cylinder (right) of the posterior toroidal surface.
Fig. 9.
Fig. 9. Power measurements of sphere (left) and cylinder (right) of the posterior spherocylindrical surface.
Fig. 10.
Fig. 10. Power measurements of sphere (left) and cylinder (right) of the posterior ellipsoidal surface.
Fig. 11.
Fig. 11. Power measurements of sphere (left) and cylinder (right) of the combined posterior surface.
Fig. 12.
Fig. 12. Contour plots of toroidal lens for average spherical power (left) and cylinder power (right).
Fig. 13.
Fig. 13. Contour plots of spherocylindrical lens for average spherical power (left) and cylinder power (right).
Fig. 14.
Fig. 14. Contour plots of ellipsoidal lens for average spherical power (left) and cylinder power (right).
Fig. 15.
Fig. 15. Contour plots of combined lens for average spherical power (left) and cylinder power (right).

Tables (3)

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Table 1. Optical Parameters of Aspherical Spectacle Lenses Used for Astigmatism Correction (unit: D, 1/m).

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Table 2. Simulation Results of Aspherical Spectacle Lenses Used for Astigmatism Correction (unit: D, 1/m).

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Table 3. Measuring Results of Aspherical Spectacle Lenses Used for Astigmatism Correction (unit: D, 1/m).

Equations (9)

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S × θ / S × θ ( S + C ) × ( θ + p i / 2 ) ( S + C ) × ( θ + p i / 2 )
{ c x  =  S / S ( n 1 ) ( n 1 ) c y  =  ( S + C ) / ( S + C ) ( n 1 ) ( n 1 )
Z =  ( c x x 2 + c y y 2 ) / ( 1 + 1 ( c x x 2  +  c y y 2 ) 2 / ( x 2  +  y 2 ) )
Z =  ( c x x 2 + c y y 2 ) / ( 1 + 1 ( 1 + K x ) c x x 2 ( 1 + K y ) c y y 2 )
Z =  ( c x x 2 + c y y 2 ) / ( 1 + 1 c x ( c x x 2  +  c y y 2 ) )
c c = C n 1
Z =  c x ( x 2  +  y 2 ) / ( 1 + 1 ( 1 + K ) c x 2 ( x 2 + y 2 ) )
Zc = cc ( y cos θ  +  x sin θ ) 2 / ( 1 + 1 ( 1 + K ) c c 2 ( y cos θ  +  x sin θ ) 2 )
Z c o n b = Z + Z c

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