Abstract

We present the design, fabrication, and characterization of a dual-surface sphero-cylindrical progressive addition lens (DSOC-PAL), which combines the progressive cylindrical addition power of both lens surfaces to give the required spherical addition power. Both the freeform lens surfaces are numerically solved with the variational-difference numerical method based on the minimization of a merit function that employs weight functions and boundary conditions to balance between the desired spherical power distribution and the necessary cylindrical power distribution. The simulation results show that the proposed DSOC-PAL design is highly tolerant to the surface alignment errors and agree well with the experimental results obtained by the lens surfacing and polishing process.

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

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References

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  1. J. E. Sheedy, “Progressive addition lenses-matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
    [Crossref]
  2. A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 6,935,744 (2005).
  3. A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 7,241,010 (2007).
  4. B. Maitenaz, “Ophthalmic lenses with a progressively varying focal power,” U.S. patent 3,687,528 (1972).
  5. J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 4,861,153 (1989).
  6. J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 5,123,725 (1992).
  7. J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
    [Crossref]
  8. J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
    [Crossref]
  9. J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
    [Crossref]
  10. W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
    [Crossref]
  11. Y. Li, W. Huang, H. Feng, and J. Chen, “Customized design and efficient machining of astigmatism-minimized progressive addition lens,” Chin. Opt. Lett. 16(11), 113302 (2018).
    [Crossref]
  12. V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
    [Crossref]
  13. J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11(7), 1949–1957 (1994).
    [Crossref]
  14. ISO, “Ophthalmic optics and instruments - Reporting aberrations of the human eye,” in ISO 24157: 2008.
  15. D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
    [Crossref]
  16. R. R. Krueger, R. A. Applegate, and S. M. MacRae, “Wavefront Customized Visual Correction: The Quest for Super Vision II,” Slack Incorporated, 2nd Edition (2003).
  17. Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
    [Crossref]
  18. D. R. Ibañez, J. A. Gómez-Pedrero, J. Alonso, and J. A. Quiroga, “Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape,” Opt. Express 24(6), 5918–5933 (2016).
    [Crossref]
  19. A. Gray, E. Abbena, and S. Salamon, “Modern Differential Geometry of Curves and Surfaces with Mathematica,” CRC Press (2006).
  20. L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
    [Crossref]
  21. G. Minkwitz, “On the surface astigmatism of a fixed symmetrical aspheric surface,” Opt. Acta 10(3), 223–227 (1963).
    [Crossref]
  22. J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
    [Crossref]
  23. Lens Processing & Technology Division of Vision Council, “Data communication standard,” version 3.12 (2018).
  24. H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
    [Crossref]

2018 (1)

2017 (1)

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

2016 (2)

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

D. R. Ibañez, J. A. Gómez-Pedrero, J. Alonso, and J. A. Quiroga, “Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape,” Opt. Express 24(6), 5918–5933 (2016).
[Crossref]

2014 (1)

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

2011 (1)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

2004 (2)

J. E. Sheedy, “Progressive addition lenses-matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref]

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

2003 (1)

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

2001 (1)

D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
[Crossref]

1998 (1)

J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
[Crossref]

1997 (1)

L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
[Crossref]

1994 (1)

1987 (1)

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

1963 (1)

G. Minkwitz, “On the surface astigmatism of a fixed symmetrical aspheric surface,” Opt. Acta 10(3), 223–227 (1963).
[Crossref]

Abbena, E.

A. Gray, E. Abbena, and S. Salamon, “Modern Differential Geometry of Curves and Surfaces with Mathematica,” CRC Press (2006).

Alonso, J.

Applegate, R. A.

R. R. Krueger, R. A. Applegate, and S. M. MacRae, “Wavefront Customized Visual Correction: The Quest for Super Vision II,” Slack Incorporated, 2nd Edition (2003).

Azus, J.

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

Bailey, I.

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

Bao, W. Z.

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

Bille, J. F.

Borish, I.

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

Buri, M.

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

Chen, H.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Chen, J.

Y. Li, W. Huang, H. Feng, and J. Chen, “Customized design and efficient machining of astigmatism-minimized progressive addition lens,” Chin. Opt. Lett. 16(11), 113302 (2018).
[Crossref]

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Chen, S.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Collins, M. J.

D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
[Crossref]

Davis, B.

D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
[Crossref]

Feng, H.

Y. Li, W. Huang, H. Feng, and J. Chen, “Customized design and efficient machining of astigmatism-minimized progressive addition lens,” Chin. Opt. Lett. 16(11), 113302 (2018).
[Crossref]

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Fleck, A.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

Goelz, S.

Gómez-Pedrero, J. A.

Gray, A.

A. Gray, E. Abbena, and S. Salamon, “Modern Differential Geometry of Curves and Surfaces with Mathematica,” CRC Press (2006).

Greiner, G.

J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
[Crossref]

Grimm, B.

Gulliver, R.

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Horner, D.

L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
[Crossref]

Huang, W.

Ibañez, D. R.

Iskander, D. R.

D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
[Crossref]

Jiang, W.

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

Kikuchi, Y.

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 6,935,744 (2005).

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 7,241,010 (2007).

Kitani, A.

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 7,241,010 (2007).

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 6,935,744 (2005).

Krueger, R. R.

R. R. Krueger, R. A. Applegate, and S. M. MacRae, “Wavefront Customized Visual Correction: The Quest for Super Vision II,” Slack Incorporated, 2nd Edition (2003).

Lakshminarayanan, V.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

Li, C.

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Li, Y.

Y. Li, W. Huang, H. Feng, and J. Chen, “Customized design and efficient machining of astigmatism-minimized progressive addition lens,” Chin. Opt. Lett. 16(11), 113302 (2018).
[Crossref]

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Liang, J.

Loos, J.

J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
[Crossref]

MacRae, S. M.

R. R. Krueger, R. A. Applegate, and S. M. MacRae, “Wavefront Customized Visual Correction: The Quest for Super Vision II,” Slack Incorporated, 2nd Edition (2003).

Maitenaz, B.

B. Maitenaz, “Ophthalmic lenses with a progressively varying focal power,” U.S. patent 3,687,528 (1972).

Minkwitz, G.

G. Minkwitz, “On the surface astigmatism of a fixed symmetrical aspheric surface,” Opt. Acta 10(3), 223–227 (1963).
[Crossref]

Quiroga, J. A.

Salamon, S.

A. Gray, E. Abbena, and S. Salamon, “Modern Differential Geometry of Curves and Surfaces with Mathematica,” CRC Press (2006).

Santosa, F.

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Seidel, H. P.

J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
[Crossref]

Sheedy, J.

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

Sheedy, J. E.

J. E. Sheedy, “Progressive addition lenses-matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref]

Tang, Q. L.

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

Thibos, L. N.

L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
[Crossref]

Wang, H. Q.

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

Wang, J.

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Wheeler, W.

L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
[Crossref]

Winthrop, J. T.

J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 5,123,725 (1992).

J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 4,861,153 (1989).

Xia, R.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Yuan, Y.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Zhu, D.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

Zhu, L.

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

Chin. Opt. Lett. (1)

Comput. Aided. Des. (2)

J. Loos, G. Greiner, and H. P. Seidel, “A variational approach to progressive lens design,” Comput. Aided. Des. 30(8), 595–602 (1998).
[Crossref]

W. Jiang, W. Z. Bao, Q. L. Tang, H. Q. Wang, and L. Zhu, “A variational-difference numerical method for designing progressive-addition lenses,” Comput. Aided. Des. 48, 17–27 (2014).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

D. R. Iskander, M. J. Collins, and B. Davis, “Optimal modeling of corneal surfaces with Zernike polynomials,” IEEE Trans. Biomed. Eng. 48(1), 87–95 (2001).
[Crossref]

Int. J Adv. Manuf. Technol. (1)

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J Adv. Manuf. Technol. 91(9-12), 3799–3806 (2017).
[Crossref]

J. Mod. Opt. (1)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58(7), 545–561 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

Math. Models Methods Appl. Sci. (1)

J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14(04), 619–640 (2004).
[Crossref]

Opt. Acta (1)

G. Minkwitz, “On the surface astigmatism of a fixed symmetrical aspheric surface,” Opt. Acta 10(3), 223–227 (1963).
[Crossref]

Opt. Express (1)

Optom. Vis. Sci. (2)

J. Sheedy, M. Buri, I. Bailey, J. Azus, and I. Borish, “The optics of progressive lenses,” Optom. Vis. Sci. 64(2), 90–99 (1987).
[Crossref]

L. N. Thibos, W. Wheeler, and D. Horner, “Power vectors: an application of fourier analysis to the description and statistical analysis of refractive error,” Optom. Vis. Sci. 74(6), 367–375 (1997).
[Crossref]

Optometry (1)

J. E. Sheedy, “Progressive addition lenses-matching the specific lens to patient needs,” Optometry 75(2), 83–102 (2004).
[Crossref]

Proc. SPIE (1)

Y. Li, R. Xia, J. Chen, H. Feng, Y. Yuan, D. Zhu, and C. Li, “Freeform surface of progressive addition lens represented by Zernike polynomials,” Proc. SPIE 9683, 96830W (2016).
[Crossref]

SIAM J. Appl. Math. (1)

J. Wang, R. Gulliver, and F. Santosa, “Analysis of a variational approach to progressive lens design,” SIAM J. Appl. Math. 64(1), 277–296 (2003).
[Crossref]

Other (9)

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 6,935,744 (2005).

A. Kitani and Y. Kikuchi, “Bi-aspherical type progressive-power lens,” U.S. patent 7,241,010 (2007).

B. Maitenaz, “Ophthalmic lenses with a progressively varying focal power,” U.S. patent 3,687,528 (1972).

J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 4,861,153 (1989).

J. T. Winthrop, “Progressive addition spectacle lens,” U.S. patent 5,123,725 (1992).

A. Gray, E. Abbena, and S. Salamon, “Modern Differential Geometry of Curves and Surfaces with Mathematica,” CRC Press (2006).

R. R. Krueger, R. A. Applegate, and S. M. MacRae, “Wavefront Customized Visual Correction: The Quest for Super Vision II,” Slack Incorporated, 2nd Edition (2003).

ISO, “Ophthalmic optics and instruments - Reporting aberrations of the human eye,” in ISO 24157: 2008.

Lens Processing & Technology Division of Vision Council, “Data communication standard,” version 3.12 (2018).

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Figures (13)

Fig. 1.
Fig. 1. The (a) weight function α(x, y), (b) weight function β(x, y) and (c) mean curvature Hr(x,y) are required in the merit function for the anterior lens surface design. The numerically solved (d) perturbation surface is combined with a spherical background surface with radius of curvature R = 151 mm to give (e) the anterior surface of DSOC-PAL.
Fig. 2.
Fig. 2. The (a) weight function α(x, y), (b) weight function β(x, y) and (c) mean curvature Hr(x,y) are required in the merit function for the posterior lens surface design. The numerically solved (d) perturbation surface is combined with a spherical background surface with radius of curvature R = 149.4 mm to give (e) the posterior surface of DSOC-PAL.
Fig. 3.
Fig. 3. Zernike coefficients of lens surfaces except mode 4 and the modes less than 3.
Fig. 4.
Fig. 4. The simulated surface power distribution of DSOC-PAL. (a) High power and (b) cylindrical power of the anterior lens surface; (c) high power and (d) cylindrical power of the posterior lens surface.
Fig. 5.
Fig. 5. The power vector representation of the designed DSOC-PAL. (a)∼(c) The anterior lens surface and (d)∼(f) the posterior lens surface are combined to give (g)∼(i) the whole lens.
Fig. 6.
Fig. 6. The sphero-cylinder representation of the surface power of DSOC-PAL, including (a) high power, (b) cylindrical power and (c) equivalent spherical power that is actually the same as Fig. 5(g).
Fig. 7.
Fig. 7. The optical performance including (a) high power, (b) astigmatism and (c) equivalent spherical power in diopters calculated by ray tracing of the designed DSOC-PAL at each gaze direction.
Fig. 8.
Fig. 8. The simulated lens power distribution influenced by lateral misalignment of −6 mm, −3 mm, 3 mm and 6 mm between the lens surfaces.
Fig. 9.
Fig. 9. The simulated lens power distribution influenced by vertical misalignment of −4 mm, −2 mm, 2 mm and 4 mm between the lens surfaces.
Fig. 10.
Fig. 10. The simulated lens power distribution influenced by azimuthal misalignment of −10°, −5°, 5° and 10° between the lens surfaces.
Fig. 11.
Fig. 11. The calculated tool path for (a) the convex anterior lens surface and (b) the concave posterior lens surface. The feed rate was set to be 2 mm per revolution just for demonstration. Black line: tool path for rough cutting; red line: tool path for finishing.
Fig. 12.
Fig. 12. The measured power distribution of the semi-finished lens blank. (a)∼(b) Only the anterior surface of lens blank is finished; (c)∼(d) Only the posterior surface of lens blank is finished.
Fig. 13.
Fig. 13. The sphero-cylinder representation of the measured DSOC-PAL power in diopters including (a) high power, (b) cylindrical power and (c) equivalent spherical power.

Equations (8)

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MF = Ω { α ( x , y ) [ κ 1 ( x , y ) κ 2 ( x , y ) 2 ] 2 + β ( x , y ) [ H ( x , y ) H r ( x , y ) ] 2 } d x d y
H ( x , y ) = κ 1 ( x , y ) + κ 2 ( x , y ) 2
A ( x , y ) = ( RI 1 ) | κ 1 ( x , y ) κ 2 ( x , y ) |
( E G F 2 ) κ 2 ( E N + G L 2 F M ) κ + ( L N M 2 ) = 0
E = 1 + S x 2 , F = S x S y , G = 1 + S y 2 ,
L = S x x 1 + S x 2 + S y 2 , M = S x y 1 + S x 2 + S y 2 , N = S y y 1 + S x 2 + S y 2
M ( x , y ) = P h ( x , y ) + P l ( x , y ) 2 J 0 ( x , y ) = A ( x , y ) 2 cos 2 φ ( x , y ) J 45 ( x , y ) = A ( x , y ) 2 sin 2 φ ( x , y )
C y l = 2 J 0 , a + p 2 + J 45 , a + p 2 H i g h P o w e r = M a + p + C y l 2

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