Abstract

Refractive parameters are the main design and evaluation parameters of freeform spectacle lenses. In this paper, the mathematical model of refractive parameters is established, and the refractive power distribution on the whole surface is drawn with a radial basis function. The measurement methods are analyzed, and typical freeform spectacle lenses are measured with a freeform verifier. The refractive power distribution on the whole surface, the cylinder view, and the refractive power curve along the progressive corridor are drawn up. There are no evident image changes on the whole surface. The refractive power smoothly varies along the progressive corridor. In comparing the results with the analysis, measurement results are in agreement with the calculation.

© 2014 Optical Society of America

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References

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  1. M. Jalie, The Principles of Ophthalmic Lenses (Association of Dispensing Opticians, 1972).
  2. M. Jalie, Ophthalmic Lenses and Dispensing (Butterworth-Heinemann, 2003).
  3. D. R. Pope, “Progressive addition lenses: history, design, wearer satisfaction and trends,” in Vision Science and Its Applications (Optical Society of America, 2000).
  4. T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
    [Crossref]
  5. F. Z. Fan, “Manufacturing of freeform optics (keynote speech),” in Ophthalmic Optics Forum, Beijing, China, September13, 2011.
  6. F. Z. Fang, “Advances in freeform optics (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, March10–11, 2012.
  7. F. Z. Fang, “Manufacturing and measurement of freeform specticles (invited presentation),” in Carl Zeiss Vision, Aalen, Germany, March15, 2012.
  8. F. Z. Fang, “Evaluation of freeform lenses (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, February28, 2013.
  9. D. J. Meister and S. W. Fisher, “Progress in the spectacle correction of presbyopia. Part 1: design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).
    [Crossref]
  10. J. Wang and F. Santosa, “A numerical method for progressive lens design,” Math. Models Methods Appl. Sci. 14, 619–640 (2004).
    [Crossref]
  11. J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
    [Crossref]
  12. W. Liru, “Questions to the evaluation method and relative standards for free form lense,” Focus 01, 12–15 (2012) (in Chinese).
  13. C. Fowler, “Technical note: apparatus for comparison of progressive addition spectacle lenses,” Ophthal. Physiol. Opt. 26, 502–506 (2006).
    [Crossref]
  14. C. Fowler and C. Sullivan, “Varifocal spectacle lens surface power measurement,” Ophthal. Physiol. Opt. 8, 231–233 (1988).
    [Crossref]
  15. M. C. Knauer, J. Kaminski, and G. Häusler, eds., “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
  16. J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43, 1305–1317 (2010).
    [Crossref]
  17. H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
    [Crossref]
  18. C. Castellini, F. Francini, and B. Tiribilli, “Hartmann test modification for measuring ophthalmic progressive lenses,” Appl. Opt. 33, 4120–4124 (1994).
    [Crossref]
  19. E. A. Villegas and P. Artal, “Comparison of aberrations in different types of progressive power lenses,” Ophthal. Physiol. Opt. 24, 419–426 (2004).
    [Crossref]
  20. C. Zhou, W. Wang, K. Yang, X. Chai, and Q. Ren, “Measurement and comparison of the optical performance of an ophthalmic lens based on a Hartmann-Shack wavefront sensor in real viewing conditions,” Appl. Opt. 47, 6434–6441 (2008).
    [Crossref]
  21. J. Arasa, J. Caum, S. Royo, and A. Cifuentes, eds., “Progressive addition lenses power map measurement using Ronchi test techniques,” in Optical Metrology (International Society for Optics and Photonics, 2003).
  22. Y. Wang, J. Cai, and F. Lu, “Freeform ophthalmic lenses power map measurement using Ronchi test techniques,” Opto-Elect. Eng.38 (2011) (in Chinese).
  23. Q. Wang, Research on the Measurements of Lens Power Based on Moiré Defection Technology (Suzhou University, 2008) (in Chinese).
  24. X. Xiao, Research on the Moiré Deflectometry Method on Measuring Spectacle Lens (University of Electronic Science and Technology of China, 2012) (in Chinese).
  25. J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
    [Crossref]
  26. J. E. Sheedy, “Progressive addition lenses—matching the specific lens to patient needs,” Opto. J. Am. Opto. Assoc. 75, 83–102 (2004).
    [Crossref]
  27. J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
    [Crossref]
  28. S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
    [Crossref]
  29. E. Acosta, S. Chamadoira, and R. Blendowske, “Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A 23, 632–637 (2006).
    [Crossref]
  30. E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
    [Crossref]
  31. T. Spiers and C. Hull, “Optical Fourier filtering for whole lens assessment of progressive power lenses,” Ophthal. Physiol. Opt. 20, 281–289 (2000).
    [Crossref]

2012 (2)

W. Liru, “Questions to the evaluation method and relative standards for free form lense,” Focus 01, 12–15 (2012) (in Chinese).

S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
[Crossref]

2011 (1)

T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
[Crossref]

2010 (2)

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43, 1305–1317 (2010).
[Crossref]

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
[Crossref]

2009 (1)

E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
[Crossref]

2008 (2)

C. Zhou, W. Wang, K. Yang, X. Chai, and Q. Ren, “Measurement and comparison of the optical performance of an ophthalmic lens based on a Hartmann-Shack wavefront sensor in real viewing conditions,” Appl. Opt. 47, 6434–6441 (2008).
[Crossref]

D. J. Meister and S. W. Fisher, “Progress in the spectacle correction of presbyopia. Part 1: design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).
[Crossref]

2006 (3)

C. Fowler, “Technical note: apparatus for comparison of progressive addition spectacle lenses,” Ophthal. Physiol. Opt. 26, 502–506 (2006).
[Crossref]

J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
[Crossref]

E. Acosta, S. Chamadoira, and R. Blendowske, “Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A 23, 632–637 (2006).
[Crossref]

2005 (1)

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

2004 (4)

J. E. Sheedy, “Progressive addition lenses—matching the specific lens to patient needs,” Opto. J. Am. Opto. Assoc. 75, 83–102 (2004).
[Crossref]

M. C. Knauer, J. Kaminski, and G. Häusler, eds., “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).

E. A. Villegas and P. Artal, “Comparison of aberrations in different types of progressive power lenses,” Ophthal. Physiol. Opt. 24, 419–426 (2004).
[Crossref]

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

2000 (1)

T. Spiers and C. Hull, “Optical Fourier filtering for whole lens assessment of progressive power lenses,” Ophthal. Physiol. Opt. 20, 281–289 (2000).
[Crossref]

1998 (1)

J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
[Crossref]

1994 (1)

1988 (1)

C. Fowler and C. Sullivan, “Varifocal spectacle lens surface power measurement,” Ophthal. Physiol. Opt. 8, 231–233 (1988).
[Crossref]

Acosta, E.

S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
[Crossref]

E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
[Crossref]

E. Acosta, S. Chamadoira, and R. Blendowske, “Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A 23, 632–637 (2006).
[Crossref]

Artal, P.

E. A. Villegas and P. Artal, “Comparison of aberrations in different types of progressive power lenses,” Ophthal. Physiol. Opt. 24, 419–426 (2004).
[Crossref]

Balzer, J.

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43, 1305–1317 (2010).
[Crossref]

Blendowske, R.

S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
[Crossref]

E. Acosta, S. Chamadoira, and R. Blendowske, “Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A 23, 632–637 (2006).
[Crossref]

Cai, J.

Y. Wang, J. Cai, and F. Lu, “Freeform ophthalmic lenses power map measurement using Ronchi test techniques,” Opto-Elect. Eng.38 (2011) (in Chinese).

Campbell, C.

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

Castellini, C.

Castillo, L. R.

E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
[Crossref]

Chai, X.

Chamadoira, S.

S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
[Crossref]

E. Acosta, S. Chamadoira, and R. Blendowske, “Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A 23, 632–637 (2006).
[Crossref]

Fan, F. Z.

F. Z. Fan, “Manufacturing of freeform optics (keynote speech),” in Ophthalmic Optics Forum, Beijing, China, September13, 2011.

Fang, F. Z.

F. Z. Fang, “Advances in freeform optics (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, March10–11, 2012.

F. Z. Fang, “Manufacturing and measurement of freeform specticles (invited presentation),” in Carl Zeiss Vision, Aalen, Germany, March15, 2012.

F. Z. Fang, “Evaluation of freeform lenses (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, February28, 2013.

Feng, P.

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
[Crossref]

Fisher, S. W.

D. J. Meister and S. W. Fisher, “Progress in the spectacle correction of presbyopia. Part 1: design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).
[Crossref]

Fowler, C.

C. Fowler, “Technical note: apparatus for comparison of progressive addition spectacle lenses,” Ophthal. Physiol. Opt. 26, 502–506 (2006).
[Crossref]

C. Fowler and C. Sullivan, “Varifocal spectacle lens surface power measurement,” Ophthal. Physiol. Opt. 8, 231–233 (1988).
[Crossref]

Francini, F.

Guo, H.

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
[Crossref]

Hardy, R. F.

J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
[Crossref]

Hayes, J. R.

J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
[Crossref]

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

Hull, C.

T. Spiers and C. Hull, “Optical Fourier filtering for whole lens assessment of progressive power lenses,” Ophthal. Physiol. Opt. 20, 281–289 (2000).
[Crossref]

Jalie, M.

M. Jalie, The Principles of Ophthalmic Lenses (Association of Dispensing Opticians, 1972).

M. Jalie, Ophthalmic Lenses and Dispensing (Butterworth-Heinemann, 2003).

King-Smith, E.

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

Liru, W.

W. Liru, “Questions to the evaluation method and relative standards for free form lense,” Focus 01, 12–15 (2012) (in Chinese).

Loos, J.

J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
[Crossref]

Lu, F.

Y. Wang, J. Cai, and F. Lu, “Freeform ophthalmic lenses power map measurement using Ronchi test techniques,” Opto-Elect. Eng.38 (2011) (in Chinese).

Meister, D. J.

D. J. Meister and S. W. Fisher, “Progress in the spectacle correction of presbyopia. Part 1: design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).
[Crossref]

Pope, D. R.

D. R. Pope, “Progressive addition lenses: history, design, wearer satisfaction and trends,” in Vision Science and Its Applications (Optical Society of America, 2000).

Raasch, T. W.

T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
[Crossref]

Ren, Q.

Santosa, F.

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

Seidel, H. P.

J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
[Crossref]

Sheedy, J.

J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
[Crossref]

Sheedy, J. E.

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

J. E. Sheedy, “Progressive addition lenses—matching the specific lens to patient needs,” Opto. J. Am. Opto. Assoc. 75, 83–102 (2004).
[Crossref]

Slusallek, P.

J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
[Crossref]

Spiers, T.

T. Spiers and C. Hull, “Optical Fourier filtering for whole lens assessment of progressive power lenses,” Ophthal. Physiol. Opt. 20, 281–289 (2000).
[Crossref]

Su, L.

T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
[Crossref]

Sullivan, C.

C. Fowler and C. Sullivan, “Varifocal spectacle lens surface power measurement,” Ophthal. Physiol. Opt. 8, 231–233 (1988).
[Crossref]

Tao, T.

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
[Crossref]

Tiribilli, B.

Vázquez, D.

E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
[Crossref]

Villegas, E. A.

E. A. Villegas and P. Artal, “Comparison of aberrations in different types of progressive power lenses,” Ophthal. Physiol. Opt. 24, 419–426 (2004).
[Crossref]

Wang, J.

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

Wang, Q.

Q. Wang, Research on the Measurements of Lens Power Based on Moiré Defection Technology (Suzhou University, 2008) (in Chinese).

Wang, W.

Wang, Y.

Y. Wang, J. Cai, and F. Lu, “Freeform ophthalmic lenses power map measurement using Ronchi test techniques,” Opto-Elect. Eng.38 (2011) (in Chinese).

Werling, S.

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43, 1305–1317 (2010).
[Crossref]

Xiao, X.

X. Xiao, Research on the Moiré Deflectometry Method on Measuring Spectacle Lens (University of Electronic Science and Technology of China, 2012) (in Chinese).

Yang, K.

Yi, A.

T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
[Crossref]

Zhou, C.

Appl. Opt. (2)

Clin. Exp. Optom. (1)

D. J. Meister and S. W. Fisher, “Progress in the spectacle correction of presbyopia. Part 1: design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).
[Crossref]

Comput. Graph. Forum (1)

J. Loos, P. Slusallek, and H. P. Seidel, “Using wavefront tracing for the visualization and optimization of progressive lenses,” Comput. Graph. Forum 17, 255–265 (1998).
[Crossref]

Focus (1)

W. Liru, “Questions to the evaluation method and relative standards for free form lense,” Focus 01, 12–15 (2012) (in Chinese).

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, 619–640 (2004).
[Crossref]

Measurement (1)

J. Balzer and S. Werling, “Principles of shape from specular reflection,” Measurement 43, 1305–1317 (2010).
[Crossref]

Ophthal. Physiol. Opt. (5)

E. A. Villegas and P. Artal, “Comparison of aberrations in different types of progressive power lenses,” Ophthal. Physiol. Opt. 24, 419–426 (2004).
[Crossref]

C. Fowler, “Technical note: apparatus for comparison of progressive addition spectacle lenses,” Ophthal. Physiol. Opt. 26, 502–506 (2006).
[Crossref]

C. Fowler and C. Sullivan, “Varifocal spectacle lens surface power measurement,” Ophthal. Physiol. Opt. 8, 231–233 (1988).
[Crossref]

E. Acosta, D. Vázquez, and L. R. Castillo, “Analysis of the optical properties of crystalline lenses by point-diffraction interferometry,” Ophthal. Physiol. Opt. 29, 235–246 (2009).
[Crossref]

T. Spiers and C. Hull, “Optical Fourier filtering for whole lens assessment of progressive power lenses,” Ophthal. Physiol. Opt. 20, 281–289 (2000).
[Crossref]

Opt. Lasers Eng. (1)

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48, 166–171 (2010).
[Crossref]

Opt. Vis. Sci. (1)

T. W. Raasch, L. Su, and A. Yi, “Whole-surface characterization of progressive addition lenses,” Opt. Vis. Sci. 88, E217–E26 (2011).
[Crossref]

Opto. J. Am. Opto. Assoc. (2)

J. Sheedy, R. F. Hardy, and J. R. Hayes, “Progressive addition lenses—measurements and ratings,” Opto. J. Am. Opto. Assoc. 77, 23–39 (2006).
[Crossref]

J. E. Sheedy, “Progressive addition lenses—matching the specific lens to patient needs,” Opto. J. Am. Opto. Assoc. 75, 83–102 (2004).
[Crossref]

Opto. Vis. Sci. (2)

J. E. Sheedy, C. Campbell, E. King-Smith, and J. R. Hayes, “Progressive powered lenses: the Minkwitz theorem,” Opto. Vis. Sci. 82, 916–922 (2005).
[Crossref]

S. Chamadoira, R. Blendowske, and E. Acosta, “Progressive addition lens measurement by point diffraction interferometry,” Opto. Vis. Sci. 89, 1532–1542 (2012).
[Crossref]

Proc. SPIE (1)

M. C. Knauer, J. Kaminski, and G. Häusler, eds., “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).

Other (11)

F. Z. Fan, “Manufacturing of freeform optics (keynote speech),” in Ophthalmic Optics Forum, Beijing, China, September13, 2011.

F. Z. Fang, “Advances in freeform optics (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, March10–11, 2012.

F. Z. Fang, “Manufacturing and measurement of freeform specticles (invited presentation),” in Carl Zeiss Vision, Aalen, Germany, March15, 2012.

F. Z. Fang, “Evaluation of freeform lenses (invited presentation),” in Ophthalmic Labs & Industry (MAFO), Milan, Italy, February28, 2013.

M. Jalie, The Principles of Ophthalmic Lenses (Association of Dispensing Opticians, 1972).

M. Jalie, Ophthalmic Lenses and Dispensing (Butterworth-Heinemann, 2003).

D. R. Pope, “Progressive addition lenses: history, design, wearer satisfaction and trends,” in Vision Science and Its Applications (Optical Society of America, 2000).

J. Arasa, J. Caum, S. Royo, and A. Cifuentes, eds., “Progressive addition lenses power map measurement using Ronchi test techniques,” in Optical Metrology (International Society for Optics and Photonics, 2003).

Y. Wang, J. Cai, and F. Lu, “Freeform ophthalmic lenses power map measurement using Ronchi test techniques,” Opto-Elect. Eng.38 (2011) (in Chinese).

Q. Wang, Research on the Measurements of Lens Power Based on Moiré Defection Technology (Suzhou University, 2008) (in Chinese).

X. Xiao, Research on the Moiré Deflectometry Method on Measuring Spectacle Lens (University of Electronic Science and Technology of China, 2012) (in Chinese).

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Figures (5)

Fig. 1.
Fig. 1.

Five zones on the PAL: distance zone, progressive corridor, near zone, and two blending zones. The refractive power varies continuously along the progressive corridor from distance to near.

Fig. 2.
Fig. 2.

Schematic of progression. The corridor length of the lens design can be defined as the vertical distance separating the minimum curvature within the distance zone and maximum curvature within the near zone of the lens surface along the umbilic.

Fig. 3.
Fig. 3.

Refractive power distribution calculated by radial basis function. (a) Refractive power of the distance is 1.50D, and the additional refractive power is 3.0D. (b) Cylindrical power of the distance is 1.50D, and the additional refractive power is 3.0D. (c) Refractive power of the distance is 1.25D, and the additional refractive power is 3.0D. (d) Cylindrical power of the distance is 1.25D, and the additional refractive power is 3.0D.

Fig. 4.
Fig. 4.

Measurement results of freeform spectacle lenses designed with the refractive power of distance 1.50D, and the additional refractive power of 3.0D. (a) Refractive power distribution. (b) Cylinder view. (c) Refractive power curve along the progressive corridor.

Fig. 5.
Fig. 5.

Measurement results of freeform spectacle lenses designed with the refractive power of distance 1.25D, and the additional refractive power of 3.0D. (a) Refractive power distribution. (b) Cylinder view. (c) Refractive power curve along the progressive corridor.

Equations (22)

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

δ=ADDL,
p=(1n)κb+(n1)κf1d(11n)κf,
limd0p=limd0(1n)κb+(n1)κf1d(11n)κf,
pthin=(n1)(κfκb).
k=κ1κ2,
H=κ1+κ22.
{κ1=H+H2Kκ2=HH2K.
Pf=(n1)(|κ⃗f1|+|κ⃗f2|)2,
Af=(n1)(κ⃗f1κ⃗f2),
κ⃗f1=|κ⃗f1|sinθ+|κ⃗f1|cosθ,
κ⃗f2=|κ⃗f2|sinϕ+|κ⃗f2|cosϕ,
Pb=(n1)(|κ⃗b1|+|κ⃗b2|)2,
Ab=(n1)(κ⃗b1κ⃗b2),
κ⃗b1=|κ⃗b1|sinθ+|κ⃗b1|cosθ,
κ⃗b2=|κ⃗b2|sinϕ+|κ⃗b2|cosϕ,
pthin=Pf+Pb,
Athin=AfAb.
J=Ω{α(x,y)(κ1κ22)+β(x,y)(κ1+κ22p(x,y))2}dxdy.
J=Ω{α(H(x,y)2K(x,y))+β(H(x,y)p(x,y))2}dxdy.
f(x)=cjΦ(xxj),
cjΦ(xkxj)=f(xk).
[ϕ(x1x1)ϕ(x1x2)ϕ(x1xn)ϕ(x2x1)ϕ(x2x2)ϕ(x2xn)ϕ(xnx1)ϕ(xnx2)ϕ(xnxn)][c1c2cn]=[f(x1)f(x2)f(xn)].

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