Abstract

With the adoption of polycarbonate lens material for injection molding of greater accuracy and at lower costs, polycarbonate has become very suitable for mass production of more economical products, such as diving goggles. However, with increasing requirements for visual quality improvement, lenses need to have not only refractive function but also thickness and spherical aberration, which are gradually being taken more seriously. For a high-power-composite lens, meanwhile, the thickness cannot be substantially reduced, and there is also the issue of severe spherical aberration at the lens edges. In order to increase the added value of the product without changing the material, the present research applied the eye model and Taguchi experiment method, combined with design optimization for hyperbolic-aspherical lens, to significantly reduce the lens thickness by more than 30%, outperforming the average thickness reduction in general aspherical lens. The spherical aberration at the lens edges was also reduced effectively during the optimization process for the nonspherical lens. Prototypes made by super-finishing machines were among the results of the experiment. This new application can be used in making a large amount of injection molds to substantially increase the economic value of the product.

© 2014 Optical Society of America

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References

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2012

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[CrossRef]

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

S. Zheng, Z. Wang, Y. Liu, and R. Li, “Aspheric spectacles for correcting presbyopia with myopia and astigmatism,” Appl. Opt. 51, 6926–6932 (2012).
[CrossRef]

2009

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

2007

2006

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

D. A. Atchison, “Optical models for human myopic eyes,” Vis. Res. 46, 2236–2250 (2006).
[CrossRef]

2002

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

2000

S.-J. Liu and J.-H. Chang, “Application of the Taguchi method to optimize the surface quality of gas assist injection molded composites,” J. Reinf. Plast. Comp. 19, 1352–1362 (2000).
[CrossRef]

1997

1995

1992

Artal, P.

Atchison, D. A.

D. A. Atchison, “Optical models for human myopic eyes,” Vis. Res. 46, 2236–2250 (2006).
[CrossRef]

Bahrami, M.

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[CrossRef]

Bradley, A.

Brennan, N. A.

Campbell, C.

Carvalho, L. A.

M. S. de Almeida and L. A. Carvalho, “Different schematic eyes and their accuracy to the in vivo eye: a quantitative comparison study,” Braz. J. Phys. 37, 378–387 (2007).
[CrossRef]

Chang, E.-H.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

Chang, H.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Chang, J.-H.

S.-J. Liu and J.-H. Chang, “Application of the Taguchi method to optimize the surface quality of gas assist injection molded composites,” J. Reinf. Plast. Comp. 19, 1352–1362 (2000).
[CrossRef]

Chang, M.-W.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Chen, Y.-C.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

Chou, J.-H.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

de Almeida, M. S.

M. S. de Almeida and L. A. Carvalho, “Different schematic eyes and their accuracy to the in vivo eye: a quantitative comparison study,” Braz. J. Phys. 37, 378–387 (2007).
[CrossRef]

Fang, Y.-C.

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

Fernández, E. J.

Goncharov, A. V.

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[CrossRef]

Greivenkamp, J. E.

Hsueh, B.-R.

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

Jiang, C.-J.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

Li, R.

Lin, C.-H.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Liou, H.-L.

Liu, S.-J.

S.-J. Liu and J.-H. Chang, “Application of the Taguchi method to optimize the surface quality of gas assist injection molded composites,” J. Reinf. Plast. Comp. 19, 1352–1362 (2000).
[CrossRef]

Liu, T.-K.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

Liu, Y.

MacDonald, J.

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

Norrby, S.

Piers, P.

Schwiegerling, J.

Sun, C.-C.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Sun, J.-H.

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

Sun, W.-S.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Thibos, L. N.

Tien, C.-L.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Tsai, H.-L.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

van der Mooren, M.

Wang, Z.

Wu, B.-W.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

Yang, T.-H.

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

Ye, M.

Zhang, X.

Zheng, S.

Appl. Opt.

Braz. J. Phys.

M. S. de Almeida and L. A. Carvalho, “Different schematic eyes and their accuracy to the in vivo eye: a quantitative comparison study,” Braz. J. Phys. 37, 378–387 (2007).
[CrossRef]

J. Biomed. Opt.

M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt. 17, 055001 (2012).
[CrossRef]

Y.-C. Chen, C.-J. Jiang, T.-H. Yang, and C.-C. Sun, “Development of a human eye model incorporated with intraocular scattering for visual performance assessment,” J. Biomed. Opt. 17, 075009 (2012).

J. Mod. Opt.

Y.-C. Fang, T.-K. Liu, J. Macdonald, J.-H. Chou, B.-W. Wu, H.-L. Tsai, and E.-H. Chang, “Optimizing chromatic aberration calibration using a novel genetic algorithm,” J. Mod. Opt. 53, 1411–1427 (2006).
[CrossRef]

J. Opt. A

J.-H. Sun, B.-R. Hsueh, Y.-C. Fang, and J. MacDonald, “Optical design and extended multi-objective optimization of miniature L-type optics,” J. Opt. A 11, 105505 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Reinf. Plast. Comp.

S.-J. Liu and J.-H. Chang, “Application of the Taguchi method to optimize the surface quality of gas assist injection molded composites,” J. Reinf. Plast. Comp. 19, 1352–1362 (2000).
[CrossRef]

Opt. Eng.

W.-S. Sun, H. Chang, C.-C. Sun, M.-W. Chang, C.-H. Lin, and C.-L. Tien, “Design of high-power aspherical ophthalmic lenses with a reduced error budget,” Opt. Eng. 41, 2809–2813 (2002).
[CrossRef]

Vis. Res.

D. A. Atchison, “Optical models for human myopic eyes,” Vis. Res. 46, 2236–2250 (2006).
[CrossRef]

Other

CODE V, Reference Manual, “Defining Surface Types,” Version 10.3, 5–14 (2011).

CODE V, “Liou human eye model:eyemodel3.len,” Version 10.3 (2011).

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Figures (6)

Fig. 1.
Fig. 1.

Original eye model.

Fig. 2.
Fig. 2.

Eye model simulating ametropes.

Fig. 3.
Fig. 3.

Postlens-fitting eye model.

Fig. 4.
Fig. 4.

Schematic diagram illustrating the relative position of the Sag and h of the surface.

Fig. 5.
Fig. 5.

Convergent curve of the error function for aspherical optimization.

Fig. 6.
Fig. 6.

Blank lens made by injection molding: left, front surface; right, rear surface.

Tables (9)

Tables Icon

Table 1. Relevant Parameters of the Liou Eye Model

Tables Icon

Table 2. Various Optic Parameters of the Original Eye Model

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Table 3. Various Optic Parameters of the Eye Model Simulating Ametropes

Tables Icon

Table 4. Various Optical Parameters of the Postlens-Fitting Eye Model

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Table 5. Taguchi Experimental Orthogonal-Array Design

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Table 6. Results of the Aspherical-Optimization Design for the First Surface of the Lens

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Table 7. Results of the Aspherical Optimization Design for the Second Surface of the Lens

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Table 8. Sag Values for the Lens Height (y surface = 66.5mm)

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Table 9. Sag Values for the Lens Height (X Surface = 86.5mm)

Equations (7)

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

GradA=n(r,z)=n0+(Nr2)z+(Nz1)z2+(Nz2)r2=1.368+(0.049057×z)(0.015427×z2)(0.001978×r2).
Grad  P=1.407(0.006605×z2)(0.001978×r2).
n(λ)=n(mediaat0.555μm)+0.0512(0.1455×λ)+(0.0961×λ2).
z=h2R+R2(1+k)h2+Ar4+Br6+Cr8+Dr10,
Sag=h2586+343396(240.0312)h2.
y  surface(66.5mm):Sag=h266.5+4422.25+(6.1895)h2,
x  surface(86.5mm):Sag=h286.5+7282.25+(0.5)h2,

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