Abstract

Injection molding is an important mass-production tool in the optical industry. In this research our aim is to develop a process of combining ultraprecision diamond turning and injection molding to create a unique low-cost manufacturing process for progressive addition lenses (PALs). In industry, it is a well-known fact that refractive index variation and geometric deformation of injection molded lenses due to the rheological properties of polymers will distort their optical performance. To address this problem, we developed a method for determining the optical aberrations of the injection molded PALs. This method involves reconstructing the wavefront pattern in the presence of uneven refractive index distribution and surface warpage using a finite element method. In addition to numerical modeling, a measurement system based on a Shack–Hartmann wavefront sensor was used to verify the modeling results. The measured spherocylindrical powers and aberrations of the PALs were in good agreement with the model. Consequently, the optical aberrations of injection molded PALs were successfully predicted by finite element modeling. In summary, it was demonstrated in this study that numerically based optimization for PAL manufacturing is feasible.

© 2013 Optical Society of America

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References

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  1. D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
    [CrossRef]
  2. W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.
  3. C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.
  4. S.-W. Kim and L.-S. Turng, “Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method,” Polym. Eng. Sci. 46, 1263–1274 (2006).
    [CrossRef]
  5. K. Park and W. Joo, “Numerical evaluation of a plastic lens by coupling injection molding analysis with optical simulation,” Jpn. J. Appl. Phys. 47, 8402–8407 (2008).
    [CrossRef]
  6. C. Huang, “Investigation of injection molding process for high precision polymer lens manufacturing,” Doctoral dissertation (The Ohio State University, 2008).
  7. C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
    [CrossRef]
  8. C. Castellini, F. Francini, and B. Tiribilli, “Hartmann test modification for measuring ophthalmic progressive lenses,” Appl. Opt. 33, 4120–4124 (1994).
    [CrossRef]
  9. E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vis. Sci. 80, 106–114 (2003).
    [CrossRef]
  10. C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
    [CrossRef]
  11. A. I. Isayev, “Orientation development in the injection molding of amorphous polymers,” Polym. Eng. Sci. 23, 271–284 (1983).
    [CrossRef]
  12. T. Raasch, “Aberrations and spherocylindrical powers within subapertures of freeform surfaces,” J. Opt. Soc. Am. A 28, 2642–2646 (2011).
    [CrossRef]
  13. L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
    [CrossRef]
  14. A. Y. Yi and L. Li, “Design and fabrication of a microlens array by use of a slow tool servo,” Opt. Lett. 30, 1707–1709 (2005).
    [CrossRef]
  15. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
  16. L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
    [CrossRef]
  17. L. Li and A. Y. Yi, “An affordable injection-molded precision hybrid glass–polymer achromatic lens,” Int. J. Adv. Manuf. Technol., doi: 10.1007/s00170-013-5128-1 (2013).
    [CrossRef]

2013 (1)

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

2012 (1)

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

2011 (3)

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

T. Raasch, “Aberrations and spherocylindrical powers within subapertures of freeform surfaces,” J. Opt. Soc. Am. A 28, 2642–2646 (2011).
[CrossRef]

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

2008 (1)

K. Park and W. Joo, “Numerical evaluation of a plastic lens by coupling injection molding analysis with optical simulation,” Jpn. J. Appl. Phys. 47, 8402–8407 (2008).
[CrossRef]

2006 (1)

S.-W. Kim and L.-S. Turng, “Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method,” Polym. Eng. Sci. 46, 1263–1274 (2006).
[CrossRef]

2005 (1)

2004 (1)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

2003 (1)

E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vis. Sci. 80, 106–114 (2003).
[CrossRef]

1994 (1)

1983 (1)

A. I. Isayev, “Orientation development in the injection molding of amorphous polymers,” Polym. Eng. Sci. 23, 271–284 (1983).
[CrossRef]

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Andre, B.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

Artal, P.

E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vis. Sci. 80, 106–114 (2003).
[CrossRef]

Bradley, A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

Bullimore, M. A.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Castellini, C.

Castro, J. M.

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

Cheng, Y.-C.

W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.

Cheung, C. F.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Dambon, O.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

Francini, F.

Georgiadis, K.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

Hanriot, F.

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

He, P.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

Ho, L. T.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

Hsu, W.-Y.

W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.

Huang, C.

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

C. Huang, “Investigation of injection molding process for high precision polymer lens manufacturing,” Doctoral dissertation (The Ohio State University, 2008).

Huang, C.-Y.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Huang, H.-X.

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

Hugonneaux, P.

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

Isayev, A. I.

A. I. Isayev, “Orientation development in the injection molding of amorphous polymers,” Polym. Eng. Sci. 23, 271–284 (1983).
[CrossRef]

Joo, W.

K. Park and W. Joo, “Numerical evaluation of a plastic lens by coupling injection molding analysis with optical simulation,” Jpn. J. Appl. Phys. 47, 8402–8407 (2008).
[CrossRef]

Kim, S.-W.

S.-W. Kim and L.-S. Turng, “Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method,” Polym. Eng. Sci. 46, 1263–1274 (2006).
[CrossRef]

Klocke, F.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

Kong, L. B.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Lai, K. T.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Li, L.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

A. Y. Yi and L. Li, “Design and fabrication of a microlens array by use of a slow tool servo,” Opt. Lett. 30, 1707–1709 (2005).
[CrossRef]

L. Li and A. Y. Yi, “An affordable injection-molded precision hybrid glass–polymer achromatic lens,” Int. J. Adv. Manuf. Technol., doi: 10.1007/s00170-013-5128-1 (2013).
[CrossRef]

Liu, Y.-L.

W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.

Lochegnies, D.

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

Moreau, P.

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

Park, K.

K. Park and W. Joo, “Numerical evaluation of a plastic lens by coupling injection molding analysis with optical simulation,” Jpn. J. Appl. Phys. 47, 8402–8407 (2008).
[CrossRef]

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Raasch, T.

Raasch, T. W.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Sheedy, J. E.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Su, G.-D.

W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.

Su, L.

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

Thibos, L. N.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

Tiribilli, B.

To, S.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Turng, L.-S.

S.-W. Kim and L.-S. Turng, “Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method,” Polym. Eng. Sci. 46, 1263–1274 (2006).
[CrossRef]

Villegas, E. A.

E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vis. Sci. 80, 106–114 (2003).
[CrossRef]

Wang, B.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

Wang, F.

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

Yang, C.

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

Yi, A. Y.

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

A. Y. Yi and L. Li, “Design and fabrication of a microlens array by use of a slow tool servo,” Opt. Lett. 30, 1707–1709 (2005).
[CrossRef]

L. Li and A. Y. Yi, “An affordable injection-molded precision hybrid glass–polymer achromatic lens,” Int. J. Adv. Manuf. Technol., doi: 10.1007/s00170-013-5128-1 (2013).
[CrossRef]

Adv. Polym. Technol. (1)

C. Yang, L. Su, C. Huang, H.-X. Huang, J. M. Castro, and A. Y. Yi, “Effect of packing pressure on refractive index variation in injection molding of precision plastic optical lens,” Adv. Polym. Technol. 30, 51–61 (2011).
[CrossRef]

Appl. Opt. (1)

J. Opt. (1)

L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt. 13, 055407 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

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

J. Vis. (1)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4(4), 9 (2004).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Park and W. Joo, “Numerical evaluation of a plastic lens by coupling injection molding analysis with optical simulation,” Jpn. J. Appl. Phys. 47, 8402–8407 (2008).
[CrossRef]

New J. Glass Ceramics (1)

D. Lochegnies, P. Moreau, F. Hanriot, and P. Hugonneaux, “3D modelling of thermal replication for designing progressive glass moulds,” New J. Glass Ceramics 3, 34–42 (2013).
[CrossRef]

Opt. Lett. (1)

Optom. Vis. Sci. (2)

E. A. Villegas and P. Artal, “Spatially resolved wavefront aberrations of ophthalmic progressive-power lenses in normal viewing conditions,” Optom. Vis. Sci. 80, 106–114 (2003).
[CrossRef]

C.-Y. Huang, T. W. Raasch, A. Y. Yi, J. E. Sheedy, B. Andre, and M. A. Bullimore, “Comparison of three techniques in measuring progressive addition lenses,” Optom. Vis. Sci. 89, 1564–1573 (2012).
[CrossRef]

Polym. Eng. Sci. (2)

A. I. Isayev, “Orientation development in the injection molding of amorphous polymers,” Polym. Eng. Sci. 23, 271–284 (1983).
[CrossRef]

S.-W. Kim and L.-S. Turng, “Three-dimensional numerical simulation of injection molding filling of optical lens and multiscale geometry using finite element method,” Polym. Eng. Sci. 46, 1263–1274 (2006).
[CrossRef]

Other (4)

L. Li and A. Y. Yi, “An affordable injection-molded precision hybrid glass–polymer achromatic lens,” Int. J. Adv. Manuf. Technol., doi: 10.1007/s00170-013-5128-1 (2013).
[CrossRef]

W.-Y. Hsu, Y.-L. Liu, Y.-C. Cheng, and G.-D. Su, “Design and fabrication of the progressive addition lens,” in Frontiers in Optics 2010/Laser Science XXVI, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FThU8.

C. F. Cheung, L. B. Kong, L. T. Ho, S. To, B. Wang, and K. T. Lai, “An integrated approach for design, ultra-precision polishing and measurement of freeform progressive lenses,” in 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT) (International Society for Optics and Photonics, 2012), p. 84160C.

C. Huang, “Investigation of injection molding process for high precision polymer lens manufacturing,” Doctoral dissertation (The Ohio State University, 2008).

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Figures (10)

Fig. 1.
Fig. 1.

Freeform surface of the backside of the PAL. The first polynomial term was removed to show the freeform geometry.

Fig. 2.
Fig. 2.

Meshed FEM model. Node(i.1) is numbered along the number i line at the bottom surface of the PAL, and Node(i.N) is the node along the number i line at its top surface.

Fig. 3.
Fig. 3.

Finished ultraprecision diamond turned mold inserts for PAL injection molding.

Fig. 4.
Fig. 4.

PALs manufactured by microinjection molding.

Fig. 5.
Fig. 5.

Schematic of the wavefront measuring system. 1, distant source; 2, PAL under test; 3 and 4, 150 mm fl lenses; 5, Shack–Hartmann sensor.

Fig. 6.
Fig. 6.

Simulated refractive index variation of an injection molded PAL.

Fig. 7.
Fig. 7.

Simulated thickness change in xy plane of the molded PAL.

Fig. 8.
Fig. 8.

Spherical power M of the molded PAL: (a) design, (b) simulation, and (c) measurement.

Fig. 9.
Fig. 9.

Cylindrical component J0 of the injection molded PAL: (a) design, (b) simulation, and (c) measurement.

Fig. 10.
Fig. 10.

Comparison of (a) design, (b) simulated, and (c) measured cylindrical component J45 of the injection molded PAL.

Tables (3)

Tables Icon

Table 1. Material Parameters of PMMA

Tables Icon

Table 2. Injection Molding Condition

Tables Icon

Table 3. Injection Molding Conditions for Design of Experiment

Equations (17)

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

z=0.462×3×(2x2+2y21),
z=0.462×3×(2x2+2y21)0.015×22(3x2yy3)0.046×22(3x2y+3y32y)+0.007×22(3x3+3xy22x)+0.007×22(x33xy2)+0.0064×23(10x4y+20x2y312x2y+10y512y3+3y).
V=V0[1Cln(1+PB)],
V0={b1S+b2ST¯,ifTTtb1L+b2LT¯,ifT>Tt,
B={b3Sexp(b4ST¯),ifTTtb3Lexp(b4LT¯),ifT>Tt,
T¯=Tb5,
Tt=b5+b6P,
η=η01+(η0γγ*)1n,
η0=Bexp(TbT),
ni=j=1Nn(i,j)N,
Δni=nij=1NAnjNA,
di=z(i,N)z(i,1),
D=(Δni+n01)×(dit0),
cc=TZ×((ZT(x,y)×cc).*rsj),
M=c2043r2,
J0=c2226r2,
J45=c2226r2,

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