Abstract

Glass compression molding is an alternative manufacturing method for efficient, high-quality, low- cost optical component manufacturing. However, in compression molding, refractive index variation is inadvertently introduced to glass, which can influence optical performance of molded glass lenses, especially for lenses used in high precision applications. In order to study refractive index variation and dispersion in molded glass lenses after cooling, a group of BK7 cylindrical glass lenses were thermally treated with various heating and cooling conditions. The molded glass lenses were measured by use of an optical setup based on a Mach–Zehnder interferometer with red, green, and blue lasers separately. Using the wavefront information extracted from fringe patterns, refractive index and dispersion variation in molded glass lenses were reconstructed using a filtered backprojection algorithm. Furthermore, refractive index and dispersion variation at different cooling rates and different soaking temperatures were investigated.

© 2009 Optical Society of America

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References

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  1. R. O. Maschmeyer, C. A. Andrysick, T. W. Geyer, H. E. Meissner, C. J. Parker, and L. M. Sanford, “Precision molded glass optics,” Appl. Opt. 22, 2410-2412 (1983).
    [CrossRef] [PubMed]
  2. A. A. Milton, G. E. Blair, and C. C. Maier, “Method for molding glass lenses,” U.S. patent 3,833,347 (3 September 1974).
  3. A. Jain, “Experimental study and numerical analysis of compression molding process for manufacturing precision aspherical glass lenses,” Ph.D. dissertation (Ohio State University, 2006).
  4. H. Vogt, “Precision molding provides compact consumer optics,” Laser Focus World 43, 115-118 (2007).
  5. U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
    [CrossRef]
  6. O. S. Narayanaswamy, “A model of structural relaxation in glass,” J. Am. Ceram. Soc. 54, 491-498 (1971).
    [CrossRef]
  7. L. J. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662-1667 (2008).
    [CrossRef] [PubMed]
  8. M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
    [CrossRef]
  9. H. Suhara, “Interferometric measurement of the refractive-index distribution in plastic lenses by use of computed tomography,” Appl. Opt. 41, 5317-5325 (2002).
    [CrossRef] [PubMed]
  10. J. H. Li and D. R. Uhlmann, “The flow of glass at high stress levels,” J. Non-Cryst. Solids 3, 127-147 (1970).
    [CrossRef]
  11. G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
    [CrossRef]
  12. A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses: a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579-586 (2005).
    [CrossRef]
  13. A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
    [CrossRef]
  14. A. Jain and A. Y. Yi, “Finite element modeling of structural relaxation during annealing of a precision molded glass lens,” J. Manuf. Sci. Eng. 128, 683-690 (2006).
    [CrossRef]
  15. W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
    [CrossRef]
  16. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
    [CrossRef]
  17. J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105-125(1998).
    [CrossRef]
  18. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  19. A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416-5420 (1998).
    [CrossRef]
  20. J. Radon, “Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. 69, 262-277(1917).
  21. S. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).
  22. R. Gardon and O. S. Narayanaswamy, “Stress and volume relaxation in annealing of flat glass,” J. Am. Ceram. Soc. 44, 305 (1961).
    [CrossRef]

2009 (1)

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

2008 (2)

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

L. J. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662-1667 (2008).
[CrossRef] [PubMed]

2007 (2)

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

H. Vogt, “Precision molding provides compact consumer optics,” Laser Focus World 43, 115-118 (2007).

2006 (2)

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

A. Jain and A. Y. Yi, “Finite element modeling of structural relaxation during annealing of a precision molded glass lens,” J. Manuf. Sci. Eng. 128, 683-690 (2006).
[CrossRef]

2005 (3)

G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[CrossRef]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses: a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579-586 (2005).
[CrossRef]

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

2002 (1)

1998 (2)

A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37, 5416-5420 (1998).
[CrossRef]

J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105-125(1998).
[CrossRef]

1983 (1)

1971 (1)

O. S. Narayanaswamy, “A model of structural relaxation in glass,” J. Am. Ceram. Soc. 54, 491-498 (1971).
[CrossRef]

1970 (1)

J. H. Li and D. R. Uhlmann, “The flow of glass at high stress levels,” J. Non-Cryst. Solids 3, 127-147 (1970).
[CrossRef]

1961 (1)

R. Gardon and O. S. Narayanaswamy, “Stress and volume relaxation in annealing of flat glass,” J. Am. Ceram. Soc. 44, 305 (1961).
[CrossRef]

1917 (1)

J. Radon, “Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. 69, 262-277(1917).

Andrysick, C. A.

Asundi, A.

Baltes, A.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Berghmans, F.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Blair, G. E.

A. A. Milton, G. E. Blair, and C. C. Maier, “Method for molding glass lenses,” U.S. patent 3,833,347 (3 September 1974).

Chen, Y.

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

L. J. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662-1667 (2008).
[CrossRef] [PubMed]

Deans, S.

S. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

Firestone, G. C.

G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[CrossRef]

Fischer, P.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Fotheringham, U.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Gardon, R.

R. Gardon and O. S. Narayanaswamy, “Stress and volume relaxation in annealing of flat glass,” J. Am. Ceram. Soc. 44, 305 (1961).
[CrossRef]

Geyer, T. W.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Höhn, P.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Huntley, J. M.

J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105-125(1998).
[CrossRef]

Jain, A.

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

A. Jain and A. Y. Yi, “Finite element modeling of structural relaxation during annealing of a precision molded glass lens,” J. Manuf. Sci. Eng. 128, 683-690 (2006).
[CrossRef]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses: a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579-586 (2005).
[CrossRef]

G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[CrossRef]

A. Jain, “Experimental study and numerical analysis of compression molding process for manufacturing precision aspherical glass lenses,” Ph.D. dissertation (Ohio State University, 2006).

Jedamzik, R.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Kemao, Q.

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

Klocke, F.

Kniazewski, P.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Krajewski, R.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Kujawinska, M.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Li, J. H.

J. H. Li and D. R. Uhlmann, “The flow of glass at high stress levels,” J. Non-Cryst. Solids 3, 127-147 (1970).
[CrossRef]

Maier, C. C.

A. A. Milton, G. E. Blair, and C. C. Maier, “Method for molding glass lenses,” U.S. patent 3,833,347 (3 September 1974).

Maschmeyer, R. O.

Meissner, H. E.

Milton, A. A.

A. A. Milton, G. E. Blair, and C. C. Maier, “Method for molding glass lenses,” U.S. patent 3,833,347 (3 September 1974).

Narayanaswamy, O. S.

O. S. Narayanaswamy, “A model of structural relaxation in glass,” J. Am. Ceram. Soc. 54, 491-498 (1971).
[CrossRef]

R. Gardon and O. S. Narayanaswamy, “Stress and volume relaxation in annealing of flat glass,” J. Am. Ceram. Soc. 44, 305 (1961).
[CrossRef]

Parker, C. J.

Pongs, G.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Radon, J.

J. Radon, “Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. 69, 262-277(1917).

Sanford, L. M.

Schenk, C.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Shen, L. G.

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

Sooryakumar, R.

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

Stolz, C.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Su, L. J.

Suhara, H.

Thienpont, H.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Uffelen, M. V.

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Uhlmann, D. R.

J. H. Li and D. R. Uhlmann, “The flow of glass at high stress levels,” J. Non-Cryst. Solids 3, 127-147 (1970).
[CrossRef]

Vogt, H.

H. Vogt, “Precision molding provides compact consumer optics,” Laser Focus World 43, 115-118 (2007).

Wensen, Z.

Westenberger, G.

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

Xie, X.

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

Yi, A. Y.

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

L. J. Su, Y. Chen, A. Y. Yi, F. Klocke, and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662-1667 (2008).
[CrossRef] [PubMed]

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

A. Jain and A. Y. Yi, “Finite element modeling of structural relaxation during annealing of a precision molded glass lens,” J. Manuf. Sci. Eng. 128, 683-690 (2006).
[CrossRef]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses: a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579-586 (2005).
[CrossRef]

G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[CrossRef]

Zhao, W.

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

Appl. Opt. (4)

Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. (1)

J. Radon, “Über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math. Phys. Kl. 69, 262-277(1917).

J. Am. Ceram. Soc. (4)

R. Gardon and O. S. Narayanaswamy, “Stress and volume relaxation in annealing of flat glass,” J. Am. Ceram. Soc. 44, 305 (1961).
[CrossRef]

U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz, and G. Westenberger, “Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool-Narayanaswamy-Moynihan model,” J. Am. Ceram. Soc. 91, 780-783 (2008).
[CrossRef]

O. S. Narayanaswamy, “A model of structural relaxation in glass,” J. Am. Ceram. Soc. 54, 491-498 (1971).
[CrossRef]

A. Y. Yi and A. Jain, “Compression molding of aspherical glass lenses: a combined experimental and numerical analysis,” J. Am. Ceram. Soc. 88, 579-586 (2005).
[CrossRef]

J. Manuf. Sci. Eng. (1)

A. Jain and A. Y. Yi, “Finite element modeling of structural relaxation during annealing of a precision molded glass lens,” J. Manuf. Sci. Eng. 128, 683-690 (2006).
[CrossRef]

J. Non-Cryst. Solids (1)

J. H. Li and D. R. Uhlmann, “The flow of glass at high stress levels,” J. Non-Cryst. Solids 3, 127-147 (1970).
[CrossRef]

J. Strain Anal. (1)

J. M. Huntley, “Automated fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105-125(1998).
[CrossRef]

Laser Focus World (1)

H. Vogt, “Precision molding provides compact consumer optics,” Laser Focus World 43, 115-118 (2007).

Meas. Tech. (1)

W. Zhao, Y. Chen, L. G. Shen, and A. Y. Yi, “Investigation of refractive index distribution in precision compression glass molding by use of 3D tomography,” Meas. Tech. 20, 055109 (2009).
[CrossRef]

Model. Simul. Mater. Sci. Eng. (1)

A. Jain, A. Y. Yi, X. Xie, and R. Sooryakumar, “Finite element modeling of stress relaxation in glass lens moulding using measured, temperature-dependent elastic modulus and viscosity data of glass,” Model. Simul. Mater. Sci. Eng. 14, 465-477 (2006).
[CrossRef]

Opt. Lasers Eng. (1)

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

Proc. SPIE (1)

M. V. Uffelen, P. Kniazewski, R. Krajewski, M. Kujawinska, F. Berghmans, and H. Thienpont, “Application of microinterferometric tomography as an evaluation tool for phase micro-objects,” Proc. SPIE 5776, 596-604 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

G. C. Firestone, A. Jain, and A. Y. Yi, “Precision laboratory apparatus for high temperature compression molding of glass lenses,” Rev. Sci. Instrum. 76, 063101 (2005).
[CrossRef]

Other (4)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

A. A. Milton, G. E. Blair, and C. C. Maier, “Method for molding glass lenses,” U.S. patent 3,833,347 (3 September 1974).

A. Jain, “Experimental study and numerical analysis of compression molding process for manufacturing precision aspherical glass lenses,” Ph.D. dissertation (Ohio State University, 2006).

S. Deans, The Radon Transform and Some of Its Applications (Wiley, 1983).

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Figures (14)

Fig. 1
Fig. 1

Precision glass molding machine.

Fig. 2
Fig. 2

Temperature history of glass molding experiments: (a) three soaking temperatures with the same cooling rate, (b) three cooling rates with the same soaking temperature.

Fig. 3
Fig. 3

Optical setup for measurement of refractive index and dispersion variation.

Fig. 4
Fig. 4

Interference fringe ( T = 700 °C , cooling rate = 10.17 ° C / min , angle = 0 ° , diameter of the glass lens = 5 mm ).

Fig. 5
Fig. 5

Phase map of the fringe pattern shown in Fig. 4.

Fig. 6
Fig. 6

Reconstructed phase map of the middle slice.

Fig. 7
Fig. 7

Refractive index distribution of the middle slice.

Fig. 8
Fig. 8

Profile of section A-A in Fig. 7.

Fig. 9
Fig. 9

Refractive index distribution of the longitudinal section.

Fig. 10
Fig. 10

Refractive index variation in the axial direction of the molded glass lens.

Fig. 11
Fig. 11

Refractive index variation and dispersion of molded glass lenses ( diameter = 5 mm ) with the same soaking temperature ( 680 °C ) and different cooling rates: (a)  T = 680 °C , cooling rate = 10.17 ° C / min ; (b)  T = 680 °C , cooling rate = 2.41 ° C / min ; (c)  T = 680 °C , cooling rate = 1.15 ° C / min .

Fig. 12
Fig. 12

Maximum difference of refractive index variation of molded glass lenses under different cooling rates.

Fig. 13
Fig. 13

Refractive index variation of molded glass lenses under different soaking temperature ( lens diameter = 5 mm , λ = 632.8 nm ).

Fig. 14
Fig. 14

Refractive index variation of molded glass lenses under different soaking temperature ( lens diameter = 7 mm , λ = 632.8 nm ).

Equations (3)

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n ( λ ) = n ( λ ) ref + n ( λ ) T f ( T f T f , ref ) ,
P ( x , y , z 0 ) = 0 π S ( f u , θ , z 0 ) | f u | exp ( j 2 π f u u ) d f u d θ = 0 π + S ( f u , θ , z 0 ) | f u | exp ( j 2 π f u ( x cos θ + y sin θ ) ) d f u d θ ,
n ( x , y , z 0 ) = P ( x , y , z 0 ) λ 2 π d ,

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