Abstract

Compression molding of glass optical components is a high volume near net-shape precision fabrication method. In a compression molding process, a variation of the refractive index occurs along the radial direction of the glass component due to thermal treatment. The variation of refractive index is an important parameter that can affect the performance of optical lenses, especially lenses used for high precision optical systems. Refractive index variations in molded glass lenses under different cooling conditions were investigated using both an experimental approach and a numerical simulation. Specifically, refractive index variations inside molded glass lenses were evaluated by measuring optical wavefront variations with a Shack–Hartmann sensor system. The measured refractive index variations of the molded glass lenses were compared with the numerical simulation as a validation of the modeling approach.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. O. S. Narayanaswamy, “A model of structural relaxation in glass,” J. Am. Ceram. Soc. 54, 491-498 (1971).
    [CrossRef]
  6. A. Jain and A. Y. Yi, “Numerical modeling of viscoelastic stress relaxation during glass lens forming process,” J. Am. Ceram. Soc. 88, 530-535 (2005).
    [CrossRef]
  7. Y. Chen, L. Su, and A. Y. Yi, “Numerical simulation and experiment study of residual stresses in compression molding of precision glass optical components,” J. Manuf. Sci. Eng. (to be published).
  8. T. Dennis, E. M. Gill, and S. L. Gilbert, “Interferometric measurement of refractive-index change in photosensitive glass,” Appl. Opt. 40, 1663-1667 (2001).
    [CrossRef]
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    [CrossRef]
  10. H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315-1322 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
    [CrossRef]

2006

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

2005

A. Jain and A. Y. Yi, “Numerical modeling of viscoelastic stress relaxation during glass lens forming process,” J. Am. Ceram. Soc. 88, 530-535 (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]

2004

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

2003

2002

2001

T. Dennis, E. M. Gill, and S. L. Gilbert, “Interferometric measurement of refractive-index change in photosensitive glass,” Appl. Opt. 40, 1663-1667 (2001).
[CrossRef]

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577 (2001).

2000

1995

1987

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

1983

1971

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

B. C. Platt and R. Shack, “Lenticular Hartmann-screen,” Opt. Sci. Cent. Newsl. Univ. Ariz. 5, 15-16 (1971).

1955

H. N. Ritland, “Relation between refractive index and density of a glass at a constant temperature,” J. Am. Ceram. Soc. 3886-88 (1955).
[CrossRef]

1946

G. Joos, “Change of refractive index, density, and molecular refraction in tempering of glasses,” Optik (Jena) 1, 320-323 (1946).

Alexandrov, S. A.

S. A. Alexandrov and I. V. Chenyh, “Interference method for determination of refractive index and thickness,” Opt. Eng. 39, 2480-2486 (2000).
[CrossRef]

Andrysick, C. A.

Atta, L. V.

Benatar, A.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Berkhson, S. M.

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

Bliss, E. S.

Busbey, R. F.

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

Chen, Y.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Y. Chen, L. Su, and A. Y. Yi, “Numerical simulation and experiment study of residual stresses in compression molding of precision glass optical components,” J. Manuf. Sci. Eng. (to be published).

Chenyh, I. V.

S. A. Alexandrov and I. V. Chenyh, “Interference method for determination of refractive index and thickness,” Opt. Eng. 39, 2480-2486 (2000).
[CrossRef]

Coppola, G.

Dailey, M. J.

Demmer, A.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Dennis, T.

Ellerbroek, B. L.

Feldman, M.

Ferraro, P.

Geyer, T. W.

Gilbert, S. L.

Gill, E. M.

Grewell, D.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Grey, A. A.

Haruna, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315-1322 (2002).
[CrossRef] [PubMed]

Holdener, F. R.

Inoue, S.

Iodice, M.

Jain, A.

A. Jain and A. Y. Yi, “Numerical modeling of viscoelastic stress relaxation during glass lens forming process,” J. Am. Ceram. Soc. 88, 530-535 (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]

A. Jain, “Experimental Study and Numerical Analysis of Compression Molding Process for Manufacturing Precision Aspherical Glass Lenses,” Ph. D. dissertation (The Ohio State University, 2006).

Joos, G.

G. Joos, “Change of refractive index, density, and molecular refraction in tempering of glasses,” Optik (Jena) 1, 320-323 (1946).

Klocke, F.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Koch, J. A.

Konishi, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

Krause, D.

H. Loch and D. Krause, Mathematical Simulation in Glass Technology (Springer, 2002).
[CrossRef]

Loch, H.

H. Loch and D. Krause, Mathematical Simulation in Glass Technology (Springer, 2002).
[CrossRef]

Markovsky, A.

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

Maruyama, H.

Maschmeyer, R. O.

Meissner, H. E.

Mitsuyama, T.

Narayanaswamy, O. S.

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

Nicola, S. D.

Nishi, H.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

Ohmi, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, and M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315-1322 (2002).
[CrossRef] [PubMed]

Parker, C. J.

Pennington, T. L.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577 (2001).

B. C. Platt and R. Shack, “Lenticular Hartmann-screen,” Opt. Sci. Cent. Newsl. Univ. Ariz. 5, 15-16 (1971).

Pongs, G.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

Presta, R. W.

Ritland, H. N.

H. N. Ritland, “Relation between refractive index and density of a glass at a constant temperature,” J. Am. Ceram. Soc. 3886-88 (1955).
[CrossRef]

Roggemann, M. C.

Sacks, R. A.

Salmon, J. T.

Sanford, L. M.

Scherer, G. W.

G. W. Scherer, Relaxation in Glass and Composites (Wiley, 1986).

Seppala, L. G.

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577 (2001).

B. C. Platt and R. Shack, “Lenticular Hartmann-screen,” Opt. Sci. Cent. Newsl. Univ. Ariz. 5, 15-16 (1971).

Soules, T. F.

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

Su, L.

Y. Chen, L. Su, and A. Y. Yi, “Numerical simulation and experiment study of residual stresses in compression molding of precision glass optical components,” J. Manuf. Sci. Eng. (to be published).

Toeppen, J. S.

Welsh, B. M.

Whistler, W. T.

Winter, S. E.

Wonterghem, B. M. V.

Woods, B. W.

Yamada, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

Yi, A. Y.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

A. Jain and A. Y. Yi, “Numerical modeling of viscoelastic stress relaxation during glass lens forming process,” J. Am. Ceram. Soc. 88, 530-535 (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]

Y. Chen, L. Su, and A. Y. Yi, “Numerical simulation and experiment study of residual stresses in compression molding of precision glass optical components,” J. Manuf. Sci. Eng. (to be published).

A. Y. Yi, “Optical fabrication,” in The Optics Encyclopedia, T. G. Brown, K. Kreath, H. Kogelnik, M. A. Kriss, J. Schmit, and M. J. Weber, eds. (Academic, 2003), pp. 1945-1959.

Zacharias, R. A.

Appl. Opt.

J. Am. Ceram. Soc.

H. N. Ritland, “Relation between refractive index and density of a glass at a constant temperature,” J. Am. Ceram. Soc. 3886-88 (1955).
[CrossRef]

T. F. Soules, R. F. Busbey, S. M. Berkhson, and A. Markovsky, “Finite element calculation of stresses in glass parts undergoing viscous relaxation,” J. Am. Ceram. Soc. 70, 90-95 (1987).
[CrossRef]

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

A. Jain and A. Y. Yi, “Numerical modeling of viscoelastic stress relaxation during glass lens forming process,” J. Am. Ceram. Soc. 88, 530-535 (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]

J. Micromech. Microeng.

A. Y. Yi, Y. Chen, F. Klocke, G. Pongs, A. Demmer, D. Grewell, and A. Benatar, “A high volume precision compression molding process of glass diffractive optics by use of micromachined fused silica wafer mold and low Tg optical glass,” J. Micromech. Microeng. 16, 2000-2005 (2006).
[CrossRef]

J. Refract. Surg.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577 (2001).

Meas. Sci. Technol.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. , 15, 1531-1535 (2004).
[CrossRef]

Opt. Eng.

S. A. Alexandrov and I. V. Chenyh, “Interference method for determination of refractive index and thickness,” Opt. Eng. 39, 2480-2486 (2000).
[CrossRef]

Opt. Sci. Cent. Newsl. Univ. Ariz.

B. C. Platt and R. Shack, “Lenticular Hartmann-screen,” Opt. Sci. Cent. Newsl. Univ. Ariz. 5, 15-16 (1971).

Optik (Jena)

G. Joos, “Change of refractive index, density, and molecular refraction in tempering of glasses,” Optik (Jena) 1, 320-323 (1946).

Other

A. Jain, “Experimental Study and Numerical Analysis of Compression Molding Process for Manufacturing Precision Aspherical Glass Lenses,” Ph. D. dissertation (The Ohio State University, 2006).

A. Y. Yi, “Optical fabrication,” in The Optics Encyclopedia, T. G. Brown, K. Kreath, H. Kogelnik, M. A. Kriss, J. Schmit, and M. J. Weber, eds. (Academic, 2003), pp. 1945-1959.

H. Loch and D. Krause, Mathematical Simulation in Glass Technology (Springer, 2002).
[CrossRef]

G. W. Scherer, Relaxation in Glass and Composites (Wiley, 1986).

Y. Chen, L. Su, and A. Y. Yi, “Numerical simulation and experiment study of residual stresses in compression molding of precision glass optical components,” J. Manuf. Sci. Eng. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Meshed numerical simulation model.

Fig. 2
Fig. 2

Temperature history of three different cooling rates.

Fig. 3
Fig. 3

Schematic of the measuring system. 1, He–Ne laser; 2, filter; 3, polarizer; 4, beam expander; 5, specimen in matching liquid; 6. lens 1; 7, lens 2; 8, SHS.

Fig. 4
Fig. 4

Reconstructed wavefront variation using the SHS.

Fig. 5
Fig. 5

Measured refractive index variations along the radial direction for three different cooling rates and an untreated glass lens (blank).

Fig. 6
Fig. 6

Predicted index variations along the radial direction for three different cooling rates.

Fig. 7
Fig. 7

Comparison of refractive index variation curves at a cooling rate of q 2 = 0.60 ° C / s

Tables (2)

Tables Icon

Table 1 Mechanical and Thermal Properties of BK7 Glass

Tables Icon

Table 2 Structural Relaxation Parameters Used in Numerical Simulation

Equations (9)

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

d n d ρ = ( n 2 1 ) ( 4 π + b n 2 b ) 8 πnρ ,
Δ n Δ ρ = ( n 2 1 ) ( 4 π + b n 2 b ) 8 πnρ ,
Δ n i , j = ( n 2 1 ) ( 4 π + b n 2 b ) 8 πn × Δ V i , j ( V i , j + Δ V i , j ) ,
Δ n i = ( j = 1 N Δ n i , j ) / N .
Δ n v , i = Δ n i Δ n 1 .
L ( x , y ) = n ( x , y ) t ( x , y ) ,
L r = n c t .
Δ L v ( x , y ) = L ( x , y ) L r = n ( x , y ) t n c t .
Δ n v ( x , y ) = n ( x , y ) n c = Δ L v ( x , y ) / t .

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