Abstract

A grinding process that uses loose abrasives for the beveling of lenses is presented. Determination of the parameters of grinding tools with loose abrasives for beveling applications with various optical elements is discussed. The process of grinding with loose abrasives for a lapping operation is analyzed by examination of the influence of optical glass material parameters on material removal and surface roughness for lens manufacturing conditions. The model established for this analysis uses the concept of lateral fracture, which is based on removal of optical glass material by rolling abrasive particles. The particles remove material by lateral cracking. The abrasive mineral Barton Garnet was used in the lapping experiments. Under specific large-diameter lens manufacturing conditions, lapping time values at the conventional removal depth have been obtained for various optical glasses.

© 2000 Optical Society of America

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References

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  1. D. Kuntz, “Specifying laser diode optics,” Laser Focus 20(3), 44–55 (1984).
  2. K. G. Krieg, Klein Einführung in die DIN-Normen (Teubner, Stuttgart/Beuth-Verlag, Berlin, Germany, 1977).
  3. H. H. Karow, Fabrication Methods for Precision Optics (Wiley, New York, 1993).
  4. G. Gräfe, H. Kuss, G. Reichelt, Feinoptiker (VEB Verlag Technik, Berlin, 1980), Vol. 3.
  5. D. F. Horne, Optical Production Technology (Adam Hilger, Bristol, UK, 1972).
  6. M. Buijs, K. Korpel-van Houten, “A model for lapping of glass,” J. Mater. Sci. 29, 3014–3020 (1993).
    [CrossRef]
  7. M. Buijs, L. Martens, “Effect of indentation interaction on cracking,” J. Am. Ceram. Soc. 75, 2809–2814 (1992).
    [CrossRef]
  8. Schott Glass Catalog (Schott Glass Technologies, Inc., Duryea, Pa., 1992).
  9. J. C. Lambropoulos, T. Fang, P. D. Funkenbusch, S. D. Jacobs, M. J. Cumbo, D. Golini, “Surface microroughness of optical glass under deterministic microgrinding,” Appl. Opt. 35, 4448–4462 (1996).
    [CrossRef] [PubMed]
  10. J. C. Lambropoulos, S. Xu, T. Fang, “Loose abrasive lapping hardness of optical glasses and its interpretation,” Appl. Opt. 36, 1501–1516 (1997).
    [CrossRef] [PubMed]
  11. D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
    [CrossRef]
  12. J. A. Williams, A. M. Hyncica, “Mechanisms of abrasive wear in lubricated contacts,” Wear 152, 57–74 (1992).
    [CrossRef]
  13. A. Broese-van Groenou, J. D. B. Veldkamp, “Grinding brittle materials,” Philips Tech. Rev. 38, 105–118 (1979).
  14. M. A. Moore, F. S. King, “Abrasive wear of brittle solids,” Wear 60, 123–140 (1980).
    [CrossRef]
  15. M. Buijs, K. Korpel-van Houten, “Three-body abrasion of brittle materials as studied by lapping,” Wear 166, 237–245 (1993).
    [CrossRef]

1997 (1)

1996 (1)

1993 (2)

M. Buijs, K. Korpel-van Houten, “Three-body abrasion of brittle materials as studied by lapping,” Wear 166, 237–245 (1993).
[CrossRef]

M. Buijs, K. Korpel-van Houten, “A model for lapping of glass,” J. Mater. Sci. 29, 3014–3020 (1993).
[CrossRef]

1992 (2)

M. Buijs, L. Martens, “Effect of indentation interaction on cracking,” J. Am. Ceram. Soc. 75, 2809–2814 (1992).
[CrossRef]

J. A. Williams, A. M. Hyncica, “Mechanisms of abrasive wear in lubricated contacts,” Wear 152, 57–74 (1992).
[CrossRef]

1984 (1)

D. Kuntz, “Specifying laser diode optics,” Laser Focus 20(3), 44–55 (1984).

1982 (1)

D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
[CrossRef]

1980 (1)

M. A. Moore, F. S. King, “Abrasive wear of brittle solids,” Wear 60, 123–140 (1980).
[CrossRef]

1979 (1)

A. Broese-van Groenou, J. D. B. Veldkamp, “Grinding brittle materials,” Philips Tech. Rev. 38, 105–118 (1979).

Broese-van Groenou, A.

A. Broese-van Groenou, J. D. B. Veldkamp, “Grinding brittle materials,” Philips Tech. Rev. 38, 105–118 (1979).

Buijs, M.

M. Buijs, K. Korpel-van Houten, “Three-body abrasion of brittle materials as studied by lapping,” Wear 166, 237–245 (1993).
[CrossRef]

M. Buijs, K. Korpel-van Houten, “A model for lapping of glass,” J. Mater. Sci. 29, 3014–3020 (1993).
[CrossRef]

M. Buijs, L. Martens, “Effect of indentation interaction on cracking,” J. Am. Ceram. Soc. 75, 2809–2814 (1992).
[CrossRef]

Cumbo, M. J.

Evans, A. G.

D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
[CrossRef]

Fang, T.

Funkenbusch, P. D.

Golini, D.

Gräfe, G.

G. Gräfe, H. Kuss, G. Reichelt, Feinoptiker (VEB Verlag Technik, Berlin, 1980), Vol. 3.

Horne, D. F.

D. F. Horne, Optical Production Technology (Adam Hilger, Bristol, UK, 1972).

Hyncica, A. M.

J. A. Williams, A. M. Hyncica, “Mechanisms of abrasive wear in lubricated contacts,” Wear 152, 57–74 (1992).
[CrossRef]

Jacobs, S. D.

Karow, H. H.

H. H. Karow, Fabrication Methods for Precision Optics (Wiley, New York, 1993).

King, F. S.

M. A. Moore, F. S. King, “Abrasive wear of brittle solids,” Wear 60, 123–140 (1980).
[CrossRef]

Korpel-van Houten, K.

M. Buijs, K. Korpel-van Houten, “Three-body abrasion of brittle materials as studied by lapping,” Wear 166, 237–245 (1993).
[CrossRef]

M. Buijs, K. Korpel-van Houten, “A model for lapping of glass,” J. Mater. Sci. 29, 3014–3020 (1993).
[CrossRef]

Krieg, K. G.

K. G. Krieg, Klein Einführung in die DIN-Normen (Teubner, Stuttgart/Beuth-Verlag, Berlin, Germany, 1977).

Kuntz, D.

D. Kuntz, “Specifying laser diode optics,” Laser Focus 20(3), 44–55 (1984).

Kuss, H.

G. Gräfe, H. Kuss, G. Reichelt, Feinoptiker (VEB Verlag Technik, Berlin, 1980), Vol. 3.

Lambropoulos, J. C.

Lawn, B. R.

D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
[CrossRef]

Marshall, D. B.

D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
[CrossRef]

Martens, L.

M. Buijs, L. Martens, “Effect of indentation interaction on cracking,” J. Am. Ceram. Soc. 75, 2809–2814 (1992).
[CrossRef]

Moore, M. A.

M. A. Moore, F. S. King, “Abrasive wear of brittle solids,” Wear 60, 123–140 (1980).
[CrossRef]

Reichelt, G.

G. Gräfe, H. Kuss, G. Reichelt, Feinoptiker (VEB Verlag Technik, Berlin, 1980), Vol. 3.

Veldkamp, J. D. B.

A. Broese-van Groenou, J. D. B. Veldkamp, “Grinding brittle materials,” Philips Tech. Rev. 38, 105–118 (1979).

Williams, J. A.

J. A. Williams, A. M. Hyncica, “Mechanisms of abrasive wear in lubricated contacts,” Wear 152, 57–74 (1992).
[CrossRef]

Xu, S.

Appl. Opt. (2)

J. Am. Ceram. Soc. (2)

M. Buijs, L. Martens, “Effect of indentation interaction on cracking,” J. Am. Ceram. Soc. 75, 2809–2814 (1992).
[CrossRef]

D. B. Marshall, B. R. Lawn, A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65, 561–566 (1982).
[CrossRef]

J. Mater. Sci. (1)

M. Buijs, K. Korpel-van Houten, “A model for lapping of glass,” J. Mater. Sci. 29, 3014–3020 (1993).
[CrossRef]

Laser Focus (1)

D. Kuntz, “Specifying laser diode optics,” Laser Focus 20(3), 44–55 (1984).

Philips Tech. Rev. (1)

A. Broese-van Groenou, J. D. B. Veldkamp, “Grinding brittle materials,” Philips Tech. Rev. 38, 105–118 (1979).

Wear (3)

M. A. Moore, F. S. King, “Abrasive wear of brittle solids,” Wear 60, 123–140 (1980).
[CrossRef]

M. Buijs, K. Korpel-van Houten, “Three-body abrasion of brittle materials as studied by lapping,” Wear 166, 237–245 (1993).
[CrossRef]

J. A. Williams, A. M. Hyncica, “Mechanisms of abrasive wear in lubricated contacts,” Wear 152, 57–74 (1992).
[CrossRef]

Other (5)

Schott Glass Catalog (Schott Glass Technologies, Inc., Duryea, Pa., 1992).

K. G. Krieg, Klein Einführung in die DIN-Normen (Teubner, Stuttgart/Beuth-Verlag, Berlin, Germany, 1977).

H. H. Karow, Fabrication Methods for Precision Optics (Wiley, New York, 1993).

G. Gräfe, H. Kuss, G. Reichelt, Feinoptiker (VEB Verlag Technik, Berlin, 1980), Vol. 3.

D. F. Horne, Optical Production Technology (Adam Hilger, Bristol, UK, 1972).

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Figures (11)

Fig. 1
Fig. 1

Typical bevel specifications.

Fig. 2
Fig. 2

(a) Biconvex lens located in a concave grinding tool with the dimensions shown. (b) Surface edge bevel after the beveling operation has been completed.

Fig. 3
Fig. 3

(a) Cross section of the collector mirror used in catopric and catadioptric systems. (b) Assembly of the collector mirror on the concave grinding tool with the dimensions shown.

Fig. 4
Fig. 4

Beveling concave rectangular lenses on a convex grinding tool.

Fig. 5
Fig. 5

Lapping operation with the loose abrasive BG with a concave grinding tool.

Fig. 6
Fig. 6

Diagram of lapping test equipment. The lens holder moves back and forth with an amplitude of A l : (a) side view, (b) top view.

Fig. 7
Fig. 7

Particle size distribution curve of BG.

Fig. 8
Fig. 8

Variation of surface roughness, average peak to valley with the glass material parameter expression (E w 1/2/H w ) from Tables 1 and 3. Solid line, constrained linear fit. The numbers refer to the glass sequence in Table 1.

Fig. 9
Fig. 9

Variation of removal rate with the glass material parameter expression (E w 5/4/K lc,w H w 2) from Tables 1 and 3. Solid line, constrained linear fit. The numbers refer to the glass sequence in Table 1.

Fig. 10
Fig. 10

Diagram of a lens sample that denotes removal depth (RD). Hatched area, the section that will be removed, which has a thickness of 0.1 mm. The tolerance values of R c and R l are different and are exaggerated in this figure.

Fig. 11
Fig. 11

Variation of measured and calculated lapping times with the glass material parameter expression (K lc,w H w 2/E w 5/4). Solid line, calculated lapping times; points, measured lapping times. The numbers refer to the glass sequence in Table 1. v = 0.50 ms-1, P tot = 53.76 N, A w = 1.14 × 104 mm2.

Tables (3)

Tables Icon

Table 1 Optical Glass Material Parameters

Tables Icon

Table 2 Chemical Compositions and Vickers’s Hardness Values at a 100-gf Load and a 15-s Dwell Time of Lapping Plates

Tables Icon

Table 3 Lapping Results with Abrasive BG for Optical Glass Samples with a Normal Load of 5.0 Na

Equations (11)

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

rb=2 cos θ-1ϕ0,  ϕ0=ϕb+ϕl/2.
w=2 sin θ-1Δϕ,  Δϕ=ϕl-ϕb.
brb1-sin θ.
rb=r12 cos θ1-ϕl24r121/2,
Hlp<Hw<Hla,
c=α1Ew3/8Klc,w1/2Hw1/2 Pi5/8,
α1=δL1/2A1/4cot ψ5/12,
Pc=δ0A2cot ψ-2/3 Klc,w4Hw3EwHw,
Rz=α2Ew1/2Hw Pi1/2,
Z=α3vPi3/4PtotRaAwEw5/4Klc,wHw2
Z=β Ew5/4Klc,wHw2,

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