Abstract

We present a nondestructive method for estimating the depth of subsurface damage (SSD) in some single crystalline optical materials (silicon, lithium niobate, calcium fluoride, magnesium fluoride, and sapphire); the method is established by correlating surface microroughness measurements, specifically, the peak-to-valley (p–v) microroughness, to the depth of SSD found by a novel destructive method. Previous methods for directly determining the depth of SSD may be insufficient when applied to single crystals that are very soft or very hard. Our novel destructive technique uses magnetorheological finishing to polish spots onto a ground surface. We find that p–v surface microroughness, appropriately scaled, gives an upper bound to SSD. Our data suggest that SSD in the single crystalline optical materials included in our study (deterministically microground, lapped, and sawed) is always less than 1.4 times the p–v surface microroughness found by white-light interferometry. We also discuss another way of estimating SSD based on the abrasive size used.

© 2005 Optical Society of America

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    [CrossRef]
  21. E. N. Pugh, L. E. Samuels, “Damaged layers in abraded silicon surfaces,” J. Electrochem. Soc. 111, 1430–1432 (1964).
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  24. Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
    [CrossRef]
  25. S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
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    [CrossRef]
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    [CrossRef]
  33. J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).
  34. Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
    [CrossRef]
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  36. J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).
  37. J. C. Lambropoulos, “From abrasive size to subsurface damage in grinding,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 17–18.
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    [CrossRef]
  47. J. A. Randi, J. C. Lambropoulos, S. D. Jacobs, “Determination of subsurface damage in optical materials using a noninvasive technique,” in Optical Fabrication and Testing Digest (Optical Society of America, Washington, D.C., 2002), pp. 61–63.
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2004 (1)

T. Juliano, V. Domnich, Y. Gogotsi, “Examining pressure-induced phase transformations in silicon by spherical indentation and Raman spectroscopy: a statistical study,” J. Mater. Res. 19, 3099–3108 (2004).
[CrossRef]

2002 (2)

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

1999 (2)

J. C. Lambropoulos, S. D. Jacobs, J. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).

F. Ebrahimi, L. Kalwani, “Fracture anisotrophy in silicon single crystal,” Mat. Sci. Eng. A 268, 116–126 (1999).
[CrossRef]

1997 (1)

A. Kailer, Y. G. Gogotsi, K. G. Nickel, “Phase transformations of silicon caused by contact loading,” J. Appl. Phys. 81, 3057–3063 (1997).
[CrossRef]

1996 (2)

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
[CrossRef]

1994 (4)

I. Blech, D. Dang, “Silicon wafer deformation after backside grinding,” Solid State Technol., August, 1994, pp. 74–76.

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News, June1994, pp. 15–19.
[CrossRef]

H. H. K. Xu, S. Jahanmir, “Simple technique for observing subsurface damage in machining of ceramics,” J. Am. Ceram. Soc. 77, 1388–1390 (1994).
[CrossRef]

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

1989 (3)

V. A. Perevoshchikov, V. D. Skupov, “Accumulation of defects in silicon wafers from operation to operation during mechanical finishing process,” Sov. J. Opt. Technol. 56, 302–305 (1989).

M. Taneya, Y. Sugimoto, K. Akita, “Characterization of subsurface damage in GaAs processed by Ga+ focused ion-beam-assisted Cl2 etching using photoluminescence,” J. Appl. Phys. 66, 1375–1381 (1989).
[CrossRef]

E. Brinksmeier, “State-of-the-art non-destructive measurement of subsurface material properties and damages,” Precis. Eng. 11, 211–224 (1989).
[CrossRef]

1988 (2)

Z. Hang, H. Shen, F. H. Pollak, “Comprehensive investigation of polish-induced surface strain in 〈100〉 and 〈111〉 GaAs and InP,” J. Appl. Phys. 64, 3233–3242 (1988).
[CrossRef]

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

1987 (2)

S. Chandrasekhar, M. C. Shaw, B. Bhushan, “Comparison of grinding and lapping of ferrites and metals,” ASME J. Eng. Ind. 109, 76–82 (1987).
[CrossRef]

D. F. Edwards, P. P. Hed, “Optical glass fabrication technology. 2. Relationship between surface roughness and subsurface damage,” Appl. Opt. 26, 4677–4680 (1987).
[CrossRef]

1986 (1)

O. Podzimek, C. J. Heuvelman, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

1985 (1)

D. F. Weirauch, “A study of lapping and polishing damage in single-crystal CdTe,” J. Electrochem. Soc. 132, 250–254 (1985).
[CrossRef]

1972 (1)

B. J. Hockey, “Observations by TEM on the subsurface damage produced in aluminum oxide by mechanical polishing and grinding,” Proc. Br. Ceram. Soc. 20, 95–115 (1972).

1970 (1)

B. G. Cohen, M. W. Frocht, “X-ray measurement of elastic strain and annealing in semiconductors,” Solid-State Electron. 13, 105–112 (1970).
[CrossRef]

1965 (1)

D. Haneman, “Strain energy of (111) and (-1-1-1) surfaces of InSb,” Brit. J. Appl. Phys. 16, 411–413 (1965).
[CrossRef]

1964 (1)

E. N. Pugh, L. E. Samuels, “Damaged layers in abraded silicon surfaces,” J. Electrochem. Soc. 111, 1430–1432 (1964).
[CrossRef]

1957 (1)

F. K. Aleinikov, “The effect of certain physical and mechanical properties on the grinding of brittle materials,” Sov. Phys. Tech. Phys. 27, 2529–2538 (1957).

1922 (1)

F. W. Preston, “Structure of abraded glass surfaces,” Trans. Opt. Soc. 23(3), 141–164 (1922).
[CrossRef]

Ahn, Y.

Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
[CrossRef]

Akita, K.

M. Taneya, Y. Sugimoto, K. Akita, “Characterization of subsurface damage in GaAs processed by Ga+ focused ion-beam-assisted Cl2 etching using photoluminescence,” J. Appl. Phys. 66, 1375–1381 (1989).
[CrossRef]

Aleinikov, F. K.

F. K. Aleinikov, “The effect of certain physical and mechanical properties on the grinding of brittle materials,” Sov. Phys. Tech. Phys. 27, 2529–2538 (1957).

Arrasmith, S. R.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

Atwood, M.

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp. 28–31. See also Ref. 2.

Bhushan, B.

S. Chandrasekhar, M. C. Shaw, B. Bhushan, “Comparison of grinding and lapping of ferrites and metals,” ASME J. Eng. Ind. 109, 76–82 (1987).
[CrossRef]

Bifano, T. G.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” ASME J. Eng. Ind.113, 184–189.

Blech, I.

I. Blech, D. Dang, “Silicon wafer deformation after backside grinding,” Solid State Technol., August, 1994, pp. 74–76.

Blessing, G. V.

J. A. Slotwincki, N. N. Hsu, G. V. Blessing, “Ultrasonic measurement of surface and subsurface structure in ceramics,” in Proceeding of the International Conference on Machining of Advanced Materials, NIST Special Publ. 847, S. Jahanmir, ed. (U. S. Gov. Printing Office, Washington, D.C., 1993).

Bowes, P.

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

Brinksmeier, E.

E. Brinksmeier, “State-of-the-art non-destructive measurement of subsurface material properties and damages,” Precis. Eng. 11, 211–224 (1989).
[CrossRef]

Chandrasekhar, S.

Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
[CrossRef]

S. Chandrasekhar, M. C. Shaw, B. Bhushan, “Comparison of grinding and lapping of ferrites and metals,” ASME J. Eng. Ind. 109, 76–82 (1987).
[CrossRef]

Chen, K.-H.

J. C. Lambropoulos, K.-H. Chen, T. J. Lambropoulos, “Deformation of silicon surfaces,” in Optical Materials and Structures Technologies, W. A. Goodman, ed., Proc. SPIE5179, 203–214 (2003).
[CrossRef]

Clarke, D. R.

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

Cleaveland, E. E.

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

Cohen, B. G.

B. G. Cohen, M. W. Frocht, “X-ray measurement of elastic strain and annealing in semiconductors,” Solid-State Electron. 13, 105–112 (1970).
[CrossRef]

Cook, R. F.

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

Dang, D.

I. Blech, D. Dang, “Silicon wafer deformation after backside grinding,” Solid State Technol., August, 1994, pp. 74–76.

Domnich, V.

T. Juliano, V. Domnich, Y. Gogotsi, “Examining pressure-induced phase transformations in silicon by spherical indentation and Raman spectroscopy: a statistical study,” J. Mater. Res. 19, 3099–3108 (2004).
[CrossRef]

Dow, T. A.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” ASME J. Eng. Ind.113, 184–189.

Dumas, P.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Ebrahimi, F.

F. Ebrahimi, L. Kalwani, “Fracture anisotrophy in silicon single crystal,” Mat. Sci. Eng. A 268, 116–126 (1999).
[CrossRef]

Edwards, D. F.

Fang, T.

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

T. Fang, “Near surface mechanical properties of optical materials in deterministic microgrinding,” Ph.D. Thesis (University of Rochester, Rochester, New York, 1997).

Farris, T. N.

Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
[CrossRef]

Ferreira, C.

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp. 28–31. See also Ref. 2.

Frocht, M. W.

B. G. Cohen, M. W. Frocht, “X-ray measurement of elastic strain and annealing in semiconductors,” Solid-State Electron. 13, 105–112 (1970).
[CrossRef]

Funkenbusch, P. D.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).

Gillman, B. E.

J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).

Gogotsi, Y.

T. Juliano, V. Domnich, Y. Gogotsi, “Examining pressure-induced phase transformations in silicon by spherical indentation and Raman spectroscopy: a statistical study,” J. Mater. Res. 19, 3099–3108 (2004).
[CrossRef]

Gogotsi, Y. G.

A. Kailer, Y. G. Gogotsi, K. G. Nickel, “Phase transformations of silicon caused by contact loading,” J. Appl. Phys. 81, 3057–3063 (1997).
[CrossRef]

Golini, D.

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News, June1994, pp. 15–19.
[CrossRef]

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

D. Golini, S. D. Jacobs, “Transition between brittle and ductile mode in loose abrasive grinding,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 80–91 (1990).
[CrossRef]

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp. 28–31. See also Ref. 2.

Gregg, L. L.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Haneman, D.

D. Haneman, “Strain energy of (111) and (-1-1-1) surfaces of InSb,” Brit. J. Appl. Phys. 16, 411–413 (1965).
[CrossRef]

Hang, Z.

Z. Hang, H. Shen, F. H. Pollak, “Comprehensive investigation of polish-induced surface strain in 〈100〉 and 〈111〉 GaAs and InP,” J. Appl. Phys. 64, 3233–3242 (1988).
[CrossRef]

Hed, P. P.

Heuvelman, C. J.

O. Podzimek, C. J. Heuvelman, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

Hockey, B. J.

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

B. J. Hockey, “Observations by TEM on the subsurface damage produced in aluminum oxide by mechanical polishing and grinding,” Proc. Br. Ceram. Soc. 20, 95–115 (1972).

Hogan, S.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Hsu, N. N.

J. A. Slotwincki, N. N. Hsu, G. V. Blessing, “Ultrasonic measurement of surface and subsurface structure in ceramics,” in Proceeding of the International Conference on Machining of Advanced Materials, NIST Special Publ. 847, S. Jahanmir, ed. (U. S. Gov. Printing Office, Washington, D.C., 1993).

Izumitani, T. S.

T. S. Izumitani, Optical Glass (American Institute of Physics, New York, 1986), Chap. 4.

Jacobs, S. D.

J. C. Lambropoulos, S. D. Jacobs, J. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).

D. Golini, S. D. Jacobs, “Transition between brittle and ductile mode in loose abrasive grinding,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 80–91 (1990).
[CrossRef]

J. A. Randi, J. C. Lambropoulos, S. D. Jacobs, “Determination of subsurface damage in optical materials using a noninvasive technique,” in Optical Fabrication and Testing Digest (Optical Society of America, Washington, D.C., 2002), pp. 61–63.

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).

Jahanmir, S.

H. H. K. Xu, S. Jahanmir, “Simple technique for observing subsurface damage in machining of ceramics,” J. Am. Ceram. Soc. 77, 1388–1390 (1994).
[CrossRef]

Juliano, T.

T. Juliano, V. Domnich, Y. Gogotsi, “Examining pressure-induced phase transformations in silicon by spherical indentation and Raman spectroscopy: a statistical study,” J. Mater. Res. 19, 3099–3108 (2004).
[CrossRef]

Kailer, A.

A. Kailer, Y. G. Gogotsi, K. G. Nickel, “Phase transformations of silicon caused by contact loading,” J. Appl. Phys. 81, 3057–3063 (1997).
[CrossRef]

Kalwani, L.

F. Ebrahimi, L. Kalwani, “Fracture anisotrophy in silicon single crystal,” Mat. Sci. Eng. A 268, 116–126 (1999).
[CrossRef]

Karow, H. H.

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

Kirchner, P. D.

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

Kordonski, W. I.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

Kozhinova, I. A.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Kroll, M. C.

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

Lambropoulos, J. C.

J. C. Lambropoulos, S. D. Jacobs, J. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).

J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).

J. C. Lambropoulos, “From abrasive size to subsurface damage in grinding,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 17–18.

J. A. Randi, J. C. Lambropoulos, S. D. Jacobs, “Determination of subsurface damage in optical materials using a noninvasive technique,” in Optical Fabrication and Testing Digest (Optical Society of America, Washington, D.C., 2002), pp. 61–63.

J. C. Lambropoulos, K.-H. Chen, T. J. Lambropoulos, “Deformation of silicon surfaces,” in Optical Materials and Structures Technologies, W. A. Goodman, ed., Proc. SPIE5179, 203–214 (2003).
[CrossRef]

Lambropoulos, T. J.

J. C. Lambropoulos, K.-H. Chen, T. J. Lambropoulos, “Deformation of silicon surfaces,” in Optical Materials and Structures Technologies, W. A. Goodman, ed., Proc. SPIE5179, 203–214 (2003).
[CrossRef]

Li, Y.

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).

Lindquist, A.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp. 28–31. See also Ref. 2.

Maltsev, A.

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

Mann, A. B.

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

Nickel, K. G.

A. Kailer, Y. G. Gogotsi, K. G. Nickel, “Phase transformations of silicon caused by contact loading,” J. Appl. Phys. 81, 3057–3063 (1997).
[CrossRef]

Perevoshchikov, V. A.

V. A. Perevoshchikov, V. D. Skupov, “Accumulation of defects in silicon wafers from operation to operation during mechanical finishing process,” Sov. J. Opt. Technol. 56, 302–305 (1989).

Pethica, J. B.

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

Podzimek, O.

O. Podzimek, C. J. Heuvelman, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

O. Podzimek, “Deformation energy under optical surfaces,” in High Power Lasers: Sources, Laser–Material Interactions, High Excitations, and Fast Dynamics, E.-W. Kreutz, D. Schuoecker, eds., Proc. SPIE801, 221–225 (1987).

Pollak, F. H.

Z. Hang, H. Shen, F. H. Pollak, “Comprehensive investigation of polish-induced surface strain in 〈100〉 and 〈111〉 GaAs and InP,” J. Appl. Phys. 64, 3233–3242 (1988).
[CrossRef]

Pollicove, H. H.

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News, June1994, pp. 15–19.
[CrossRef]

Preston, F. W.

F. W. Preston, “Structure of abraded glass surfaces,” Trans. Opt. Soc. 23(3), 141–164 (1922).
[CrossRef]

Pugh, E. N.

E. N. Pugh, L. E. Samuels, “Damaged layers in abraded silicon surfaces,” J. Electrochem. Soc. 111, 1430–1432 (1964).
[CrossRef]

Quesnel, D. J.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Randi, J. A.

J. A. Randi, J. C. Lambropoulos, S. D. Jacobs, “Determination of subsurface damage in optical materials using a noninvasive technique,” in Optical Fabrication and Testing Digest (Optical Society of America, Washington, D.C., 2002), pp. 61–63.

Romanofsky, H. J.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Ruckman, J.

J. C. Lambropoulos, S. D. Jacobs, J. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News, June1994, pp. 15–19.
[CrossRef]

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).

Saka, H.

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

Samuels, L. E.

E. N. Pugh, L. E. Samuels, “Damaged layers in abraded silicon surfaces,” J. Electrochem. Soc. 111, 1430–1432 (1964).
[CrossRef]

Scattergood, R. O.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” ASME J. Eng. Ind.113, 184–189.

Shaw, M. C.

S. Chandrasekhar, M. C. Shaw, B. Bhushan, “Comparison of grinding and lapping of ferrites and metals,” ASME J. Eng. Ind. 109, 76–82 (1987).
[CrossRef]

Shen, H.

Z. Hang, H. Shen, F. H. Pollak, “Comprehensive investigation of polish-induced surface strain in 〈100〉 and 〈111〉 GaAs and InP,” J. Appl. Phys. 64, 3233–3242 (1988).
[CrossRef]

Shimatani, A.

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

Shorey, A. B.

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

Skupov, V. D.

V. A. Perevoshchikov, V. D. Skupov, “Accumulation of defects in silicon wafers from operation to operation during mechanical finishing process,” Sov. J. Opt. Technol. 56, 302–305 (1989).

Slotwincki, J. A.

J. A. Slotwincki, N. N. Hsu, G. V. Blessing, “Ultrasonic measurement of surface and subsurface structure in ceramics,” in Proceeding of the International Conference on Machining of Advanced Materials, NIST Special Publ. 847, S. Jahanmir, ed. (U. S. Gov. Printing Office, Washington, D.C., 1993).

Stevens, H. J.

J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).

Suganuma, M.

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

Sugimoto, Y.

M. Taneya, Y. Sugimoto, K. Akita, “Characterization of subsurface damage in GaAs processed by Ga+ focused ion-beam-assisted Cl2 etching using photoluminescence,” J. Appl. Phys. 66, 1375–1381 (1989).
[CrossRef]

Suprijadi,

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

Taneya, M.

M. Taneya, Y. Sugimoto, K. Akita, “Characterization of subsurface damage in GaAs processed by Ga+ focused ion-beam-assisted Cl2 etching using photoluminescence,” J. Appl. Phys. 66, 1375–1381 (1989).
[CrossRef]

van Heerden, D.

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

Weihs, T. P.

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

Weirauch, D. F.

D. F. Weirauch, “A study of lapping and polishing damage in single-crystal CdTe,” J. Electrochem. Soc. 132, 250–254 (1985).
[CrossRef]

Xu, H. H. K.

H. H. K. Xu, S. Jahanmir, “Simple technique for observing subsurface damage in machining of ceramics,” J. Am. Ceram. Soc. 77, 1388–1390 (1994).
[CrossRef]

Xu, S.

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

Zhou, Y.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Ann. CIRP (1)

O. Podzimek, C. J. Heuvelman, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

Appl. Opt. (1)

Appl. Optics (1)

J. C. Lambropoulos, S. Xu, T. Fang, D. Golini, “Twyman effect mechanics in grinding and microgrinding,” Appl. Optics 35, 5704–5713 (1996).
[CrossRef]

ASME J. Eng. Ind. (1)

S. Chandrasekhar, M. C. Shaw, B. Bhushan, “Comparison of grinding and lapping of ferrites and metals,” ASME J. Eng. Ind. 109, 76–82 (1987).
[CrossRef]

Brit. J. Appl. Phys. (1)

D. Haneman, “Strain energy of (111) and (-1-1-1) surfaces of InSb,” Brit. J. Appl. Phys. 16, 411–413 (1965).
[CrossRef]

Ceram. Trans. (1)

J. C. Lambropoulos, S. D. Jacobs, J. Ruckman, “Material removal mechanisms from grinding to polishing,” Ceram. Trans. 102, 113–128 (1999).

J. Am. Ceram. Soc. (1)

H. H. K. Xu, S. Jahanmir, “Simple technique for observing subsurface damage in machining of ceramics,” J. Am. Ceram. Soc. 77, 1388–1390 (1994).
[CrossRef]

J. Amer. Ceram. Soc. (1)

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Amer. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

J. Appl. Phys. (3)

A. Kailer, Y. G. Gogotsi, K. G. Nickel, “Phase transformations of silicon caused by contact loading,” J. Appl. Phys. 81, 3057–3063 (1997).
[CrossRef]

Z. Hang, H. Shen, F. H. Pollak, “Comprehensive investigation of polish-induced surface strain in 〈100〉 and 〈111〉 GaAs and InP,” J. Appl. Phys. 64, 3233–3242 (1988).
[CrossRef]

M. Taneya, Y. Sugimoto, K. Akita, “Characterization of subsurface damage in GaAs processed by Ga+ focused ion-beam-assisted Cl2 etching using photoluminescence,” J. Appl. Phys. 66, 1375–1381 (1989).
[CrossRef]

J. Electrochem. Soc. (2)

E. N. Pugh, L. E. Samuels, “Damaged layers in abraded silicon surfaces,” J. Electrochem. Soc. 111, 1430–1432 (1964).
[CrossRef]

D. F. Weirauch, “A study of lapping and polishing damage in single-crystal CdTe,” J. Electrochem. Soc. 132, 250–254 (1985).
[CrossRef]

J. Manuf. Sci. Eng. (1)

Y. Ahn, S. Chandrasekhar, T. N. Farris, “Determination of surface residual stresses in machined ceramics using indentation fracture,” J. Manuf. Sci. Eng. 118, 483–489 (1996).
[CrossRef]

J. Mater. Res. (1)

T. Juliano, V. Domnich, Y. Gogotsi, “Examining pressure-induced phase transformations in silicon by spherical indentation and Raman spectroscopy: a statistical study,” J. Mater. Res. 19, 3099–3108 (2004).
[CrossRef]

Mat. Sci. Eng. A (1)

F. Ebrahimi, L. Kalwani, “Fracture anisotrophy in silicon single crystal,” Mat. Sci. Eng. A 268, 116–126 (1999).
[CrossRef]

Opt. Photon. News (1)

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News, June1994, pp. 15–19.
[CrossRef]

Philos. Mag. (2)

A. B. Mann, D. van Heerden, J. B. Pethica, P. Bowes, T. P. Weihs, “Contact resistance and phase transformations during nanoindentation of silicon,” Philos. Mag. A82, 1921–1929 (2002).
[CrossRef]

H. Saka, A. Shimatani, M. Suganuma, Suprijadi, “Transmission electron microscopy of amorphization and phase transformation beneath indents in Si,” Philos. Mag. A82, 1971–1982 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

D. R. Clarke, M. C. Kroll, P. D. Kirchner, R. F. Cook, B. J. Hockey, “Amorphization and conductivity of silicon and germanium induced by indentation,” Phys. Rev. Lett. 60, 2156–2159 (1988).
[CrossRef] [PubMed]

Precis. Eng. (1)

E. Brinksmeier, “State-of-the-art non-destructive measurement of subsurface material properties and damages,” Precis. Eng. 11, 211–224 (1989).
[CrossRef]

Proc. Br. Ceram. Soc. (1)

B. J. Hockey, “Observations by TEM on the subsurface damage produced in aluminum oxide by mechanical polishing and grinding,” Proc. Br. Ceram. Soc. 20, 95–115 (1972).

Solid State Technol. (1)

I. Blech, D. Dang, “Silicon wafer deformation after backside grinding,” Solid State Technol., August, 1994, pp. 74–76.

Solid-State Electron. (1)

B. G. Cohen, M. W. Frocht, “X-ray measurement of elastic strain and annealing in semiconductors,” Solid-State Electron. 13, 105–112 (1970).
[CrossRef]

Sov. J. Opt. Technol. (1)

V. A. Perevoshchikov, V. D. Skupov, “Accumulation of defects in silicon wafers from operation to operation during mechanical finishing process,” Sov. J. Opt. Technol. 56, 302–305 (1989).

Sov. Phys. Tech. Phys. (1)

F. K. Aleinikov, “The effect of certain physical and mechanical properties on the grinding of brittle materials,” Sov. Phys. Tech. Phys. 27, 2529–2538 (1957).

Trans. Opt. Soc. (1)

F. W. Preston, “Structure of abraded glass surfaces,” Trans. Opt. Soc. 23(3), 141–164 (1922).
[CrossRef]

Other (23)

J. A. Slotwincki, N. N. Hsu, G. V. Blessing, “Ultrasonic measurement of surface and subsurface structure in ceramics,” in Proceeding of the International Conference on Machining of Advanced Materials, NIST Special Publ. 847, S. Jahanmir, ed. (U. S. Gov. Printing Office, Washington, D.C., 1993).

T. S. Izumitani, Optical Glass (American Institute of Physics, New York, 1986), Chap. 4.

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

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” ASME J. Eng. Ind.113, 184–189.

D. Golini, S. D. Jacobs, “Transition between brittle and ductile mode in loose abrasive grinding,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 80–91 (1990).
[CrossRef]

J. C. Lambropoulos, Y. Li, P. D. Funkenbusch, J. Ruckman, “Non-contact estimate of grinding-induced subsurface damage,” in Optical Instrumentation and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 41–50 (1999).

J. C. Lambropoulos, “From abrasive size to subsurface damage in grinding,” in Optical Fabrication and Testing, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 17–18.

J. C. Lambropoulos, B. E. Gillman, S. D. Jacobs, H. J. Stevens, “Deterministic microgrinding, lapping, and polishing of glass-ceramics,” J. Amer. Ceram. Soc. (to be published).

O. Podzimek, “Deformation energy under optical surfaces,” in High Power Lasers: Sources, Laser–Material Interactions, High Excitations, and Fast Dynamics, E.-W. Kreutz, D. Schuoecker, eds., Proc. SPIE801, 221–225 (1987).

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing Workshop, Vol. 13 of 1994 OSA Technical Digest Series, (Optical Society of America, Washington, D.C., 1994), pp. 28–31. See also Ref. 2.

S. R. Arrasmith, S. D. Jacobs, J. C. Lambropoulos, A. Maltsev, D. Golini, W. I. Kordonski, E. E. Cleaveland, “The use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers,” in Optical Manufacturing and Testing IV, H. P. Stahl, ed., Proc. SPIE4451, 286–294 (2001).
[CrossRef]

J. C. Lambropoulos, K.-H. Chen, T. J. Lambropoulos, “Deformation of silicon surfaces,” in Optical Materials and Structures Technologies, W. A. Goodman, ed., Proc. SPIE5179, 203–214 (2003).
[CrossRef]

T. Fang, “Near surface mechanical properties of optical materials in deterministic microgrinding,” Ph.D. Thesis (University of Rochester, Rochester, New York, 1997).

Optipro Systems, 6368 Dean Parkway, Ontario, N.Y. 14519-8939, www.optipro.com .

NewView 5000: Objective, 20× Mirau; FDA resolution, high; scan length, 20 µm bipolar; min mod, 2.00; min area size, 7 (Zygo Corp., Laurel Brook Road, Middlefield, Conn. 06455, www.zygo.com ).

S. R. Arrasmith, I. A. Kozhinova, L. L. Gregg, A. B. Shorey, H. J. Romanofsky, S. D. Jacobs, D. Golini, W. I. Kordonski, S. Hogan, P. Dumas, “Details of polishing spot in magnetorheological finishing (MRF),” in Optical Manufacturing and Testing III, H. Stahl, ed., Proc. SPIE3782, 92–100 (1999).
[CrossRef]

J. A. Randi, J. C. Lambropoulos, S. D. Jacobs, “Determination of subsurface damage in optical materials using a noninvasive technique,” in Optical Fabrication and Testing Digest (Optical Society of America, Washington, D.C., 2002), pp. 61–63.

Form Talysurf Series 2, Taylor/Hobson, Suite 350, 2100 Golf Road, Rolling Meadows, Ill. 60008.

Olympus Vanox-T Model:AHMT, Olympus Optical Co., Inc.22-2, Nishishinjuka 1-chrome, Shinjuku-ku Tokyo, Japan.

Ono Sokki EG-133, 1-16-1 Hakusan, Midori-ku, Yokohama 226-8507, Japan.

ISP Optics, 1 Bridge St., Irvington, N.Y. 10533, www.ispoptics.com .

Crystal Systems, 27 Congress St., Salem, Mass. 01970, www.crystalsystems.com .

Crystal Technology Inc., 1040 East Meadow Circle, Palo Alto, Calif. 94303-4230.

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Figures (7)

Fig. 1
Fig. 1

COM ball dimple on MgF2 with a 1.59-mm diameter, viewed at 50× magnification.

Fig. 2
Fig. 2

Optical microscope view of a MRF spot at 15× magnification. The magnetorheological fluid enters from the left and exits to the right. The length of the spot is 1.2 cm.

Fig. 3
Fig. 3

Depth profile of a MRF spot taken across the centerline with a Taylor–Hobson Talysurf profilometer.

Fig. 4
Fig. 4

Leading edge of a spot on 10–20-µm abrasive ground fused silica at 50× magnification.

Fig. 5
Fig. 5

Trailing edge of a spot on 10–20-µm abrasive ground fused silica at 100× magnification. The 360-µm distance is measured with a digital indicator.

Fig. 6
Fig. 6

SSD measurements by the MRF technique, collected on BK7, with four spots being placed in etched and unetched regions, respectively.

Fig. 7
Fig. 7

SSD versus p–v surface microroughness, and the boundary of the inequality SSD ≤ 1.4 × p–v SR. The p–v microroughness is determined with white-light interferometry.

Tables (2)

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Table 1 Micromechanical Properties of the Single Crystals Useda

Tables Icon

Table 2 SSD Measurements by the COM Ball Dimple and MRF Spot Technique along the Leading Edge (LE) and Trailing Edge (TE)

Equations (3)

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SSD SR = 2.33 α K 2 / 3 ( E H ) ( 2 5 m ) / 3 ( cot ψ ) 1 / 9 ( sin ψ ) 1 / 2 [ P ( K c 4 / H 3 ) ] 1 / 6 ,
0.3 L 0.68 < SSD ( µ m ) < 2 L 0.85 ,
SSD ( µ m ) < 1.4 × SR ( p v , µ m ) ,

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