Abstract

The design and properties of an optical probe for on-line measurement of surface roughness are discussed. Based on light scattering, a probe that consists of a laser diode, a measuring lens, and a linear photodiode array was designed to detect surface roughness, in which the light scattered from a test surface at a relatively large scattering angle φ (=28°) can be collected to enhance measuring range and repeatability. A coaxial design that incorporates a dual-laser probe and compressed air makes the proposed system insensitive to the position of the test surface and to surface conditions such as the presence of debris, vibration, and lubricants that result from machining. The results from measurements of several sets of specimens have demonstrated the feasibility of measuring surface roughness by using light scattering. On-line measurement on a diamond-turning lathe has shown that the proposed technique is stable and compact enough to be applicable to on-line measurement of surface roughness of an engineering surface.

© 2003 Optical Society of America

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References

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  1. D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
    [CrossRef]
  2. D. J. Whitehouse, “Stylus contact method for surface metrology in the ascendancy,” Meas. Control. 31, 48–50 (1998).
  3. J. M. Bennett, “Recent developments in surface roughness characterization,” Meas. Sci. Technol. 3, 1119–1127 (1992).
    [CrossRef]
  4. J. Kangami, Hatazawa, “Measurement of surface profiles by the focus method,” Wear 134, 221–229 (1989).
    [CrossRef]
  5. C. J. Tay, S. L. Toh, H. M. Shang, J. B. Zhang, “Whole-field determination of surface roughness by speckle correlation,” Appl. Opt. 34, 2324–2335 (1995).
    [CrossRef] [PubMed]
  6. J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
    [CrossRef]
  7. T. V. Vorburger, E. Marx, T. R. Lettieri, “Regimes of surface roughness measurable with light scattering,” Appl. Opt. 32, 3401–3408 (1993).
    [CrossRef] [PubMed]
  8. U. Persson, “Measurement of surface roughness using infrared scattering,” Measurement 18, 109–116 (1996).
    [CrossRef]
  9. S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
    [CrossRef]
  10. P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
    [CrossRef]
  11. T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1980).
    [CrossRef]
  12. F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
    [CrossRef]
  13. O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
    [CrossRef]
  14. J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
    [CrossRef]
  15. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).
  16. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
    [CrossRef]
  17. V. S. Pugachev, Probability Theory and Mathematical Statistics for Engineers (Pergamon, Oxford, 1984).
  18. S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
    [CrossRef]
  19. R. Brodmann, O. Gerstorfer, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
    [CrossRef]
  20. J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
    [CrossRef]
  21. K. Takami, “Defect inspection of wafers by laser scattering,” Mater. Sci. Technol. B 44, 181–187 (1997).
  22. P. Sandland, “Automated defect inspection: past, present and future,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed. Proc. SPIE3332, 296–308 (1998).
    [CrossRef]
  23. G. J. Dixon, “Light scattering maps surface imperfections,” Laser Focus World 34, 89–93 (1998).
  24. S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
    [CrossRef]

2002 (1)

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

2001 (1)

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

2000 (2)

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

1998 (3)

O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
[CrossRef]

G. J. Dixon, “Light scattering maps surface imperfections,” Laser Focus World 34, 89–93 (1998).

D. J. Whitehouse, “Stylus contact method for surface metrology in the ascendancy,” Meas. Control. 31, 48–50 (1998).

1997 (2)

K. Takami, “Defect inspection of wafers by laser scattering,” Mater. Sci. Technol. B 44, 181–187 (1997).

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

1996 (2)

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

U. Persson, “Measurement of surface roughness using infrared scattering,” Measurement 18, 109–116 (1996).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

J. M. Bennett, “Recent developments in surface roughness characterization,” Meas. Sci. Technol. 3, 1119–1127 (1992).
[CrossRef]

1989 (1)

J. Kangami, Hatazawa, “Measurement of surface profiles by the focus method,” Wear 134, 221–229 (1989).
[CrossRef]

1987 (2)

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
[CrossRef]

1985 (1)

R. Brodmann, O. Gerstorfer, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

1980 (1)

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1980).
[CrossRef]

1979 (2)

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

Bennett, J. M.

J. M. Bennett, “Recent developments in surface roughness characterization,” Meas. Sci. Technol. 3, 1119–1127 (1992).
[CrossRef]

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
[CrossRef]

Brodmann, R.

R. Brodmann, O. Gerstorfer, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

Bukthat, J. E.

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Church, E. L.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Dixon, G. J.

G. J. Dixon, “Light scattering maps surface imperfections,” Laser Focus World 34, 89–93 (1998).

Docchio, F.

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

Elson, J. M.

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
[CrossRef]

Fine, J.

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

Gerstorfer, O.

R. Brodmann, O. Gerstorfer, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

Giusti, F.

F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
[CrossRef]

Hatazawa,

J. Kangami, Hatazawa, “Measurement of surface profiles by the focus method,” Wear 134, 221–229 (1989).
[CrossRef]

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Kangami, J.

J. Kangami, Hatazawa, “Measurement of surface profiles by the focus method,” Wear 134, 221–229 (1989).
[CrossRef]

Kasashima, N.

O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
[CrossRef]

King, R. L.

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

Kusy, R. P.

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Lettieri, T. R.

Lorincik, J.

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

Marton, D.

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

Marx, E.

Mayhew, M. J.

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Mori, K.

O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
[CrossRef]

Persson, U.

U. Persson, “Measurement of surface roughness using infrared scattering,” Measurement 18, 109–116 (1996).
[CrossRef]

Pugachev, V. S.

V. S. Pugachev, Probability Theory and Mathematical Statistics for Engineers (Pergamon, Oxford, 1984).

Quan, C.

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

Rovati, L. G.

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

Ryabov, O.

O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
[CrossRef]

Sandland, P.

P. Sandland, “Automated defect inspection: past, present and future,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed. Proc. SPIE3332, 296–308 (1998).
[CrossRef]

Sansoni, G.

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

Santochi, M.

F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
[CrossRef]

Shang, H. M.

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

C. J. Tay, S. L. Toh, H. M. Shang, J. B. Zhang, “Whole-field determination of surface roughness by speckle correlation,” Appl. Opt. 34, 2324–2335 (1995).
[CrossRef] [PubMed]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

Takami, K.

K. Takami, “Defect inspection of wafers by laser scattering,” Mater. Sci. Technol. B 44, 181–187 (1997).

Tantussi, G.

F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
[CrossRef]

Tay, C. J.

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

C. J. Tay, S. L. Toh, H. M. Shang, J. B. Zhang, “Whole-field determination of surface roughness by speckle correlation,” Appl. Opt. 34, 2324–2335 (1995).
[CrossRef] [PubMed]

Teague, E. C.

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1980).
[CrossRef]

Toh, S. L.

Tomassini, P.

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

Vorburger, T. V.

T. V. Vorburger, E. Marx, T. R. Lettieri, “Regimes of surface roughness measurable with light scattering,” Appl. Opt. 32, 3401–3408 (1993).
[CrossRef] [PubMed]

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1980).
[CrossRef]

Wang, S. H.

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

Whitehouse, D. J.

D. J. Whitehouse, “Stylus contact method for surface metrology in the ascendancy,” Meas. Control. 31, 48–50 (1998).

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Whitley, J. Q.

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

Zhang, J. B.

Ann. CIRP (1)

F. Giusti, M. Santochi, G. Tantussi, “On-line sensing of flank and crater wear of cutting tools,” Ann. CIRP 36, 41–44 (1987).
[CrossRef]

Appl. Opt. (2)

J. Nondestruct. Eval. (1)

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Using laser scattering for detection of cracks on a micro-solderball surface,” J. Nondestruct. Eval. 20, 145–151 (2002).
[CrossRef]

J. Vac. Sci. Technol. B (1)

J. Lorincik, D. Marton, R. L. King, J. Fine, “Scanning scattering microscope for surface microtopography and defect imaging,” J. Vac. Sci. Technol. B 14, 2417–2423 (1996).
[CrossRef]

Laser Focus World (1)

G. J. Dixon, “Light scattering maps surface imperfections,” Laser Focus World 34, 89–93 (1998).

Mater. Sci. Technol. B (1)

K. Takami, “Defect inspection of wafers by laser scattering,” Mater. Sci. Technol. B 44, 181–187 (1997).

Meas. Control. (1)

D. J. Whitehouse, “Stylus contact method for surface metrology in the ascendancy,” Meas. Control. 31, 48–50 (1998).

Meas. Sci. Technol. (2)

J. M. Bennett, “Recent developments in surface roughness characterization,” Meas. Sci. Technol. 3, 1119–1127 (1992).
[CrossRef]

D. J. Whitehouse, “Surface metrology,” Meas. Sci. Technol. 8, 955–972 (1997).
[CrossRef]

Measurement (1)

U. Persson, “Measurement of surface roughness using infrared scattering,” Measurement 18, 109–116 (1996).
[CrossRef]

Opt. Eng. (4)

S. H. Wang, C. Quan, C. J. Tay, H. M. Shang, “Surface roughness measurement in the submicrometer range using laser scattering,” Opt. Eng. 39, 1597–1601 (2000).
[CrossRef]

J. M. Elson, J. M. Bennett, “Vector scattering theory,” Opt. Eng. 18, 116–124 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship between surface scattering and microtopographic features,” Opt. Eng. 18, 125–136 (1979).
[CrossRef]

R. Brodmann, O. Gerstorfer, “Optical roughness measuring instrument for fine-machined surfaces,” Opt. Eng. 24, 408–413 (1985).
[CrossRef]

Opt. Laser Technol. (1)

J. Q. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Bukthat, “Surface roughness of stainless steel and electroformed nickel standards using a HeNe laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Opt. Lasers Eng. (2)

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Collimating of diverging laser beam using graded-index optical fiber,” Opt. Lasers Eng. 34, 121–127 (2000).
[CrossRef]

O. Ryabov, K. Mori, N. Kasashima, “Laser displacement meter application for milling diagnostics,” Opt. Lasers Eng. 30, 251–263 (1998).
[CrossRef]

Precis. Eng. (1)

T. V. Vorburger, E. C. Teague, “Optical techniques for on-line measurement of surface topography,” Precis. Eng. 3, 61–83 (1980).
[CrossRef]

Rev. Sci. Instrum. (1)

P. Tomassini, L. G. Rovati, G. Sansoni, F. Docchio, “Novel optical sensor for the measurement of surface texture,” Rev. Sci. Instrum. 72, 2207–2213 (2001).
[CrossRef]

Wear (1)

J. Kangami, Hatazawa, “Measurement of surface profiles by the focus method,” Wear 134, 221–229 (1989).
[CrossRef]

Other (3)

V. S. Pugachev, Probability Theory and Mathematical Statistics for Engineers (Pergamon, Oxford, 1984).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, Norwood, Mass., 1987).

P. Sandland, “Automated defect inspection: past, present and future,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed. Proc. SPIE3332, 296–308 (1998).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Laser beam scattered from a rough surface and its corresponding light distribution.

Fig. 2
Fig. 2

Schematic of the proposed optical probe.

Fig. 3
Fig. 3

Block diagram of the processing circuit.

Fig. 4
Fig. 4

Schematic diagram of a protection cap.

Fig. 5
Fig. 5

Configuration of the on-line measurement on a diamond-turning lathe.

Fig. 6
Fig. 6

S d versus R a for several machining processes: (a) lapping, (b) diamond turning, (c) flat grinding, and (d) planning.

Fig. 7
Fig. 7

Influence of workpiece diameter D on scattered light-distribution value S d .

Fig. 8
Fig. 8

Comparison of results with and without ambient disturbances.

Fig. 9
Fig. 9

Change of S d obtained from an aluminum workpiece on a diamond-turning lathe in different cutting stages corresponding to different turning speeds.

Tables (1)

Tables Icon

Table 1 Comparison of the Proposed Optical Probe and Stylus Data

Equations (7)

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

Pϕ= Iφ-π/2π/2 Iφdφ.
S=-π/2π/2 PφIφ-Ī2dφ,
Sd=k2i=1nIi-i¯2Pi,
Sd=982.8Ra+0.526,
Sd=648Ra+1.63,
Sd=6.7Ra+43
Sd=5Ra+52,

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