Abstract

In an interferometer which uses a reference surface, the measured surface heights correspond to the difference between the test and reference surfaces. To accurately determine the rms roughness of supersmooth surfaces, the effects of the reference surface roughness need to be removed. One technique for doing this involves averaging a number of uncorrelated measurements of a mirror to generate a reference surface profile which can then be subtracted from subsequent measurements so that they do not contain errors due to the reference surface. The other technique provides an accurate rms roughness of the surface by taking two uncorrelated measurements of the surface. These two techniques for measurement of supersmooth surfaces are described in detail, and results of the measurement of a 0.7-Å rms roughness mirror are presented. The expected error in the rms roughness measurement of a supersmooth mirror due to instrument noise is 0.02 Å.

© 1990 Optical Society of America

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References

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  1. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, DC, 1989).
  2. J. M. Bennett, “Comparison of Techniques for Measuring the Roughness of Optical Surfaces,” Opt. Eng. 24, 380–387 (1985).
    [CrossRef]
  3. W. T. Welford, “Noncontacting Measurement of Surface Roughness,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 118–121 (1980).
  4. G. E. Sommargren, “Optical Heterodyne Profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  5. B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489–1497 (1985).
    [CrossRef] [PubMed]
  6. J. M. Zavisland, J. M. Eastman, “Measurement and Effects of Surface Defects and Quality of Polish,” Proc. Soc. Photo-Opt. Instrum. Eng. 525, 169–173 (1985).
  7. D. Pantzer, J. Politch, L. Ek, “Heterodyne Profiling Instrument for the Angstrom Region,” Appl. Opt. 25, 4168–4172 (1986).
    [CrossRef] [PubMed]
  8. F. Laeri, T. C. Strand, “Angstrom Resolution Optical Profilometry for Microscopic Objects,” Appl. Opt. 26, 2245–2249 (1987).
    [CrossRef] [PubMed]
  9. J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
    [CrossRef]
  10. J. F. Biegen, R. A. Smythe, “High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology,” in Proceedings, Fourth International Conference on Metrology and Properties of Engineering Surfaces (National Bureau of Standards, Washington, DC, 13–15Apr.1988).
  11. J. C. Wyant, “Measurement of Roughness of Supersmooth Optical Surfaces,” Acta Polytech. Scand., Proc. Image Science ’85, Helsinki, Finland Ph 150, 241–244 (1985).
  12. P. Beckman, Elements of Applied Probability Theory (Harcourt, Brace & World, New York, 1968).
  13. Correlation length is defined as the distance over which the autocovariance function falls to 0.1 of its maximum value (ANSI Standard B46.1-1978, Surface Texture, p. 34). It can be calculated from a measured profile of the surface.
  14. K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
    [CrossRef]

1988 (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

1987 (1)

F. Laeri, T. C. Strand, “Angstrom Resolution Optical Profilometry for Microscopic Objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

1986 (2)

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

D. Pantzer, J. Politch, L. Ek, “Heterodyne Profiling Instrument for the Angstrom Region,” Appl. Opt. 25, 4168–4172 (1986).
[CrossRef] [PubMed]

1985 (4)

J. C. Wyant, “Measurement of Roughness of Supersmooth Optical Surfaces,” Acta Polytech. Scand., Proc. Image Science ’85, Helsinki, Finland Ph 150, 241–244 (1985).

J. M. Bennett, “Comparison of Techniques for Measuring the Roughness of Optical Surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef] [PubMed]

J. M. Zavisland, J. M. Eastman, “Measurement and Effects of Surface Defects and Quality of Polish,” Proc. Soc. Photo-Opt. Instrum. Eng. 525, 169–173 (1985).

1981 (1)

1980 (1)

W. T. Welford, “Noncontacting Measurement of Surface Roughness,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 118–121 (1980).

Basila, D.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

Beckman, P.

P. Beckman, Elements of Applied Probability Theory (Harcourt, Brace & World, New York, 1968).

Bennett, J. M.

J. M. Bennett, “Comparison of Techniques for Measuring the Roughness of Optical Surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, DC, 1989).

Bhushan, B.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef] [PubMed]

Biegen, J. F.

J. F. Biegen, R. A. Smythe, “High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology,” in Proceedings, Fourth International Conference on Metrology and Properties of Engineering Surfaces (National Bureau of Standards, Washington, DC, 13–15Apr.1988).

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Eastman, J. M.

J. M. Zavisland, J. M. Eastman, “Measurement and Effects of Surface Defects and Quality of Polish,” Proc. Soc. Photo-Opt. Instrum. Eng. 525, 169–173 (1985).

Ek, L.

Koliopoulos, C. L.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef] [PubMed]

Laeri, F.

F. Laeri, T. C. Strand, “Angstrom Resolution Optical Profilometry for Microscopic Objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, DC, 1989).

Pantzer, D.

Politch, J.

Smythe, R. A.

J. F. Biegen, R. A. Smythe, “High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology,” in Proceedings, Fourth International Conference on Metrology and Properties of Engineering Surfaces (National Bureau of Standards, Washington, DC, 13–15Apr.1988).

Sommargren, G. E.

Strand, T. C.

F. Laeri, T. C. Strand, “Angstrom Resolution Optical Profilometry for Microscopic Objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

Welford, W. T.

W. T. Welford, “Noncontacting Measurement of Surface Roughness,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 118–121 (1980).

Wyant, J. C.

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurement of Surface Topography of Magnetic Tapes by Mirau Interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef] [PubMed]

J. C. Wyant, “Measurement of Roughness of Supersmooth Optical Surfaces,” Acta Polytech. Scand., Proc. Image Science ’85, Helsinki, Finland Ph 150, 241–244 (1985).

Zavisland, J. M.

J. M. Zavisland, J. M. Eastman, “Measurement and Effects of Surface Defects and Quality of Polish,” Proc. Soc. Photo-Opt. Instrum. Eng. 525, 169–173 (1985).

Appl. Opt. (1)

F. Laeri, T. C. Strand, “Angstrom Resolution Optical Profilometry for Microscopic Objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Tribol. (1)

J. C. Wyant, C. L. Koliopoulos, B. Bhushan, D. Basila, “Development of a Three-Dimensional Noncontact Digital Optical Profiler,” Trans. ASME, J. Tribol. 108, 1–8 (1986).
[CrossRef]

Opt. Eng. (1)

J. M. Bennett, “Comparison of Techniques for Measuring the Roughness of Optical Surfaces,” Opt. Eng. 24, 380–387 (1985).
[CrossRef]

Proc. Image Science ’85, Helsinki, Finland (1)

J. C. Wyant, “Measurement of Roughness of Supersmooth Optical Surfaces,” Acta Polytech. Scand., Proc. Image Science ’85, Helsinki, Finland Ph 150, 241–244 (1985).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. M. Zavisland, J. M. Eastman, “Measurement and Effects of Surface Defects and Quality of Polish,” Proc. Soc. Photo-Opt. Instrum. Eng. 525, 169–173 (1985).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

W. T. Welford, “Noncontacting Measurement of Surface Roughness,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 118–121 (1980).

Prog. Opt. (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[CrossRef]

Other (4)

P. Beckman, Elements of Applied Probability Theory (Harcourt, Brace & World, New York, 1968).

Correlation length is defined as the distance over which the autocovariance function falls to 0.1 of its maximum value (ANSI Standard B46.1-1978, Surface Texture, p. 34). It can be calculated from a measured profile of the surface.

J. F. Biegen, R. A. Smythe, “High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology,” in Proceedings, Fourth International Conference on Metrology and Properties of Engineering Surfaces (National Bureau of Standards, Washington, DC, 13–15Apr.1988).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, DC, 1989).

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Figures (7)

Fig. 1
Fig. 1

Error in the rms roughness measured for a reference surface with 5-Å rms roughness.

Fig. 2
Fig. 2

Measurement of supersmooth mirror including the reference surface.

Fig. 3
Fig. 3

Profile of reference surface generated by averaging sixteen uncorrelated measurements of the supersmooth mirror.

Fig. 4
Fig. 4

Difference between Figs. 2 and 3 showing the supersmooth mirror without the effects of the reference surface on the same scale as Figs. 2 and 3.

Fig. 5
Fig. 5

Same as Fig. 4 plotted on a different height scale. Profile and roughness of surface can be seen.

Fig. 6
Fig. 6

Different between two consecutive data sets taken at a single location on a mirror indicating the noise level of the measurements.

Fig. 7
Fig. 7

Absolute measurement of the supersmooth mirror made with two uncorrelated measurements.

Equations (17)

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meas ( x ) = test ( x ) + ref ( x ) .
σ meas = σ test 2 + σ ref 2 ,
meas ( x ) i = mirror ( x ) i + ref ( x ) ,
genref ( x ) = 1 N i = 1 N meas ( x ) i = 1 N i = 1 N mirror ( x ) i + ref ( x ) ,
genref ( x ) 2 = [ 1 N i = 1 N mirror ( x ) i ] 2 + ref ( x ) 2 ,
genref ( x ) 2 = 1 N 2 i = 1 N mirror ( x ) 2 + ref ( x ) 2 = 1 N mirror ( x ) 2 + ref ( x ) 2 .
σ genref = ( σ mirror N ) 2 + σ ref 2 ,
meas ( x ) - genref ( x ) = test ( x ) - error ( x ) ,
error ( x ) = 1 N i = 1 N mirror ( x ) i .
σ test = σ meas - genref 2 + σ error 2 ,
σ error = σ mirror N ,
meas ( x ) 1 = test ( x ) 1 + ref ( x ) , meas ( x ) 2 = test ( x ) 2 + ref ( x ) ,
diff ( x ) = meas ( x ) 1 - meas ( x ) 2 = test ( x ) 1 - test ( x ) 2 .
diff ( x ) = test ( x ) 1 + [ - test ( x ) 2 ] ,
σ diff 2 = σ test 1 2 + σ test 2 2 .
σ test 1 = σ test 2 .
σ test = σ diff 2 .

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