Abstract

An experimental investigation is made of a technique for measurement of surface roughness. A speckle pattern is formed near the image plane of a lens in spatially coherent light having a broad spectral bandwidth. The contrast of the speckle is found to be related to surface roughness when the roughness and the coherence length of illumination are comparable in magnitude. Implementation techniques are discussed and results shown that indicate good correlation with profilometer measurements for a wide range of roughness values produced with a variety of finishing procedures.

© 1972 Optical Society of America

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References

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  1. Surface Roughness Standard USAS B46.1
  2. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
    [Crossref]
  3. H. Davies, Proc. Inst. Elec. Eng. 101, 209 (1954).
  4. R. C. Birkebak, Appl. Opt. 10, 1070 (1971).
    [Crossref]
  5. P. Beckmann, A. Spizzichens, The Scattering of Electromagnetic Waves From Rough Surfaces (Macmillan, New York, 1963).
  6. J. B. P. Williamson, J. Pullen, R. T. Hunt, Proc. Inst. Mech. Eng. 182, 21 (fi967).
  7. D. P. Greenwood, E. J. Powers, J. Opt. Soc. Am. 61, 1589A (1971).
  8. R. C. Birkebak, Ph.D. dissertation, University of Minnesota (1962).
  9. R. A. Semplak, Bell Syst. Tech. J. 44, 1659 (1965).
  10. P. Beckmann, in Prõgress in Optics, E. Wolf, Ed. (Wiley, New York, 1967).
  11. C. R. Munnerlyn, M. Latta, Appl. Opt. 7, 1858 (1968).
    [Crossref] [PubMed]
  12. C. H. F. Velze, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, Newcastle-upon-Tyne, 1969).
  13. W. Ribbens, Appl. Opt. 8, 2173 (1969).
    [Crossref] [PubMed]
  14. W. Ribbens, Appl. Opt. 11, 807 (1972).
    [Crossref] [PubMed]
  15. B. J. Thompson, Ind. Photogr. 15, 24 (1966).
  16. J. W. Goodman, Stanford Electronics Lab Tech. Report 2303-1 (1963).
  17. R. A. Sprague, J. Opt. Soc. Am. 62, 723A (1972).
  18. M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).
  19. J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).
  20. T. J. Skinner, Ph.D. Dissertation, Boston University (1964).
  21. D. R. Craig, Sci. Eng. 5, 337 (1961).
  22. C. E. K. Mees, T. H. James, Eds., The Theory of the Photographic Process (Macmillan, New York, 1966), p. 582.

1972 (3)

W. Ribbens, Appl. Opt. 11, 807 (1972).
[Crossref] [PubMed]

R. A. Sprague, J. Opt. Soc. Am. 62, 723A (1972).

M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).

1971 (2)

R. C. Birkebak, Appl. Opt. 10, 1070 (1971).
[Crossref]

D. P. Greenwood, E. J. Powers, J. Opt. Soc. Am. 61, 1589A (1971).

1969 (1)

1968 (1)

1966 (1)

B. J. Thompson, Ind. Photogr. 15, 24 (1966).

1965 (1)

R. A. Semplak, Bell Syst. Tech. J. 44, 1659 (1965).

1962 (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

1961 (2)

1954 (1)

H. Davies, Proc. Inst. Elec. Eng. 101, 209 (1954).

Beckmann, P.

P. Beckmann, A. Spizzichens, The Scattering of Electromagnetic Waves From Rough Surfaces (Macmillan, New York, 1963).

P. Beckmann, in Prõgress in Optics, E. Wolf, Ed. (Wiley, New York, 1967).

Bennett, H. E.

Birkebak, R. C.

R. C. Birkebak, Appl. Opt. 10, 1070 (1971).
[Crossref]

R. C. Birkebak, Ph.D. dissertation, University of Minnesota (1962).

Craig, D. R.

D. R. Craig, Sci. Eng. 5, 337 (1961).

Davies, H.

H. Davies, Proc. Inst. Elec. Eng. 101, 209 (1954).

Elbaum, M.

M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).

Goodman, J. W.

J. W. Goodman, Stanford Electronics Lab Tech. Report 2303-1 (1963).

Gordon, E. I.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Greenebaum, M.

M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).

Greenwood, D. P.

D. P. Greenwood, E. J. Powers, J. Opt. Soc. Am. 61, 1589A (1971).

Hunt, R. T.

J. B. P. Williamson, J. Pullen, R. T. Hunt, Proc. Inst. Mech. Eng. 182, 21 (fi967).

King, M.

M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).

Latta, M.

Munnerlyn, C. R.

Porteus, J. O.

Powers, E. J.

D. P. Greenwood, E. J. Powers, J. Opt. Soc. Am. 61, 1589A (1971).

Pullen, J.

J. B. P. Williamson, J. Pullen, R. T. Hunt, Proc. Inst. Mech. Eng. 182, 21 (fi967).

Ribbens, W.

Rigden, J. D.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Semplak, R. A.

R. A. Semplak, Bell Syst. Tech. J. 44, 1659 (1965).

Skinner, T. J.

T. J. Skinner, Ph.D. Dissertation, Boston University (1964).

Spizzichens, A.

P. Beckmann, A. Spizzichens, The Scattering of Electromagnetic Waves From Rough Surfaces (Macmillan, New York, 1963).

Sprague, R. A.

R. A. Sprague, J. Opt. Soc. Am. 62, 723A (1972).

Thompson, B. J.

B. J. Thompson, Ind. Photogr. 15, 24 (1966).

Velze, C. H. F.

C. H. F. Velze, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, Newcastle-upon-Tyne, 1969).

Williamson, J. B. P.

J. B. P. Williamson, J. Pullen, R. T. Hunt, Proc. Inst. Mech. Eng. 182, 21 (fi967).

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

R. A. Semplak, Bell Syst. Tech. J. 44, 1659 (1965).

Ind. Photogr. (1)

B. J. Thompson, Ind. Photogr. 15, 24 (1966).

J. Opt. Soc. Am. (4)

H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
[Crossref]

D. P. Greenwood, E. J. Powers, J. Opt. Soc. Am. 61, 1589A (1971).

R. A. Sprague, J. Opt. Soc. Am. 62, 723A (1972).

M. Elbaum, M. King, M. Greenebaum, J. Opt. Soc. Am. 62, 732A (1972).

Proc. Inst. Elec. Eng. (1)

H. Davies, Proc. Inst. Elec. Eng. 101, 209 (1954).

Proc. Inst. Mech. Eng. (1)

J. B. P. Williamson, J. Pullen, R. T. Hunt, Proc. Inst. Mech. Eng. 182, 21 (fi967).

Proc. IRE (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Sci. Eng. (1)

D. R. Craig, Sci. Eng. 5, 337 (1961).

Other (8)

C. E. K. Mees, T. H. James, Eds., The Theory of the Photographic Process (Macmillan, New York, 1966), p. 582.

Surface Roughness Standard USAS B46.1

C. H. F. Velze, in Optical Instruments and Techniques, J. H. Dickson, Ed. (Oriel Press, Newcastle-upon-Tyne, 1969).

T. J. Skinner, Ph.D. Dissertation, Boston University (1964).

P. Beckmann, A. Spizzichens, The Scattering of Electromagnetic Waves From Rough Surfaces (Macmillan, New York, 1963).

R. C. Birkebak, Ph.D. dissertation, University of Minnesota (1962).

P. Beckmann, in Prõgress in Optics, E. Wolf, Ed. (Wiley, New York, 1967).

J. W. Goodman, Stanford Electronics Lab Tech. Report 2303-1 (1963).

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Figures (6)

Fig. 1
Fig. 1

Apparatus used to measure speckle contrast by scanning speckle pattern past a point detector.

Fig. 2
Fig. 2

Modulated portions of speckle pattern scans made with illumination having a coherence length of 1.5 μm. σr is the average surface roughness as measured with a profilometer. All these speckle patterns have the same mean intensity.

Fig. 3
Fig. 3

Speckle pattern scans made with different coherence lengths of illumination for two surfaces having different roughness values.

Fig. 4
Fig. 4

Speckle contrast vs surface roughness as measured with a profilometer. The contrast is seen to become small when the roughness is comparable in magnitude with the coherence length of illumination (1.5 μm) and when the roughness is less than a quarter of the mean wavelength of illumination (λ = 0.5 μm).

Fig. 5
Fig. 5

Apparatus used to measure speckle contrast with nonlinear photoconductive cells.

Fig. 6
Fig. 6

Photocell difference reading vs surface roughness as measured with a profilometer. The coherence length of illumination was approximately 8.5 μm, with a mean wavelength of 0.75 μm. The apparent linearity of response is due to the combination of nonlinear photocell response with a nonlinear contrast curve.

Equations (6)

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

L c = c / Δ ν ,
D = 2 λ Z / d ,
Δ Z = Z M Δ X / D ,
P 1 P 2 / Δ Z = D / Z ,
P 1 P 2 / P 1 P 2 = P 1 P 2 / Δ X = M ,
Δ Z = Z M Δ X / D .

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