Abstract

Expressions relating the roughness of a plane surface to its specular reflectance at normal incidence are presented and are verified experimentally. The expressions are valid for the case when the root mean square surface roughness is small compared to the wavelength of light. If light of a sufficiently long wavelength is used, the decrease in measured specular reflectance due to surface roughness is a function only of the root mean square height of the surface irregularities. Long-wavelength specular reflectance measurements thus provide a simple and sensitive method for accurate measurement of surface finish. This method is particularly useful for surface finishes too fine to be measured accurately by conventional tracing instruments. Surface roughness must also be considered in precise optical measurements. For example, a non-negligible systematic error in specular reflectance measurements will be made even if the root mean square surface roughness is less than 0.01 wavelength. The roughness of even optically polished surfaces may thus be important for measurements in the visible and ultraviolet regions of the spectrum.

PDF Article

References

  • View by:
  • |
  • |

  1. Lord Rayleigh, Nature 64, 385 (1901).
  2. F. Jentzsch, Z. tech. Physik 7, 310 (1926).
  3. H. Hasunuma and J. Nara, J. Phys. Soc. Japan 11, 69 (1956).
  4. W. E. K. Middleton and G. Wyszecki, J. Opt. Soc. Am. 47, 1020 (1957).
  5. R. S. Hunter, J. Opt. Soc. Am. 36, 178 (1946).
  6. J. Guild, J. Sci. Instr. 17, 178 (1940).
  7. E. A. Ollard, J. Electrodepositor's Tech. Soc. 24, 1(1949).
  8. J. Halling, J. Sci. Instr. 31, 318 (1954).
  9. R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 41.
  10. H. Davies, Proc. Inst. Elec. Engrs. 101, 209 (1954).
  11. Davies refers to this function as the autocorrelation function. However, we shall use the term autocovariance function as a more appropriate name when the function in question is not normalized. For a discussion of the properties of such functions see J. H. Laning, Jr., and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill Book Company, Inc., New York, 1956); and R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, New York, 1958).
  12. E. Engelhard, Natl. Bur. Standards Circ. No. 581, 1 (1957).
  13. H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).
  14. F. W. Preston, Trans. Opt. Soc. (London) 23, 141 (1922).
  15. W. F. Koehler and W. C. White, J. Opt. Soc. Am. 45, 1011 (1955).
  16. W. F. Koehler, J. Opt. Soc. Am. 43, 743 (1953).
  17. S. Bochner and K. Chandrasekharan, Fourier Transforms (Princeton University Press, Princeton, New Jersey, 1949), p. 67.

Battin, R. H.

Davies refers to this function as the autocorrelation function. However, we shall use the term autocovariance function as a more appropriate name when the function in question is not normalized. For a discussion of the properties of such functions see J. H. Laning, Jr., and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill Book Company, Inc., New York, 1956); and R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, New York, 1958).

Bennett, H. E.

H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).

Bochner, S.

S. Bochner and K. Chandrasekharan, Fourier Transforms (Princeton University Press, Princeton, New Jersey, 1949), p. 67.

Chandrasekharan, K.

S. Bochner and K. Chandrasekharan, Fourier Transforms (Princeton University Press, Princeton, New Jersey, 1949), p. 67.

Davies, H.

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

Engelhard, E.

E. Engelhard, Natl. Bur. Standards Circ. No. 581, 1 (1957).

Guild, J.

J. Guild, J. Sci. Instr. 17, 178 (1940).

Halling, J.

J. Halling, J. Sci. Instr. 31, 318 (1954).

Hasunuma, H.

H. Hasunuma and J. Nara, J. Phys. Soc. Japan 11, 69 (1956).

Hunter, R. S.

R. S. Hunter, J. Opt. Soc. Am. 36, 178 (1946).

Jentzsch, F.

F. Jentzsch, Z. tech. Physik 7, 310 (1926).

Koehler, W. F.

H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).

W. F. Koehler, J. Opt. Soc. Am. 43, 743 (1953).

W. F. Koehler and W. C. White, J. Opt. Soc. Am. 45, 1011 (1955).

Laning, Jr., J. H.

Davies refers to this function as the autocorrelation function. However, we shall use the term autocovariance function as a more appropriate name when the function in question is not normalized. For a discussion of the properties of such functions see J. H. Laning, Jr., and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill Book Company, Inc., New York, 1956); and R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, New York, 1958).

Middleton, W. E. K.

W. E. K. Middleton and G. Wyszecki, J. Opt. Soc. Am. 47, 1020 (1957).

Nara, J.

H. Hasunuma and J. Nara, J. Phys. Soc. Japan 11, 69 (1956).

Ollard, E. A.

E. A. Ollard, J. Electrodepositor's Tech. Soc. 24, 1(1949).

Preston, F. W.

F. W. Preston, Trans. Opt. Soc. (London) 23, 141 (1922).

Rayleigh, Lord

Lord Rayleigh, Nature 64, 385 (1901).

White, W. C.

W. F. Koehler and W. C. White, J. Opt. Soc. Am. 45, 1011 (1955).

Wood, R. W.

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 41.

Wyszecki, G.

W. E. K. Middleton and G. Wyszecki, J. Opt. Soc. Am. 47, 1020 (1957).

Other

Lord Rayleigh, Nature 64, 385 (1901).

F. Jentzsch, Z. tech. Physik 7, 310 (1926).

H. Hasunuma and J. Nara, J. Phys. Soc. Japan 11, 69 (1956).

W. E. K. Middleton and G. Wyszecki, J. Opt. Soc. Am. 47, 1020 (1957).

R. S. Hunter, J. Opt. Soc. Am. 36, 178 (1946).

J. Guild, J. Sci. Instr. 17, 178 (1940).

E. A. Ollard, J. Electrodepositor's Tech. Soc. 24, 1(1949).

J. Halling, J. Sci. Instr. 31, 318 (1954).

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd ed., p. 41.

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

Davies refers to this function as the autocorrelation function. However, we shall use the term autocovariance function as a more appropriate name when the function in question is not normalized. For a discussion of the properties of such functions see J. H. Laning, Jr., and R. H. Battin, Random Processes in Automatic Control (McGraw-Hill Book Company, Inc., New York, 1956); and R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, New York, 1958).

E. Engelhard, Natl. Bur. Standards Circ. No. 581, 1 (1957).

H. E. Bennett and W. F. Koehler, J. Opt. Soc. Am. 50, 1 (1960).

F. W. Preston, Trans. Opt. Soc. (London) 23, 141 (1922).

W. F. Koehler and W. C. White, J. Opt. Soc. Am. 45, 1011 (1955).

W. F. Koehler, J. Opt. Soc. Am. 43, 743 (1953).

S. Bochner and K. Chandrasekharan, Fourier Transforms (Princeton University Press, Princeton, New Jersey, 1949), p. 67.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.