OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 25 — Sep. 1, 2000
  • pp: 4473–4485

Angular distribution of light scattered from a sinusoidal grating

Egon Marx, Thomas A. Germer, Theodore V. Vorburger, and Byong C. Park  »View Author Affiliations

Applied Optics, Vol. 39, Issue 25, pp. 4473-4485 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (184 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The angular distributions of light scattered by gold-coated and aluminum-coated gratings with amplitudes of ∼90 nm and periods of 6.67 µm were measured and calculated for light incident from a He–Ne laser at an angle of 6°. Experimental results are compared with predictions of Beckmann’s scalar theory and Rayleigh’s vector theory. The measured scattering pattern has a background of scattered light due mainly to residual surface roughness. Also the power in the higher-order peaks is larger by several orders of magnitude than the computed one, which can be attributed mainly to the low-order contributions of the harmonics in the profile.

© 2000 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings

Original Manuscript: January 14, 2000
Revised Manuscript: May 2, 2000
Published: September 1, 2000

Egon Marx, Thomas A. Germer, Theodore V. Vorburger, and Byong C. Park, "Angular distribution of light scattered from a sinusoidal grating," Appl. Opt. 39, 4473-4485 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Marx, T. R. Lettieri, T. V. Vorburger, M. McIntosh, “Sinusoidal surfaces as standards for BRDF instruments,” in Optical Scattering: Applications, Measurement, and Theory, J. C. Stover, ed., Proc. SPIE1530, 15–21 (1991).
  2. E. Marx, T. V. Vorburger, “Windowing effects on light scattered by sinusoidal surfaces,” in Optical Scattering: Applications, Measurement, and Theory II, J. C. Stover, ed., Proc. SPIE1995, 2–14 (1993).
  3. E. Marx, T. R. Lettieri, T. V. Vorburger, “Light scattering by sinusoidal surfaces: illumination windows and harmonics in standards,” Appl. Opt. 34, 1269–1277 (1995). [CrossRef] [PubMed]
  4. B. C. Park, T. V. Vorburger, T. A. Germer, E. Marx, “Scattering from sinusoidal gratings,” in Scattering and Surface Roughness, Z.-H. Gu, A. Maradudin, eds., Proc. SPIE3141, 65–77 (1997). [CrossRef]
  5. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Chaps. 4 and 5.
  6. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institute of Physics, Bristol, 1991), Chap. 4, pp. 80–84.
  7. Ref. 6, p. 42.
  8. J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, New York, 1990), p. 219.
  9. R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 16–17.
  10. Ref. 5, p. 81 or Ref. 6, p. 89.
  11. Ref. 8, p. 60.
  12. D. Maystre, “Integral methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 76–81.
  13. G. R. Jiracek, “Numerical comparisons of a modified Rayleigh approach with other rough surface EM scattering solutions,” IEEE Trans. Antennas Propag. 21, 393–396 (1973). [CrossRef]
  14. Certain commercial equipment is identified to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by NIST or does it imply that the equipment is necessarily the best available for the purpose.
  15. C. C. Asmail, C. L. Cromer, J. E. Proctor, J. J. Hsia, “Instrumentation at the National Institute of Standards and Technology for bidirectional reflectance distribution function (BRDF) measurements,” in Stray Radiation in Optical Systems III, R. P. Breault, ed., Proc. SPIE2260, 52–61 (1994). [CrossRef]
  16. T. A. Germer, C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999). [CrossRef]
  17. J. E. Harvey, C. L. Vernold, A. Krywonos, P. L. Thompson, “Diffracted radiance: a fundamental quantity of nonparaxial scalar diffraction theory,” Appl. Opt. 38, 6469–6481 (1999). [CrossRef]
  18. E. D. Palik, Handbook of Optical Constants (Academic, San Diego, Calif., 1985), pp. 286–295, 369–406.
  19. Ref. 8, pp. 112–115.
  20. A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt. Soc. Am. 73, 1028–1041 (1983). [CrossRef]
  21. D. A. Content, “Diffraction grating groove analysis used to predict efficiency and scatter performance,” in Gradient Index, Miniature, and Diffractive Optical Systems, A. D. Kathman, ed., Proc. SPIE3778, 19–30 (1999). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited