OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 40, Iss. 33 — Nov. 20, 2001
  • pp: 6072–6080

Width of the Specular Peak Perpendicular to the Principal Plane for Rough Surfaces

Gerhard Meister, André Rothkirch, Hartwig Spitzer, and Johann Bienlein  »View Author Affiliations


Applied Optics, Vol. 40, Issue 33, pp. 6072-6080 (2001)
http://dx.doi.org/10.1364/AO.40.006072


View Full Text Article

Acrobat PDF (293 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The bidirectional reflectance distribution function (BRDF) model developed by Torrance and Sparrow [J. Opt. Soc. Am. <b>57,</b> 1105–1114 (1967)] is used to describe the specular reflection of rough surfaces. We compare this model with the BRDF measurements of four manmade surfaces with different roughnesses. The model can be used to describe the basic features of the measured BRDFs. We found that the width of the specular peak perpendicular to the principal plane decreases strongly with an increasing illumination zenith angle in the data as well as in the model. A model analysis shows that the width is approximately proportional to the cosine of the illumination angle θ<sub><i>i</i></sub>, and the deviations are determined by the roughness of the surface. This relationship is accompanied by an increase in reflectance in the specular direction in the principal plane that is 1/cos θ<sub><i>i</i></sub> stronger than the increase for a perfectly smooth surface.

© 2001 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(150.0150) Machine vision : Machine vision
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(290.5880) Scattering : Scattering, rough surfaces

Citation
Gerhard Meister, André Rothkirch, Hartwig Spitzer, and Johann Bienlein, "Width of the Specular Peak Perpendicular to the Principal Plane for Rough Surfaces," Appl. Opt. 40, 6072-6080 (2001)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-33-6072


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Institut of Physics Publishing, Bristol, UK, 1992), pp. 1–250.
  2. J. C. Stover, Optical Scattering—Measurement and Analysis (The International Society for Optical Engineering, Bellingham, Wash., 1995), 2nd ed. pp. 1–321.
  3. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 81.
  4. J. M. Soto-Crespo and M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
  5. M. Saillard and D. Maystre, “Scattering from metallic and dielectric rough surfaces,” J. Opt. Soc. Am. A 7, 982–990 (1990).
  6. J. A. Sanchez-Gil and M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1285 (1991).
  7. M. E. Knotts, T. R. Michel, and K. A. Donnel, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” J. Opt. Soc. Am. A 10, 928–941 (1993).
  8. K. A. O’Donnell and E. R. Mendez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
  9. M. E. Knotts and K. A. Donnel, “Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness,” J. Opt. Soc. Am. A 11, 697–710 (1994).
  10. J. M. Bennett and L. Mattson, Introduction to Rough Surface Scattering (Optical Society of America, Washington, D.C., 1989).
  11. K. Torrance and E. Sparrow, “Theory for off-specular reflection from rough surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
  12. B. V. Ginneken, M. Stavridi, and J. J. Koenderink, “Diffuse and specular reflectance from rough surfaces,” Appl. Opt. 37, 130–139 (1998).
  13. G. Meister, A. Rothkirch, H. Spitzer, and J. Bienlein, “BRDF field studies for remote sensing of urban areas,” Remote Sens. Rev. 19, 37–57 (2000).
  14. S. Solheim, B. Hosgood, G. Andreoli, and J. Piironen, “Calibration and characterization of data from the European Goniometric Facility (EGO),” Report Eur 17268 en. (Space Applications Institute, Joint Research Centre, Ispra, Italy, 1996), pp. 1–31.
  15. G. Meister, “Bidirectional reflectance of urban surfaces,” Ph.D. dissertation, (Universität Hamburg, Hamburg, Germany, 2000), pp. 15–78, http://www.sub.uni-hamburg.de/disse/253/diss.pdf.
  16. M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vision 14, 227–251 (1995).
  17. K. J. Dana, B. v. Ginneken, S. K. Nayar, and J. J. Koenderink, “Reflectance and texture of real world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
  18. A. Rothkirch, G. Meister, B. Hosgood, H. Spitzer, and J. Bienlein, “BRDF measurements on urban materials using laser light,” Remote Sens. Rev. 19, 21–35 (2000).
  19. B. Phong, “Illumination for computer generated pictures,” Commun. ACM (Association for Computing Machinery) 18, 311–317 (1975).
  20. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Lamperis, “Geometric considerations and nomenclature for reflectance,” Monogram 160:52 (U. S. Department of Commerce, National Bureau of Standards, 1977), pp. 1–33.
  21. G. Meister, A. Rothkirch, H. Spitzer, and J. Bienlein, “The shape of the specular peak of rough surfaces,” in Proceedings of the Nineteenth Congress of the International Society for Photogrammetry and Remote Sensing (ISPRS), 16–23 July 2000, Amsterdam, Vol. 33 of International Archives of Photogrammetry and Remote Sensing (2000), pp. 852–860.
  22. G. Meister, A. Rothkirch, B. Hosgood, H. Spitzer, and J. Bienlein, “Error analysis for BRDF measurements at the European Goniometric Facility,” Remote Sens. Rev. 19, 111–131 (2000).
  23. A. Rothkirch, G. Meister, H. Spitzer, and J. Bienlein, “BRDF measurements of urban surface materials at the EGO facility using a laser source,” in Proceedings of the Nineteenth Congress of the International Society for Photogrammetry and Remote Sensing (ISPRS), 16–23 July 2000, Amsterdam, Vol. 33 of International Archives of Photogrammetry and Remote Sensing, (2000), pp. 777–784.
  24. S. Brandt, Data Analysis (Springer-Verlag, Berlin, 1999), pp. 1–652.
  25. L. B. Wolff, “On the relative brightness of specular and diffuse reflection,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 369–376.
  26. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
  27. W. Wanner, A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. Schaaf, and M. J. Barnsley, “Global retrieval of bidirectional reflectance and albedo over land from EOS modis and MISR data: theory and algorithm,” J. Geophys. Res. 102, 17143–17161 (1997).

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