OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 8 — Aug. 1, 1994
  • pp: 2286–2297

Backscattering cross section of a roughened sphere

Donald J. Schertler and Nicholas George  »View Author Affiliations

JOSA A, Vol. 11, Issue 8, pp. 2286-2297 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (1682 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The backscattering cross section of a perfectly conducting, roughened sphere is presented. It is derived from the calculation of the electric-field cross correlation at two temporal frequencies and at two points in the backscatter direction. Careful treatment has been given to the calculation of the ensemble average of the surface height and slope terms, particularly in the backscatter from the off-axis regions of the sphere where the angles of illumination become large. At these large angles significant portions of the surface are in shadow and fail to contribute to the backscatter. The effect of shadowing is treated as a multiplying factor of the percentage of the surface that is illuminated. The cross correlation of the field is reduced to give the backscattering cross section. Both Gaussian and exponential surface correlations are considered, representing extremes in surface structure. The cross sections of both surfaces are shown to increase for certain ranges of rms roughness and correlation length. This increase is due to the backscatter from the annular regions of the sphere, which, when viewed as an image, would appear as a bright ring or halo. These results are supported by experimental measurements taken from roughened disks as a function of the illumination angle.

© 1994 Optical Society of America

Original Manuscript: November 29, 1993
Manuscript Accepted: March 16, 1994
Published: August 1, 1994

Donald J. Schertler and Nicholas George, "Backscattering cross section of a roughened sphere," J. Opt. Soc. Am. A 11, 2286-2297 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Physik 25, 377–445 (1908). [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  4. L. Brillouin, “The scattering cross section of spheres for electromagnetic waves,” J. Appl. Phys. 20, 1110–1125 (1949). [CrossRef]
  5. B. R. Levy, J. B. Keller, “Diffraction by a smooth object,” Commun. Pure Appl. Math. 12, 159–209 (1959). [CrossRef]
  6. D. L. Sengupta, “The sphere,” in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. A. Senior, P. L. E. Uslenghi, eds. (North-Holland, Amsterdam, 1969), Chap. 10, pp. 353–415.
  7. T. Hagfors, “Relations between rough surfaces and their scattering properties as applied to radar astronomy,” in Radar Astronomy, J. V. Evans, T. Hagfors, eds. (McGraw-Hill, New York, 1968), Chap. 4 pp. 187–209.
  8. P. Beckmann, “Shadowing of random rough surfaces,” IEEE Trans. Antennas Propag. AP-13, 384–388 (1965). [CrossRef]
  9. R. J. Wagner, “Shadowing of randomly rough surfaces,” J. Acoust. Soc. Am. 41, 138–147 (1967). [CrossRef]
  10. B. G. Smith, “Geometric shadowing of a random rough surface,” IEEE Trans. Antennas Propag. AP-15, 668–671 (1967). [CrossRef]
  11. M. J. Sancer, “Shadow-corrected electromagnetic scattering from a randomly rough surface,” IEEE Trans. Antennas Propag. AP-17, 577–585 (1969). [CrossRef]
  12. R. Schiffer, K. O. Thielheim, “Light reflection from randomly oriented convex particles with rough surface,” J. Appl. Phys. 53, 2825–2830 (1982). [CrossRef]
  13. E. Bahar, S. Chakrabarti, “Scattering and depolarization by large conducting spheres with rough surfaces,” Appl. Opt. 24, 1820–1825 (1985). [CrossRef] [PubMed]
  14. E. Bahar, “Scattering cross sections for random rough surfaces: full wave analysis,” Radio Sci. 16, 331–341 (1981). [CrossRef]
  15. E. Bahar, D. E. Barrick, “Scattering cross sections for composite surfaces that cannot be treated as perturbed-physical optics problems,” Radio Sci. 18, 129–137 (1983). [CrossRef]
  16. N. C. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991). [CrossRef]
  17. N. C. Bruce, J. C. Dainty, “Multiple scattering from rough dielectric and metal surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 1471–1481 (1991). [CrossRef]
  18. N. George, A. C. Livanos, J. A. Roth, C. H. Papas, “Remote sensing of large roughened spheres,” Opt. Acta 23, 367–387 (1976). [CrossRef]
  19. N. George, “Speckle from rough, moving objects,” J. Opt. Soc. Am. 66, 1182–1194 (1976). [CrossRef]
  20. J. C. Erdmann, R. I. Gellert, “Speckle field of curved, rotating surfaces of Gaussian roughness illuminated by a laser light spot,” J. Opt. Soc. Am. 66, 1194–1204 (1976). [CrossRef]
  21. R. Schiffer, K. O. Thielheim, “Scattering of scalar waves by an impenetrable rough sphere,” Opt. Acta 31, 1085–1100 (1984). [CrossRef]
  22. R. Schiffer, “The coherent scattering cross-section of a slightly rough sphere,” Opt. Acta 33, 959–980 (1986). [CrossRef]
  23. R. Schiffer, “Light scattering by perfectly conducting statistically irregular particles,” J. Opt. Soc. Am. A 6, 385–402 (1989). [CrossRef]
  24. R. E. Hiatt, T. B. A. Senior, V. H. Weston, “A study of surface roughness and its effects on the backscattering cross section of spheres,” Proc. IRE 48, 2008–2016 (1960). [CrossRef]
  25. V. H. Weston, “Pulse return from a sphere,” IRE Trans. Antennas Propag. AP-7, S43–S51 (1959). [CrossRef]
  26. E. M. Kennaugh, “The impulse response concept in single-body scattering,” in Electromagnetic Scattering, R. L. Rowell, R. S. Stein, eds. (Gordon & Breach, New York, 1965), pp. 217–236.
  27. E. M. Kennaugh, D. L. Moffatt, “Transient and impulse response approximations,” Proc. IEEE 53, 893–901 (1965). [CrossRef]
  28. J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. AP-16, 89–97 (1968). [CrossRef]
  29. D. J. Schertler, N. George, “Backscattering cross section of a tilted, roughened disk,” J. Opt. Soc. Am. A 9, 2056–2066 (1992). [CrossRef]
  30. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  31. N. George, A. Jain, “Space and wavelength dependence of speckle intensity,” Appl. Phys. 4, 201–212 (1974). [CrossRef]
  32. L. Shaw, “Comments on ‘Shadowing of random surfaces,’” IEEE Trans. Antennas Propag. AP-14, 253 (1966). [CrossRef]
  33. R. A. Brockelman, T. Hagfors, “Note on the effect of shadowing on the backscattering of waves from a random rough surface,” IEEE Trans. Antennas Propag. AP-14, 621–629 (1966). [CrossRef]
  34. P. J. Welton, K. E. Hawker, H. G. Frey, “Experimental shadowing measurements on randomly rough surfaces,” J. Acoust. Soc. Am. 54, 446–450 (1973). [CrossRef]
  35. G. T. Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Handbook (Plenum, New York, 1970).
  36. M. M. Beal, “Serrated circular apertures: optical Fourier transforms and fractal analysis,” Ph.D. dissertation (University of Rochester, Rochester, N.Y., 1990).
  37. J. J. Bowman, T. B. A. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North-Holland, Amsterdam, 1969).
  38. T. Hagfors, “Backscattering from an undulating surface with applications to radar returns from the moon,”J. Geophys. Res. 69, 3779–3784 (1964). [CrossRef]
  39. A. Stogryn, “Electromagnetic scattering from rough, finitely conducting surfaces,” Radio Sci. 2, 415–428 (1967).
  40. D. E. Barrick, W. H. Peake, “A review of scattering from surfaces with different roughness scales,” Radio Sci. 3, 865–868 (1968).
  41. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, San Diego, Calif., 1978).
  42. M. K. Abdelazeez, “Wave scattering from a large sphere with rough surface,” IEEE Trans. Antennas Propag. AP-31, 375–377 (1983). [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