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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 52, Iss. 10 — Oct. 1, 1962
  • pp: 1093–1104

Elementary Results for Scattering by Large Cones

J. E. BURKE, L. MOWER, and V. TWERSKY  »View Author Affiliations

JOSA, Vol. 52, Issue 10, pp. 1093-1104 (1962)

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Elementary results for scattering by finite cones whose length and base dimensions are large compared to wavelength are obtained by approximating the surface fields in the integral representation by their geometrical-optics values. Both singly and doubly truncated cones are considered. A general expression is obtained for the location of the “specular beam” (i.e., the surface generated by the geometrically reflected rays), and simple results for the field on and off the “beam” are developed. In particular, it is shown that for many practical purposes a universal curve exists for the scattering pattern. This curve, which depends on a parameter involving the cone’s length and half-angle, falls more or less between the Fraunhofer “aperture” patterns for the strip and disk, and differs essentially in that the minima are not zero. Numerical illustrations are given.

J. E. BURKE, L. MOWER, and V. TWERSKY, "Elementary Results for Scattering by Large Cones," J. Opt. Soc. Am. 52, 1093-1104 (1962)

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  1. V. A. Fock, "The Distribution of Currents by a Plane Wave on the Surface of a Conductor," J. Phys. 10, 130 (1946). J. B. Keller, "A Geometrical Theory of Diffraction," in Calculus of Variation and its Applications, Proceedings of the Symposium in Applied Mathematics (McGraw-Hill Book Company, Inc., New York, 1958), Vol. 8, pp. 27–52. An elementary survey of approximation procedures is given in V. Twersky, "Electromagnetic Waves," Phys. Today 13, 30 (1960). Recent developments are reviewed by L. B. Felsen and K. M. Siegel, "Diffraction and Scattering," J. Research Natl. Bur. Standards 64D, 707 (1960).
  2. K. M. Siegel et al., "Studies in Radar Cross Sections VIII" (Willow Run Research Center, Ann Arbor, Michigan, 1953).
  3. L. Mower and V. Twersky, "Scattering by a Finite Cone" (Report EDL-E4, Sylvania Electronic Defense Laboratories, 1955), Sec. 3.4.
  4. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1949), 1380 ff. and 1551 ff.
  5. S. Silver, Microwave Anttenna Theory and Design (McGraw-Hill Book Company, Inc., New York, 1949).
  6. J. B. Keller, "Back Scattering from a Finite Cone" (New York University, Institute of Mathematical Sciences, Division of Electromagnetic Research, Research Report No. EM-127, 1959).
  7. K. M. Siegel, Appl. Sci. Research B7, 293 (1959).
  8. K. M. Siegel, R. F. Goodrich, and V. H. Weston, Appl. Sci. Research B8, (1959).
  9. J. E. Burke and J. B. Keller, "Diffraction by Finite Bodies of Revolution" (Report EDL-E49, Sylvania Electronic Defense Laboratories, 1960).
  10. R. C. Bartle, C. I. Beard, J. E. Burke, M. E. Juza, and V. Twersky, "Optical Scattering Range, and Studies on Simple Shapes" (Report EDL-M258, Sylvania Electronic Defense Laboratories, 1960).
  11. See for example, D. D. Saxon, "Lectures on the Scattering of Light" (Scientific Report No. 9, University of California, Los Angeles, Department of Meteorology, 1955); see also C. I. Beard T. H. Kays, and V. Twersky, J. Appl. Phys. 33, 2851 (1962).
  12. In practice, photo-optical techniques facilitate determining θ(S) and σ(S). Thus one can illuminate a silvered cone with a distant point source of light and record the specular beams on photographic paper or film. If the paper is oriented perpendicular to the cone's axis, then the recorded traces give directly the variation of θ(S) (essentially as in Figs. 5 and 6). Using positive transparencies and controlled processing yields traces which can be measured on an optical densitometer for direct determinations of σ(S).

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