An Efficient and Analytical Solution to the Integral on Truncated-Wedge ILDCs for Polygonal Surfaces
Keywords:
Closed form, linear division, TWILDCsAbstract
A new method is proposed to analytically evaluate the line integral on truncated-wedge incremental length diffraction coefficients (TW-ILDCs). By utilizing the coherence of a geometry, the trailing edges can be divided into several linear segments, and the line integrals can be reduced as the two end-point contributions for each segment based on the mathematical model derived in this paper. Thus, the efficiency is greatly enhanced in comparison with the traditional numerical techniques. Numerical results for the bistatic radar cross sections show excellent performance of the proposed method both in accuracy and efficiency.
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References
P. Y. Ufimtsev, “Method of edge waves in the physical theory of diffraction,” U.S. Air Force, Foreign Technology Div., Wright-Patterson AFB, OH, Sept. 7, 1971 (transl. from Russian).
K. M. Mitzner, Incremental length diffraction coefficients, Report AFAL-TR-73-296, Northrop Corporation, 1974.
A. Michaeli, “Elimination of infinities in equivalent edge currents, part I: Fringe current components,” IEEE Trans. Antennas and Propagat., vol. 34, no. 7, pp. 912-918, July 1986.
R. A. Shore and A. D. Yaghjian, “Incremental diffraction coefficients for planar surfaces,” IEEE Trans. Antennas and Propagat., vol. 37, no. 1, pp. 55-70, Jan. 1988.
R. A. Shore and A. D. Yaghjian, “Correction to Incremental diffraction coefficients for planar surfaces,” IEEE Trans. Antennas and Propagat., vol. 37, pp. 1342, Jan. 1989.
O. Breinbjerg, “Higher-order equivalent edge currents for fringe wave radar scattering by perfectly conducting polygonal plates,” IEEE Trans. Antennas and Propagat., vol. 40, pp. 1543- 1544, Dec. 1992.
R. A. Shore and A. D. Yaghjian, “Incremental diffraction coefficients for plane conformal strips with application to bistatic scattering from the disk,” J. Electromagn. Waves Applicat., vol. 6, no. 3, pp. 359-396, Mar. 1992.
M. G. Cote, M. B. Woodworth, and A. D. Yaghjian, “Scattering from the perfectly conducting cube,” IEEE Trans. Antennas and Propagat., vol. 36, pp. 1321-1329, Sept. 1988.
A. Michaeli, “Equivalent currents for second-order diffraction by the edges of perfectly conducting polygonal surfaces,” IEEE Trans. Antennas and Propagat., vol. 35, no. 2, pp. 183-190, Feb. 1987.
P. M. Johansen, “Uniform physical theory of diffraction equivalent edge currents for truncated wedge strips,” IEEE Trans. Antennas and Propagat., vol. 44, no. 7, pp. 989-995, July 1996.
W. Pauli, “On asymptotic series for functions in the theory of diffraction of light,” Phys. Rev., vol. 54, pp. 924-931, Dec. 1938.
A. Michaeli, “Equivalent edge currents for arbitrary aspects of observation,” IEEE Trans. Antennas and Propagat., vol. 32, pp. 252-258, Mar. 1984.
V. A. Borovikov, “Uniform stationary phase method,” IEEE Electromagn. Waves, 1994.
P. Ya. Ufimtsev, “The 50-year anniversary of the PTD: Comments on the PTD’s origin and development,” IEEE Antennas and Propagat. Magazine, vol. 55, no. 3, June 2013.
G. L. James, Geometrical Theory of Diffraction for Electromagentic Waves. Hertfordshire, England: Peter Peregrinus, 1976.
J. T. Moore, A. D. Yaghjian, and R. A. Shore, “Shadow boundary and truncated wedge ILDCs in Xpatch,” in Proc. IEEE Antennas and Propag. Society Int. Symp., 2005, vol. 1, pp. 10-13, July 1986.
R. A. Shore and A. D. Yaghjian, “A comparison of high-frequency scattering determined from PO fields enhanced with alternative ILDCs,” IEEE Trans. Antennas and Propagat., vol. 52, no. 1, pp. 336-341, Jan. 2004.
B. Robert and F. E. Thomas, “Investigation of equivalent edge currents for improved radar cross section predictions,” Proc. 8th Eur Conf. Antennas Propag. (EuCAP), pp. 2321-2325, 2014.
P. C. Gao, Y. B. Tao, Z. H. Bai, and H. Lin, “Mapping the SBR and TW-ILDCs to heterogeneous CPU-GPU architecture for fast computation of electromagnetic scattering,” Progress Electromagn. Res. (PIER), vol. 122, pp. 137-154, 2012.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. Norwood, MA, USA: Dover, 1972.
E. W. Ng and M. Geller, “A table of integrals of the error functions,” Joural of Research of the National Bureau of Standards - B. Mathematical Sciences, vol. 73B, no. 1, Jan.-Mar. 1969.
