288
Views
3
CrossRef citations to date
0
Altmetric
Articles

Multi-parameter identification and shape reconstruction for unbounded fractal rough surfaces with tapered wave incidence

, , &
Pages 1282-1301 | Received 28 Sep 2014, Accepted 14 May 2016, Published online: 30 May 2016

References

  • Bao G, Li P, Lv J. Numerical solution of an inverse diffraction grating problem from phaseless data. J. Opt. Soc. Am. A. 2013;30:293–299.
  • Bao G, Bonnetier E. Optimal design of periodic diffractive structures. Appl. Math. Opt. 2001;43:103–116.
  • Bao G, Huang K, Schmidt G. Optimal design of nonlinear diffraction gratings. J. Comput. Phys. 2003;184:106–121.
  • Bao G, Cowsar L, Masters W. Mathematical modeling in optical science. Philadelphia: SIAM; 2001.
  • Bao G, Li P, Wu H. A computational inverse diffraction grating problem. J. Opt. Soc. Am. A. 2012;29:394–399.
  • Cai Z, Chen D, Lu S. Reconstruction of a fractal rough surface. Phys. D: Nonlinear Phenom. 2006;213:25–30.
  • Ammari H, Bao G, Wood A. An integral equation method for the electromagnetic scattering from cavities. Math. Meth. Appl. Sci. 2000;23:1057–1072.
  • Zhang HW, Zhang B. A novel integral equation for scattering by locally rough surfaces and application to the inverse problem. SIAM J. Appl. Math. 2013;73:1811–1829.
  • Bao G, Li P. Near-field imaging of infinite rough surfaces. SIAM J. Appl. Math. 2013;73:2162–2187.
  • Bahar E, El-Shenawee M. Enhanced backscatter from one dimensional random rough surfaces-stationary phase approximations to full wave solutions. J. Opt. Soc. Am. A. 1995;12:151–161.
  • Colton D, Monk P. Target identification of coated objects. IEEE Trans. Antennas Propag. 2006;54:1232–1242.
  • Fung K, Shah MR, Tjuatja S. Numerical simulations of scattering from three-dimensional randomly rough surfaces. IEEE Trans. Geosci. Remote Sens. 1994;32:986–994.
  • Johnson JT, Tsang L, Shin RT, et al. Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data. IEEE Trans. Antennas Propag. 1996;44:748–756.
  • Tsang L, Chan CH, Pak K, et al. Monte Carlo simulations of large-scale composite random rough-surface scattering based on the banded-matrix iterative approach. J. Opt. Soc. Amer. 1994;11:691–696.
  • Tsang L, Kong JA, Ding KH. Scattering of electromagnetic waves. Vol. 2, Numerical simulations. New York (NY): Wiley Interscience; 2001.
  • Thorsos EI. The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum. J. Acoust. Soc. Amer. 1988;83:78–92.
  • Wombell RJ, DeSanto JA. Reconstruction of rough-surface profiles with the Kirchhoff approximation. J. Opt. Soc. Amer. 1991;8:1892–1897.
  • Wombell RJ, DeSanto JA. The reconstruction of shallow rough-surface profiles from scattered field data. Inverse Prob. 1991;7:L7–L12.
  • Franceschetti G, Iodice A, Riccio D. Scattering from dielectric random fractal surfaces via method of moments. IEEE Trans. Geosci. Remote Sens. 2010;38:1644–1655.
  • Kress R, Rundell W. Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Inverse Prob. 2005;21:1207–1223.
  • Colton D, Giebermann K, Monk P. A regularized sampling method for solving three-dimensional inverse scattering problems. SIAM J. Sci. Comput. 2000;21:2316–2330.
  • Potthas R. A survey on sampling and probe methods for inverse problems. Inverse Prob. 2006;22:R1–R47.
  • Zhang L, Ma FM, Wang J. Regularized conjugate gradient method with fast multipole acceleration for wave scattering from 1D fractal rough surface. Wave Motion. 2013;50:41–55.
  • Fletcher R. Practical methods of optimization. New York (NY): Wiley; 2000.
  • El-Shenawee M, Miller E. Multiple-incidence/multi-frequency for profile reconstruction of random rough surfaces using the three-dimensional electromagnetic fast multipole model. IEEE Trans. Geosci. Remote Sens. 2004;42:2499–2510.
  • Franceschetti G, Riccio D. Scattering, natural surfaces, and fractals. London: Academic Press; 2006.
  • Jaggard D, Sun X. Scattering from fractally corrugated surfaces. J. Opt. Soc. Am. A. 1990;7:1131–1139.
  • Thorsos EI, Jackson DR. Studies of scattering theory using numerical methods. Waves Random Media. 1991;1:S165–S190.
  • Ye H, Jin Y. Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface. IEEE Trans. Antennas Propag. 2005;53:1234–1237.
  • Arens T, Hohage T. On radiation conditions for rough surface scattering problems. IMA J. Appl. Math. 2005;70:839–847.
  • DeSanto JA, Martin PA. On angular-spectrum representations for scattering by infinite rough surfaces. Wave Motion. 1996;24:421–433.
  • DeSanto JA, Martin PA. On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface. J. Acoust. Soc. Amer. 1997;102:67–77.
  • Zhang L, Ma FM. Boundary integral equation methods for the scattering problem by an unbounded sound soft rough surface with tapered wave incidence. J. Comput. Appl. Math. 2015;277:1–16.
  • DeSanto JA. Exact boundary integral equations for scattering of scalar waves from infinite rough interfaces. Wave Motion. 2010;47:139–145.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.