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Some Extensions to the Integral Equation Method for Electromagnetic Scattering from Rough Surfaces Yang Du [email_address] Zhejiang University, Hangzhou, China 2011.7.25
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Conventional Analytical Models ,[object Object],[object Object]
The Unifying Models ,[object Object],[object Object]
The IEM and AIEM Models ,[object Object],[object Object],Ref:  [1] A. K. Fung, Z. Q. Li, and K. S. Chen, “Backscattering from a randomly rough dielectric surface,”  IEEE Trans. Geosci. Remote Sensing , vol. GE-30, no. 2, pp. 356–369, Mar. 1992. [2] K. S. Chen, T. D. Wu, L. Tsang, Q. Li, J. C. Shi, and A. K. Fung, “ Emission of rough surfaces calculated by the integral equation method with comparison to three-dimensional moment method simulations,” IEEE Trans. Geosci. Remote Sensing , vol. GE-41, no. 1, pp. 90–101, Jan. 2003.
Assumptions Underlying IEM ,[object Object],[object Object],[object Object],[object Object],[object Object]
Observation One ,[object Object]
Correlation Coefficients between Slopes at Different Points
The Significance of Slope Statistics If the conventional KA approach is incorporated with the surface slope statistics, the resulting model appears almost immune to the Brewster angle effect for vertical polarization.  This feature is expected since the directions of the unit normal which lead the local angles of incidence to approach the Brewster angle occupy only a small portion of the directional distribution; contributions from the rest of the distribution become appreciable in this new treatment.
Smooth surface Rougher surface slope accounted No slope accounted Data: DeRoo, R.D., and F.T. Ulaby, “Bistatic Specular Scattering from Rough Dielectric Surfaces,”  IEEE Transactions on Antennas and Propagation, Vol. 42, No. 2, 1994, pp. 1743–1755. Added by KSC
The Statistical IEM Model Development of the statistical IEM (SIEM) model is motivated by the observation that slope statistics has appreciable impact on the Kirchhoff approximation, which forms the Kirchhoff part of the IEM formalism, and by the intuition that incorporating shadow effect directly into field rather than scattered power may provide more physical results.  Details of the SIEM model can be found in [3].  [3] Y. Du, J. A. Kong, Z. Y. Wang, W. Z. Yan, and L. Peng, “A statistical integral equation  model for shadow-corrected EM scattering from a Gaussian rough surface,”  IEEE Trans.  Antennas and Propagation , vol. 55, no. 6, pp. 1843-1855, June 2007.
Testing Cases of SIEM
SIEM  –  Simulation I
SIEM Simulation II
Some Concluding Remarks on SIEM ,[object Object],[object Object],[object Object],[object Object]
Observation Two ,[object Object],[object Object]
Observation Two (Cont.) ,[object Object],[object Object],[object Object]
Spectral form of Green’s function Added by KSC @ksc 2003 Propagator in upper and lower medium, respectively Upward, downward
An Illustrative Computation to Show the Inclusion of the Error Function I is the Heavyside function,  . Transformation of variables leads to the factorization where
An Illustrative Computation to Show the Inclusion of the Error Function II can be readily obtained as while where  erf  is the error function defined as
The Extended AIEM Model ,[object Object],[object Object],[object Object],[object Object],[object Object],Ref:  [4] Y. Du, “A new bistatic model for electromagnetic scattering from randomly rough surfaces,”  Waves in Random and Complex Media , vol. 18, no. 1, pp. 109-128, Feb. 2008.
Some Observations on the Cross Scattering Coefficient ,[object Object],[object Object],[object Object]
Some Observations on the Complementary Scattering Coefficient ,[object Object],[object Object],[object Object]
EAIEM Simulation I Macelloni, G., Nesti, G., Pampaloni, P., Sigismondi, S., Tarchi, D. and Lolli, S., 2000, Experimental validation of surface scattering and emission models. IEEE Transactions on Geoscience and Remote Sensing, 38, 459–469.
EAIEM Simulation II
Some Concluding Remarks on EAIEM ,[object Object]
[object Object]

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RoughSurfaceModels.ppt

  • 1. Some Extensions to the Integral Equation Method for Electromagnetic Scattering from Rough Surfaces Yang Du [email_address] Zhejiang University, Hangzhou, China 2011.7.25
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  • 8. Correlation Coefficients between Slopes at Different Points
  • 9. The Significance of Slope Statistics If the conventional KA approach is incorporated with the surface slope statistics, the resulting model appears almost immune to the Brewster angle effect for vertical polarization. This feature is expected since the directions of the unit normal which lead the local angles of incidence to approach the Brewster angle occupy only a small portion of the directional distribution; contributions from the rest of the distribution become appreciable in this new treatment.
  • 10. Smooth surface Rougher surface slope accounted No slope accounted Data: DeRoo, R.D., and F.T. Ulaby, “Bistatic Specular Scattering from Rough Dielectric Surfaces,” IEEE Transactions on Antennas and Propagation, Vol. 42, No. 2, 1994, pp. 1743–1755. Added by KSC
  • 11. The Statistical IEM Model Development of the statistical IEM (SIEM) model is motivated by the observation that slope statistics has appreciable impact on the Kirchhoff approximation, which forms the Kirchhoff part of the IEM formalism, and by the intuition that incorporating shadow effect directly into field rather than scattered power may provide more physical results. Details of the SIEM model can be found in [3]. [3] Y. Du, J. A. Kong, Z. Y. Wang, W. Z. Yan, and L. Peng, “A statistical integral equation model for shadow-corrected EM scattering from a Gaussian rough surface,” IEEE Trans. Antennas and Propagation , vol. 55, no. 6, pp. 1843-1855, June 2007.
  • 13. SIEM – Simulation I
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  • 18. Spectral form of Green’s function Added by KSC @ksc 2003 Propagator in upper and lower medium, respectively Upward, downward
  • 19. An Illustrative Computation to Show the Inclusion of the Error Function I is the Heavyside function, . Transformation of variables leads to the factorization where
  • 20. An Illustrative Computation to Show the Inclusion of the Error Function II can be readily obtained as while where erf is the error function defined as
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  • 24. EAIEM Simulation I Macelloni, G., Nesti, G., Pampaloni, P., Sigismondi, S., Tarchi, D. and Lolli, S., 2000, Experimental validation of surface scattering and emission models. IEEE Transactions on Geoscience and Remote Sensing, 38, 459–469.
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