RANDOM ROUGH SURFACE SIMULATIONS in .NET

Draw qrcode in .NET RANDOM ROUGH SURFACE SIMULATIONS
4
QR Code 2d Barcode implement on .net
use visual studio .net qr code implementation toassign qr-code on .net
RANDOM ROUGH SURFACE SIMULATIONS
Qr-codes reader for .net
Using Barcode recognizer for visual .net Control to read, scan read, scan image in visual .net applications.
Perfect Electric Conductor (Non-Penetrable Surface)
Visual Studio .NET bar code integrating in .net
generate, create bar code none on .net projects
1.1 1.2 1.3 1.4
.net Framework barcode decoder for .net
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Integral Equation Matrix Equation: Dirichlet Boundary Condition (EFIE for TE Case) Tapering of Incident Waves and Calculation of Scattered Waves Random Rough Surface Generation
Control qr code jis x 0510 data on visual c#.net
to use qr code and qr-codes data, size, image with visual c#.net barcode sdk
114 116 118 124 124 132 134
Control qr-codes size for .net
to print qr code jis x 0510 and qr code data, size, image with .net barcode sdk
1.4.1 Gaussian Rough Surface 1.4.2 Fractal Rough Surface
Control qr-code image in visual basic.net
use visual studio .net qr-code integrated toencode denso qr bar code on vb
Neumann Boundary Condition (MFIE for TM Case)
Attach pdf-417 2d barcode in .net
using .net crystal tobuild pdf-417 2d barcode on asp.net web,windows application
Two-Media Problem
Barcode integrated with .net
using visual .net crystal todraw barcode with asp.net web,windows application
2.1 2.2 2.3 2.4
Visual Studio .NET ansi/aim code 39 maker with .net
using vs .net togenerate code-39 on asp.net web,windows application
TE and TM Waves Absorptivity, Emissivity and Reflectivity Impedance Matrix Elements: Numerical Integrations Simulation Results
Barcode generator for .net
generate, create barcode none in .net projects
139 141 143 145 145 150 151
.net Framework barcode 2 of 5 printer in .net
using barcode development for .net vs 2010 control to generate, create 2/5 industrial image in .net vs 2010 applications.
2.4.1 Gaussian Surface and Comparisons with Analytical Methods 2.4.2 Dirichlet Case of Gaussian Surface with Ocean Spectrum and Fractal Surface 2.4.3 Bistatic Scattering for Two Media Problem with Ocean Spectrum
Visual Studio .NET (WinForms) ansi/aim code 128 encoding in .net
using windows forms todeploy code 128 code set b on asp.net web,windows application
Topics of Numerical Simulations
ANSI/AIM Code 39 barcode library on .net
use web pages ansi/aim code 39 printing toencode 3 of 9 barcode for .net
3.1 3.2 3.3
Periodic Boundary Condition MFIE for TE Case of PEC Impedance Boundary Condition
Generate datamatrix 2d barcode with c#
using barcode drawer for .net framework control to generate, create ecc200 image in .net framework applications.
Microwave Emission of Rough Ocean Surfaces
ASP.NET datamatrix implementation with .net
using asp.net web pages toincoporate data matrix for asp.net web,windows application
- 111-
Barcode decoder in .net
Using Barcode scanner for visual .net Control to read, scan read, scan image in visual .net applications.
154 158 161
Access upc a with c#
using barcode encoding for vs .net control to generate, create upc a image in vs .net applications.
4 RANDOM ROUGH SURFACE SIMULATIONS
Bar Code implement in .net
generate, create barcode none with .net projects
Waves Scattering from Real-Life Rough Surface Profiles 166
5.1 5.2 5.3
Introduction Rough Surface Generated by Three Methods Numerical Results of the Three Methods
References and Additional Readings
166 167 169
4 RANDOM ROUGH SURFACE SIMULATIONS
In this chapter we study random rough surface simulations of onedimensional surface for two-dimensional scattering problem. The simulations of rough surface scattering started in the late 1970's and continue to the present day [Axline and Fung, 1978; Thorsos, 1988; Thorsos and Jackson, 1991; Maystre et al. 1991; Devayya and Wingham, 1992; Thorsos and Jackson, 1989; Thorsos and Broschat, 1995; Maradudin et al. 1990; Michel and O'Donnell, 1992; McGurn and Maradudin, 1993; Chan et al. 1991; NietoVesperinas and Soto-Crespo, 1987]. The main purposes of the early simulations were to validate analytic scattering theory and to investigate backscattering enhancement. The numerical method in this chapter is based on the formulation of integral equations and converting the integral equations into matrix equations using the method of moments. We discuss the Dirichlet problem and Neumann problem and illustrate the results using Gaussian surfaces, surfaces with ocean spectrum, and fractal surfaces. Next, we discuss dielectric surface and the calculation of emissivity for applications in passive remote sensing. In particular, we address the accuracy issue in the calculation of emissivity. The accurate calculation of emissivity distinguishes the emphasis of rough surface simulations in this book. Most researchers on rough surface simulations emphasize on bistatic scattering and backscattering, which are usually measured and plotted in dB scale. For such simulations, an accuracy of 25% or 1 dB is acceptable. However, for passive remote sensing calculations, the physics is based on energy conservation. The key result in passive remote sensing is the difference of emissivity between a rough surface and a flat surface. The difference is small and can be a few percent to less than 1%. For ocean remote sensing, that difference is particularly small, e.g., 0.003 or 0.3%. This corresponds to a brightness temperature difference of less than a Kelvin between a rough surface and a flat surface. The ability to distinguish that small difference actually forms the basis of passive remote sensing of ocean wind. This means that for passive remote sensing numerical simulations, energy conservation has to be within 0.3%. Such a stringent requirement is not needed in active remote sensing simulations, where an energy conservation of 96% is deemed to be good. Thus numerical methods of simulations for active remote sensing can be different from passive remote sensing because of the large difference in accuracy requirements. One key implication for calculations in passive remote sensing is that the rough surface needs to have a fine discretization. In this chapter, we will also introduce examples of real life surface profiles measured for rocky surfaces, soil surfaces, and snow surfaces.
4 RANDOM ROUGH SURFACE SIMULATIONS
Perfect Electric Conductor (Non-Penetrable Surface)
1.1 Integral Equation
Consider an incident wave 1f;inc(r) impinging upon a random surface (Fig. 4.1.1) with height profile z = f (x). In two-dimensional scattering problem r = xx + ZZ, the wavefunction '!/J(r) is (4.1.1) where '!/Js(r) is the scattered wave. The wavefunction obeys the equation
(\72
+ k2) '!/J = 0
(4.1.2)
The two-dimensional Green's function obeys the equation (4.1.3) and
g(r,r')
~H61)(klr-r'i)
(4.1.4)
o (Va)
Let the spaces above and below the rough surface be denoted by region and region 1 (VI)' We use the Green's theorem to get