_ uf3

.NET qr printing with .netusing barcode encoding for .net framework control to generate, create qr-codes image in .net framework applications.

Un+1 1/Jn+1

QR Code 2d Barcode scanner with .netUsing Barcode reader for .net vs 2010 Control to read, scan read, scan image in .net vs 2010 applications.

+ Un+2 + ." + u n+ n ,

Bar Code generating on .netusing .net vs 2010 toget bar code on asp.net web,windows application

(5.2.26)

Visual .net bar code recognizer in .netUsing Barcode scanner for visual .net Control to read, scan read, scan image in visual .net applications.

(5.2.27) nl We calculate Green's functio~ of the upper medium on the coarse grid. These are represented by CL a f3 and baf3 .

QR encoding for c#using visual studio .net toinsert qr code on asp.net web,windows application

<rf3 _ aaf3 -

Control qrcode data with .netto build quick response code and qr code 2d barcode data, size, image with .net barcode sdk

+ 1/Jn+2 + ... + 'l/Jn+n,

Control qr code jis x 0510 size in vb.netto attach qr codes and qr-code data, size, image with vb barcode sdk

{b..X~H61)(kraf3) 4

Visual .net Crystal ean / ucc - 14 maker in .netusing barcode creation for vs .net crystal control to generate, create gtin - 128 image in vs .net crystal applications.

r a f3

Barcode drawer in .netuse .net vs 2010 crystal barcode generation toencode bar code on .net

> rf

Compose barcode in .netusing .net vs 2010 toreceive bar code on asp.net web,windows application

(5.2.28)

Develop datamatrix 2d barcode in .netgenerate, create data matrix barcodes none on .net projects

r f3 a

ITF-14 printing on .netuse visual .net crystal itf creation toassign upc shipping container symbol itf-14 for .net

r a f3 ::::; rf

Control ean-13 supplement 2 data with .netto add european article number 13 and ean-13 data, size, image with .net barcode sdk

_ baf3

QR Code integrated in visual basicusing visual studio .net todraw qr code on asp.net web,windows application

{ -b..x ik j'(xf3)(xf3 - x a ) - [j(xf3) - j(x a )] Hi l ) (kr f3) a 4 r a f3

VS .NET bar code implementation for visual basicgenerate, create barcode none with visual basic projects

~f3::::;~

Control ucc - 12 data with visual c#.netto generate ucc - 12 and upc symbol data, size, image with .net c# barcode sdk

(5.2.29)

EAN / UCC - 13 barcode library for .netusing barcode maker for visual studio .net (winforms) control to generate, create ean-13 supplement 2 image in visual studio .net (winforms) applications.

2.4 Bistatic Scattering Coefficient and Emissivity

Control quick response code size on c# qr bidimensional barcode size for visual c#

where ~x is the coarse grid sampling, ~x = n1~x, and ~x is the dense grid sampling. Thus we use this averaging for the second terms of both (5.2.20) and (5.2.21). Equation (5.2.13) becomes

Get barcode in javausing birt todraw bar code on asp.net web,windows application

[~a:nnu(xn) + ~b:nn'Mxn)] + [t,a~~u(x~) + tb~~~'(X~)]

Jasper barcode writer for javause jasper barcode implementation tomake barcode on java

= 1/Jinc(X m )

(5.2.30)

In (5.2.30) we use subscript "intp" to represent linear interpolation. Note in (5.2.30) that L::~g1 a:nnu(xn) has N dg values of m = 1,2, ... , N dg , while L:~=1 a~!il(x(3) only has N values ofa = 1,2, ... , N. Thus we first compute

(3=1

a~(3u(x(3) = d(x a )

(5.2.30a)

for a = 1,2, , N on the coarse grid. To find d(x m ) on the dense grid of X m , m = 1,2, ,Ndg , we use linear interpolation of d(xa)'s to get d(xm)'s. We further use BMIAjCAG to solve matrix equation. We divide nonnear-field interactions into two regions which are separated by Td. We now have three distance ranges for the upper medium Green's function, 0 :S T :S Tj, Tj < T :S Td, and T > Td with different operations. For 0 :S T :S Tj known as very near-field region, we use direct matrix and column vector product on the dense grid. For Tj < T :S Td known as near-field region, we use direct matrix and column vector product on the coarse grid and interpolation as in (5.2.30). For T > Td known as non-near-field region, we expand aa(3 and ba (3 in Taylor series as in the BMIAjCAG so that the FFTs can be used to compute this part of the matrix-vector multiplication. The Taylor series expansion is as in Section 1

Here

(kVX~+Z~) ~ ~ Om(Xd)

(5.2.31)

Hrepresents both H6

2.4 Bistatic Scattering Coefficient and Emissivity

After the matrix equation is solved, the surface field can be calculated. The bistatic scattering coefficient ()( Bs , B ) for the spectral domain tapered wave i is given in (4.1.57). We next illustrate the numerical simulation results of wave scattering from a rough lossy dielectric surface for both TE and TM waves [Tsang and

5 FAST METHODS FOR ROUGH SURFACE SCATTERING

scatlerlngangle (degree)

Figure 5.2.1 Comparison of the bistatic scattering coefficients between the single dense grid of 30 points per wavelength and the single coarse grid of 10 points per wavelength. TE wave, rms h = 0.5>", correlation length of I = 0.6>", dielectric constant of Er = 25 + i, surface length of L = 100>.., and tapering parameter of 9 = L/4 at incidence angle of (Ji. (a) One realization, (b) 20 realizations.

Li, 1997; Li et al. 1999]. Simulations are based on Gaussian random rough surfaces with Gaussian correlation functions. First, we show the comparisons of bistatic scattering coefficients and surface fields based on a single dense grid (SDG) and a single coarse grid (SCG) with a complex dielectric constant of 25 + i, surface length of 100 wavelengths, and at an incidence angle of 30 . The results show that the dense grid is required for the case with large dielectric constant. We shall regard the SDG results to be correct. Next, we compare the results based on PBTG-BMIAICAG with that of SDG. Then we use the PBTG-BMIAICAG method to calculate the cases with large surface length and compare with SDG. The tapering parameter was taken to be L I 4 for the case of surface length of 100 wavelengths and L 18 for the case of surface length of 500 wavelengths at near-grazing incidence. The critical distance r f that defines the very near field is fixed at 1 wavelength. The cases with a surface length of 100 wavelengths were run on a SPARC 20 workstation, and the cases with a surface length of 500 wavelengths were run on a Pentium-Pro Personal Computer with a clock rate of 200 MHz.