n x H = 2n x H inc in .NET

Implement DataMatrix in .NET n x H = 2n x H inc
n x H = 2n x H inc
Data Matrix 2d Barcode generation on .net
using vs .net tocreate data matrix barcodes in asp.net web,windows application
(9.4.10)
scanning ecc200 in .net
Using Barcode recognizer for .net vs 2010 Control to read, scan read, scan image in .net vs 2010 applications.
For one-dimensional surface, the tangential H field (n x H) is proportional to N x "V x (fJ'ljJ) = N X (\7 'ljJ X fJ). Since N . fJ = 0, the tangential H field is proportional to -fJ(N . \7 E). Hence for the tangential plane approximation of Fig. 9.4.1, we have (9.4.11) The approximation is exact if we do have an infinite plane with normal n. Thus the region of validity of the Kirchhoff approximation is that the radius of curvature must be much larger than the wavelength. It also requires that shadowing and multiple scattering are negligible. For a curve given by z = f(x), the tangent vector is the rate of change of position vector with respect to the arc length s.
decoding bar code with .net
Using Barcode scanner for visual .net Control to read, scan read, scan image in visual .net applications.
A dX A dZ A [A t = -x + - Z = x
.net Vs 2010 Crystal barcode integration in .net
generate, create bar code none for .net projects
+ f'( x )A]dX Zds
Gs1 Datamatrix Barcode barcode library in visual c#
using barcode implementation for visual .net control to generate, create data matrix barcode image in visual .net applications.
(9.4.12)
Aspx datamatrix encoding for .net
use aspx data matrix barcodes encoder toencode data matrix barcodes with .net
9 l-D RANDOM ROUGH SURFACE SCATTERING
Control data matrix ecc200 data with vb
to encode barcode data matrix and 2d data matrix barcode data, size, image with vb barcode sdk
Using the chain rule of differentiation and ds ,--,--,---::-dx = + (J'(x))2
39 Barcode generation with .net
using barcode creator for .net crystal control to generate, create code 39 image in .net crystal applications.
(9.4.13)
Matrix Barcode barcode library for .net
using vs .net todraw matrix barcode for asp.net web,windows application
gives
Bar Code barcode library on .net
generate, create bar code none with .net projects
A x t = [A
Barcode writer with .net
using barcode printer for visual studio .net control to generate, create barcode image in visual studio .net applications.
1 + f'() z -r==;=::=;=~ x A] VI + (J'(x))2
Print planet with .net
using barcode integrating for visual .net crystal control to generate, create planet image in visual .net crystal applications.
(9.4.14)
Create data matrix 2d barcode with visual basic
using barcode development for aspx.net crystal control to generate, create datamatrix image in aspx.net crystal applications.
The curvature is the rate of change of the tangent vector with respect to arc length s. Hence
Embed 39 barcode for word documents
generate, create code 39 none with word documents projects
= Ids =
Aspx qr code jis x 0510 encoder for .net
using barcode writer for web pages control to generate, create qr code image in web pages applications.
dt I
Build qr bidimensional barcode in microsoft excel
using barcode creator for excel spreadsheets control to generate, create qr barcode image in excel spreadsheets applications.
VI + (J'(x))2 = [1 + (J'(x))2]3/2
Barcode integrated in .net
use .net winforms bar code maker toinclude barcode on .net
[1 + (J'(X))2] 3/2 1f"(x)1 = a and p = 00, showing that
1f"(x)1
Control upc code data with microsoft excel
to print upc a and upc a data, size, image with microsoft excel barcode sdk
(9.4.15)
2D Barcode generation for .net
using barcode implement for rdlc reports control to generate, create 2d barcode image in rdlc reports applications.
The radius of curvature p is the reciprocal of the curvature. (9.4.16)
For a straight line, f"(x) Kirchhoff approximation is good for a surface that can be represented by its tangent plane. To estimate p, we note that for C(x) = exp( -x 2 /1 2 ), from Section 2.1, we have
I d2 f 2V3h rms of dx 2 = -12
df rmS of - =
h V2-
(9.4.17a) (9.4.I7b)
Hence p is of the order of
= _1_
2V3h
(1 + 2h 2 ) 3/2 l2
(9.4.18)
For example, if h = 1,)" I = 4,)" then p = 5.5,), and is much bigger than wavelength. For h = 0.5,), and l = 1), we have p = 1.06\ which is comparable to a wavelength. Besides the radius of curvature condition, the Kirchhoff approximation also ignores shadowing and multiple scattering. Since the Kirchhoff approximation ignores shadowing, the region of validity is also dependent on incident angle. Using (9.4.1) in (9.4.4), we have
N . \l'ljJ ~ 2(N . iki ) if,.r
(9.4.19)
From (9.4.8) and (9.4.19), the scattered field for z'
'ljJsCr')
> f(x') is
(9.4.20)
dx g(r, r')(N . kd eiki r
4.1 Dirichlet Problem for l-D Surface
with r = (x, f(x)). In the spectral domain, the two-dimensional Green's function is 00 i eikx(x'-x)+ikxlz'-zl (9.4.21) g(r, r') = -4 dk x k
Substituting (9.4.21) into (9.4.20) gives, for z'
'l/Js(r') =
> z = f(x),
(9.4.22)
dk x eikxx'+ikxz' 'l/Js(kx )
dx ei(kiX-kx)x-i(kx+kiX)f(x) [:~ kix + kiZ] (9.4.23) z We cast (9.4.22) and (9.4.23) in the forms that are similar to the small perturbation method of Section 3.1. Define 'l/Js (k x ) = - 2:k
k s = kxx + kzz
kd = ki - k s = kdx X + kdzZ = (kix - kx)x - (kiz
(9.4.24)
+ kz)z
(9.4.25)
To treat the df /dx term in (9.4.23), we perform integration by parts and ignore "edge" effects. Ignoring edge effects implies that
Thus
1r z
dx (ikdx
+ ikdz df ) eikdXX+ikdxf(x)
(9.4.26)
1 'l/Js(kx ) = 2 k k
(-kizkdz
+ kixkdx)
1 _=
dx eikdxX+ikdxf(x)
(9.4.27)
It is interesting to digress to make a small height approximation in (9.4.26) and see how the results compare with SPM. Then we have
(kixkdx - kizkdz)F( -kdx) (9.4.28) z In the vicinity of the specular direction kdx ~ 0, kdz ~ -2kiz, and k z ~ kiz, from (9.4.28) we obtain 'l/Js(k x ) ~ -<5(kdx) 'l/Js(k x ) ~ -<5(kdx)
+ 2ikizF( -kdx)
(9.4.29)
We note that from the small perturbation method, Eqs. (9.3.10) and (9.3.13), we have (9.4.30) Thus we know that the Kirchhoff approximation result generally is different from that of the small perturbation method. They are close to each in the vicinity of the specular direction for the case of small height. Comparison of Monte Carlo simulation shows that the small perturbation method, within
9 l-D RANDOM ROUGH SURFACE SCATTERING
its domain of validity (kh 1 and s 1), gives better solution than Kirchhoff approximation. The Kirchhoff approximation has a partially overlapping region of validity with SPM (for example, the correlation length l must be much larger than the wavelength). Note that (9.4.27) of the Kirchhoff approximation is applicable to large height. Taking the average of (9.4.27) to obtain the coherent field and using (9.2.44), an important consequence is that the average of (exp(ikdzf(x))) is independent of x and can be taken outside the integral sign. ('tps(k x )) =
27T zkdz = -6(kdx) exp( -2k;zh2 )