[Ct+1 e- ik (l+l).d l in .NET

Integration DataMatrix in .NET [Ct+1 e- ik (l+l).d l
[Ct+1 e- ik (l+l).d l
VS .NET barcode data matrix development on .net
use .net data matrix writer toaccess data matrix barcodes on .net
(5.2.21)
Datamatrix 2d Barcode reader on .net
Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications.
+ DZ+l eik(l+l).dl ]
Barcode implementation with .net
using visual studio .net crystal toprint barcode on asp.net web,windows application
with A o = RTE , Bo = 1, At = 0, B t = TTE, Co = R , Do = 1, Ct = 0, and D t = TTM. The wave amplitudes can now be determined using the propagating matrices. The reflection coefficients RTE and RTM are dual of each other and
Bar Code maker for .net
using barcode generating for visual .net control to generate, create barcode image in visual .net applications.
5 SCATTERING AND EMISSION BY LAYERED MEDIA
Control 2d data matrix barcode size for c#
to print datamatrix 2d barcode and gs1 datamatrix barcode data, size, image with visual c#.net barcode sdk
can be calculated by the recurrence relation of (5.2.12). However, because we are deriving the electric dyadic Green's function, the amplitudes Gl, Dl, and TTM are not dual of A l , B l , and TTE. We define
Control datamatrix 2d barcode image for .net
generate, create data matrix 2d barcode none in .net projects
R _ kl z - k(l+l)z l(l+l) - k k lz (l+l)z
Control datamatrix 2d barcode image in visual basic
use visual studio .net 2d data matrix barcode implement todevelop barcode data matrix on vb.net
(5.2.22a) (5.2.22b)
GS1 128 encoding with .net
using .net framework toencode ean128 in asp.net web,windows application
El+1 k lz - Elk(l+l)z 8 l (l+1) = ------'---'El+1 k lz El k(l+l)z
Visual .net bar code implement for .net
using barcode creation for vs .net control to generate, create barcode image in vs .net applications.
Rl(l+l) and 8 l (l+1) are the reflection coefficients for TE and TM waves, respectively, between regions I and 1+ 1. The wave amplitudes in regions 1+ 1 and I are related by the TE and TM propagating matrices.
Gs1 Datamatrix Barcode integrated for .net
using vs .net crystal toincoporate data matrix 2d barcode in asp.net web,windows application
(5.2.23a)
Build barcode standards 128 in .net
use .net framework barcode code 128 encoder toprint barcode code 128 with .net
(5.2.23b)
Insert ean-8 supplement 2 add-on in .net
using barcode generating for .net vs 2010 control to generate, create ean8 image in .net vs 2010 applications.
where
Deploy pdf417 on .net
using barcode generator for sql server reporting service control to generate, create pdf417 2d barcode image in sql server reporting service applications.
V (l+l) l
Control gs1 - 12 data in excel spreadsheets
upc-a supplement 5 data in excel spreadsheets
is called the TE forward propagation matrix and is given by -2
Control upc-a image for c#.net
using visual studio .net toinsert upc-a supplement 2 in asp.net web,windows application
V(l+l)l =
Control ean 128 barcode image with .net
using aspx.cs page todisplay ean 128 in asp.net web,windows application
1 + -k-(l+l)z
Control uss code 128 data on vb
to include code 128a and code 128b data, size, image with visual basic barcode sdk
kl Z
Bar Code integrating for .net
using report rdlc toprint barcode in asp.net web,windows application
e-ik(l+1)% (d'+1 -d,) [ R(l+l) l e ik (l+1).(d 1 1-d,) +
An Asp.net Form bar code implementation with .net
using asp.net web pages tointegrate barcode with asp.net web,windows application
R(l+l)l e-ik(l+1)%(dl+1-dl)]
Control barcode 3 of 9 image for java
use java code 3/9 generator toget bar code 39 on java
e1'k (l+1). (d 1+1 -
dI )
(5.2.24a)
and, similarly,
V (l+1) l =
2 k(l+l)
1 + -El- k(l+l)z
E(l+l)
k lz
e-ik(l+1).(dl+1-dl) +1-d1) [ 8(l+ 1) l eik (l+1).(d1
8(l+1) l e- ik (l+1).(d 1+ 1-dz)]
eik (l+1)' (d1+1-d,)
(5.2.24b)
Using reciprocity and k1.. --t -k1.. and the property that e( -k x , -ky , k z ) = -e(k x , k y , k z ) and h( -k x , -ky , k z ) = h(k x , k y , -k z ), we have
COl(1', r') = GOt (1', 1")
C~oCr', 1') = 8~2
d;z1..
i k .r 90zCk1.., z')e-ik.L.r'.L
(5.2.25)
= C:O(1", 1') =
d:zJ..
eik.r 9olk J.., z')e-ik.L.r'.L (5.2.26)
2.2 Dyadic Green'8 Function for Stratified Medium
where
gozCkl.., z') = e(k z ) [Ale l (_klz)eiklZZ'
+ Blel(klZ)e-iklzZ']
(5.2.27)
+ h(k z ) [Czht(-ktz)eikIZZ' + Dtht(ktz)e-ikIZZ']
gotCkl.., z') = e(kz)et(ktz)e-iktzZ'TTE + h(kz)ht(ktz)e-iktzZ'TTM (5.2.28)
Numerical solution of the Green's functions of layered media for arbitrary field point can be done by performing numerical integration of Sommerfield integral. In the past, this was usually done by computing the mixed potentials in the spatial domain [Mosig, 1989; Michalski and Mosig, 1997]. Recently, it is shown that the electric field dyadic Green's function of layered media can be computed in the spatial domain by using the Sommerfield integral with extractions [Tsang et al. 2000] For remote sensing, the observation point r in.-:.egion 0 is in the far-field. It is useful to have a far-field approximation for GOl(r, r') with r r'. We may evaluate GOl(r, r') by the stationary-phase method. The exponent is
kxx + kyY + (k 2
Then the stationary point is at
k~ - k;)~z
(5.2.29a) (5.2.29b) (5.2.29c) (5.2.30a) (5.2.30b) (5.2.30c)
kx = k sin ecos <p
k y = k sin esin <p k z = kcose
where
x = r sin ecos <p Y = r sin esin <p z = rcose
This gives the asymptotic result of = - -') eikr G01 (r, r = =
411T
_ .- -, = (k l.., z ') e -zk,L r ,L gOI
(5.2.31a) (5.2.31b)
eikr _ .- -, Got(r,r') = -4 gOt(kl..,z')e-zk,L.r,L
where the value of kl.. = kxx + kyY in gOI(kl.., z') and got(kl.., z') is to be evaluated at the stationary phase point given by (5.2.29).
5 SCATTERING AND EMISSION BY LAYERED MEDIA
2.3 Brightness Temperatures for a Stratified Medium with Temperature Distribution
Using the result of fluctuation dissipation theorem in 3, we have
TBV(So)] l' ~) 1m 167f211r; ~ [ TBh ( So = To-+OO A 0 cos 00 L
dxdy d"( Z )rJ"1 (Z ) ZWEI .11 (5.2.32)
[~(so) GOl(ro,r) . Gzt(ro,r) '~(So)]
h(so) . GOl(ro, 1') . GOl(ro,r) . h(so)
where GOI is the dyadic Green's function for stratified medium with SOurce point in region l. Using the asymptotic formula of (5.2.31), we have
211 167f ; Aocos
fff dx dy dz WE1'(Z)1l (z)G Ol (ro,r) . G~;(ro,1')
ko = -0-
dz--1}(z)gOI(k.L, z) . gOI(k.L, z)
Ei'(z)
-*t -
(5.2.33)
Hence, using (5.2.27) and (5.2.28) in (5.2.33) gives
k TBh(k,w) = -0cos 0
L:L j-dl-1dz'TI(Z')
1=1 Eo -d l
IAI l( -klz ) eiklzZI
+ BI el(kIZ)e-iklzzI12
(5.2.34)
k TBv(k, w) = -0cos 0
L :L j-dl-1dz' 7Hz')
1=1 Eo
-d l
leI hl(-kl z) eiklZZI
+ D I hl(klz)e-iklzzl
(5.2.35)
Carrying out the integrations in (5.2.34) and (5.2.35), we find the brightness temperature as observed from a radiometer at an angle 00 to be
2.3 Brightness Temperatures for Stratified Medium
for horizontal polarization, and
(5.2.36b)
for vertical polarization where kx = ksinO o . In the derivation of (5.2.36), we made use of the identities 2k~zk~~ = w2p,E~ and Ik tz l 2 + k~ = w2p,(E~k~z + E~/k~~)/k~z' The procedure for evaluating these expressions is as follows: (1) Both reflection coefficients R TE and R are evaluated by the recurrence relation method as given in (5.2.12). (2) The propagation matrix formalism of (5.2.23) and (5.2.24) are used to calculate the upward and downward wave amplitudes Al' El' GI, and Dl in each layer, as well as the transmitted wave amplitudes in the bottom layer TTE and TTM. That is, A o = RTE, B o = 1, Co = R , and Do = 1 are known from step (1), we can use (5.2.23a) and (5.2.23b) to calculate AI, B I , CI and D I and then A 2, B 2, C 2 and D 2, and so on. (3) The temperature Tl and permittivity El in each layer are used to perform the summation with the wave amplitudes previously obtained, as done in (5.2.36a) and (5.2.36b). When the medium is of constant temperature T, then the brightness temperatures are given simply by
TBh(Oo)