Fluctuating Fields in .NET

Attach Data Matrix 2d barcode in .NET Fluctuating Fields
Fluctuating Fields
Paint data matrix with .net
generate, create data matrix ecc200 none on .net projects
In random scattering problems, since the inhomogeneities are randomly distributed, the fields and intensity are fluctuating. In the case of random discrete scatterers, the particles are randomly distributed in positions, shapes, sizes, and orientations so that the scattered fields are randomly fluctuating. For the case of random rough surface, the height profile is randomly distributed. In this section, we examine some of the basic relations of fluctuating fields. The concept of random fields is the foundation of random media and random rough surface scattering problems. Unlike deterministic problem in which there is only one solution, random media problem only has an unique solution for a single realization. As realization changes, the positions of the scatterers change and the height profiles change, and the fields will fluctuate. Realization changes can be due to the motion of the random media and rough surfaces or to the motion of the transmitter and receiver as they would view different parts of the surfaces and random media. Classic works on the concept of random fields include Booker and Gordon [1950], Foldy [1945], Lax [1951, 1952], Twersky [1962, 1964], Keller [1964], Frisch [1968], Beran [1968], Tatarskii [1971], and Ishimaru [1978].
.net Vs 2010 2d data matrix barcode scanner on .net
Using Barcode decoder for visual .net Control to read, scan read, scan image in visual .net applications.
3.1 Coherent and Incoherent Fields
decoding barcode with .net
Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications.
Let E(r) be the field. In general, E(r) is a random function of position. We can write E(r) as an average field (E) and the fluctuating field :
Bar Code barcode library for .net
generate, create barcode none on .net projects
E(r)
.net Vs 2010 data matrix writer for visual c#
use .net vs 2010 data matrix barcodes creator tocreate data matrix barcode for c#.net
(E(r))
Barcode Data Matrix barcode library on .net
using barcode integrated for web control to generate, create data matrix barcode image in web applications.
+ (r)
Create barcode data matrix for vb
using vs .net todisplay data matrix ecc200 on asp.net web,windows application
(3.3.1) (3.3.2)
Incoporate pdf417 in .net
using barcode creation for .net vs 2010 control to generate, create pdf417 image in .net vs 2010 applications.
( (r)) = 0
.net Framework Crystal barcode encoder on .net
using barcode encoder for visual .net crystal control to generate, create barcode image in visual .net crystal applications.
where angular bracket ( ) stands for ensemble averaging. The average field is also called the coherent field, and the fluctuating field is called the incoherent
.net Framework Crystal barcode data matrix writer with .net
using .net framework crystal toattach datamatrix in asp.net web,windows application
3 FUNDAMENTALS OF RANDOM SCATTERING
PDF417 integration in .net
using vs .net crystal toaccess pdf417 2d barcode in asp.net web,windows application
field. However, although the fluctuating field is called the "incoherent" field, it can contain partial coherent effects. From (3.3.1)
USD-8 generator for .net
using visual .net toadd code 11 for asp.net web,windows application
EE* = (E)(E*)
Control ucc-128 data for excel
ucc.ean - 128 data with office excel
Thus
+ (E) * + (E*) + ( *) + ( (rl) *(r2))
Aspx gs1 datamatrix barcode writer on .net
use asp.net web service data matrix barcode implementation tomake barcode data matrix on .net
(3.3.3)
Word Documents code 3/9 generating with word documents
generate, create code-39 none in word projects
(E(rI)E*(r2)) = (E(rl))(E*(r2))
Produce qr barcode for .net c#
generate, create qr code none with visual c#.net projects
(3.3.4)
Control qr code iso/iec18004 data in java
to attach qr-codes and qr code data, size, image with java barcode sdk
The quantity (E(rI)E*(r2)) is called the field correlation function at rl and r2. It is the sum of a coherent part represented by the first term of (3.3.4) and the incoherent part as represented by the second term of (3.3.4). When rl = r2, we get the intensity from (3.3.4). Let
Control qr code image with .net
using asp.net web pages togenerate qr code for asp.net web,windows application
I = E(r)E* (r)
Bar Code barcode library in .net
generate, create bar code none in .net projects
be the intensity. Then
(3.3.5)
(1) = Ie + If
where
(3.3.6)
Ie = I(E(r))1
is the coherent intensity and
(3.3.7) (3.3.8)
If = (1 (r)1
is the incoherent intensity. The intensity can also be fluctuating. The variance a} of the intensity fluctuation is given by
a} = (1 2 ) -
(1)2 = (IEI
(Ie + I f )2 = (IEI 4 )
(I(E(r))1
+ (1 (r)1 2)
(3.3.9)
3.2 Probability Distribution of Scattered Fields and Polarimetric Description
Consider; a random field created by scattering from many different particles or by random rough surface
E = Aexp(i4 = X
+ iY
(3.3.10)
where A is amplitude, 4> is the phase, and X and Yare called the quadrature components. Since E is sum of fields from many different particles or from many peaks and valleys in random rough surfaces, we can write [Ishimaru, 1978; Sarabandi, 1992]
L (Xn+ iYn)= LAn exp(i4>n)
n=l n=l
(3.3.11)
3.2 Probability Distribution
where n is the particle index and N is the number of particles. It is assumed that the Xn's and Yn's are independent random variables. Then, the central limit theorem states that the probability distribution of a sum of Nindependent random variables will approach a normal distribution as N - t 00, regardless of the probability distribution of each random variable. Based on this, X and Yare normally distributed. It is further assumed that the phase has no preferred value and is uniformly distributed between 0 and 27r. The uniform distribution of p( ) is independent of A. Thus, the joint probability density function p(A, ) is
p(A, ) = p(A)p( ) 1 p( ) = 27r 0 ::; ::; 27r
(3.3.12) (3.3.13)
If we take an average using the probability density function above, we obtain
(X) = (A cos ) = (A) (cos )
Similarly,
loo dAp(A) l27r d p( ) cos = 0
(Y) = 0
(XY) = (A sin cos )
(3.3.14)
(3.3.15) (3.3.16)