RADIATIVE TRANSFER THEORY in .NET

Deploy Data Matrix 2d barcode in .NET RADIATIVE TRANSFER THEORY
7
Build data matrix barcode with .net
using visual studio .net todisplay data matrix 2d barcode on asp.net web,windows application
RADIATIVE TRANSFER THEORY
2d Data Matrix Barcode reader on .net
Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Scalar Radiative Transfer Theory Vector Radiative Transfer Theory Phase Matrix of Independent Scattering Extinction Matrix Emission Vector Boundary Conditions References and Additional Readings
VS .NET bar code drawer on .net
using visual .net toembed bar code in asp.net web,windows application
260 269 269 272 275 283 286
scan bar code with .net
Using Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.
2.1 2.2 2.3 2.4
Control datamatrix size with visual c#.net
to create data matrix barcodes and data matrix 2d barcode data, size, image with visual c#.net barcode sdk
- 259-
Gs1 Datamatrix Barcode barcode library on .net
generate, create data matrix barcodes none in .net projects
7 RADIATIVE TRANSFER THEORY
Control datamatrix size for visual basic.net
barcode data matrix size with visual basic.net
Radiative transfer theory is an important method to treat multiple scattering in medium consisting of random discrete scatteries. Classic books on the subject include Chandrasekhar [1960]; Ishimaru [1978]; Case and Zweifel [1967]. The theory has been extensively applied [Tsang et al., 1977; Tsang et al. 1985; Fung, 1994; Ulabyet al. 1990; Burke et al. 1979]. In this chapter, we derive the equation that governs the propagation of specific intensity in a medium containing random distribution of particles. The particles scatter and absorb the wave energy, and these characteristics should be included in a differential equation to be satisfied by the specific intensity. This equation is called the radiative transfer equation. There are three constituents of the radiative transfer equation. The extinction matrix describes the attenuation of specific intensity due to absorption and scattering. The phase matrix characterizes the coupling of intensities in two different directions due to scattering. The emission vector gives the thermal emission source of the specific intensity. Since the specific intensity is a four-element Stokes vector, the extinction and phase matrices are 4 x 4 matrices and the emission vector is a 4 X 1 column matrix. For spherical particles, the extinction matrix is diagonal and is a constant times the unit matrix. The emission vector has the first two elements equal and the last two elements equal to zero. For nonspherical particles, the extinction matrix is generally nondiagonal and the four elements of the emission vector are all nonzero. The resultant equations are called vector radiative transfer equations to distinguish them from the scalar transfer equation. We also define phase matrix as the averaged scattering cross section per unit volume of space where the volume is larger than many wavelengths and also large enough to include many particles. In this new definition, the coherent wave interactions among particles within wavelength scales can be included, and the collective scattering effects of particles in the neighborhood of each other are included. This is unlike the classical definition in which only the single-particle scattering characteristics are included in the phase matrix definition. Likewise, the extinction coefficient is defined as the average extinction cross section per unit volume of space, and the absorption coefficient is average absorption cross section per unit volume of space.
Visual Studio .NET Crystal ean-13 writer on .net
using vs .net crystal todeploy ean13+2 for asp.net web,windows application
Scalar Radiative Transfer Theory
.NET Crystal barcode pdf417 generating on .net
use visual studio .net crystal pdf417 2d barcode integration tobuild pdf417 2d barcode in .net
Radiative Dansler Equation
Visual Studio .NET uss code 128 generator in .net
using barcode writer for .net vs 2010 control to generate, create uss code 128 image in .net vs 2010 applications.
Radiative transfer equation is an integra-differential equation that governs the propagation of specific intensity.
Barcode writer on .net
generate, create bar code none with .net projects
1 Scalar Radiative Transfer Theory
Visual Studio .NET Crystal usps postnet barcode writer in .net
using vs .net crystal todraw delivery point barcode (dpbc) with asp.net web,windows application
0 '
Java matrix barcode development with java
use java matrix barcode maker toget 2d barcode on java
. . ' '. '0: 0
ANSI/AIM Code 128 barcode library for .net
generate, create code-128 none in .net projects
.. .0 .' '.
Matrix Barcode barcode library with .net
using barcode integrated for asp.net aspx control to generate, create 2d barcode image in asp.net aspx applications.
' ' '
Control upc a image on .net
use .net windows forms upc-a supplement 2 development toinclude gtin - 12 in .net
10 ' .
Control qr codes size on .net
qr-code size with .net
0 ' . : 0 :
Control ean / ucc - 13 image for word
using barcode integrated for word documents control to generate, create gs1 - 13 image in word documents applications.
0 :
Control 2d data matrix barcode data for .net
data matrix 2d barcode data in .net
'., '.
..:.
0 :
'0. ",'
0 ':.
' . '
.0:"
00 '0 0 :
....
. . . .' ...... : . :
,0'.
: .:.::'0: 0 :,,:
'0 ... '0'
0
:
..... ' . 0 . 0 :0'.: . .. : :: .. ..
' 0
' : . ' 0
Figure 7.1.1 Specific intensity 1(8) in direction 8 in and out of elemental volume. Many
particles are inside the elemental volume.
Consider a medium consisting of a large number of particles (Fig. 7.1.1). We have I(r, s) at all r and for all s due to scattering. We consider a "small" volume element dV = dAdl, and dl is along the direction s. The small volume element is centered at r. We consider the differential change in specific intensity 1(s) as it passes through dV (Fig. 7.1.1). The differential change of power in direction s is
dP = -1in(s)dAdO + 1out(s) dAdO = -I(r, s) dAdO + I(r + dls, s) dAdO
Radiative Change In Medium Containing Many Particles
(7.1.1)
The volume dV contains many particles that are randomly positioned. The volume dV is much bigger than ..\3 so that random phase prevails and the input and output relation of dV can be expressed in terms of intensities instead of fields. Thus dV, though called a "small" volume element, is really "not that small." There are three kinds of changes that will occur to 1(r, s) in the small volume element: (i) Extinction that contributes a negative change (ii) Emission by the particles inside the volume dV that contributes a positive change (iii) Bistatic scattering from direction Sf into direction s that contributes a positive change