1. FUNDAMENTALS AND PROPERTIES FOR RADIATION IN ABSORBING, EMITTING, AND SCATTERING MEDIA
Attenuation by absorption and scattering
Absorption and scattering coefficients
Augmentation of intensity by emission
Augmentation of intensity by incoming
scattering

2. Attenuation by Absorption and Scattering
(experimental
observation) or s
s + ds
: extinction coefficient, units of
reciprocal length [cm-1]

3. al : absorption coefficient
sl : scattering coefficient
Bouguer’s law

4. Radiation mean penetration distance
energy absorbed and scattered at s
fraction of energy absorbed and scattered at s

5. Mean penetration depth
when kl = constant
lm : average penetration distance
before absorption or scattering

6. Optical thickness (Opacity)
for a uniform gas
the number of mean penetration distances

7. : optically thick (photon continuum)
A volume element within the material
is only influenced by surrounding
neighbors.
diffusion approximation (Rosseland
approximation)
: optically thin
interact directly with medium boundary
Radiation emitted within the material is
not reabsorbed by the material.
negligible self-absorption

8. Limiting cases
: transparent medium
: completely opaque

9. The absorption and Scattering Coefficients
Absorption coefficient
if no scattering,
in the case of a uniform medium
in the electromagnetic theory of radiant energy propagation in conducting media

10. True absorption coefficient
ordinary or spontaneous emission
stimulated or induced emission
(negative absorption): resulting from the presence of the radiation field. At the same frequency and in the same direction as the incident photon
The observed emerging intensity is the result of the actual absorption modified by the addition of induced emission along the path

11. actual absorbed energy :
true absorption coefficient
larger than al calculated by using observed attenuation media
for a gas with reflective index n = 1
except at a large value of lT
1% deviation lT < 3120 mm
within 5% deviation lT < 4800 mm

12. Mie Solution
1) Definitions
Cs : scattering cross-section
the ratio of the rate of scattered energy by a spherical particle to the incident energy rate per unit area
Ca : absorption cross-section
Ce : extinction cross-section

13. Q : efficiency factor
the ratio of the cross-section to the geometric cross-section
r : radius of the sphere
: absorption efficiency factor
: scattering efficiency factor

14. 2) Mie’s solution
Re : real part
x : size parameter,
an, bn: Mie coefficient (Riccati-Bessel function)

15. z = x or y, y = mx, m = n - ik

16. Basic parameters
index of refraction m = n - ik relative to the surrounding medium
(k = 0 : pure scatter)
2) size parameter:
3) scattering angle q : phase function
For a medium containing N particles per unit volume of the same composition and uniform size

17. For a cloud of particles of different sizes

18. Increase of Intensity by Emission
spherical black
enclosure at T
nonparticipating
medium
volume element dV
dAs dA dw
ilb ds
s = ds
s = 0
dAs: a projected area normal to il(0)

19. ▪ spectral intensity incident at a location of dAs on dV, from element dA on the surface of the black enclosure:
▪ the change of this intensity in dV as a result of absorption

20. ▪ the energy absorbed by the differential subvolume dsdAs :
▪ the energy emitted by dA and absorbed by all of dV,

21. ▪ for all energy incident upon dV from the entire spherical enclosure

22. ▪ in equilibrium the energy spontaneously emitted by an isothermal volume element

23. dAp: the projected area of dV normal to the direction of emission
▪ the radiation intensity emitted by a volume element into any direction
dAp: the projected area of dV normal to the direction of emission
: the mean thickness of dV parallel
to the direction of emission or

24. Increase of Intensity by Incoming Scatteringdw ds
scattered intensity in the W direction

25. where
phase function: directional distribution of scattered radiation

26. isotropic scattering
physical interpretation
: probability that the incident radiation at will be scattered into the element of solid angle dw about the direction W W

27. Augmentation by incoming scatteringdw ds
scattering of the incident radiation per unit time, per unit wavelength, per unit volume, into an element of solid angle dw about W

28. All scattered intensity in the W directionds dw
All scattered intensity in the W direction or

29. Radiative Transfer Equation (RTE)