Black body radiation,planck's radiation, wien's law, stephen boltzmann law ,P K MANI

1. Remote Sensing and its Applications in Soil
Resource Mapping(ACSS-754)(2+1)
Dr. P. K. Mani
Bidhan Chandra Krishi Viswavidyalaya
E-mail: pabitramani@gmail.com
Website: www.bckv.edu.in

2. B. Radiation & Atmosphere
Remote sensing is affected by how well the illuminating energy
penetrates the atmosphere. This is especially important when the
distance involved is great, such as from a satellite.

3. The Nature of Light
• In the 1860s, the Scottish mathematician and physicist James
Clerk Maxwell succeeded in describing all the basic properties of
electricity and magnetism in four equations
• This mathematical achievement demonstrated that electric and
magnetic forces are really two aspects of the same phenomenon,
which we now call electromagnetism

5. Kirchhoff’s Laws

6. Kirchoff’s First Spectral Law
• Any hot body produces a continuous spectrum
– if it’s hot enough it looks something like this
– digitally like this
Intensity
Wavelength

7. Kirchoff’s Second Spectral Law
• Any gas to which energy is applied, either as
heat or a high voltage, will produce an
emission line spectrum like this
– or digitally like this
Intensity
Wavelength

8. Kirchoff’s Third Spectral Law
• Any gas placed between a continuous
spectrum source and the observer will produce
a absorption line spectrum like this
– or digitally like this
Intensity
Wavelength

9. Astronomers’ Observations

11. A perfect radiator, “one that radiates the maximum number of photons in
a unit time from a unit area in a specified spectral interval into a
hemisphere that any body at thermodynamic equilibrium at the same
temperature can radiate.”

12. Black Body Radiation:
Blackbody radiation field is characterised as:
Isotropic and nonpolarized;
Independent of shape of cavity;
Depends on only temperature
(T).
In a perfect blackbody emisivity is equal to unity due to
thermodynamic equilibirium.
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13. Kirchoff’s law:
Since no real body is perfect
emitter, its emittance is less than
that of a black body (Mb). Thus
the emissivity of a real (gray,Mg)
body is defined by εg= Mg/Mb

14. • As the temperature
increases, the peak
wavelength emitted by the
black body decreases.
• As temperature increases,
the total energy emitted
increases, because the
total area under the curve
increases.
• The curve gets infinitely
close to the x-axis but
never touches it.

16. Derivation of Planck’s radiation law
Assumptions:
A cavity in a material that is maintained
at constant temperature T
The emission of radiation from the
cavity walls is in equilibrium with the
radiation that is absorbed by the walls
Blackbody cavity: schematic
The radiation field in an empty volume
in thermal equilibrium with a container at
T can be viewed as a superposition of
standing harmonic waves
M. Planck, Ann. Phys. Vol. 4, p.553 (1901)

24. Rayleigh–Jeans Law:
it describes the spectral radiance of
electromagnetic radiation at all
wavelengths from a black body at a given
temperature:
c is the speed of light,
k is Boltzmann's constant
T is the temperature in kelvins.
It predicts an energy output that diverges towards infinity as
wavelengths grow smaller. This was not supported by experiments
and the failure has become known as the ultraviolet catastrophe.

25. The energy density (i.e., the energy per unit volume) is therefore
given by
a relation known as Rayleigh-Jeans' law. The expression is valid
for
but incorrect for
, as it predicts that in this
case the energy density should become infinite. This physically
incorrect property of the equation would lead to what has
been termed “UV catastrophy".

27. Planck 1900: ...the whole procedure
Wilhelm Wien (1864-1928).
was an act of despair
because a theoretical interpretation had to be found
at any price, no matter how high that might be...

28. Planck’s radiation law
The Planck’s radiation law can be written in
dependence on frequency or on wavelength
With
L = spectral radiance
(energy / unit time / unit surface area
/ unit solid angle / unit wavelenth),
λ = wavelength, T = temperature,
h = Planck const
(6.62606896×10−34 J·s),
c = speed of light (299,792,458 m/s),
k =Boltzmann constant
(1.380 6504 × 10−23 J /K)
ν = frequency (c = λν).
u = spectral energy density as energy / unit volume /unit wavelength
2 interpretations of Planck’s law:
1) A surface of a solid body with the highest possible emissivity emits exactly the
radiation calculated from the Planck’s law.
2) Within a box with walls which have all the same temperature we get a gas of
electromagnetic photons which are in equilibrium with the walls, meaning that in any
time interval the walls absorb and emit an equal amount of photons. The energy
density and spectral distribution of the photons are described by u .

29. Planck’s radiation Law:
For a radiating body with emissivity ε, the spectral radiant
excitance (emittance) is given by Planck’s radiation law as:
ε 8π hc
1
Mλ =
⋅ hc / λkT
5
λ
e
−1
W/(m2-μm)
Using the relationship between frequency and wavelength of the
electromagnetic radiation ν = c/λ, Planck’s law can be written as
ε 8πh
ν
M ν = 3 ⋅ hν / kT
c
e
−1
3
W/(m2-Hz)

30. Black-body radiation is the type of electromagnetic radiation within
or surrounding a body in thermodynamic equilibrium with its
environment, or emitted by a black body (an opaque and nonreflective body) held at constant, uniform temperature. The radiation
has a specific spectrum and intensity that depends only on the
temperature of the body

31. Planck to Einstein: I hereby award you the Planck Medal because you
expanded my desperate idea of quantum of energy to the even more
desperate idea of quantum of light.

32. Stefan- Boltzmann Law:
If we integrate Mλ or Mν over all wavelength or all frequencies, the
total radiant emittance M will obtained for a radiating body of unit
area i.e.,
M = ∫ M λ dλ = ∫ M v dv = (ε 8π κ / h c )T
5
= σεT ,...........W / m
4
4
3 3
4
2
Where σ is the Stefan-Boltzmann radiation constant, and has the
numerical value = 5.669 10-8 W/(M2-K4)
Wien’s Displacement Law:
To obtain the peak spectral radiant emittance, we differentiate M λ with
respect to λ and set it equal to 0 and the resulting equation is solved
for λmax . Thus we get
λmax = a / T ...............µm

33. Radiance of EMR
A black body is hypothetical material that absorbs and
re-radiates ALL incident EMR.
The Stephan-Boltzman equation describes the total
amount of radiation emitted by a black body as a
function of its surface temperature:
M = σT4
where:
M = energy (Wm-2)
σ = Stephan-Boltzman constant
T = temperature (K)

34. • Wien’s Displacement Law
λm = b/T
λm = µm
b = 2898 µm K
• λ m(Sun) = 2898/6000
= 0.48 µm
• λ m(Earth) = 2898/300
= 9.66 µm

35. • Stefan-Boltzmann law
MT = σT4
MT = W m-2
σ = 5.669 x 10-8 W m-2 K-4
λm(Sun) = 5.669e-8 X 60004
MT = 7.3 x 107 W m-2
• λm (Earth) = 5.669e-8 x 3004
MT = 4.6 x 102 W m-2

37. Total EMR Emitted
The higher the
temperature
the more total
energy
Total Energy = Area
Under Curve

38. Spectral Distribution of Energy Radiated
from Blackbodies at Various Temperatures

39. Wavelength of EMR Emitted
The higher the
temperature the
lower/shorter the
wavelength of
maximum radiance
• Wein’ Law states
that λm = A/T
where: A is a
constant
Shortwave
EMR
Longwave
EMR

48. Radiometric Quantities
Quantities
Radiant Energy
(Q)
Definition
Unit
Energy transferred by electromagnetic J
waves
Radiant Flux
(Φ )
Rate of transfer of radiant energy
(Φ = dQ/dt)
W
Radiant emittance/
Radiant excitance
(M)
Radiant flux emitted per unit area of a
source
(M = dΦ/ dA)
W cm -2
Radiant Intensity
(I)
Radiant flux/ unit solid angle
(I = dΦ/dω)
W sr-1
Radiance
(L)
Radiant flux / unit solid angle/ unit area W cm-2 sr-1
(L=dI/dA Cosθ )
Irradiance
(E)
Radiant flux incident / unit area
(E = dΦ/dA)
W cm-2

49. Selective transmission of EMR by Earth’s
atmosphere
Transmission through the atmosphere is very selective.
Very high for wavelengths 0.3-1 µm and >1cm,
moderately good for 1-20 µm and 0.1-1 cm, and
very poor for <0.3 µm and 20-100 µm. This defines the
“ATMOSPHERIC WINDOWS”.

50. Absorption.
Scattering

51. Rayleigh Scattering: why the sky is blue

54. The atmosphere affects electromagnetic energy through absorption, scattering
and reflection.
How these processes affect radiation seen by the satellite depends on the path
length, the presence of particulates and absorbing gases, and wavelengths
involved.
transmitted
absorbed,
emitted and
scattered by
aerosols and
molecules
transmitted
absorbed
&scattered
emitted
reflected
transmitted
reflected
absorbed
emitted
Land
emitted
reflected
transmitted absorbed
Ocean
Figure-... Process of Atmospheric Radiation

55. EM radiation from the sun interacts with the atmospheric constituents
and gets absorbed or scattered. Essentially two types of scattering
takes place:
Elastic scattering in which the energy of radiation is not changed due
to the scattering, and
inelastic scattering in which the energy of the scattered radiation is
changed.
3 types of elastic scattering
is recognized in atmospheric scattering
Rayleigh scattering
Mie scattering
Nonselective scattering

56. Radiation scattered from a particle depends on:
Size;
Shape;
Index of refraction;
Wavelength of radiation;
View geometry.
For Rayleight scattering, λ >> φ
•Scattering is diffuse (in all directions) and λ dependent or selective
• Scattering = 1/ λ4
For Mie scattering,
λ ≈φ
Where φ is particle size.
 Scattering properties of such aerosols as smoke, dust, haze in
the visible part of the spectrum and of cloud droplets in the IR
region can be explanined by Mie scattering,
While of air molecules in the visible part can be explained by
Rayleigh Scattering

57. Rayleigh scattering refers to the scattering of light off of the molecules of the air, and
can be extended to scattering from particles up to about a tenth of the wavelength of
the light. It is Rayleigh scattering off the molecules of the air which gives us the
blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much
smaller than the wavelength to be:
Rayleigh scattering can be considered to be elastic scattering since the photon
energies of the scattered photons is not changed.
Scattering in which the scattered photons have either a higher or lower photon
energy is called Raman scattering. Usually this kind of scattering involves exciting
some vibrational mode of the molecules, giving a lower scattered photon energy, or
scattering off an excited vibrational state of a molecule which adds its vibrational
energy to the incident photon.

59. Nonselective Scattering
• Particles are much larger than the wavelength d>>l
• All wavelength are scattered equally
Effects of scattering
• It causes haze in remotely sensed images
• It decreases the spatial detail on the images
• It also decreases the contrast of the images

60. Mie Scattering
The scattering from molecules and very tiny particles
(< 1/10 wavelength) is predominantly Rayleigh scattering. For
particle sizes larger than a wavelength, Mie scattering predominates. This
scattering produces a pattern like an antenna lobe, with a sharper and more
intense forward lobe for larger particles.
Mie scattering is not strongly wavelength dependent and produces the almost
white glare around the sun when a lot of particulate material is present in the air. It
also gives us the white light from mist and fog.
Greenler in his "Rainbows, Haloes and Glories" has some excellent color plates
demonstrating Mie scattering and its dramatic absence in the particle-free air of
the polar regions.

61. Atmospheric scattering process
Scattering
process
Rayleigh
Mie
Nonselective
Wavelength Particle size
dependence
μm
λ-4
<<0.1
λ0 to λ-4
0.1-10
λ0
>10
Kind of
particles
Air molecules
Smoke ,
fume, Haze
Dust , Fog,
Cloud
Nonselective scattering occurs when the particles are much larger
than the wavelength of the radiation. Water droplets and large dust
particles can cause this type of scattering. Nonselective scattering gets
its name from the fact that all wavelengths are scattered about equally.
This type of scattering causes fog and clouds to appear white to our
eyes because blue, green, and red light are all scattered in
approximately equal

62. Atmospheric Windows




Atmospheric windows define wavelength ranges in
which the atmosphere is particularly transmissive of
energy.
Visible region of the electromagnetic spectrum
resides within an atmospheric window with
wavelengths of about 0.3 to 0.9 µm
Emitted energy from the earth's surface is sensed
through windows at 3 to 5 µm and 8 to 14 µm.
Radar and passive microwave systems operate
through a window region of 1 mm to 1 m.

63. Atmospheric Windows
The dominant
windows in the
atmosphere are in
the visible and radio
frequency regions,
while X-Rays and
UV are very strongly
absorbed and
Gamma Rays and
IR are somewhat
less strongly
absorbed.

65. Those wavelength ranges in which radiation can pass
through the atmosphere with relatively little attenuation.
atmospheric windows.

66. Atmospheric Windows
• Those wavelengths that are relatively easily
transmitted through the atmosphere
http://www.crisp.nus.edu.sg/~research/tutorial/atmoseff.htm#windows

68. Examples of Passive Sensors:
• Advanced Very High Resolution Radiometer
(AVHRR) Sea Surface Temperature
• Sea-viewing Wide Field-of-View Sensor
(SeaWiFS) Ocean Color

69. Remote Sensing Examples
•Global maps of land cover/land cover change from
MODIS …..
•http://earthobservatory.nasa.gov/Newsroom/LCC/
69

70. Key: land cover
classes

71. Geostationary vs. polar orbiting
sensors
Geostationary sensors
orbit with the earth
continually viewing the
same hemispheric area
Polar orbiters,
continually view new
areas of the earth as the
planet rotates underneath
the sensor. Keeps the
same general solar time
as it cross the equator on
each orbit - called sun
synchronous
Polar
orbit

72. Many different systems - which to
choose?

73. ikonos-abbottabad-pakistan

74. ikonos-fukushimadaiichi-after-web

75. ikonosmanhattan-newyork-9-11-2001web

76. IKONOS

77. Remote Sensor Types:
non-imaging
non-scaning
passive
Monochrom
IR
imaging Camera
imaging
Sensor
types
Microwave radiometer
Magnatic ensor
Gravimeter
Fourier spectrum
scanning
TV camera
image plane scanning
object plane scanning
Solid scanner
Optical mechanical scan.
Microwave radiometer
non-scaning non-imaging Microwave radiometer
Microwave altimeter
aktive
scanning imaging
image plane scanning
object plane scanning
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Passive phased array radar
Real aperture radar
Synthetic aperture radar

78. Orbits:
The motion of the satellites around the earth is governed
by the Newton’s law of motion.
The attractive force is:
r
satellite
earth
Satellite orbit
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gMem
F =
r2

79. However, real satellite orbit is nerly elliptical due to
the external foreces(e.g. gravitational potential of earth, solar
pressure). Eliptical orbit is to be explained by Kepler’s law.
Six orbital elements are used to express the spacecraft position
given by:
•Semimajor axis,a (km);
•Eccentricity,e;
•Inclination,i (degree);
•Right ascensing of ascending node, Ω (degree);
•Argument of perigee, ω (degree);
•And true anomaly, ν, degree.
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80. Z
spacecraft
apogee
earth
a
ν
perigee
Y
ω
Ascending node
Orbit plane
X
Ω
i
Equator plane
Ascending node
For the meteorological satellites, mainly two orbits are used:
and sunsynchronous and geostationary.
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81. Sunsynchronous orbit have high inclination angle (e.g
98.7 for NOAA sat), pass the equator at the same local time,
and located in the lower orbit (e.g . 850 km).
Geostationary orbit consides with the earth’s equatorial plane,
located nearly 36 km above the equator. Geostationary satellites
drift from the desired orbit so that periodic orbit manoeuvres are
needed in the east-west and north-south directions and vise versa.
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