NR401 Dr. A.
Bhattacharya 1
ELECTROMAGNETIC THEORY
LECTURE 4
Lecture 4
EM radiation
2
Electromagnetic (EM) forms the basic source of remote
sensing observation.
Understanding basic properties of EM waves
Produced by
Motion of electric charge
Changing electrical field are set up by oscillating charged
particles
Changing electrical fields induces changing magnetic fields in
the surrounding medium.
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EM radiation
3
Time varying electric field produces a time varying
magnetic fields and vice-versa
Once generated, the EM wave is self propagating
Wave energy travels across space
Waves Electric + Magnetic fields
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EM radiation
4
Propagation in homogenous + isotropic media
direction of the 2 fields are at right angles to each
other
Electric and Magnetic fields are right angle to the
propagation direction
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EM fields and waves
5
First order Maxwell-Lorentz equation
Equating A set of second-order
differential
equations for the fields E and B
Second-order equations wave equation
Maxwell equations are postulates
Axiomatic foundation of classical electrodynamics
Describe in scalar and vector differential equations in
time t and x 3
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6
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Maxwell equations
7
Maxwell equations are 4 first-order differential
equations that are coupled
2 Scalar equations 3D Euclidean vector
form representing 3
scalar equations
each
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Maxwell equations
8
In the process of de-coupling
the equations,
we obtain one
second-order equation in E and one in B
These second-order partial differential equations are wave
equation
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Maxwell equations
9
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Maxwell equations
10
General wave equations for the electromagnetic fields,
generated in regions where there exist sources
and x, t of any kind j ( x, t )
Outside source region x, t =0 j ( x, t ) =0
Uncoupled homogenous equation
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Maxwell equations
11
EM waves are vector waves exhibit wave
polarization
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Speed of light
12
Various properties of EM waves can be deduced
from Maxwell’s equations
1
cm
0 8.85 x 10-12 Farad/m
0 4π x 10-7 Henry/m
1
c 3 x 108 m/s
0 0
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Refractive index/Dielectric constant
13
r and r
r is the relative permittivity (called dielectric constant)
r is the relative permeability
1 1 1
cm
r 0 r 0 r r 00
c c
cm
r r n
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Refractive index/Dielectric constant
14
n is referred to as refractive index
The media we consider are generally non-magnetic and
hence r 1
n r
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Permittivity/Permeability
15
Permittivity:
The property of a medium which influences the force between
electrical charges.
The permittivity of a medium/material is usually referred with
respect to permittivity of free space Relative permittivity
(Dielectric constant)
Permeability:
Magnetic property of the material
Measure of ‘conducting’ the magnetic lines of forces into the
material
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Propagation of EM waves from one
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medium to another
EM wave falls on a boundary between 2 lossless
homogenous media with different refractive
index
Part reflected back to incident medium (Fresnel
reflection)
Transmitted on second medium
Absorbed and emitted by the surface
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Propagation of EM waves from one
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medium to another
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Interaction of EM waves with Earth's
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surface
EM on interaction experiences :
Changes in magnitude
Changes in direction
Changes in wavelength
Changes in phase
Changes in polarization
Changes detected by remote sensors
Interpreter to obtain useful information about the object of
interest
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Interaction of EM waves with Earth's
19
surface
Viewpoint of interaction mechanism
Visible
----------- Infrared wavelengths (0.3µm –
16µm) 3 regions
0.3µm – 3µm Reflective region
3µm – 5.5µm Reflection/Self emission
8µm – 14µm Thermal infrared
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Reflection
20
Surface reflection are most useful in RS applications
The reflection intensity depends on the surface
refractive index/absorption coefficient/angle of
incidence
a. Perfect specular
b. Near perfect specular
c. Lambertian
d. Quasi-Lambertian
e. Complex/Diffused
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Spectral Signature
21
Spectral reflectance ρ(λ) is the ratio of reflected
energy to incident energy as a function of
wavelength
E R ( )
( ) 100
E I ( )
( ) Spectral reflectance at a particular wavelength
E R ( ) Energy of wavelength reflected from a object
E I ( ) Energy of wavelength incident upon a object
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Absorption
22
In EM domain materials broadly classified as
conductors and dielectrics (insulators)
There is no sharp distinction between dielectrics and
conductors
1 Conductor
1 Dielectric
: Conductivi ty
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Absorption
23
A lossy dielectric can be characterized by a
complex dielectric constant
' i ''
'
The real part correspond to the loss-less
component
"
The real part correspond to the lossy
component
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Absorption
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Refractive index :
n Complex quantity
n n ' in "
n
'
n ( Ulaby,
' 2 " 2
1986 )
" ' "
2n n
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Absorption
25
In a lossy medium as the wave propagates
Amplitude Intensity gets progressively reduced
The power density EZ at a point z
E Z E0 e K a z
Kais the power absorption coefficient and has
the unit of inverse of length
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Absorption
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Penetration depth
Defined as the depth at which the power is reduced
by 1
e
For " '
1 0 '
la
Ka 2 "
0 : Free space wavelength
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Scattering
27
If the medium is not homogenous Dielectric
discontinuities
EM radiation Absorbed + Scattered
Intensity reduced
Radiation scattered out to other direction reducing
the amount of radiation in the incident direction
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Scattering
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Scattering coefficient K S
Scattering length ls
The combined effect of scattering + absorption
Attenuation
In RS Inhomogeneous medium
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Scattering
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K e K a K s
Ks
Single scattering albedo : 0
Ke
0 is essentially the probability that given an interaction
between a photon and a particle, the photon will be scattered
rather than absorbed
0 1 : Attenuation by scattering
0 0 : Attenuation by absorption
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Quantum nature of EM radiation
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EM radiation Dual nature Wave and Particle
Wave nature Interference, diffraction,
polarization
Particle nature Photoelectric effect
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Quantum nature of EM radiation
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Quantum theory EM radiation moves in space
as discrete packets or quanta of energy
Each quantum of radiation Photon
Energy
c
Q h h
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Quantum nature of EM radiation
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Q Energy of quanta, joules (J)
h Planck' s constant, 6.626 10 34 J sec
Frequency
The longer the wavelength involved, the lower its
energy content.
Naturally emitted long wavelength radiation
Microwave emission from terrain feature is more
difficult to sense than radiation of shorter
wavelengths emitted Thermal IR energy
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Thermal Radiation
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Any object above absolute zero (0 K or -273 ˚C)
emits radiation
An ideal thermal radiator is called a black-body
emits radiation as per Plank’s law
2 1
2hc 2 M Spectral radiant exitance (Wm m )
M
5 ch k Boltzman's constant (1.3805 10 23WsK 1 )
exp 1
kT
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Thermal Radiation
34
A blackbody is an ideal surface such that
It
absorbs all incident radiation regardless of the
wavelength or direction of incident radiation
Fora given temperature and wavelength, no body
can emit more energy than a black body
Black body is diffuse emitter
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Thermal Radiation
35
The total emission within all the wavelength can
be found out by integrating Planck’s equation
2hc 2
0M 0 5 ch d
exp 1
kT
M Total T 4 ; : Stefan - Boltzman's constant
Stefan-Boltzman’s Law
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The Sun produces a
continuous spectrum
36 of energy from gamma
rays to radio waves
Various parts of the
EM spectrum may
differentiated using
wavelength (measured
in micrometers or
nanometers, i.e., λm or
nm) or electron volts
(eV).
2 Visible portion – 0.4 to
0.7 λm (~10-7 m range)
Jensen 2005
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Spectral Bandwidths of Landsat and SPOT
Sensor Systems
37
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Thermal Radiation
38
In addition to computing the total amount of energy
exiting a theoretical blackbody such as the Sun, we
can determine its dominant wavelength (λmax) based
on Wein's displacement law:
k
max
T
where k is a constant = 2898 mm K, and T is the
absolute temperature in Kelvin
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Blackbody radiation curves
39
•The area under each curve may
be summed to compute the total
radiant energy exiting each object.
•The Sun produces more radiant
exitance than the Earth because
its temperature is greater.
•As the temperature of an object
increases, its dominant
wavelength (λmax ) shifts toward
the shorter wavelengths of the
spectrum.
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Radiation curves of the earth and Sun
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Thermal Radiation
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The value of the exitance at the peak wavelength
is given by max
M max bT 5
b 1.286 10-11 Wm 2 m 1 K 5
All the equations assumes that the black body emits radiation
in vacuum. For a medium with refractive index n
k
max
nT
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Atmospheric Scattering
42
Scattering is the process by which small particles suspended
in a medium of a different index of refraction diffuse a
portion of the incident radiation in all directions.
Incident
sunlight
Scattered light
Atmospheric
particles
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Atmospheric Scattering
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Scattering not only reduces the image contrast but also
changes the spectral signature of ground objects seen
Scatter differs from reflection in that the direction associated
with scattering is unpredictable, whereas the direction of
reflection is predictable.
With scattering, there is no energy transformation, but a
change in the spatial distribution of the energy.
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Atmospheric Scattering
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Type of scattering is a function of:
• The wavelength of the incident radiant energy
• Their abundance
• The size of the particles
• The depth of the atmosphere
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Rayleigh scattering occurs when the diameter of the matter
Rayleigh (usually air molecules) are many times smaller than the
wavelength of the incident electromagnetic radiation.
scattering
It is impossible to predict the direction in which a specific atom
45 or molecule will emit a photon, hence scattering.
The approximate amount of Rayleigh scattering in the
atmosphere in optical wavelengths (0.4 – 0.7 mm) may be
computed using the Rayleigh scattering cross-section algorithm:
m
8 3 n 2 1 2
3N 2 4
where n = refractive index, N = number of air molecules per
unit volume, and λ = wavelength.
The amount of scattering is inversely related to the fourth power
of the radiation's wavelength. For example, blue light (0.4 m)
is scattered 16 times more than near-infrared light (0.8 m).
0.7
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Rayleigh scattering - effects
46
• Haze in satellite imagery, which diminishes crispness or
contrast of an image.
• Images taken in shorter wavelengths are more strongly
affected by Rayleigh scattering
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Mie scattering
47
• Mie scattering takes place when there are essentially spherical particles
present in the atmosphere with diameters approximately equal to the
wavelength of radiation being considered.
• For visible light, water vapor, dust, and other particles ranging from a
few tenths of a micrometer (Visible) to several micrometers (NIR) in
diameter are the main scattering agents.
• It influences the entire spectral region from UV IR regions
• Leads to diffused images, especially in overcast conditions.
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Non-selective scattering
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• Non-selective scattering is produced by particles several times the
diameter of the radiation being transmitted.
• This type of scattering is non-selective, i.e. all wavelengths of light are
scattered, not just blue, green, or red wavelength independent
• For example, water droplets, which make up clouds and fog banks,
scatter all wavelengths of visible light with equal intensity. These
objects therefore appear white Clouds
• Scattering can severely reduce the information content of remotely
sensed data to the point that the imagery looses contrast and it is
difficult to differentiate one object from another.
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Summary
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• The sensor to be used for the given remote sensing task
cannot be selected arbitrarily.
• One must consider:
• the spectral sensitivity of the sensor available,
• the presence or absence of atmospheric windows in the
spectral range(s) one wishes to sense,
• the source, magnitude, and spectral composition of the
energy available in these ranges.
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