ELECTROMAGNETIC THEORY LECTURE 4avikb/GNR401/RS/RS_401_lecture_4.pdf · wavelength of the incident electromagnetic radiation. It is impossible to predict the direction in which a

ELECTROMAGNETIC THEORYLECTURE 4

NR401 Dr. A. Bhattacharya 1

Lecture 4

EM radiation

NR401 Dr. A. Bhattacharya

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.

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

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

EM fields and waves


5

First order Maxwell-Lorentz equation Equating A set of second-order differential

equations for the fields and Second-order equations wave equation

Maxwell equations are postulates Axiomatic foundation of classical electrodynamics Describe in scalar and vector differential equations in

time and

E

B

t 3x


6

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

Maxwell equations

In the process of de-coupling the equations, we obtain one second-order equation in and one in

These second-order partial differential equations are wave equation

E

B


8

Maxwell equations


9

Maxwell equations

General wave equations for the electromagnetic fields, generated in regions where there exist sources and of any kind

Outside source region =0 =0

Uncoupled homogenous equation

tx, ),( txj


10

tx, ),( txj

Maxwell equations


11

EM waves are vector waves exhibit wave polarization

Speed of light


12

Various properties of EM waves can be deduced from Maxwell’s equations

1

mc

0 8.85 x 10-12 Farad/m

0 4π x 10-7 Henry/m

00

1

c 3 x 108 m/s

Refractive index/Dielectric constant

and

is the relative permittivity (called dielectric constant)

is the relative permeability

rr


13

r r

nccc

c

rrm

rrrrm

0000

111

Refractive index/Dielectric constant

n is referred to as refractive index

The media we consider are generally non-magnetic and hence 1r


14

rn

Permittivity/Permeability


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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

Propagation of EM waves from one medium to another


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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

Propagation of EM waves from one medium to another


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Interaction of EM waves with Earth's surface


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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

Interaction of EM waves with Earth's surface


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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

Reflection


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Surface reflection are most useful in RS applications

The reflection intensity depends on the surface refractive index/absorption coefficient/angle of incidence

a. Perfect specularb. Near perfect specularc. Lambertiand. Quasi-Lambertiane. Complex/Diffused

Spectral Signature


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Spectral reflectance ρ(λ) is the ratio of reflected energy to incident energy as a function of wavelength

100)()()(

I

R

EE

object aupon incident h wavelengtofEnergy )(object a from reflectedh wavelengtofEnergy )(

h wavelengtparticular aat ereflectanc Spectral)(

I

R

EE

Absorption


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In EM domain materials broadly classified as conductors and dielectrics (insulators)

There is no sharp distinction between dielectrics and conductors

tyConductivi :

Dielectric 1

Conductor 1

Absorption


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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

'

"

Absorption


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Refractive index :

)1986 Ulaby,(2

quantityComplex

"'"

2"2''

"'

nnnn

innn

n

Absorption


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In a lossy medium as the wave propagates

Amplitude Intensity gets progressively reduced

The power density at a point ZE

zKZ

aeEE 0

is the power absorption coefficient and has the unit of inverse of length

aK

z

Absorption


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Penetration depth Defined as the depth at which the power is reduced

by e1

h wavelengtspace Free :"2

1

For

0

'0

'"

aa K

l

Scattering


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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

Scattering


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Scattering coefficient

Scattering length

The combined effect of scattering + absorption Attenuation

In RS Inhomogeneous medium

SK

sl

Scattering


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sae KKK

Single scattering albedo :

is essentially the probability that given an interaction between a photon and a particle, the photon will be scattered rather than absorbed

e

s

KK

0

0

absorptionby n Attenuatio : 0scatteringby n Attenuatio : 1

0

0

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 theory EM radiation moves in space as discrete packets or quanta of energy

Each quantum of radiation Photon

Energy

chhQ



32

Frequency sec10626.6 constant, sPlanck'

(J) joules quanta, ofEnergy 34

Jh

Q

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

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

)103805.1(constant sBoltzman' )( exitanceradiant Spectral

1exp

2123

12

5

2

WsKk

mWmM

kTch

hcM

Thermal Radiation


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A blackbody is an ideal surface such that

It absorbs all incident radiation regardless of the wavelength or direction of incident radiation

For a given temperature and wavelength, no body can emit more energy than a black body

Black body is diffuse emitter

Thermal Radiation


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The total emission within all the wavelength can be found out by integrating Planck’s equation

constant sBoltzman'-Stefan : ;

1exp

2

4

0 5

2

0

TM

d

kTch

hcM

Total

Stefan-Boltzman’s Law


36

2

The Sun produces a continuous spectrumof 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).

Visible portion – 0.4 to 0.7 λm (~10(~10--7 7 m range)m range)

Jensen 2005Jensen 2005

Spectral Bandwidths of Landsat and SPOT Sensor Systems


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Thermal Radiation


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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:

Tk

max

where k is a constant = 2898 mm K, and T is the absolute temperature in Kelvin

Blackbody radiation curves


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•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.

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

512 11-

5

101.286

max

KmWmb

bTM

All the equations assumes that the black body emits radiation in vacuum. For a medium with refractive index n

nTk

max

Atmospheric Scattering


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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.

Atmospheric particles

Incident sunlight

Scattered light



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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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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 atmosphereThe depth of the atmosphere


45

0.7

Rayleigh scattering occurs when the diameter of the matter (usually air molecules) are many times smaller than the wavelength of the incident electromagnetic radiation.

It is impossible to predict the direction in which a specific atom 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:

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).

42

223

318

Nn

m

Rayleigh scattering

Rayleigh scattering - effects


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• Haze in satellite imagery, which diminishes crispness or contrast of an image.

• Images taken in shorter wavelengths are more strongly affected by Rayleigh scattering

Mie scattering


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• 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.

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.

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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ELECTROMAGNETIC THEORY LECTURE 4avikb/GNR401/RS/RS_401_lecture_4.pdf · wavelength of the incident electromagnetic radiation. It is impossible to predict the direction in which a