2-1

EE/Ae 157a

Introduction to the Physics and Techniques of

Remote Sensing

Week 2: Nature and Properties of Electromagnetic

Waves

2-2

TOPICS TO BE COVERED

• Fundamental Properties of Electromagnetic Waves

– Electromagnetic Spectrum, Maxwell’s Equations, Wave Equation,

Quantum Properties of EM Radiation, Polarization, Coherency, Group

and Phase Velocity, Doppler Effect

• Nomenclature and Definition of Radiation Quantities

– Radiation Quantities, Spectral Quantities, Luminous Quantities

• Generation of Electromagnetic Radiation

• Detection of Electromagnetic Radiation

• Overview of Interaction of EM Waves with Matter

• Interaction Mechanisms Throughout the Electromagnetic

Spectrum

2-3

ELECTROMAGNETIC SPECTRUM

2-4

MAXWELL’S EQUATIONS

0

0

0

0

B

E

ED

HB

JD

H

BE

r

r

t

t

2-5

WAVE EQUATION

EEE

E

HE

2

2

2

00

0

t

t

rr

r

2E 0 r0r

2E

t2 0

From Maxwell’s Equations, we find:

This is the free-space wave equation

2-6

SOLUTION TO THE WAVE EQUATION

2E

2

cr

2 E 0

For a sinusoidal field, the wave equation reduces to

The solution to this equation is of the form

E Aei kr t

The speed of light is given by

cr 1

0 r 0r

c0

r r

2-7

QUANTUM PROPERTIES OF EM RADIATION

• Maxwell’s equations describe mathematically smooth motion of

fields.

• For very short wavelengths, it fails to describe certain significant

phenomena when the wave interacts with matter.

• In those cases, a quantum description is more appropriate.

• In this description, the EM radiation is presented by a quantized

burst with energy Q proportional to the frequency of the wave:

• The energy in the wave train is delivered to a receiver on a

probabilistic basis

• Only when a large number of wave trains are present, will the

overall average effect be described by Maxwell’s equations

Q h; h Planck' s constant 6.626 1034

Joules/second

2-8

WAVE POLARIZATION

vyy

hxx

v

i

vh

i

h tkzAE

tkzAEeAeA vh

cos

coseeA

From the solution to the wave equation, we can write

This can be written as

vhvh

v

v

h

h

v

v

h

h

A

E

A

E

A

E

A

E

2

22

sincos2

This is the expression of an ellipse, and the wave is said to be

elliptically polarized

2-9

POLARIZATION ELLIPSE

v

av

ah

POLARIZATION

ELLIPSE

MAJOR

AXIS

MINOR

AXIS

h

2-10

SPECIAL POLARIZATIONS

m ; m 0,1, 2,

When

the wave is said to be linearly polarized. In this case, the ellipse

collapses to form a line.

When

Ax Ay and m 2, m 1,2,

the wave is said to be circularly polarized.

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HORIZONTAL (LINEAR) VERTICAL (LINEAR)

RIGHT-HAND CIRCULAR LEFT-HAND CIRCULAR

SPECIAL POLARIZATIONS

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Stokes Parameters

2 20

2 21

2

3

2 cos

2 sin

h v

h v

h v h v

h v h v

S a a

S a a

S a a

S a a

1 0

2 0

3 0

cos 2 cos 2

cos 2 sin 2

sin 2

S S

S S

S S

Another way to describe the polarization of a wave, particularly appropriate for the case of partially polarized waves, is through

the use of the Stokes parameters of the wave. For a monochromatic wave, these four parameters are defined as

Note that for such a fully polarized wave, only three of the Stokes parameters are independent, since

Using the relations between the ellipse orientation and ellipticity angles and the wave amplitudes and relative phases, it

can be shown that the Stokes parameters can also be written as

2 2 2 20 1 2 3S S S S

,

These relations lead to a simple geometric interpretation of polarization states. The Stokes parameters can be regarded as

the Cartesian coordinates of a point on a sphere, known as the Poincaré sphere, of radius 0S

2-13

Poincare Sphere

2

2

Linear

Polarization

(Horizontal)

Right-Hand

Circular

Left-Hand

Circular

Linear

Polarization

(Vertical)

1S

0S

3S

2S

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COHERENCY

• The coherence time of two waves of frequency n and nDn is the

time after which the waves are out of phase by exactly one cycle

• The coherence length is defined as:

• If two waves are coherent, there is a systematic relationship

between their instantaneous amplitudes.

nDt 1 n Dn Dt DnDt 1 Dt 1

Dn

Dl cDt c

Dn

2-15

COHERENCY

• Assume the total electric field is the sum of two component fields:

• The average power is

• If the two waves are incoherent, then

• If the waves are coherent, then

E t E1 t E2 t

P ~ E2

t E1

2t E2

2t 2 E1 t E2 t

E1 t E2 t 0 P P1 P2

E1 t E2 t 0 P P1 P2 or P P1 P2

2-16

Example of Coherence

2-17

PHASE VELOCITY

• The phase velocity of a wave is the velocity at which a constant

phase front progresses

D kDz Dt 0 Dz

Dt v p

k

vpDt

z

2-18

GROUP VELOCITY

• The group velocity is the velocity at which a plane of constant

amplitude progresses

• In the limit, this becomes

E z,t Aei k Dk z D t

Aei kDk z D t

2 Aei kz wt

cos Dkz Dt

DkDz DDt 0 Dz

Dt vg

D

Dk

z

vgDt

vg

k

2-19

PHASE vs GROUP VELOCITY

• Group velocity represents the velocity at which energy is

transported by a wave

• As such, the group velocity must be less than or equal to the

speed of light

• For certain media, the phase velocity can be greater than the

speed of light

• For non-dispersive media, the group and phase velocity are the

same and equal to the speed of light

ck

v p

k c

vg

k c

2-20

DOPPLER EFFECT

• If the relative difference between a source radiating a wave with a

fixed frequency n and an observer changes with time, the

frequency of the signal observed will be different than n

• This difference in frequency is known as the Doppler shift

• If the distance between the source and the observer is decreasing,

the Doppler shift is positive, i.e. the observed frequency is higher

than the transmitted one

• If the distance is increasing, the Doppler shift is negative

• The Doppler shift is used in remote sensing to measure target

motion

• It is also the effect used in Synthetic Aperture Radar to achieve

high resolution in the along-track direction

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DOPPLER EFFECT

l

Constant Amplitudes

c

v

q

Observer

c T v T cosq l

c

n

v

n cosq

c

n

n n nv

ccosq

nd nv

ccosq

For radars:

n d 2nv

ccosq

2-22

RADIANT ENERGY

• Radiant energy is the energy carried by the electromagnetic wave

• The amount of energy per unit volume is called radiant energy

density

• Radiant energy Q is measured in

• Radiant energy density W is measured in

joule

joule m3

W dQ

dV

2-23

RADIANT FLUX

• Radiant flux is the time rate at which radiant energy passes a

certain location

• Radiant flux density is the radiant flux intercepted by a unit area of

a plane surface

• The flux density incident upon a surface is called irradiance, M

• The flux density leaving a surface is called emittance, E

dQ

dtwatt

E, M d

dAwatt m

2

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SOLID ANGLE

• The solid angle W subtended by an area A on a spherical surface

is that area divided by the radius of the sphere squared

W

A

Area of Sphere

4R2

W A

R2

R

2-25

RADIANT INTENSITY

• The radiant intensity of a point source in a given direction is the

radiant flux per unit solid angle leaving the source in that direction

I d

dWwatt steradian

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RADIANCE

• Radiance is the radiant flux per unit solid angle leaving an

extended source in a given direction per unit projected area in that

direction

• If the radiance does not change as a function of direction of

emission, the source is called Lambertian

Wq

Source Area

A

Projected Source Area

Acosq

Flux, Surface Normal

L dI

dA cosqwatt steradianm

2

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REFLECTANCE, TRANSMITTANCE and

ABSORPTANCE

• Reflectance r is the ratio of the reflected exitance from a plane of

material to the irradiance on that plane

• Transmittance t is the ratio of the transmitted exitance, leaving

the opposite side of the plane, to the irradiance

• Absorptance a is the flux density that is absorped over the

irradiance

r t a 1

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SPECTRAL QUANTITIES

• Electromagnetic waves are usually made up of a collection of

sinusiods of slightly different frequencies, each carrying a part of

the radiant flux of the total wave

• The spectral band over which these components extend is called

the bandwidth of the signal

• All radiance quantities have equivalent spectral quantities that

correspond to the density as a function of frequency

Spectral flux l Flux in waves in band l Dl to l Dl

2Dl

Total flux in Bandwidth = l1 to l2 l dll 1

l 2

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LUMINOUS QUANTITIES

• Luminous quantities are related to the characteristic of the human

eye to perceive radiative quantities

• The relative effectiveness of the eye in converting radiant flux to

visual response is called the spectral luminous efficiency

• This function is used as a weighting function in relating radiant

quantities to luminous quantities

V l

n 680 e l V l dl0

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SPECTRAL LUMINOUS EFFICIENCY

2-31

COMPONENTS OF A REMOTE SENSING

SYSTEM

Source

Scattering Object

Waves Emitted

Collecting

Aperture

Detector

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GENERATION OF EM RADIATION

• A variety of techniques are used to generate electromagnetic

radiation in the different parts of the EM spectrum

• At radio frequencies, waves are generated by alternating currents

in wires, electron beams, or on the surfaces of antennas

• At microwave frequencies, electron tubes (e.g. TWTs) or

molecular exitation (e.g. masers) are used

• In the infrared and visible, waves are generated by molecular

excitation (vibrational or rotational) followed by decay. The

frequency of the waves generated is exactly related to the

difference between the two energy levels of the molecules

• Lasers use the exitation of molecules and atoms and selective

decay to generate narrow bandwidth EM radiation, and are used

from the UV to the high submillimeter

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GENERATION OF EM RADIATION

• Molecules in a gaseous state tend to have narrow, well-defined

emission lines

• In the solid phase, the close packing of atoms or molecules distort

their electron orbits, leading to a large number of characteristic

frequencies

• In the case of liquids, the situation is further complicated by the

random motion of molecules relative to each other

• At higher energies, gamma rays are generated in the natural

environment by radioactive decay of uranium, thorium or

potassium.

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GENERATION OF EM RADIATION

• Heat energy is a special case of EM radiation

• The random motion (due to collisions) of the molecules due to

kinetic energy results in exitation (electronic, vibrational and

rotational) followed by random emissions during decay

• This leads to radiation over a large bandwidth according to

Planck’s law for an ideal source (called a black body)

• Thermal emission is usually unpolarized

S l 2hc

2

l5

1

ech lkT 1

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IDEAL BLACK BODY RADIATION

2-36

SUN SPECTRAL IRRADIANCE AT EARTH’S

SURFACE

2-37

DETECTION OF EM RADIATION

• Any remote sensing system uses a collector, followed by a

detector, to measure the radiation from the source to be studied.

• The collector is an aperture that intercepts part of the radiated

field.

• In the radio and microwave regions of the spectrum, antennas

(dipoles, arrays, dishes) are used as collectors.

• In the IR, visible and UV regions, the collector is usually a lens or

reflecting surface focussing the energy onto the detector. The

energy is then transformed into another form such as heat,

electric current, or state change.

• Types of detectors include photomultiplier tubes, photodiodes,

and charge coupled devices (CCDs).

2-38

BOLTZMANN’S LAW

• In the case of thermal

equilibrium, the density of

population at any energy level is

proportional to

• The energy required to excite

from level i to level j is

Ni ~ e E i kT

E0

E

E2

E3

E1

Energy

Population

Nhn Ej Ei

2-39

ABSORPTION AND EMISSION

Ei

Ek

El

Ej

n ij n ij

n jk

n ki

n li

n jl

n lk

n ki

n jl

2-40

WAVE-MATTER INTERACTIONS

Spe ctral Re gion Main Inte raction Me chanisms Example Applications

Gamma Rays, X-Rays Atomic Proce sse s Mapping radioactive mate rials

Ultraviole t E le ctronic Proce sse s Pre se nce of H and He in

atmosphe re s

V isible and Ne ar IR E le ctronic and Vibrational Mole cular

Proce sse s

Surface che mical composition,

ve ge tation cove r, and biological

prope rtie s

Mid - IR V ibrational, V ibrational-Rotational

mole cular proce sse s

Surface che mical composition,

atmosphe ric che mical composition

The rmal IR The rmal Emission, V ibrational and

Rotational Proce sse s

Surface he at capacity, surface

te mpe rature , atmosphe ric

te mpe rature , atmosphe ric and

surface constitue nts

Microwave Rotational Proce sse s, The rmal

Emission, Scatte ring, Conduction

Atmosphe ric constitue nts, surface

te mpe rature , surface physical

prope rtie s, atmosphe ric

pre cipitation

Radio Fre que ncy Scatte ring, Conduction, Ionosphe ric

Effe cts

Surface physical prope rtie s,

subsurface sounding, ionosphe ric

sounding

2-41

WAVE-MATTER INTERACTIONS