Transcript Chapter 2 EMR

Lecture #2
The Fundamentals of
Electromagnetic Radiation Principles
Contributions from R. Pu and M. D. King
Outline
1. Electromagnetic energy interactions
2. Electromagnetic radiation models (wave/particle)
3. Atmospheric refraction
4. Atmospheric scattering
5. Atmospheric absorption (“atmospheric
windows”)
6. Radiometric quantities and reflectance
7. Radiance and atmospheric transfer/correction
8. Summary
1. Electromagnetic Energy
Interactions
1. Electromagnetic Energy Interactions
• When the energy being remotely sensed comes
from the Sun, the energy:
– Propagates through the vacuum of space
– Interacts with the Earth's atmosphere, surface, and
atmosphere
– Reaches the remote sensor (interacts with various
optical systems, filters, emulsions, or detectors)
Energy-matter
interactions in the
atmosphere, at the
study area, and at
the remote sensor
detector
Pictorial Explanation
2. Electromagnetic Radiation Models
Fundamental Properties of
Electromagnetic Radiation
• The three basic ways in which energy can be transferred
include radiation, convection and conduction.
• The transfer of energy by electromagnetic radiation is of
primary interest to remote sensing because it is the only
form of energy transfer that can take place in a vacuum
such as the region between the Sun and the Earth
• The Sun bathes the Earth’s surface with radiant energy
causing the air near the ground to increase in temperature
– The less dense air rises, creating convectional currents in the
atmosphere
• Energy may be conducted directly from one object to
another as when a pan is in direct physical contact with a
hot burner
Fundamental Properties of
Electromagnetic Radiation
• The energy can be transferred in the three basic
ways: conduction, convection, and radiation
Electromagnetic Radiation Models
To understand how electromagnetic radiation is
created, how it propagates through space, and
how it interacts with other matter, it is useful to
describe the processes using two different
models:
• the wave model, and
• the particle model
Wave Model of EM Energy
An electromagnetic wave is composed of electric and
magnetic vectors that are orthogonal to one another and
travel from the source at the speed of light (3 x 108 m s-1)
The Wave Model of
Electromagnetic
Energy
• Frequency: the number of wavelengths that pass a point
per unit time
• Wavelength: the mean distance between maximums (or
minimums)
• Common units: micrometers (m) or nanometers (nm)
• One cycle per second is termed one hertz (1 Hz)
Wave Model of Electromagnetic Energy
The relationship between the wavelength, , and frequency, , of
electromagnetic radiation is based on the following formula, where
c is the speed of light:
c = l ×v
v=
c
l
v
l=
c
Note that frequency,  is inversely proportional to wavelength, 
The longer the wavelength, the lower the frequency, and vice-versa
Wave Model of Electromagnetic Energy
Sources of Electromagnetic Energy
• The Sun yields a
continuous spectrum
of EM energy
• This process produces
a large amount of
short wavelength
energy (from 0.4 - 0.7
m; blue, green, and
red light)
• Interacts with the atmosphere and surface materials
(reflect, absorb)
• Absorption: absorb the short wavelength energy and
then re-emit it at a longer wavelength
Electromagnetic (EM) Spectrum
The Sun produces a
continuous spectrum of
energy from gamma
rays to radio waves that
continually bathe the
Earth in energy
The visible portion of the
spectrum may be
measured using
wavelength (measured
in m or nm) or electron
volts (eV)
– All units are
interchangeable
Stefan-Boltzmann Law
• The total emitted radiation (M) from a blackbody is
proportional to the fourth power of its absolute temperature
– This is known as the Stefan-Boltzmann law and is expressed as:
M = sT 4
where s is the Stefan-Boltzmann constant = 5.6697 x 10-8 W m-2 K-4
– T = absolute temperature (in Kelvin)
• The greater the T, the greater the amount of radiant energy
exiting the object
– The temperature 0°C (in the common Celsius scale) corresponds to 273 K
Wien’s Displacement Law
• To compute its dominant wavelength (max) as:
max = k / T
where k is a constant equaling 2898 m K, and T is temperature in
degrees Kelvin
• The Sun approximates a 6,000 K blackbody, therefore its
dominant wavelength is:
0.483 m = 2898 m K / 6000 K
– T determines the wavelength
Blackbody
Radiation Curves
• Blackbody radiation curves
for the Sun: temperature
approximate 6,000 K
• For Earth: 300 K
• As the temperature of the
object increases, its
dominant wavelength shifts
toward the short
wavelength portion of the
spectrum
Radiant Intensity
of the Sun
• The Sun (6,000 K blackbody)
dominant: 0.5 µm
• Earth (300 K blackbody)
• Dominant: 9.7 µm
• Sun: 41%: visible region from
0.4 - 0.7 µm
• The other 59% (<0.4 µm)
and (>0.7 µm)
• Eyes are only sensitive to
light from the 0.4 to 0.7 µm
• Remote sensor detectors
can be made sensitive to
energy in the non-visible
regions of the spectrum
Particle Model of EM Energy
• Quantum theory of electromagnetic radiation: energy
is transferred in discrete packets called quanta or
photons
• The relationship between the frequency of radiation
and the quantum is:
Q=h
• where Q is the energy of a quantum measured in
Joules (J), h is the Planck constant (6.626 x 10-34 J s-1),
and  is the frequency of the radiation
3. Atmospheric Refraction
Atmospheric Refraction
The Speed of Light in a Vacuum and in the Atmosphere
• The speed of light c is 3 x 108 m s-1 (same as
Electromagnetic Radiation EMR)
• When encounters substances of different density (air and
water), refraction may take place
• Refraction: bending of light when it passes from one
medium to another
– Refraction occurs because the media are of differing densities and
the speed of EMR is different in each
• The index of refraction, n: measure of the optical density of
a substance
– This index is the ratio of c, to the speed of light in the substance, cn:
c
n = __
cn
Index of Refraction and Snell’s Law
Atmospheric Refraction
Incident
Norm al t o
radiant energy t he surface
n = index of
1
refraction for
t his layer of

1
t he at mosphere
Optically
less dense
atmosphere
n
2
Optically
more dense
atmosphere
n
3
Optically
less dense
atmosphere
P at h of
energ y in
h omo g en eo u s
atmos p here

2
Snell’s law
– for a given frequency
of light, the product of
the index of refraction
and the sine of the
angle between the ray
and a line normal to the
interface is constant
n1 sin 1 = n2 sin 2

3
P ath of radiant energy affected
by atmospheric refraction
4. Atmospheric Scattering
Atmospheric Scattering
Electromagnetic radiation is propagated through
the earth's atmosphere almost at the speed of light
in a vacuum
• Unlike a vacuum in which nothing happens, however,
the atmosphere may affect
 speed of radiation
 intensity
 spectral distribution
 direction
Atmospheric Scattering
The type of scattering is a function of:
• The wavelength of the incident radiant energy
• The size of the gas molecule, dust particle, or
water droplet encountered
Atmospheric Layers and Constituents
Major subdivisions of the atmosphere and the types of
molecules and aerosols found in each layer
Atmospheric Scattering
Reflection: the direction
predictable
Scattering: direction
unpredictable
Water
Droplets
Based on wavelength of incident
radiant energy, the size of the
gas molecule, dust particle, or
water vapor droplet essentially
three types of scattering:
• Rayleigh
• Mie
• non-selective scattering
Rayleigh Scattering
• Rayleigh scattering occurs when the
diameter of the matter (usually air
molecules) are many times smaller than the
wavelength of the incident electromagnetic
radiation
• Rayleigh named after the English physicist
Intensity of Rayleigh Scattering
-4
Varies Inversely with  
3 2.75 2.5 2.25
Intensity of Scattered Light
100
2
1.75
En ergy i n
e le ctron vol ts (e V)
80
60
40
20
0
V
B
G
YO R
0.4
0.5
0.6
0.7
W ave le n gth in Microm e te rs
Rayleigh Scattering
• The amount of
scattering is inversely
related to the fourth
power of the radiation's
wavelength (-4)
• For example, blue light
(0.4 m) is scattered 16
times more than nearinfrared light (0.8 m)
Mie Scattering
• Mie scattering: when essentially spherical particles present in
the atmosphere with diameters approximately equal to the
wavelength of radiation
• For visible light, water droplets, dust, and other particles ranging
from a few tenths of a micrometer to several micrometers in
diameter are the main scattering agents
– The amount of scatter is greater than Rayleigh scatter and the wavelengths
scattered are longer
• Pollution also contributes to beautiful sunsets and sunrises
– The greater the amount of smoke and dust particles in the atmospheric
column, the more violet and blue light will be scattered away and only the
longer orange and red wavelength light will reach our eyes
Non-selective Scattering
• Non-selective scattering: when particles in the
atmosphere are several times (>10) greater than the
wavelength of the radiation
– All wavelengths of light are scattered, not just blue, green, or red
 Thus, water droplets scatter all wavelengths of visible light
equally well, causing the cloud to appear white (a mixture of
all colors of light in approximately equal quantities produces
white)
– Scattering can severely reduce the information content of
remotely sensed data to make it difficult to differentiate one object
from another
Color of the Sky
Two questions:
• Why is the sky blue?
• Why is the sunset orange?
Color of the Sky
• Why is the sky blue?
– A clear cloudless day-time sky is blue because
molecules in the air scatter blue light from the sun
more than they scatter red light
• Why is the sunset orange ?
– When we look towards the sun at sunset, we see red
and orange colors because the blue light has been
scattered out and away from the line of sight
• http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html
Angular Scattering Coefficient [(Q)]
– Fractional amount of energy scattered into the direction Q per
unit solid angle per unit length of transit [m-1 sr-1]
Q
dW
Unit length
Propagating beam
f
Scattering center
Solid Angle Representation of
Spherical Coordinates
dW = sinddf
Z
rsindf
rsin
rd
df

dW
d
x
f
df
y
Volume Scattering and Extinction Coefficient
• Volume scattering coefficient [ssca]
– Fractional amount of energy scattered in all directions per unit length of
transit [m-1]
ssca = (Q)dW
2 
(Q)sinQdQdf
=
0 0
• Volume absorption coefficient [sabs]
– Fractional amount of energy absorbed per unit length of transit [m-1]
• Volume extinction coefficient [sext]
– Fractional amount of energy attenuated per unit length of transit [m-1]
sext = ssca + sabs
• Single scattering albedo [0]
– Fraction of energy scattered to that attenuated
0 = ssca/(ssca + sabs)
Optical Thickness
• Optical depth [t]
– Total attenuation along a path length, generally a function of wavelength
[dimensionless]
X
t() = sextdx
0
• Total optical thickness of the atmosphere [tt]
– Total attenuation in a vertical path from the top of the atmosphere down to
the surface

tt() =
sextdz
0
• Transmission of the direct solar beam
t = exp[-tt()/µ0]
t = exp[-tt()]
0
µ0 = cos0
Scattering Phase Function
• Scattering phase function is defined as the ratio of the energy scattering per
unit solid angle into a particular direction to the average energy scattered per
unit solid angle into all directions
F(cosQ) =
(Q)
(Q)dW
=
4(Q)
ssca
4
with this definition, the phase function obeys the following normalization
4
1
1 =
F(cosQ)dW
4 0
1
1
=
F(cosQ)dcosQ
2 -1
• Rayleigh (molecular) scattering phase function
F(cosQ) =
3
(1 + cos2Q)
4
Shapes of Scattering Phase Function
Rayleigh (molecular)
90°
135°
Composite
45°
dW
180°
0°
225°
315°
270°
Shapes of Scattering Phase Function
Rayleigh (molecular)
90°
90°
135°
135°
Composite
Nonselective scattering
45°
45°
Mie scattering
dW
180°
0°
0°
180°
225°
315°
270°
225°
315°
270°
5. Atmospheric Absorption
Atmospheric Absorption
• Absorption is the process by which radiant energy is
absorbed and converted into other forms of energy
– An absorption band is a range of wavelengths (or frequencies) in the
electromagnetic spectrum within which radiant energy is absorbed by
substances such as water (H2O), carbon dioxide (CO2), oxygen (O2),
ozone (O3), and nitrous oxide (N2O)
• The cumulative effect of the absorption by the various
constituents can cause the atmosphere to close down in
certain regions of the spectrum
– This is bad for remote sensing because no energy is available to be
sensed
Absorption
• In certain parts of the spectrum such as the visible region
(0.4 - 0.7 m), the atmosphere does not absorb much of the
incident energy but transmits it effectively
• Parts of the spectrum that transmit energy effectively are
called “atmospheric windows”
• The combined effects
of atmospheric
absorption, scattering,
and reflectance reduce
the amount of solar
irradiance reaching the
Earth’s surface at sea
level
Rotational and Vibrational Modes of Molecules
6. Radiometric Quantities
and Reflectance
Definition of Solar Zenith, View Zenith,
and Relative Azimuth Angle
z
dW = sinddf
0
rsin


W

rd
df
dW
f0
f
rsind
f
d
Df
S
y
N
E
Definition of Reflection Function
The reflection function is usually a function of at least 5 variables
R(tt, 0; µ, µ0, f)
where
tt
0
µ
µ0
f
=
=
=
=
=
total optical thickness
the single scattering albedo (ratio of scattering to total extinction)
absolute value of the cosine of the zenith angle |cos|
cosine of the solar zenith angle cos0
relative azimuth angle between the direction of propagation of the
emerging radiation and the incident solar direction
Note: R, tt, 0 are all functions of wavelength 
Radiometric Quantities
• Radiometric quantities: recording the incident and exiting
radiant flux
• The simple radiation budget equation:
– the total amount of radiant flux incident to the ground (I) in
specific wavelengths
– the amount of energy reflected from the surface (r)
– the amount of energy absorbed by the surface ()
– the amount of radiant energy transmitted through the surface
(t); therefore, the radiation budget equation:
I r+  + t
Flux (Irradiance) on a Horizontal
Surface at the Surface of the Earth
The transmitted flux (irradiance) at the Earth’s surface can be calculated as:
2 
E(tt , 0; µ0, µ, f) =
I(tt, 0; µ, µ0, f)µdµdf + µ0F0exp(-tt/µ0)
0 0
2 
1
= µ0F0 [
0
T(tt, 0; µ, µ0, f)µdµdf + exp(-tt/µ0)]
0
where the transmission function is defined in an analogous manner to reflection
function
T(tt, 0; µ, µ0, f) =
I(tt, µ, f)
µ0F0
Radiometric Quantities
• The radiometric quantities are based on the amount of radiant
incident to a surface from any angle in a hemisphere (i.e. a half
of a sphere)
Hemispherical reflectance (rl) or albedo is defined as the
dimensionless ratio of the radiant flux reflected from a surface
to the radiant flux incident to it
Freflected
r

Radiometric Quantities
Hemispherical transmittance (t) is defined as the
dimensionless ratio of the radiant flux transmitted
through a surface to the radiant flux incident to it
Freflected
r

Radiometric Quantities
• Hemispherical absorption () is defined by the
dimensionless relationship
 rt
• Radiant energy must be conserved
• The net effect of absorption of radiation is that the
energy is converted into heat, causing a subsequent
rise in the substance's temperature
Concept of R adiant Flux Density
Radiant flux,F
Irradiance
F
E =
 
Area, A
Radiant flux,F
Exitance
F
M =
 
Area, A
• The concept of radiant flux
density for an area on the
surface of the earth
• Irradiance is a measure of
the amount of incoming
energy in Watts m-2
• Exitance is a measure of
the amount of energy
leaving in Watts m-2
7. Radiance and Atmospheric
Transfer/Correction
Radiance
The concept of radiance (L)
leaving a specific projected
source area (A) on the
ground, in a specific direction
(), and within a specific solid
angle (W)
The L is measured in watts
per meter squared per
steradian (W m-2 sr -1 )
– We are only interested in
the radiant flux in certain
wavelengths (F) leaving
the projected source area
(A) within a certain direction
() and solid angle (W)
Reflectance
• Specular reflection (a):
smooth (i.e., the average
surface profile is several
times smaller than the
wavelength of radiation)
• Diffuse reflection (b): rough,
the reflected rays go in many
directions
• Lambertian surface (d) the
radiant flux leaving the
surface is constant for any
angle of reflectance to the
surface normal
Path 1 contains spectral solar
irradiance (E0) that was
attenuated very little before
illuminating the terrain within
the IFOV
– Notice in this case that we
are interested in the solar
irradiance from a specific
solar zenith angle (0) and
that the amount of
irradiance reaching the
surface is a function of the
atmospheric transmittance
at this angle (T0)
– If all of the irradiance
makes it to the ground, then
the atmospheric
transmittance (T0) equals
one
– If none of the irradiance
makes it to the ground, then
the atmospheric
transmittance is zero
Path 2 contains spectral diffuse
sky irradiance (Ed) that never
even reaches the Earth’s surface
(the target study area) because
of scattering in the atmosphere
– The energy is often
scattered directly into the
IFOV of the sensor system
in the form of Rayleigh
scattering of diffuse sky
irradiance
– It contains much unwanted
diffuse sky irradiance that
was inadvertently scattered
into the IFOV of the sensor
system
– Therefore, if possible, we
want to minimize its Ed
effects
Path 3 contains energy from the
Sun that has undergone some
Rayleigh, Mie, and/or
nonselective scattering and
perhaps some absorption and
reemission before illuminating
the study area
– Thus, its spectral
composition and
polarization may be
somewhat different from the
energy that reaches the
ground from path 1
– It is referred to as the
downward reflectance of the
atmosphere (Edd)
Path 4 contains radiation that
was reflected or scattered by
nearby terrain (rn) covered by
snow, concrete, soil, water,
and/or vegetation into the IFOV
of the sensor system
– The energy does not
actually illuminate the study
area of interest
– Therefore, if possible, we
would like to minimize its
effects
Path 2 and Path 4 combine to
produce what is commonly
referred to as Path Radiance, Lp
Path 5 is energy that was also
reflected from nearby terrain
into the atmosphere, but then
scattered or reflected onto the
study area
• Adjacency effect
Atmospheric Correction Using ATCOR
a) Image containing substantial haze prior to atmospheric correction. b) Image after
atmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the
German Aerospace Centre)
Atmospheric Correction
• Atmospheric correction of ALI imagery (Beijing,
China, May 3, 2001)
Before
After
Before
After
SL Liang, University of Maryland, College Park
Atmospheric Correction
• MODIS imagery of Chinese northeastern coast,
(False color composite, May 7, 2000)
(Before AC)
(After AC)
SL Liang, University of Maryland, College Park
Atmospheric Correction
• MODIS imagery of Chinese northeastern coast,
(False color composite, May 7, 2000)
(Before AC)
(After AC)
SL Liang, University of Maryland, College Park
8. Summary
1. Electromagnetic energy interactions: interaction with atmosphere, earth,
atmosphere, sensor system components (camera, film, emulsion, etc.)
2. Electromagnetic radiation models (wave/particle): three energy transfer
ways (conduction, convection & radiation), two EM models (wave (c=v.), particle
(Q=h.v), Q~), S. B. law (total emitted radiance) & Wien’s law (peak-wavelength),
3. Atmospheric refraction: n1.sine1= n2.sine2= n3.sine3
4. Atmospheric scattering: Rayleigh (d<<), Mie (d~), non-selective (d>>), blue
sky phenomenon at noon, yellow/radish phenomenon at sunrise/set
5. Atmospheric absorption (“atmospheric windows”): ‘close down’
regions, ‘atmospheric windows’
6. Radiometric quantities and
reflectance:1=refectance+absorption+transmittance, three type reflectances
(specular, diffuse & lambertian)
7. Radiance and atmospheric transfer/correction: irradiance, exitance
and radiance, atmospheric transfer (path radiance, total radiance, etc.)