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Electromagnetic Radiation PrinciplesElectromagnetic Radiation Principles
Dr. John R. JensenDr. John R. Jensen
Department of GeographyDepartment of Geography
University of South CarolinaUniversity of South Carolina
Columbia, SC 29208Columbia, SC 29208
Jensen, J. R., 2007,Jensen, J. R., 2007,Remote Sensing ofRemote Sensing of
Environment: An Earth Resource PerspectiveEnvironment: An Earth Resource Perspective,,
Upper Saddle River: Prentice-Hall, Inc.Upper Saddle River: Prentice-Hall, Inc.
Jensen, 2Jensen, 2
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Electromagnetic Energy InteractionsElectromagnetic Energy Interactions
EnergyEnergy recorded by remote sensing systems undergoes fundamentalrecorded by remote sensing systems undergoes fundamentalinteractionsinteractions that should be understood to properly interpret the remotelythat should be understood to properly interpret the remotely
sensed data. For example, if the energy being remotely sensed comessensed data. For example, if the energy being remotely sensed comes
from the Sun, the energy:from the Sun, the energy:
is radiated by atomic particles at the source (the Sun),is radiated by atomic particles at the source (the Sun),
propagates through the vacuum of space at the speed of light,propagates through the vacuum of space at the speed of light,
interacts with the Earth's atmosphere,interacts with the Earth's atmosphere,
interacts with the Earth's surface,interacts with the Earth's surface,
interacts with the Earth's atmosphere once again, andinteracts with the Earth's atmosphere once again, andfinally reaches the remote sensor where it interacts with variousfinally reaches the remote sensor where it interacts with various
optical systems, filters, emulsions, or detectors.optical systems, filters, emulsions, or detectors.
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Solar and Heliospheric Observatory (SOHO)Solar and Heliospheric Observatory (SOHO)
Image of the Sun Obtained on September 14, 1999Image of the Sun Obtained on September 14, 1999
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Energy-matterEnergy-matter
interactions in theinteractions in the
atmosphere, at theatmosphere, at the
study area, and at thestudy area, and at the
remote sensor detectorremote sensor detector
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Jensen 2007Jensen 2007
How is Energy Transferred?How is Energy Transferred?
Energy may be transferred three ways:Energy may be transferred three ways: conductionconduction,, convectionconvection, and, and radiationradiation..
a) Energy may bea) Energy may be conductedconducteddirectly from one object to another as when a pan is indirectly from one object to another as when a pan is in
direct physical contact with a hot burner. b) The Sun bathes the Earths surface withdirect physical contact with a hot burner. b) The Sun bathes the Earths surface with
radiant energy causing the air near the ground to increase in temperature. The less denseradiant energy causing the air near the ground to increase in temperature. The less dense
air rises, creatingair rises, creating convectionalconvectionalcurrents in the atmosphere. c) Electromagnetic energy incurrents in the atmosphere. c) Electromagnetic energy in
the form ofthe form ofelectromagneticelectromagnetic waves may be transmitted through the vacuum of space fromwaves may be transmitted through the vacuum of space from
the Sun to the Earth.the Sun to the Earth.
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Jensen 2007Jensen 2007
Electromagnetic Radiation ModelsElectromagnetic Radiation Models
To understand how electromagnetic radiation is created,To understand how electromagnetic radiation is created,how it propagates through space, and how it interactshow it propagates through space, and how it interacts
with other matter, it is useful to describe the processeswith other matter, it is useful to describe the processes
using two different models:using two different models:
thethe wavewave model, andmodel, and thethe particleparticle model.model.
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Jensen, 2007Jensen, 2007
Wave Model of Electromagnetic RadiationWave Model of Electromagnetic Radiation
In the 1860s,In the 1860s, James Clerk MaxwellJames Clerk Maxwell (18311879) conceptualized electromagnetic(18311879) conceptualized electromagnetic
radiation (EMR) as an electromagnetic wave that travels through space at the speed ofradiation (EMR) as an electromagnetic wave that travels through space at the speed oflight,light, cc, which is 3 x 10, which is 3 x 1088 meters per second (hereafter referred to as m smeters per second (hereafter referred to as m s-1-1) or) or
186,282.03 miles s186,282.03 miles s-1-1. A useful relation for quick calculations is that light travels about. A useful relation for quick calculations is that light travels about
1 ft per nanosecond (101 ft per nanosecond (10-9-9 s). Thes). The electromagnetic waveelectromagnetic wave consists of two fluctuatingconsists of two fluctuating
fieldsonefieldsone electricelectric and the otherand the othermagneticmagnetic. The two vectors are at right angles. The two vectors are at right angles
(orthogonal) to one another, and both are perpendicular to the direction of travel.(orthogonal) to one another, and both are perpendicular to the direction of travel.
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Electromagnetic radiationElectromagnetic radiation is generated when an electrical charge isis generated when an electrical charge is
accelerated.accelerated.
TheThe wavelengthwavelength of electromagnetic radiation (of electromagnetic radiation () depends upon the length) depends upon the length
of time that the charged particle is accelerated and its frequency (of time that the charged particle is accelerated and its frequency ( vv) depend) depends
on the number of accelerations per second.on the number of accelerations per second.
WavelengthWavelength is formally defined as the mean distance between maximumsis formally defined as the mean distance between maximums
(or minimums) of a roughly periodic pattern and is normally measured in(or minimums) of a roughly periodic pattern and is normally measured in
micrometers (micrometers (m) or nanometers (nm).m) or nanometers (nm).
FrequencyFrequency is the number of wavelengths that pass a point per unit time. Ais the number of wavelengths that pass a point per unit time. A
wave that sends one crest by every second (completing one cycle) is said towave that sends one crest by every second (completing one cycle) is said to
have a frequency of one cycle per second or one hertz, abbreviated 1 Hz.have a frequency of one cycle per second or one hertz, abbreviated 1 Hz.
The Wave Model of Electromagnetic EnergyThe Wave Model of Electromagnetic Energy
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The relationship between the wavelength,The relationship between the wavelength, , and frequency,, and frequency,, of, ofelectromagnetic radiation is based on the following formula, whereelectromagnetic radiation is based on the following formula, where cc
is the speed of light:is the speed of light:
Wave Model of Electromagnetic EnergyWave Model of Electromagnetic Energy
cv=vc =
cv =
Note that frequency,Note that frequency,,, is inversely proportional to wavelength,is inversely proportional to wavelength, ..
The longer the wavelength, the lower the frequency, and vice-versa.The longer the wavelength, the lower the frequency, and vice-versa.
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Wave Model of Electromagnetic EnergyWave Model of Electromagnetic Energy
This cross-section of an electromagneticThis cross-section of an electromagnetic
wave illustrates the inverse relationshipwave illustrates the inverse relationship
betweenbetween wavelengthwavelength (() and) andfrequencyfrequency((). The longer the wavelength the). The longer the wavelength the
lower the frequency; the shorter thelower the frequency; the shorter the
wavelength, the higher the frequency.wavelength, the higher the frequency.
The amplitude of an electromagneticThe amplitude of an electromagneticwave is the height of the wave crestwave is the height of the wave crest
above the undisturbed position.above the undisturbed position.
Successive wave crests are numbered 1,Successive wave crests are numbered 1,
2, 3, and 4. An observer at the position2, 3, and 4. An observer at the position
of the clock records the number ofof the clock records the number of
crests that pass by in a second. Thiscrests that pass by in a second. This
frequency is measured in cycles perfrequency is measured in cycles persecond, or hertzsecond, or hertz
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The electromagnetic energy from the Sun travels in eight minutes acrossThe electromagnetic energy from the Sun travels in eight minutes across
the intervening 93 million miles (150 million km) of space to the Earth.the intervening 93 million miles (150 million km) of space to the Earth.
The Sun produces aThe Sun produces a continuous spectrumcontinuous spectrum of electromagnetic radiationof electromagnetic radiation
ranging from very short, extremely high frequency gamma and cosmicranging from very short, extremely high frequency gamma and cosmic
waves to long, very low frequency radio waveswaves to long, very low frequency radio waves
TheThe EarthEarth approximates a 300 K (27 C) blackbody and has a dominantapproximates a 300 K (27 C) blackbody and has a dominant
wavelength at approximatelywavelength at approximately 9.79.7 m.m.
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Using theUsing thewave modelwave model, it is possible to characterize the energy of the Sun, it is possible to characterize the energy of the Sun
which represents the initial source of much of the electromagnetic energywhich represents the initial source of much of the electromagnetic energy
recorded by remote sensing systems (except RADAR, LIDAR, SONAR).recorded by remote sensing systems (except RADAR, LIDAR, SONAR).
We may think of the Sun as a 6,000 KWe may think of the Sun as a 6,000 K blackbodyblackbody (a theoretical construct(a theoretical construct
which radiates energy at the maximum possible rate per unit area at eachwhich radiates energy at the maximum possible rate per unit area at each
wavelength for any given temperature). Thewavelength for any given temperature). The total emitted radiationtotal emitted radiation ((MM
))
from a blackbody is proportional to the fourth power of its absolutefrom a blackbody is proportional to the fourth power of its absolute
temperature. This is known as thetemperature. This is known as the Stefan-Boltzmann lawStefan-Boltzmann law and is expressedand is expressed
as:as:
wherewhere is the Stefan-Boltzmann constant, 5.6697 x 10is the Stefan-Boltzmann constant, 5.6697 x 10 -8-8 W mW m-2-2 KK -4-4..
Thus, the amount of energy emitted by an object such as the Sun or theThus, the amount of energy emitted by an object such as the Sun or the
Earth is a function of its temperature.Earth is a function of its temperature.
Stephen Boltzmann LawStephen Boltzmann Law
4TM =
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Sources of Electromagnetic EnergySources of Electromagnetic Energy
Thermonuclear fusion taking place on the surface of the Sun yields a continuous spectrum ofThermonuclear fusion taking place on the surface of the Sun yields a continuous spectrum of
electromagnetic energy. The 5770 6000 kelvin (K) temperature of this process produces a largeelectromagnetic energy. The 5770 6000 kelvin (K) temperature of this process produces a large
amount of relatively short wavelength energy that travels through the vacuum of space at the speedamount of relatively short wavelength energy that travels through the vacuum of space at the speed
of light. Some of this energy is intercepted by the Earth, where it interacts with the atmosphere andof light. Some of this energy is intercepted by the Earth, where it interacts with the atmosphere and
surface materials. The Earth reflects some of the energy directly back out to space or it may absorbsurface materials. The Earth reflects some of the energy directly back out to space or it may absorb
the short wavelength energy and then re-emit it at a longer wavelengththe short wavelength energy and then re-emit it at a longer wavelength
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ElectromagneticElectromagnetic
SpectrumSpectrum
The Sun produces aThe Sun produces a
continuous spectrumcontinuous spectrum of energyof energy
from gamma rays to radiofrom gamma rays to radio
waves that continually bathewaves that continually bathe
the Earth in energy. Thethe Earth in energy. The
visible portion of the spectrumvisible portion of the spectrummay be measured usingmay be measured using
wavelength (measured inwavelength (measured in
micrometers or nanometers,micrometers or nanometers,
i.e.,i.e., m or nm) or electronm or nm) or electronvolts (eV). All units arevolts (eV). All units are
interchangeable.interchangeable.
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Spectral Bandwidths of Landsat and SPOT Sensor SystemsSpectral Bandwidths of Landsat and SPOT Sensor Systems
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Weins Displacement LawWeins Displacement Law
In addition to computing the total amount of energy exiting a theoretical blackbody suchIn addition to computing the total amount of energy exiting a theoretical blackbody suchas the Sun, we can determine its dominant wavelength (as the Sun, we can determine its dominant wavelength (maxmax) based on) based on Wein'sWein's
displacement lawdisplacement law::
wherewhere kk is a constant equaling 2898is a constant equaling 2898 m K, andm K, and TT is the absolute temperature in kelvin.is the absolute temperature in kelvin.Therefore, as the Sun approximates a 6000 K blackbody, its dominant wavelength (Therefore, as the Sun approximates a 6000 K blackbody, its dominant wavelength ( maxmax))
is 0.48is 0.48 m:m:
T
k=
max
K
Kmm
6000
2898483.0
=
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Blackbody Radiation CurvesBlackbody Radiation Curves
Blackbody radiation curves for several objectsBlackbody radiation curves for several objectsincluding the Sun and the Earth whichincluding the Sun and the Earth which
approximate 6,000 K and 300 K blackbodies,approximate 6,000 K and 300 K blackbodies,
respectively.respectively. The area under each curve may beThe area under each curve may be
summed to compute the total radiant energy (summed to compute the total radiant energy (MM
) exiting each object. Thus, the Sun produces) exiting each object. Thus, the Sun produces
more radiant exitance than the Earth because itsmore radiant exitance than the Earth because itstemperature is greater. As the temperature of antemperature is greater. As the temperature of an
object increases, its dominant wavelength (object increases, its dominant wavelength (maxmax))
shifts toward the shorter wavelengths of theshifts toward the shorter wavelengths of the
spectrum.spectrum.
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Radiant IntensityRadiant Intensity
of the Sunof the Sun
The Sun approximates a 6,000 KThe Sun approximates a 6,000 K
blackbody with a dominantblackbody with a dominantwavelength of 0.48wavelength of 0.48 m (green light).m (green light).
Earth approximates a 300 KEarth approximates a 300 K
blackbody with a dominantblackbody with a dominant
wavelength of 9.66wavelength of 9.66 m . The 6,000m . The 6,000
K Sun produces 41% of its energy inK Sun produces 41% of its energy in
the visible region from 0.4 - 0.7the visible region from 0.4 - 0.7 mm
(blue, green, and red light). The other(blue, green, and red light). The other59% of the energy is in wavelengths59% of the energy is in wavelengths
shorter than blue light (0.7 m). Eyesm). Eyes
are only sensitive to light from theare only sensitive to light from the
0.4 to 0.70.4 to 0.7 m. Remote sensorm. Remote sensor
detectors can be made sensitive todetectors can be made sensitive to
energy in the non-visible regions ofenergy in the non-visible regions of
the spectrum.the spectrum.
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For a 100 years before 1905, light was thought of as a smooth andFor a 100 years before 1905, light was thought of as a smooth and
continuous wave as discussed. Then,continuous wave as discussed. Then, Albert EinsteinAlbert Einstein (1879-1955) found(1879-1955) found
that when light interacts with electrons, it has a different character.that when light interacts with electrons, it has a different character.
He found that when light interacts with matter, it behaves as though it isHe found that when light interacts with matter, it behaves as though it is
composed of many individual bodies calledcomposed of many individual bodies calledphotonsphotons, which carry such, which carry suchparticle-like properties as energy and momentum. As a result, mostparticle-like properties as energy and momentum. As a result, most
physicists today would answer the questionphysicists today would answer the question What is light?What is light? as as LightLightis ais a
particularparticularkind of matter.kind of matter.
Thus, we sometimes describe electromagnetic energy in terms of itsThus, we sometimes describe electromagnetic energy in terms of itswave-like properties. But, when the energy interacts with matter it iswave-like properties. But, when the energy interacts with matter it is
useful to describe it as discrete packets of energy, oruseful to describe it as discrete packets of energy, or quantaquanta..
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
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Niels Bohr (18851962) and Max Planck recognized the discrete nature ofNiels Bohr (18851962) and Max Planck recognized the discrete nature ofexchanges of radiant energy and proposed theexchanges of radiant energy and proposed the quantum theoryquantum theory ofof
electromagnetic radiation. This theory states that energy is transferred inelectromagnetic radiation. This theory states that energy is transferred in
discrete packets calleddiscrete packets called quantaquanta ororphotonsphotons, as discussed. The relationship, as discussed. The relationship
between the frequency of radiation expressed by wave theory and the between the frequency of radiation expressed by wave theory and the
quantum is:quantum is:
wherewhere QQ is the energy of a quantum measured in joules,is the energy of a quantum measured in joules, hh is the Planckis the Planck
constant (6.626constant (6.626 1010-34-34 J s), andJ s), and is the frequency of the radiation.is the frequency of the radiation.
vhQ =
Quantum Theory of EMRQuantum Theory of EMR
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Referring to the previous formulas, we can multiply the equation byReferring to the previous formulas, we can multiply the equation by h/hh/h, or, or
1, without changing its value:1, without changing its value:
By substitutingBy substituting QQ forfor hh, we can express the wavelength associated with a, we can express the wavelength associated with a
quantum of energy as:quantum of energy as:
oror
Thus, the energy of a quantum is inversely proportional to its wavelengthThus, the energy of a quantum is inversely proportional to its wavelength ,,
i.e., the longer the wavelength involved, the lower its energy content.i.e., the longer the wavelength involved, the lower its energy content.
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
vh
ch=
Q
ch=
chQ =
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ElectronsElectrons are the tiny negatively charged particles that move around the positivelyare the tiny negatively charged particles that move around the positively
chargedchargednucleusnucleus of an atom. Atoms of different substances are made up of varyingof an atom. Atoms of different substances are made up of varying
numbers of electrons arranged in different ways. The interaction between the positivelynumbers of electrons arranged in different ways. The interaction between the positively
charged nucleus and the negatively charged electron keep the electron in orbit. While itscharged nucleus and the negatively charged electron keep the electron in orbit. While its
orbit is not explicitly fixed, each electrons motion is restricted to a definite range fromorbit is not explicitly fixed, each electrons motion is restricted to a definite range from
the nucleus. The allowable orbital paths of electrons about an atom might be thought ofthe nucleus. The allowable orbital paths of electrons about an atom might be thought of
asas energy classes or levelsenergy classes or levels. In order for an electron to climb to a higher class, work must. In order for an electron to climb to a higher class, work must
be performed. However, unless an amount of energy is available to move the electronbe performed. However, unless an amount of energy is available to move the electron
up at least one energy level, it will accept no work. If a sufficient amount of energy isup at least one energy level, it will accept no work. If a sufficient amount of energy is
received, the electron will jump to a new level and the atom is said to bereceived, the electron will jump to a new level and the atom is said to be excitedexcited. Once an. Once an
electron is in a higher orbit, it possesseselectron is in a higher orbit, it possesses potential energypotential energy. After about. After about 1010-8-8 secondsseconds, the, the
electron falls back to the atom's lowest empty energy level or orbit and gives offelectron falls back to the atom's lowest empty energy level or orbit and gives off
radiation.radiation. The wavelength of radiation given off is a function of the amount of work doneThe wavelength of radiation given off is a function of the amount of work done
on the atomon the atom, i.e., the, i.e., the quantum of energyquantum of energy it absorbed to cause the electron to be moved to ait absorbed to cause the electron to be moved to a
higher orbit.higher orbit.
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
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MatterMattercan be heated to such high temperatures that electrons which normallycan be heated to such high temperatures that electrons which normally
move in captured non-radiating orbits are broken free. When this happens, themove in captured non-radiating orbits are broken free. When this happens, theatom remains with a positive charge equal to the negatively charged electronatom remains with a positive charge equal to the negatively charged electron
which escaped. The electron becomes awhich escaped. The electron becomes a free electronfree electron and the atom is called anand the atom is called an
ionion. In the ultraviolet and visible (. In the ultraviolet and visible (blueblue,, greengreen, and, and redred) parts of the) parts of the
electromagnetic spectrum,electromagnetic spectrum, radiationradiation is produced by changes in the energy levelsis produced by changes in the energy levels
of the outer,of the outer, valence electronsvalence electrons. The wavelengths of energy produced are a. The wavelengths of energy produced are a
function of the particular orbital levels of the electrons involved in the excitationfunction of the particular orbital levels of the electrons involved in the excitation
process. If the atoms absorb enough energy to becomeprocess. If the atoms absorb enough energy to become ionizedionized and if aand if a freefree
electronelectron drops in todrops in to fill the vacant energy levelfill the vacant energy level, then the radiation given off is, then the radiation given off is
unquantizedunquantizedandandcontinuous spectrumcontinuous spectrum is produced rather than a band or a seriesis produced rather than a band or a series
of bands. Every encounter of one of the free electrons with a positively chargedof bands. Every encounter of one of the free electrons with a positively charged
nucleus causes rapidly changing electric and magnetic fields so that radiation atnucleus causes rapidly changing electric and magnetic fields so that radiation at
all wavelengths is produced. The hot surface of theall wavelengths is produced. The hot surface of the SunSun is largely ais largely a plasmaplasma inin
which radiation of all wavelengths is produced. The spectra of a plasma is awhich radiation of all wavelengths is produced. The spectra of a plasma is a
continuous spectrumcontinuous spectrum..
Particle Model of Electromagnetic Energy
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Creation of LightCreation of Light
from Atomicfrom Atomic
ParticlesParticles
AA photonphoton of electromagnetic energy isof electromagnetic energy is
emitted when an electron in an atom oremitted when an electron in an atom ormolecule drops from a higher-energy statemolecule drops from a higher-energy state
to a lower-energy state.to a lower-energy state. The light emittedThe light emitted
(i.e., its wavelength) is a function of the(i.e., its wavelength) is a function of the
changes in the energy levels of the outer,changes in the energy levels of the outer,
valence electron. For example, yellow lightvalence electron. For example, yellow light
may be produced from a sodium vapormay be produced from a sodium vapor
lamp. Matter can also be subjected to suchlamp. Matter can also be subjected to such
high temperatures that electrons, whichhigh temperatures that electrons, which
normally move in captured, non-radiatingnormally move in captured, non-radiating
orbits, are broken free. When this happens,orbits, are broken free. When this happens,
the atom remains with a positive chargethe atom remains with a positive charge
equal to the negatively charged electronequal to the negatively charged electron
that escaped. The electron becomes a freethat escaped. The electron becomes a free
electron, and the atom is called an ion. Ifelectron, and the atom is called an ion. If
another free electron fills the vacant energyanother free electron fills the vacant energy
level created by the free electron, thenlevel created by the free electron, then
radiation from all wavelengths is produced,radiation from all wavelengths is produced,i.e., a continuous spectrum of energy. Thei.e., a continuous spectrum of energy. The
intense heat at the surface of the Sunintense heat at the surface of the Sun
produces aproduces a continuous spectrumcontinuous spectrum in thisin this
manner.manner.
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Electron orbits are like the rungs of a ladderElectron orbits are like the rungs of a ladder. Adding energy moves the. Adding energy moves the
electron up the energy ladder; emitting energy moves it down. The energyelectron up the energy ladder; emitting energy moves it down. The energyladder differs from an ordinary ladder in that its rungs are unevenlyladder differs from an ordinary ladder in that its rungs are unevenly
spaced. This means that the energy an electron needs to absorb, or to givespaced. This means that the energy an electron needs to absorb, or to give
up, in order to jump from one orbit to the next may not be the same as theup, in order to jump from one orbit to the next may not be the same as the
energy change needed for some other step. Also, an electron does notenergy change needed for some other step. Also, an electron does not
always use consecutive rungs. Instead, it follows what physicists callalways use consecutive rungs. Instead, it follows what physicists callselection rulesselection rules. In many cases, an electron uses one sequence of rungs as it. In many cases, an electron uses one sequence of rungs as it
climbs the ladder and another sequence as it descends. The energy that isclimbs the ladder and another sequence as it descends. The energy that is
left over when the electrically charged electron moves from an excitedleft over when the electrically charged electron moves from an excited
state to a de-excited state isstate to a de-excited state is emittedemittedby the atom as aby the atom as apacket of electro-packet of electro-
magnetic radiationmagnetic radiation; a particle-like unit of light called a; a particle-like unit of light called aphotonphoton..Every timeEvery timean electron jumps from a higher to a lower energy level, a photon movesan electron jumps from a higher to a lower energy level, a photon moves
away at the speed of lightaway at the speed of light..
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
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SubstancesSubstances havehave colorcolorbecause ofbecause ofdifferences in their energy levelsdifferences in their energy levels
and the selection rulesand the selection rules..
For example, consider energizedFor example, consider energized sodium vaporsodium vaporthat produces athat produces a
bright yellow light that is used in some street lamps. When abright yellow light that is used in some street lamps. When a
sodium-vapor lamp is turned on, several thousand volts of electricitysodium-vapor lamp is turned on, several thousand volts of electricity
energize the vapor. The outermost electron in each energized atomenergize the vapor. The outermost electron in each energized atom
of sodium vapor climbs to a high rung on the energy ladder and thenof sodium vapor climbs to a high rung on the energy ladder and then
returns down the ladder in a certain sequence of rungs, the last tworeturns down the ladder in a certain sequence of rungs, the last two
of which areof which are 2.1 eV2.1 eV apart. The energy released in this last leapapart. The energy released in this last leap
appears as a photon ofappears as a photon of
yellowyellow
light with a wavelength oflight with a wavelength of
0.580.58
mm
with 2.1 eV of energy.with 2.1 eV of energy.
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
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Creation of LightCreation of Light
Creation of light from atomic particlesCreation of light from atomic particles
in ain a sodium vapor lampsodium vapor lamp. After being. After being
energized by several thousand volts ofenergized by several thousand volts of
electricity, the outermost electron inelectricity, the outermost electron in
each energized atom of sodium vaporeach energized atom of sodium vapor
climbs to a high rung on the energyclimbs to a high rung on the energy
ladder and then returns down theladder and then returns down the
ladder in a predictable fashion. Theladder in a predictable fashion. The
last two rungs in the descent are 2.1last two rungs in the descent are 2.1eV apart. This produces a photon ofeV apart. This produces a photon of
yellowyellowlight, which has 2.1 eV oflight, which has 2.1 eV of
energy.energy.
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Energy ofEnergy of
QuantaQuanta
(Photons)(Photons)
The energy of quantaThe energy of quanta
(photons) ranging(photons) ranging
from gamma rays tofrom gamma rays to
radio waves in theradio waves in the
electromagneticelectromagnetic
spectrum.spectrum.
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Somehow an electron might disappear from its original orbit andSomehow an electron might disappear from its original orbit andreappear in its destination orbit without ever having to traverse anyreappear in its destination orbit without ever having to traverse any
of the positions in between. This process is called aof the positions in between. This process is called a quantum leapquantum leap oror
quantum jumpquantum jump. If the electron leaps from its highest excited state to. If the electron leaps from its highest excited state to
the ground state in a single leap it will emit a single photon ofthe ground state in a single leap it will emit a single photon of
energy. It is also possible for the electron to leap from an excitedenergy. It is also possible for the electron to leap from an excitedorbit to the ground state in a series of jumps, e.g. from 4 to 2 to 1. Iforbit to the ground state in a series of jumps, e.g. from 4 to 2 to 1. If
it takes two leaps to get to the ground state then each of these jumpsit takes two leaps to get to the ground state then each of these jumps
will emit photons of somewhat less energy. The energies emittedwill emit photons of somewhat less energy. The energies emitted ininthe two different jumps must sum to the total of the single largethe two different jumps must sum to the total of the single large
jump.jump.
Particle Model of Electromagnetic EnergyParticle Model of Electromagnetic Energy
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ScatteringScattering
Once electromagnetic radiation is generated, it is propagatedOnce electromagnetic radiation is generated, it is propagated
through the earth's atmosphere almost at the speed of light in athrough the earth's atmosphere almost at the speed of light in a
vacuum.vacuum.
Unlike a vacuum in which nothing happens, however, theUnlike a vacuum in which nothing happens, however, theatmosphere may affect not only the speed of radiation but also itsatmosphere may affect not only the speed of radiation but also its
wavelengthwavelength,, intensityintensity,, spectral distributionspectral distribution, and/or, and/or directiondirection..
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ScatterScatterdiffers fromdiffers from reflectionreflection in that the direction associated within that the direction associated with
scattering isscattering is ununpredictable, whereas the direction of reflection ispredictable, whereas the direction of reflection is
predictable. There are essentially three types of scattering:predictable. There are essentially three types of scattering:
Rayleigh,Rayleigh,
Mie,Mie, andand
Non-selectiveNon-selective..
ScatteringScattering
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Major subdivisions of theMajor subdivisions of the
atmosphere and the types ofatmosphere and the types of
molecules and aerosols found inmolecules and aerosols found in
each layer.each layer.
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Atmospheric Layers
and Constituents
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Rayleigh scatteringRayleigh scattering occurs when the diameter of the matter (usually airoccurs when the diameter of the matter (usually airmolecules) aremolecules) are many times smaller than the wavelength of the incidentmany times smaller than the wavelength of the incident
electromagnetic radiationelectromagnetic radiation. This type of scattering is named after the English. This type of scattering is named after the English
physicist who offered the first coherent explanation for it. All scattering isphysicist who offered the first coherent explanation for it. All scattering is
accomplished through absorption and re-emission of radiation by atoms oraccomplished through absorption and re-emission of radiation by atoms or
molecules in the manner described in the discussion on radiation from atomicmolecules in the manner described in the discussion on radiation from atomic
structures. It is impossible to predict the direction in which a specific atom orstructures. It is impossible to predict the direction in which a specific atom ormolecule will emit a photon, hence scattering.molecule will emit a photon, hence scattering.
The energy required to excite an atom is associated with short-wavelength, highThe energy required to excite an atom is associated with short-wavelength, high
frequency radiation.frequency radiation. The amount of scattering is inversely related to the fourthThe amount of scattering is inversely related to the fourth
power of the radiation's wavelengthpower of the radiation's wavelength.. For example, blue light (0.4For example, blue light (0.4 m) ism) is
scattered 16 times more than near-infrared light (0.8scattered 16 times more than near-infrared light (0.8 m).m).
Rayleigh ScatteringRayleigh Scattering
At h i S tt iAt h i S tt i
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Atmospheric ScatterinAtmospheric Scattering
Type of scattering is a function of:Type of scattering is a function of:
thethe wavelengthwavelength of the incidentof the incident
radiant energy, andradiant energy, and
thethesizesize of the gas molecule,of the gas molecule,
dust particle, and/or waterdust particle, and/or water
vapor droplet encountered.vapor droplet encountered.
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RayleighRayleigh
ScatteringScattering
The intensity ofThe intensity of
Rayleigh scatteringRayleigh scattering
varies inversely withvaries inversely with
the fourth power of thethe fourth power of the
wavelength (wavelength (-4-4
).).
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R l i h S i
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Rayleigh ScatteringRayleigh Scattering
Rayleigh scatteringRayleigh scattering is responsible for theis responsible for the blueblue skysky. The short violet and. The short violet and
blue wavelengths are more efficiently scattered than the longer orangeblue wavelengths are more efficiently scattered than the longer orangeand red wavelengths. When we look up on cloudless day and admire theand red wavelengths. When we look up on cloudless day and admire the
blue sky, we witness the preferential scattering of the short wavelengthblue sky, we witness the preferential scattering of the short wavelength
sunlight.sunlight.
Rayleigh scattering is responsible forRayleigh scattering is responsible forredredsunsetssunsets.. Since theSince theatmosphere is a thin shell of gravitationally bound gas surrounding theatmosphere is a thin shell of gravitationally bound gas surrounding the
solid Earth, sunlight must pass through a longer slant path of air atsolid Earth, sunlight must pass through a longer slant path of air at
sunset (or sunrise) than at noon. Since the violet and blue wavelengthssunset (or sunrise) than at noon. Since the violet and blue wavelengths
are scattered even more during their now-longer path through the airare scattered even more during their now-longer path through the air
than when the Sun is overhead, what we see when we look toward thethan when the Sun is overhead, what we see when we look toward theSun is the residue - the wavelengths of sunlight that are hardly scatteredSun is the residue - the wavelengths of sunlight that are hardly scattered
away at all, especially the oranges and reds (Sagan, 1994).away at all, especially the oranges and reds (Sagan, 1994).
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The approximate amount of Rayleigh scattering in theThe approximate amount of Rayleigh scattering in theatmosphere in optical wavelengths (0.4 0.7atmosphere in optical wavelengths (0.4 0.7 m) may bem) may be
computed using thecomputed using theRayleigh scattering cross-sectionRayleigh scattering cross-section ((mm))
algorithm:algorithm:
wherewhere nn = refractive index= refractive index,,NN= number of air molecules per unit= number of air molecules per unit
volumevolume, and, and = wavelength= wavelength. The amount of scattering is. The amount of scattering is
inversely related to the fourth power of the radiationsinversely related to the fourth power of the radiations
wavelength.wavelength.
( )( )42223
3
18
N
nm
=
Rayleigh ScatteringRayleigh Scattering
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Mie ScatteringMie Scattering
Mie scatteringMie scattering takes place when there are essentiallytakes place when there are essentially sphericalspherical particlesparticles
present in the atmospherepresent in the atmosphere with diameters approximately equal to thewith diameters approximately equal to the
wavelength of radiation being consideredwavelength of radiation being considered. For visible light, water vapor,. For visible light, water vapor,
dust, and other particles ranging from a few tenths of a micrometer todust, and other particles ranging from a few tenths of a micrometer to
several micrometers in diameter are the main scattering agents. Theseveral micrometers in diameter are the main scattering agents. The
amount of scatter is greater than Rayleigh scatter and the wavelengthsamount of scatter is greater than Rayleigh scatter and the wavelengths
scattered are longer.scattered are longer.
PollutionPollution also contributes to beautifulalso contributes to beautiful sunsetssunsets andand sunrisessunrises. The greater. The greater
the amount of smoke and dust particles in the atmospheric column, thethe amount of smoke and dust particles in the atmospheric column, the
more violet and blue light will be scattered away and only the longermore violet and blue light will be scattered away and only the longer
orangeorange andand redredwavelength light will reach our eyes.wavelength light will reach our eyes.
N l ti S tt iN l ti S tt i
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Non-selective ScatteringNon-selective Scattering
Non-selective scatteringNon-selective scattering is produced when there are particles in theis produced when there are particles in the
atmosphereatmosphere several times the diameter of the radiation beingseveral times the diameter of the radiation being
transmittedtransmitted. This type of scattering is non-selective, i.e. all wavelengths. This type of scattering is non-selective, i.e. all wavelengths
of light are scattered, not just blue, green, or red. Thus, water droplets,of light are scattered, not just blue, green, or red. Thus, water droplets,
which make up clouds and fog banks, scatter all wavelengths of visiblewhich make up clouds and fog banks, scatter all wavelengths of visible
light equally well, causing the cloud to appear white (a mixture of alllight equally well, causing the cloud to appear white (a mixture of all
colors of light in approximately equal quantities produces white).colors of light in approximately equal quantities produces white).
Scattering can severely reduce the information content of remotelyScattering can severely reduce the information content of remotely
sensed data to the point that the imagery looses contrast and it is difficultsensed data to the point that the imagery looses contrast and it is difficult
to differentiate one object from another.to differentiate one object from another.
Atmospheric ScatterinAtmospheric Scattering
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Atmospheric ScatterinAtmospheric Scattering
Type of scattering is a function of:
the wavelength of the incident
radiant energy, and
the size of the gas molecule,
dust particle, and/or water
vapor droplet encountered.
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AbsorptionAbsorption is the process by which radiant energy isis the process by which radiant energy isabsorbed and converted into other forms of energy. Anabsorbed and converted into other forms of energy. An
absorption bandabsorption bandis a range of wavelengths (or frequencies) inis a range of wavelengths (or frequencies) in
the electromagnetic spectrum within which radiant energy isthe electromagnetic spectrum within which radiant energy is
absorbed by substances such as water (Habsorbed by substances such as water (H22O), carbon dioxideO), carbon dioxide
(CO(CO22), oxygen (O), oxygen (O22), ozone (O), ozone (O33), and nitrous oxide (N), and nitrous oxide (N22O).O).
The cumulative effect of the absorption by the variousThe cumulative effect of the absorption by the various
constituents can cause the atmosphere toconstituents can cause the atmosphere toclose downclose down inin
certain regions of the spectrum. This is bad for remotecertain regions of the spectrum. This is bad for remote
sensing because no energy is available to be sensed.sensing because no energy is available to be sensed.
AbsorptionAbsorption
AbsorptionAbsorption
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In certain parts of the spectrum such as the visible region (0.4 - 0.7In certain parts of the spectrum such as the visible region (0.4 - 0.7 m), them), the
atmosphere does not absorb all of the incident energy but transmits it effectively. Partsatmosphere does not absorb all of the incident energy but transmits it effectively. Partsof the spectrum that transmit energy effectively are calledof the spectrum that transmit energy effectively are called atmospheric windows.atmospheric windows.
AbsorptionAbsorption occurs when energy of the same frequency as the resonant frequency ofoccurs when energy of the same frequency as the resonant frequency of
an atom or molecule is absorbed, producing anan atom or molecule is absorbed, producing an excited stateexcited state. If, instead of re-radiating. If, instead of re-radiating
a photon of the same wavelength, the energy is transformed into heat motion and isa photon of the same wavelength, the energy is transformed into heat motion and is
reradiated at a longer wavelength, absorption occurs. When dealing with a medium likereradiated at a longer wavelength, absorption occurs. When dealing with a medium likeair, absorption and scattering are frequently combined into anair, absorption and scattering are frequently combined into an extinction coefficientextinction coefficient..
TransmissionTransmission is inversely related to the extinction coefficient times the thickness ofis inversely related to the extinction coefficient times the thickness of
the layer. Certain wavelengths of radiation are affected far more by absorption than bythe layer. Certain wavelengths of radiation are affected far more by absorption than by
scattering. This is particularly true of infrared and wavelengths shorter than visiblescattering. This is particularly true of infrared and wavelengths shorter than visible
light.light.
AbsorptionAbsorption
Absorption of the Suns Incident Electromagnetic Energy in theAbsorption of the Suns Incident Electromagnetic Energy in the
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Absorption of the Sun s Incident Electromagnetic Energy in theAbsorption of the Sun s Incident Electromagnetic Energy in the
Region from 0.1 to 30Region from 0.1 to 30 m by Various Atmospheric Gasesm by Various Atmospheric Gases
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window
a)a) TheThe absorptionabsorption of the Suns incidentof the Suns incident
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electromagnetic energy in the regionelectromagnetic energy in the region
from 0.1 to 30from 0.1 to 30 m by variousm by various
atmospheric gases. The first four graphatmospheric gases. The first four graph
depict the absorption characteristics ofdepict the absorption characteristics of
NN22O, OO, O22 and Oand O33, CO, CO22, and H, and H22O, whileO, whilethe final graphic depicts the cumulativethe final graphic depicts the cumulative
result of all these constituents being inresult of all these constituents being in
the atmosphere at one time. Thethe atmosphere at one time. The
atmosphere essentially closes down inatmosphere essentially closes down in
certain portions of the spectrum whilecertain portions of the spectrum while
atmospheric windows exist in otheratmospheric windows exist in other
regions that transmit incident energyregions that transmit incident energy
effectively to the ground. It is withineffectively to the ground. It is within
these windows that remote sensingthese windows that remote sensing
systems must function.systems must function.
b)b) The combined effects of atmosphericThe combined effects of atmospheric
absorption, scattering, and reflectanceabsorption, scattering, and reflectance
reduce the amount of solar irradiancereduce the amount of solar irradiance
reaching the Earths surface at sea levereaching the Earths surface at sea level
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ReflectanceReflectance is the process whereby radiationis the process whereby radiation bounces offbounces off ananobject like a cloud or the terrain. Actually, the process is moreobject like a cloud or the terrain. Actually, the process is more
complicated, involvingcomplicated, involving re-radiation of photons in unison byre-radiation of photons in unison by
atoms or molecules in a layer one-half wavelength deepatoms or molecules in a layer one-half wavelength deep..
Reflection exhibits fundamental characteristics that areReflection exhibits fundamental characteristics that areimportant in remote sensing. First, the incident radiation, theimportant in remote sensing. First, the incident radiation, the
reflected radiation, and a vertical to the surface from which thereflected radiation, and a vertical to the surface from which the
angles of incidence and reflection are measured all lie in theangles of incidence and reflection are measured all lie in the
same plane. Second, the angle of incidence and the angle ofsame plane. Second, the angle of incidence and the angle of
reflection are equal.reflection are equal.
ReflectanceReflectance
ReflectanceReflectance
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There are various types of reflecting surfaces:There are various types of reflecting surfaces:
WhenWhenspecular reflectionspecular reflection occurs, the surface from which the radiation is reflected isoccurs, the surface from which the radiation is reflected is
essentiallyessentially smoothsmooth (i.e. the average surface profile is several times smaller than the(i.e. the average surface profile is several times smaller than the
wavelength of radiation striking the surface).wavelength of radiation striking the surface).
If the surface isIf the surface is roughrough, the reflected rays go in many directions, depending on the, the reflected rays go in many directions, depending on the
orientation of the smaller reflecting surfaces. This diffuse reflection does not yield aorientation of the smaller reflecting surfaces. This diffuse reflection does not yield a
mirror image, but instead producesmirror image, but instead produces diffused radiationdiffused radiation. White paper, white powders and. White paper, white powders and
other materials reflect visible light in this diffuse manner.other materials reflect visible light in this diffuse manner.
If the surface is so rough that there are no individual reflecting surfaces, thenIf the surface is so rough that there are no individual reflecting surfaces, then
scattering may occur. Lambert defined ascattering may occur. Lambert defined aperfectly diffuse surfaceperfectly diffuse surface; hence the commonly; hence the commonly
designateddesignated
Lambertian surfaceLambertian surface
is one for which the radiant flux leaving the surface isis one for which the radiant flux leaving the surface is
constant for any angle of reflectance to the surface normal.constant for any angle of reflectance to the surface normal.
ReflectanceReflectance
ReflectancReflectanc
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Jensen 2007Jensen 2007
Terrain Energy-Matter InteractionsTerrain Energy-Matter Interactions
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Radiometric quantities have been identified that allow analystsRadiometric quantities have been identified that allow analysts
to keep a careful record of the incident and exiting radiant flux.to keep a careful record of the incident and exiting radiant flux.We begin with the simpleWe begin with the simple radiation budget equationradiation budget equation,, whichwhich
states that the total amount of radiant flux in specificstates that the total amount of radiant flux in specific
wavelengths (wavelengths () incident to the terrain ( ) must be accounted) incident to the terrain ( ) must be accounted
for by evaluating the amount of radiant flux reflected from thefor by evaluating the amount of radiant flux reflected from thesurface ( ), the amount of radiant flux absorbed by thesurface ( ), the amount of radiant flux absorbed by the
surface ( ), and the amount of radiant flux transmittedsurface ( ), and the amount of radiant flux transmitted
through the surface ( ):through the surface ( ):
Terrain Energy-Matter InteractionsTerrain Energy Matter Interactions
i
reflected
absorbed
dtransmitte
dtransmitteabsorbedreflectedi++=
Terrain Energy Matter InteractionsTerrain Energy Matter Interactions
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The time rate of flow of energy onto, off of, or through a surface isThe time rate of flow of energy onto, off of, or through a surface is
calledcalled radiant fluxradiant flux (() and is measured in) and is measured in wattswatts ((WW). The). Thecharacteristics of the radiant flux and what happens to it as itcharacteristics of the radiant flux and what happens to it as it
interacts with the Earths surface is of critical importance in remoteinteracts with the Earths surface is of critical importance in remote
sensing. In fact, this is the fundamental focus of much remotesensing. In fact, this is the fundamental focus of much remote
sensing research. By carefully monitoring the exact nature of thesensing research. By carefully monitoring the exact nature of the
incoming (incident) radiant flux in selective wavelengths and how itincoming (incident) radiant flux in selective wavelengths and how itinteracts with the terrain, it is possible to learn importantinteracts with the terrain, it is possible to learn important
information about the terrain.information about the terrain.
Terrain Energy-Matter InteractionsTerrain Energy-Matter Interactions
H i h i l R fl Ab d T iH i h i l R fl t Ab t d T itt
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Hemispherical Reflectance, Absorptance, and TransmittanceHemispherical Reflectance, Absorptance, and Transmittance
TheTheHemispherical reflectanceHemispherical reflectance (()) is defined as the dimensionless ratio of the radiantis defined as the dimensionless ratio of the radiant
flux reflected from a surface to the radiant flux incident to it:flux reflected from a surface to the radiant flux incident to it:
Hemispherical transmittanceHemispherical transmittance (()) is defined as the dimensionless ratio of the radiant fluxis defined as the dimensionless ratio of the radiant flux
transmitted through a surface to the radiant flux incident to it:transmitted through a surface to the radiant flux incident to it:
Hemispherical absorptanceHemispherical absorptance (()) is defined by the dimensionless relationship:is defined by the dimensionless relationship:
i
reflected
=
i
dtransmitte
=
i
absorbed
=
H i h i l R fl t Ab t d T ittH i h i l R fl t Ab t d T itt
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Hemispherical Reflectance, Absorptance, and TransmittanceHemispherical Reflectance, Absorptance, and Transmittance
These radiometric quantities are useful for producing general statements about theThese radiometric quantities are useful for producing general statements about the
spectral reflectance, absorptance, and transmittance characteristics of terrain features. Inspectral reflectance, absorptance, and transmittance characteristics of terrain features. In
fact, if we take the simple hemispherical reflectance equation and multiply it by 100, wefact, if we take the simple hemispherical reflectance equation and multiply it by 100, we
obtain an expression forobtain an expression forpercent reflectancepercent reflectance ( ):( ):
This quantity is used in remote sensing research to describe the general spectralThis quantity is used in remote sensing research to describe the general spectral
reflectance characteristics of various phenomena.reflectance characteristics of various phenomena.
100%
=
i
reflected
%
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Typical spectralTypical spectral
reflectance curvesreflectance curves
for urbansuburbanfor urbansuburban
phenomena in thephenomena in the
region 0.4 0.9region 0.4 0.9 mm
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Irradiance and ExitanceIrradiance and Exitance
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Irradiance and ExitanceIrradiance and Exitance
The amount of radiant flux incident upon a surface per unit area of thatThe amount of radiant flux incident upon a surface per unit area of that
surface is calledsurface is calledIrradianceIrradiance ((EE),), where:where:
The amount of radiant flux leaving per unit area of the plane surface isThe amount of radiant flux leaving per unit area of the plane surface is
calledcalledExitanceExitance ((MM).).
Both quantities are measured inBoth quantities are measured in watts per meter squared (W mwatts per meter squared (W m -2-2))..
Jensen 200Jensen 200
AE
=
AM
=
Radiant Flux DensityRadiant Flux Density
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The concept ofThe concept ofradiant flux densityradiant flux density for anfor an
area on the surface of the Earth.area on the surface of the Earth.
IrradianceIrradiance is a measure of the amounis a measure of the amoun
of radiant flux incident upon aof radiant flux incident upon a
surface per unit area of the surfacesurface per unit area of the surface
measured in watts mmeasured in watts m-2-2..
ExitanceExitance is a measure of the amountis a measure of the amount
of radiant flux leaving a surface perof radiant flux leaving a surface per
unit area of the surface measured inunit area of the surface measured in
watts mwatts m-2-2..
Jensen 200
Radiant Flux DensityRadiant Flux Density
RadianceRadiance
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RadianceRadiance
Radiance (LRadiance (L)) is the radiant flux per unit solid angle leaving an extendedis the radiant flux per unit solid angle leaving an extended
source in a given direction per unit projected source area in that direction andsource in a given direction per unit projected source area in that direction and
is measured in watts per meter squared per steradian (W mis measured in watts per meter squared per steradian (W m -2-2 srsr -1-1 ). We are). We are
only interested in the radiant flux in certain wavelengths (only interested in the radiant flux in certain wavelengths (LL) leaving the) leaving the
projected source area (projected source area (AA) within a certain direction () within a certain direction () and solid angle () and solid angle ():):
LL = ______= ______
coscos
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cosA
L
=
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The concept ofThe concept ofradianceradianceleaving a specific projectedleaving a specific projected
source area on the ground,source area on the ground,
in a specific direction, andin a specific direction, and
within a specific solid angle.within a specific solid angle.
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RadianceRadiance ((LLTT)) from paths 1, 3,from paths 1, 3,
and 5 contains intrinsic valuableand 5 contains intrinsic valuable
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spectral information about thespectral information about the
target of interest. Conversely, thtarget of interest. Conversely, th
path radiancepath radiance ((LLpp)) from paths 2from paths 2
and 4 includes diffuse skyand 4 includes diffuse skyirradiance or radiance fromirradiance or radiance from
neighboring areas on the groundneighboring areas on the ground
This path radiance generallyThis path radiance generally
introduces unwanted radiometricintroduces unwanted radiometric
noise in the remotely sensed datnoise in the remotely sensed dat
and complicates the imageand complicates the imageinterpretation process.interpretation process.
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RadiometricRadiometric
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VariablesVariables
Jensen 20Jensen 20
Path 1Path 1 contains spectral solarcontains spectral solar
irradiance ( ) that wasirradiance ( ) that was
tt t d littl b ftt t d littl b fo
E
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attenuated very little beforeattenuated very little before
illuminating the terrain withinilluminating the terrain within
the IFOV. Notice in this case thathe IFOV. Notice in this case tha
we are interested in the solarwe are interested in the solarirradiance from a specific solarirradiance from a specific solar
zenith angle ( ) and that thezenith angle ( ) and that the
amount of irradiance reachingamount of irradiance reaching
the terrain is a function of thethe terrain is a function of the
atmospheric transmittance at thiatmospheric transmittance at thi
angle ( ). If all of theangle ( ). If all of theirradiance makes it to the groundirradiance makes it to the ground
then the atmosphericthen the atmospheric
transmittance ( ) equals one.transmittance ( ) equals one.
If none of the irradiance makes iIf none of the irradiance makes i
to the ground, then theto the ground, then the
atmospheric transmittance is zeratmospheric transmittance is zer
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o
oT
oT
Path 2Path 2 contains spectral diffuse skycontains spectral diffuse sky
irradiance ( ) that never evenirradiance ( ) that never even
reaches the Earths surface (thereaches the Earths surface (thed
E
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reaches the Earth s surface (thereaches the Earth s surface (the
target study area) because oftarget study area) because of
scattering in the atmosphere.scattering in the atmosphere.
Unfortunately, such energy is oftenUnfortunately, such energy is often
scattered directly into the IFOV ofscattered directly into the IFOV ofthe sensor system. As previouslythe sensor system. As previously
discussed, Rayleigh scattering ofdiscussed, Rayleigh scattering of
blue light contributes much to thisblue light contributes much to this
diffuse sky irradiance. That is whydiffuse sky irradiance. That is why
the blue band image produced by athe blue band image produced by a
remote sensor system is often muchremote sensor system is often much
brighter than any of the other bandsbrighter than any of the other bands
It contains much unwanted diffuseIt contains much unwanted diffuse
sky irradiance that was inadvertentlsky irradiance that was inadvertentl
scattered into the IFOV of the sensoscattered into the IFOV of the senso
system. Therefore, if possible, wesystem. Therefore, if possible, we
want to minimize its effects. Greenwant to minimize its effects. Green
(2003) refers to the quantity as the(2003) refers to the quantity as theupward reflectance of theupward reflectance of the
atmosphere ( ).atmosphere ( ).duE
Path 3Path 3 contains energy from thecontains energy from the
Sun that has undergone someSun that has undergone some
Rayleigh Mie and/orRayleigh Mie and/or
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Rayleigh, Mie, and/orRayleigh, Mie, and/or
nonselective scattering andnonselective scattering and
perhaps some absorption andperhaps some absorption and
reemission before illuminatingreemission before illuminatingthe study area. Thus, its spectralthe study area. Thus, its spectral
composition and polarizationcomposition and polarization
may be somewhat different frommay be somewhat different from
the energy that reaches thethe energy that reaches the
ground from path 1. Greenground from path 1. Green
(2003) refers to this quantity as(2003) refers to this quantity asthe downward reflectance of thethe downward reflectance of the
atmosphere ( ).atmosphere ( ).ddE
Jensen 20Jensen 20
Path 4Path 4 contains radiation thatcontains radiation that
was reflected or scattered bywas reflected or scattered by
nearby terrain ( ) covered bynearby terrain ( ) covered by
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nearby terrain ( ) covered bynearby terrain ( ) covered by
snow, concrete, soil, water,snow, concrete, soil, water,
and/or vegetation into the IFOVand/or vegetation into the IFOV
of the sensor system. The energyof the sensor system. The energydoes not actually illuminate thedoes not actually illuminate the
study area of interest. Thereforestudy area of interest. Therefore
if possible, we would like toif possible, we would like to
minimize its effects.minimize its effects.
Path 2 and Path 4 combine toPath 2 and Path 4 combine toproduce what is commonlyproduce what is commonly
referred to asreferred to as Path Radiance, LPath Radiance, Lpp
n
Jensen 20Jensen 20
Path 5Path 5 is energy that was alsois energy that was also
reflected from nearby terrain intreflected from nearby terrain int
the atmosphere but thenthe atmosphere but then
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the atmosphere, but thenthe atmosphere, but then
scattered or reflected onto thescattered or reflected onto the
study area.study area.
Jensen 20
The total radiance reaching the sensor fromThe total radiance reaching the sensor from
the target is:the target is:
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gg
pTS LLL +=
The total radiance recordedThe total radiance recorded
by the sensor becomes:by the sensor becomes:
( )
dETETLdooovT
+=
cos
12
1
Jensen 20
Atmospheric Correction Using ATCORAtmospheric Correction Using ATCOR
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a) Image containing substantial haze prior to atmospheric correction. b) Image aftera) Image containing substantial haze prior to atmospheric correction. b) Image afteratmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, theatmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the
German Aerospace Centre).German Aerospace Centre).Je
2
Empirical Line CalibrationEmpirical Line Calibration
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a) Landsat Thematic Mapper imagea) Landsat Thematic Mapper image
acquired on February 3, 1994 wasacquired on February 3, 1994 was
radiometrically corrected usingradiometrically corrected using empiricaempirica
line calibrationline calibration and paired NASA JPL anand paired NASA JPL anJohns Hopkins University spectral librarJohns Hopkins University spectral library
beach and waterbeach and water in situin situ spectroradiometespectroradiomete
measurements and Landsat TM imagemeasurements and Landsat TM image
brightness values (brightness values (BVBVi,j,ki,j,k).).
b) A pixel of loblolly pine with itsb) A pixel of loblolly pine with its
original brightness values in six bandsoriginal brightness values in six bands(TM band 6 thermal data were not used)(TM band 6 thermal data were not used)
c) The same pixel after empirical linec) The same pixel after empirical line
calibration tocalibration to scaled surface reflectance.scaled surface reflectance.
Note the correct chlorophyll absorption iNote the correct chlorophyll absorption i
the blue (band 1) and red (band 3)the blue (band 1) and red (band 3)
portions of the spectrum and the increaseportions of the spectrum and the increase
in near-infrared reflectance.in near-infrared reflectance.
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Index of RefractionIndex of Refraction
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TheThe index of refraction (nindex of refraction (n)) is a measure of the optical density of a substance. This indexis a measure of the optical density of a substance. This index
is the ratio of the speed of light in a vacuum,is the ratio of the speed of light in a vacuum, cc, to the speed of light in a substance such as, to the speed of light in a substance such asthe atmosphere or water,the atmosphere or water, ccnn (Mulligan, 1980):(Mulligan, 1980):
The speed of light in a substance can never reach the speed of light in a vacuum.The speed of light in a substance can never reach the speed of light in a vacuum.
Therefore, its index of refraction must always be greater than 1. For example, the index oTherefore, its index of refraction must always be greater than 1. For example, the index of
refraction for the atmosphere is 1.0002926 and 1.33 for water. Light travels more slowlyrefraction for the atmosphere is 1.0002926 and 1.33 for water. Light travels more slowly
through water because of waters higher density.through water because of waters higher density.
nc
cn =
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Snells LawSnells Law
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Refraction can be described by Snells law, which states that for a given frequency oRefraction can be described by Snells law, which states that for a given frequency of
light (we must use frequency since, unlike wavelength, it does not change when the speedlight (we must use frequency since, unlike wavelength, it does not change when the speedof light changes), the product of the index of refraction and the sine of the angle betweenof light changes), 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:the ray and a line normal to the interface is constant:
From the accompanying figure, we can see that a nonturbulent atmosphere can be thoughtFrom the accompanying figure, we can see that a nonturbulent atmosphere can be thought
of as a series of layers of gases, each with a slightly different density. Anytime energy isof as a series of layers of gases, each with a slightly different density. Anytime energy is
propagated through the atmosphere for any appreciable distance at any angle other thanpropagated through the atmosphere for any appreciable distance at any angle other than
vertical, refraction occurs.vertical, refraction occurs.
2211sinsin nn =
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AtmosphericAtmospheric
RefractionRefraction
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Refraction in three nonturbulentRefraction in three nonturbulent
atmospheric layers. The incidentatmospheric layers. The incidentenergy is bent from its normalenergy is bent from its normal
trajectory as it travels from onetrajectory as it travels from one
atmospheric layer to another.atmospheric layer to another.
Snells law can be used to predictSnells law can be used to predict
how much bending will takehow much bending will take
place, based on a knowledge ofplace, based on a knowledge of
thethe angle of incidence (angle of incidence ()) and theand theindex of refraction of eachindex of refraction of each
atmospheric level,atmospheric level, nn11,, nn22,, nn33..
Jensen 2007Jensen 2007
Snells LawSnells Law
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The amount of refraction is a function of the angle made with the vertical (The amount of refraction is a function of the angle made with the vertical (), the distance), the distance
involved (in the atmosphere the greater the distance, the more changes in density), andinvolved (in the atmosphere the greater the distance, the more changes in density), and
the density of the air involved (air is usually more dense near sea level). Serious errors inthe density of the air involved (air is usually more dense near sea level). Serious errors in
location due to refraction can occur in images formed from energy detected at highlocation due to refraction can occur in images formed from energy detected at high
altitudes or at acute angles. However, these location errors are predictable by Snells lawaltitudes or at acute angles. However, these location errors are predictable by Snells law
and thus can be removed. Notice thatand thus can be removed. Notice that
Therefore, if one knows the index of refraction of mediumTherefore, if one knows the index of refraction of medium nn11 andand nn22 and the angle oand the angle of
incidence of the energy to mediumincidence of the energy to medium nn11, it is possible to predict the amount of refraction, it is possible to predict the amount of refraction
that will take placethat will take place ((sinsin 22) in medium) in medium nn22 using trigonometric relationships. It is useful tousing trigonometric relationships. It is useful to
note, however, that most image analysts never concern themselves with computing thenote, however, that most image analysts never concern themselves with computing theindex of refraction.index of refraction.
2
11
2
sin
sin n
n
=
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