Download - _Chapter 2 2008

8/14/2019 _Chapter 2 2008

1/71

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

8/14/2019 _Chapter 2 2008

2/71

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.

8/14/2019 _Chapter 2 2008

3/71

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

8/14/2019 _Chapter 2 2008

4/71

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

8/14/2019 _Chapter 2 2008

5/71

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.

8/14/2019 _Chapter 2 2008

6/71


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.

8/14/2019 _Chapter 2 2008

7/71

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.

8/14/2019 _Chapter 2 2008

8/71

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

8/14/2019 _Chapter 2 2008

9/71

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.

8/14/2019 _Chapter 2 2008

10/71

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


8/14/2019 _Chapter 2 2008

11/71

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.

8/14/2019 _Chapter 2 2008

12/71

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 =

8/14/2019 _Chapter 2 2008

13/71

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


8/14/2019 _Chapter 2 2008

14/71

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.


8/14/2019 _Chapter 2 2008

15/71

Spectral Bandwidths of Landsat and SPOT Sensor SystemsSpectral Bandwidths of Landsat and SPOT Sensor Systems


8/14/2019 _Chapter 2 2008

16/71

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

=

8/14/2019 _Chapter 2 2008

17/71

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.


8/14/2019 _Chapter 2 2008

18/71

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.


8/14/2019 _Chapter 2 2008

19/71

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

8/14/2019 _Chapter 2 2008

20/71

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

8/14/2019 _Chapter 2 2008

21/71

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.


vh

ch=

Q

ch=

chQ =

8/14/2019 _Chapter 2 2008

22/71

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.


8/14/2019 _Chapter 2 2008

23/71

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

8/14/2019 _Chapter 2 2008

24/71

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.


8/14/2019 _Chapter 2 2008

25/71

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..


8/14/2019 _Chapter 2 2008

26/71

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.


8/14/2019 _Chapter 2 2008

27/71

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.


8/14/2019 _Chapter 2 2008

28/71

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.

8/14/2019 _Chapter 2 2008

29/71

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.


8/14/2019 _Chapter 2 2008

30/71

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..

8/14/2019 _Chapter 2 2008

31/71

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..


A h i L

8/14/2019 _Chapter 2 2008

32/71

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.


Atmospheric Layers

and Constituents

8/14/2019 _Chapter 2 2008

33/71

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

8/14/2019 _Chapter 2 2008

34/71

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.


8/14/2019 _Chapter 2 2008

35/71

RayleighRayleigh


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

).).


R l i h S i

8/14/2019 _Chapter 2 2008

36/71


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).

8/14/2019 _Chapter 2 2008

37/71

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

=


Mi S iMi S tt i

8/14/2019 _Chapter 2 2008

38/71

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

8/14/2019 _Chapter 2 2008

39/71

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.


8/14/2019 _Chapter 2 2008

40/71


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.


8/14/2019 _Chapter 2 2008

41/71

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


8/14/2019 _Chapter 2 2008

42/71

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.


Absorption of the Suns Incident Electromagnetic Energy in theAbsorption of the Suns Incident Electromagnetic Energy in the

8/14/2019 _Chapter 2 2008

43/71

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


window

a)a) TheThe absorptionabsorption of the Suns incidentof the Suns incident

l i i h il i i h i

8/14/2019 _Chapter 2 2008

44/71

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

8/14/2019 _Chapter 2 2008

45/71

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


8/14/2019 _Chapter 2 2008

46/71

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.


ReflectancReflectanc

8/14/2019 _Chapter 2 2008

47/71


Terrain Energy-Matter InteractionsTerrain Energy-Matter Interactions

8/14/2019 _Chapter 2 2008

48/71

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

8/14/2019 _Chapter 2 2008

49/71

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

8/14/2019 _Chapter 2 2008

50/71

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

8/14/2019 _Chapter 2 2008

51/71

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

%

8/14/2019 _Chapter 2 2008

52/71

Typical spectralTypical spectral

reflectance curvesreflectance curves

for urbansuburbanfor urbansuburban

phenomena in thephenomena in the

region 0.4 0.9region 0.4 0.9 mm


8/14/2019 _Chapter 2 2008

53/71

Irradiance and ExitanceIrradiance and Exitance

8/14/2019 _Chapter 2 2008

54/71

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))..


AE

=

AM

=

Radiant Flux DensityRadiant Flux Density

8/14/2019 _Chapter 2 2008

55/71

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

8/14/2019 _Chapter 2 2008

56/71

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

Jensen 2007

cosA

L

=

8/14/2019 _Chapter 2 2008

57/71

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.


RadianceRadiance ((LLTT)) from paths 1, 3,from paths 1, 3,

and 5 contains intrinsic valuableand 5 contains intrinsic valuable

8/14/2019 _Chapter 2 2008

58/71

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.


RadiometricRadiometric

8/14/2019 _Chapter 2 2008

59/71

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

8/14/2019 _Chapter 2 2008

60/71

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


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

8/14/2019 _Chapter 2 2008

61/71

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

8/14/2019 _Chapter 2 2008

62/71

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

8/14/2019 _Chapter 2 2008

63/71

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

8/14/2019 _Chapter 2 2008

64/71

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:

8/14/2019 _Chapter 2 2008

65/71

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

8/14/2019 _Chapter 2 2008

66/71

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

8/14/2019 _Chapter 2 2008

67/71

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.

Jensen 20Jensen 20

Index of RefractionIndex of Refraction

8/14/2019 _Chapter 2 2008

68/71

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 =

Jensen 20

Snells LawSnells Law

8/14/2019 _Chapter 2 2008

69/71

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 =

Jensen 20

AtmosphericAtmospheric

RefractionRefraction

8/14/2019 _Chapter 2 2008

70/71

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..


Snells LawSnells Law

8/14/2019 _Chapter 2 2008

71/71

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

=

Jensen 20