Optical Radiation Models - University of Arizona

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ECE/OPTI 531 – Image Processing Lab for Remote Sensing Fall 2005

Optical Radiation Models

Reading: Chapter 2

Fall 2005Optical Radiation Models 2


• Energy Sources• VSWIR Modeling• MWIR-LWIR Modeling

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Quantifying Radiation

• Radiant energy (Q in joules) is a measure of the capacityof an EM wave to do work by moving an object, heating,or changing its state.

• Radiant flux (Φ in watts) is the time rate (flow) of energypassing through a certain location.

• Radiant flux density (watts/m2) is the flux intercepted bya planar surface of unit area.– Irradiance (E) is flux density incident upon a surface.– Exitance (M) or emittance is flux density leaving a surface.

• The solid angle (Ω in steradians) subtended by an area Aon a spherical surface of radius r is A/r2.– Radiant intensity (I in watts/sr) is the flux per unit solid

angle in a given direction.– Radiance (L in watts/m2/sr) is the intensity per unit

projected area.• Radiance from source to object is conserved!


0

500

1000

1500

2000

2500

0.4 0.8 1.2 1.6 2 2.4

5900K BB at earth-sun distance

MODTRAN

irra

dia

nce

(W

-m-2

-µm

-1)

wavelength (µm)

solar spectrum and blackbody approximation

Spectral Radiant Exitance• Spectral distribution of radiation flux• Planck’s equation (Eq. 2–1) for perfect radiator

(blackbody)

– T is the blackbody’s temperature in Kelvin (K),T=5900K for sun, 300K for Earth,

• Mλ is a function of both wavelength of radiationand temperature of the source– usually plotted as function of wavelength, for given

temperature

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Three Spectral Regions

• VSWIR (Visible-ShortWave IR, 0.4 to 2.4µm, 400to 2400nm)– Solar radiation dominates

• MWIR (MidWave IR, 3 to 5µm, 3000 to 5000nm)– Mixture of solar and thermal radiation

• LWIR (LongWave IR, 8 to 14µm, 8000 to14000nm)– Thermal radiation dominates– Emitted by objects on Earth’s surface as a function of

their temperature and emissivity




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sensor

!

IFOV

!

L"sp

E"

L"su

L"sd

nadir

E"0

down-scatteredunscattered path-scattered

surface-reflected

direct skylightpath

radiance

Top-Of-the-Atmosphere (TOA)

VSWIR Modeling

• Three components reach sensor– Direct component is unscattered from source– Skylight is scattered down onto the target (Why are

shadows not black?)– Path radiance is scattered along path up into the

sensor


Direct Component

• Related to the signal of interest, i.e. surface reflectance• Top-Of-the-Atmosphere (TOA) irradiance modified by

atmospheric transmittance along solar path

• Earth surface irradiance depends on the angleof incidence, which in-turn, depends on solar angle andtopography

0

0.2

0.4

0.6

0.8

1

0.4 0.8 1.2 1.6 2 2.4

tran

smit

tance

wavelength (µm)

CO2

H2O

H2O

H2O

H2O

CO2

CO2

CO2,

H2O

CO2,

Normal to solar path:

Earth surface:

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irradiance at earth surface

view vector (to sensor)

(x,y)

incident irradiance does not depend on the view angle, φ

surface normal vector

solar vector (to sun)

solar elevation angle α

flux density normal to solar path

flux density at earth surfaceflux is spread over

larger area at earth surface

solar incident angle θ

view angle φ


Example: Shaded Relief

• Solar incident angle– solar elevation– local topography

(slope, aspect)• Simulate incident

angle effect onirradiance– calculate cos[θ(x,y)]

for every pixel at(x,y) using solarelevation angle fromTM image and DEM —>“shaded-relief” image

digital elevation model (DEM) shaded-relief image

TM image contrast-stretched TM image

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self-shadowed pixels projected shadows

total shadowed area = union(self-shadowed area, projected shadow area)

Shadowing

• Another incident geometry effect


Temporal Changes

October 20, 1980June 11, 1981

shading and shadowing 5 months apartLandsat MSS image of Grand Canyon, AZ

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View Path

• Incident irradiance reflects at Earth surface tobecome surface radiance

• Surface radiance modified by atmospherictransmittance along sensor view path tobecome at-sensor radiance

Earth surface:

At-sensor:


Angle Dependency

• Atmospheric transmittance varies with viewangle (and solar angle)– particularly important for wide-FOV sensors, such as

AVHRR and MODIS

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0.2

0.4

0.6

0.8

1

0.4 0.8 1.2 1.6 2 2.4

view path, nadirview path, view angle = 40 degrees

tran

smit

tance

wavelength (µm)

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Direct Component Summary

sensor

Earth surface irradiance

surface radiance

at-sensor radiance


Indirect Components

• Skylight component– secondary signal component

– where F is the fraction of sky visible at a given earthsurface point

• Path radiance component– assumed independent of (x,y) here– atmospheric scattering (“haze”)

• Rayleigh scattering for a clear atmosphere (moleculesonly)

• Mie scattering for an atmosphere with aerosols (watervapor) or particulates (dust, smoke)

• real atmospheres exhibit both Rayleigh and Mie scattering

At-sensor:

At-sensor:

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Total At-Sensor Radiance

: surface diffuse reflectance (unitless): view path atmospheric transmittance (unitless): solar path atmospheric transmittance (unitless): incident, exo-atmospheric spectral irradiance (W·m-2·µm-1): cosine of angle between solar vector and surface normal: fraction of sky hemisphere visible from surface point: downwelling atmospheric spectral irradiance (W·m-2·µm-1): upwelling atmospheric path spectral radiance

(W·m-2·µm-1 ·sr-1)


MODTRAN Simulation

0

500

1000

1500

2000

2500

0

50

100

150

200

250

400 800 1200 1600 2000 2400

AVIRIS DN

MODTRAN radiance

AV

IRIS

DN

MO

DT

RA

N rad

iance (W

-m-2-sr

-1-µm

-1)

wavelength (nm)

0

20

40

60

80

100

120

0.4 0.8 1.2 1.6 2 2.4

path-scattered

ground-reflected

radia

nce

(W

-m-2

-sr-1

-µm

-1)

wavelength (µm)

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Broad Radiation Regime

• 2.4 to14µm (2400 to 14000nm)• Solar and thermal radiation mixed in MWIR• Thermal radiation in LWIR• Measured geophysical variables:

– reflectance– spectral emissivity (thermal analogy to reflectance)– temperature

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10

100

1000

104

1

10

100

1000

104

0.1 1 10

solar irradiance

earth emission

irra

dia

nce

(W

-m-2

-µm

-1)

radian

t exitan

ce (W-m

-2-µm

-1)

wavelength (µm)

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Thermal Radiation

• Perfect radiator– “blackbody”– emissivity = 1 (ratio of spectral radiant exitance of

given object to that of a blackbody at the sametemperature)

– obeys Planck’s Law• Imperfect radiator

– “graybody”– emissivity ≤ 1 (radiates less efficiently than a

blackbody)– obeys scaled Planck’s Law

• Need to separate emissivity effects (surfaceproperty) from temperature effects (bulkproperty) – not easy!– usually assume one or the other is constant for all

objects in the scene


LWIR Radiation Components

: spectral emissivity (unitless): downwelling atmospheric-emitted spectral radiance (W·m-2·µm-1

·sr-1): upwelling atmospheric-emitted path spectral radiance

(W·m-2·µm-1 ·sr-1): linear approximation to spectral radiance for blackbody

temperature T (W·m-2·µm-1 ·sr-1)

L!ed

L!eu

T ",

L!ep

surface-emitted down-emitted path-emitted

#

MWIR:

LWIR:

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Thermal Examples

TM band 4 TM band 6

cloud shadow clouds

Clouds and their shadows (Fig. 2–19)


Thermal Examples (cont.)

MSS band 4

HCMM LWIR

nuclear power plant

cooling ponds

Lake used to cool nuclear power plant (Fig. 2–20)

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Thermal Examples (cont.)

TM band 2

TM band 6

city park

Mississippi River

New Orleans, LA, an example of a urban “heat island”(Fig. 2–21)

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Optical Radiation Models - University of Arizona