Lecture 5: Radiative transfer theory where light comes from and how it gets to where it’s going
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Transcript of Lecture 5: Radiative transfer theory where light comes from and how it gets to where it’s going
Lecture 5: Radiative transfer theory
where light comes from and how it gets to where it’s going
Wednesday, 19 January 2010
Ch 1.2 review, 1.3, 1.4http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/blusky.html (scattering)http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/refraction1.html (refraction)http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/snellsLaw/snellsLaw1.html (Snell’s Law)Review On Solid Angles, (class website -- Ancillary folder: Steradian.ppt)
Reading
http://javaboutique.internet.com/ColorFinder/
Here is a website where you can experiment with additive color mixing
What was covered in the previous lecture
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LECTURESJan 05 1. IntroJan 07 2. ImagesJan 12 3. Photointerpretation
• Jan 14 4. Color theory previous• Jan 19 5. Radiative transfer today
Jan 21 6. Atmospheric scatteringJan 26 7. Lambert’s LawJan 28 8. Volume interactionsFeb 02 9. SpectroscopyFeb 04 10. Satellites & ReviewFeb 09 11. MidtermFeb 11 12. Image processingFeb 16 13. Spectral mixture analysisFeb 18 14. ClassificationFeb 23 15. Radar & LidarFeb 25 16. Thermal infraredMar 02 17. Mars spectroscopy (Matt Smith)Mar 04 18. Forest remote sensing (Van Kane)Mar 09 19. Thermal modeling (Iryna Danilina)Mar 11 20. ReviewMar 16 21. Final Exam
Today
•The atmosphere and energy budgeting •Modeling the atmosphere•Radiative transfer equation•“Radiosity”
Friday’s lecture:
•Color and the spectrum•Color perception•Additive & subtractive color mixing•Ternary diagrams and color transformations•Selective absorption of light
The Electromagnetic Spectrum (review)
Units:Micrometer (m) = 10-6 mNanometer (nm) = 10-9 m
Light emitted by the sun
The Sun
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This graph is a spectrum
This chart shows the spectrum
Light from Sun – Light Reflected and Emitted by Earth
Wavelength, μm
W m
-2 μ
m -
1
W m
-2 μ
m-1 s
r-1
The sun is not an ideal blackbody – the 5800 K figure and graph are simplifications
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Atmospheric Constituents
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50
90
Troposphere
Stratosphere
Mesosphere
Thermosphere
Almost allH2O
He
igh
t (km
)
Temperature (K)
280200
Ozone
Constant Nitrogen (78.1%) Oxygen (21%) Argon (0.94%) Carbon Dioxide (0.033%) Neon Helium Krypton Xenon Hydrogen Methane Nitrous Oxide
Variable Water Vapor (0 - 0.04%) Ozone (0 – 12x10-4%) Sulfur Dioxide Nitrogen Dioxide Ammonia Nitric Oxide
All contribute to scatteringFor absorption, O2, O3, and N2 are important in the UVCO2 and H2O are important in the IR (NIR, MIR, TIR)
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Solar spectra before and after passage through the atmosphere
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Atmospheric transmission
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Modeling the atmosphere
dz
e
To calculate we need to know how k in the Beer-Lambert-Bouguer Law (called here) varies with altitude. Modtran models the atmosphere as thin homogeneous layers.
L
L z
e
L
LsL z
e)(
Modtran calculates k or for each layer using the vertical profile of temperature, pressure, and composition (like water vapor).
This profile can be measured made using a balloon, or a standard atmosphere can be assumed.
o is the incoming flux
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Radiosonde dataA
ltit
ud
e (k
m)
Alt
itu
de
(km
)
Relative Humidity (%) Temperature (oC)
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15
10
5
0
20
15
10
5
00 20 40 60 80 100 -80 -40 0 40
Mt Everest
Mt Rainier
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Radiant energy – Q (J) - electromagnetic energy
Solar Irradiance – Itoa(W m-2) - Incoming radiation (quasi directional) from the sun at the top of the atmosphere.
Irradiance – Ig (W m-2) - Incoming hemispheric radiation at ground. Comes from: 1) direct sunlight and 2) diffuse skylight (scattered by atmosphere).
Downwelling sky irradiance – Is↓(W m-2) – hemispheric radiation at ground
Path Radiance - Ls↑ (W m-2 sr-1 ) (Lp in text) - directional radiation scattered into the camera from the atmosphere without touching the ground
Transmissivity – - the % of incident energy that passes through the atmosphere
Radiance – L (W m-2 sr-1) – directional energy density from an object.
Reflectance – r -The % of irradiance reflected by a body in all directions (hemispheric: r·I) or in a given direction (directional: r·I·-1)
Note: reflectance is sometimes considered to be the reflected radiance. In this class, its use is restricted to the % energy reflected.
Ig
Ls↑
Itoa
0.5º
Is↓
L
Terms and units used in radiative transfer calculations
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DN = a·Ig·r + b
Radiative transfer equation
Ig is the irradiance on the groundr is the surface reflectancea & b are parameters that relate to instrument and atmospheric characteristics
This is what we want
Parameters that relate to instrument and atmospheric characteristics
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DN = g·(e·r · i·Itoa·cos(i)/ + e· r·Is↓/ + Ls↑) + o
g amplifier gainatmospheric transmissivitye emergent anglei incident angler reflectanceItoa solar irradiance at top of atmosphereIg solar irradiance at ground Is↓ down-welling sky irradianceLs↑ up-welling sky (path) radianceo amplifier bias or offset
Radiative transfer equation
DN = a·Ig·r + b
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The factor of
Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that reflects equally in all directions.
Lambert
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The factor of
Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that reflects equally in all directions.
If irradiance on the surface is Ig, then the irradiance from the surface is r·Ig = Ig W m-2.
The radiance intercepted by a camera would be r·Ig/ W m-2 sr-1.
The factor is the ratio between the hemispheric radiance (irradiance) and the directional radiance. The area of the sky hemisphere is 2 sr (for a unit radius).So – why don’t we divide by 2 instead of ?
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∫ ∫ L sin cos ddL2
0 0
•Incoming directional radiance L at elevation angle is isotropic
•Reflected directional radiance L cos is isotropic
•Area of a unit hemisphere:
∫ ∫ sin dd 2
0 0
The factor of
Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that reflects equally in all directions.
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i Itoa cos(i)
Itoa
gi Itoa cos(i)
i
r reflectance
r (i Itoa cos(i)) / reflected light
“Lambertian” surface
e
e
Ls↑ (Lp)
i
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Measured Ltoa
DN(Itoa) = a Itoa + b
Ltoae r (i Itoa cos(i)) / +
e r Is↓ / + Ls↑
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What was covered in today’s lecture?
•The atmosphere and energy budgeting •Modeling the atmosphere•Radiative transfer equation•“Radiosity”
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•Atmospheric scattering and other effects
- where light comes from and how it gets there - we will trace radiation from its source to camera - the atmosphere and its effect on light - the basic radiative transfer equation: DN = a·Ig·r + b
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What will be covered in next Tueday’s lecture?
Mauna Loa, Hawaii