#### Transcript Lecture 5:

```Tuesday, 20 January
where light comes from and how it gets to where it’s going
http://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)
Last lecture: color theory, data spaces,
color mixtures, absorption, photogrammetry
The Electromagnetic
Spectrum (review)
Units:
Micrometer = 10-6 m
Nanometer = 10-9 m
Light emitted by the sun
W m-2 μm-1 sr-1
W m-2 μm -1
Light from Sun – Light Reflected and Emitted by Earth
Wavelength, μm
Atmospheric Constituents
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
Thermosphere
90
Height (km)
Constant
Mesosphere
50
Stratosphere
Ozone
10
All contribute to scattering
For absorption, O2, O3, and N2 are important in the UV
CO2 and H2O are important in the IR (NIR, MIR, TIR)
Almost all
H2O
Troposphere
200
Temperature (K)
280
Atmospheric transmission
Modeling the atmosphere
To calculate  we need to know
how k in the Beer-LambertBouguer Law (called  here)
varies with altitude. Modtran
models the atmosphere as thin
homogeneous layers.
Modtran calculates k or  for
each layer using the vertical
profile of temperature,
pressure, and composition
(like water vapor).
  e
 dz
 e
Fo is the incoming flux
 e
 L z
L
( sL  L ) z
L
This profile can be measured
made using a balloon, or a
standard atmosphere can be
assumed.
20
20
15
15
Altitude (km)
Altitude (km)
10
5
0
0
20 40
60
80
100
Relative Humidity (%)
10
Mt Everest
5
Mt Rainier
0
-80
-40
0
40
Temperature (oC)
Terms and units
transfer calculations
0.5º
Radiant energy – Q (J) - electromagnetic energy
(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) –
Itoa
L
Ls↑
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·p-1)
Is↓
Ig
Note: reflectance is sometimes considered to be the
reflected radiance. In this class, its use is restricted to
the % energy reflected.
Parameters that relate to
instrument and
atmospheric
characteristics
DN = a·Ig·r + b
This is what we want
Ig is the irradiance on the ground
r is the surface reflectance
a & b are parameters that relate to
instrument and atmospheric
characteristics
DN = a·Ig·r + b
DN = g·(e·r · i·Itoa·cos(i)/p + e· r·Is↓/p + Ls↑) + o
g

e
i
r
Itoa
Ig
Is↓
Ls↑
o
amplifier gain
atmospheric transmissivity
emergent angle
incident angle
reflectance
solar irradiance at top of atmosphere
amplifier bias or offset
The factor of p
Consider a perfectly reflective (r=100%) diffuse “Lambertian” surface that
reflects equally in all directions.
2p p/2
∫ ∫ L sin
then
cos
d dwpL
is
I
,
the
from the surface is
g
0 0
r·Ig = Ig W m-2.
•Incoming directional radiance L at elevation angle  is isotropic
The radiance intercepted by a camera would be r·Ig/p W m-2 sr-1.
•Reflected directional radiance L cos  is isotropic
The factor p is the ratio between the hemispheric radiance (irradiance) and
the directional
The area of the sky hemisphere is 2p sr (for a unit
of a unit hemisphere:
So – why don’t we divide2pbyp/22p instead of p?
∫ ∫ sin Lambert
 d dw2p
0
0
Measured Ltoa
DN(Itoa) = a Itoa + b
Itoa
Ltoae r (i Itoa cos(i)) /p + e r Is↓ /p + Ls↑
Itoa cos(i)
i
Highlighted terms
relate to the surface
i
Ls↑=r Is↓ /p
Ls↑ (Lp)
e
i
e
Igi Itoa cos(i)
Lambert
Is↓
r reflectance
r (i Itoa cos(i)) /p
reflected light
“Lambertian” surface
Next lecture: Atmospheric
scattering and other effects
Rayleigh Scattering
l>>d
Mauna Loa, Hawaii
```