Download The essence of radiometric correction

Radiometric Correction
Remote sensing signals are essentially the amount of energy received at the sensor from
the target in a given spectral width. However, the signals we get directly the satellite are
usually noisy. The noise is usually of two types: internal and external noise. Internal
noise is from the sensor and external noise from the atmosphere and the areas adjacent to
the target.
What we received from satellite is DN values, not
the amount of radiance directly. Why?
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The number of DN values that a sensor can detect is
called the sensor radiometric resolution. Why do the
satellite send the DN values to the ground instead of
radiance?
The amount of energy was converted to DN value first
on board the satellite as shown to the right.
0
the detector Gain and Offset (Bias)
DN  Gd L  Bd
Lmin
Lmax
Figure 1
where
 L  Lmin 
L   max
 DN  Lmin
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

Spectral radiance measured over the spectral
bandwidth of the channel.
Gd: slope of response function
Bd: Bias
For Landsat 5, there are 16 detectors for each reflective band, and 4 detectors for the
thermal band. For the convenience of users, the DN was calibrated (DNcal) as
DN cal  ( DN   ref ) /  ref or DN   ref DN cal   ref
so that a single gain and bias can be used for each band.
DN cal  GL  B
For the remote sensing signals to be useful, the sensor must produce consistently the
same DN at a given amount of energy received. Therefore, G and B must remain a
constant for as long as the sensor is working. Each sensor on-board a satellite has been
very carefully tested, and its gain and bias were accurately measured before it was put on
the satellite. This is called pre-launch calibration. However, nothing is perfect, after the
sensors is launched, the sensor gain and bias may change. In remote sensing, we called it
sensor degradation.
To trace the change of sensors on board, on-board calibration is needed.
Landsat 5: on-board there are three tungsten lights whose intensity is very stable. Each
light can be turned on/off. With three lights on board, we can calibrate the gains and
offset frequently. How can we calibrate the gain and bias in Figure 1 with the three
lights?
Over the years, the sensors on-board Landsat five have been found to be drifting with
time. In the meantime, scientists found that the Internal Calibration light was not
constant, indicating the pre-launch sensor gain and bias do not apply with time. Scientists
have been constantly monitoring the change in the gain and bias of Landsat 5 sensor. The
most recent document recording the sensor gain and bias with is can be found in
http://landsat.usgs.gov. In order to use the most recent sensor gain and bias, the sensor
gain and bias produced earlier needs to be undone.
L*new  ( ref DN cal   ref  3) / Gnew
However, we may not have αref and βref. We will rely on a simple correction:
L*new  ( L*old )Gold / Gnew
Where Gold is provided by USGS in a look-up-table and Gnew can be calculated based on
Chander et al., 2007.
Landsat 7: on-board there are two tungsten lights and a blackbody and a shutter flag.
Shutter flag is used to block the external light source during internal calibration.
Similar to the three tungsten lights for Landsat 5, they are used to calibrate the gains and
offset frequently. The blackbody is set at temperature 30, 37 and 46oC to calibrate the
thermal channels. Landsat 7 ETM+ sensors have been proven to be very stable since its
launch. No sensor degradation has been found!
Ground monitoring:
In addition to the on-board calibration, there are a group of scientists who used some well
defined ground feature whose surface reflectance is known and stable. These objects are
used to monitor satellite performance.
Atmosphere Correction:
Remote Sensing Signals
Figure 2 source of energy at the target surface and at the sensor
Solar energy arrived on the target ground surface consists of two components:
direct and diffuse solar radiation. The direct solar radiation on the ground is
E 0 cos( z )T
where E0 is solar constant, z is solar zenith angle, and Tz is the atmospheric
transmissivity in the solar direction and can be estimated as
Tz  e  cos( z )
Assuming the surface reflectance s, the amount of energy leaving the surface would be
 s [ E0 cos( z )Tz  Edown ]
The energy leaving the surface will be attenuated again before reaching the satellite
sensor. In addition, the sensor will also receive path radiance that is scattered directly
from the atmosphere to the sensor. Therefore, the radiance received at the satellite is
Lsat 
s
[ E0 cos( z )Tz  Edown ]Tv  L path

where Lpath is the path radiance, and Tv is the atmosphere transmisssivity in the sensor
direction, and can be estimated as
Tv  e 
cos( v )
Solving for the surface reflectance s, we have
s 
 ( Lsat  Lpath )
Tv [ E0 cos( z )Tz  Edown ]
where Lsat=GL+B is at-satellite radiance (he sensor degradation effects gets in here). To
correct for atmospheric effects, we need to know the path radiance, aerosol optical depth
and the zenith angles from both sun and sensor directions.
If we assume Tz=Tv=1.0, Lpath=0, Edown=0, the reflectance is called apparent reflectance
(at satellite reflectance).
* 
Lsat
E0 cos( z )
The correct for the atmosphere effect, we need to understand how solar radiation interacts
with the atmosphere.
Scattering:
Rayleigh Scattering: occurs when solar radiation interacts with atmospheric molecules
and other tiny particles that are much smaller in diameter than the wavelength of the
interacting radiation. It is strong in the blue region of the solar spectrum, thus the sky
looks blue during clear days.
Mie Scattering: occurs when solar radiation interacts with atmospheric particles whose
diameters are essentially equal to the wavelength of solar radiation.
Absorption:
The spectral ranges of remote sensing are always carefully chosen to avoid
atmospheric absorption. Therefore, it is less of a problem than scattering
to remotely sensed imagery.
Extinction Cross Section
  r 2Qext ( , r )
where Qext(, r) is nondimensional
efficiency factor with values in [0,4].
Volume Extinction Coefficient (Ke)

K e    (r )n(r )dr
0
r 
r 
r
Optical Depth (Thickness):
TOA

 ( z )   K e ( z )dz
z
(z)
z
0
Atmospheric Transmissivity
T ( z )  e  ( z ) / cos( z )
where z is the solar zenith angle.