The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
what makes it difficult to correct the images afterwards. Apart
from a better contrast atmospherically corrected images can be
more easily mosaicked and compared with each other for
change detection. Atmospheric correction is also a prerequisite
for quantitative remote sensing methods, which require images
calibrated to ground reflectance.
For wide-angle sensors like the ADS40 the correction of the
anisotropic reflectance (BRDF) of the ground is just as
important for creating homogeneous images. Unfortunately the
anisotropic reflectance is very much dependent on the subpixel
surface structure of the ground which is also unknown.
So it is necessary to derive the necessary parameters for
atmospheric and bidirectional reflectance correction from the
image data itself.
For the case of atmospheric correction a number of all-purpose
software packages exist (ATCOR, ATREM/TAFKAA, ACORN,
FLAASH, etc). Those packages were developed for imaging
spectrometers or multispectral sensors with relatively low
spatial resolution and data volume. Therefore we decided to
implement a set of rather simple but efficient algorithms to
process the hundreds of Gigabytes of data of a typical high
resolution image block. In order to find a compromise between
a fast but insufficient contrast stretch and a time consuming
radiation transfer model, methods from satellite remote sensing
have been adapted to the specifics of airborne imagery and to
the actual ADS40 spectral bands. The implementation follows
the radiometric imaging chain proposed by (Beisl, 2006a).
A satellite version of the two methods has already been applied
to MERIS data over land (Telaar and Schonermark, 2006).
and NIR band are calculated. Examples have been shown
already in (Beisl, 2006a).
2.2 Physical Models
For large homogeneous surfaces the measured radiance at the
sensor is (Kaufman and Sendra, 1988, Fraser et al., 1992).
J PSTd 0W Jup
0 7t{\. ~ sp)
(1)
where L m = measured at-sensor radiance
L 0 = path radiance for zero surface reflectance
p = surface reflectance
S = mean solar spectral irradiance
Tdown = total downward transmittance from top of the
atmosphere (TOA) to the ground
T up = total upward transmittance from ground to sensor
s = spherical albedo of the atmosphere, i.e. the fraction
of the upward radiance which is backscattered by the
atmosphere
This equation can be solved for the reflectance p
P =
f
1 + 5/
where
J cj- j
u ± down ± up
(2)
(3)
2. ATMOSPHERIC EFFECTS
2.1 Empirical Models
Without any external data the atmospheric effects can only be
determined using statistical methods working on the image data
itself. Histograms of air- or spacebome data show a band
specific offset where the population starts. This is due to
scattered light from below the sensor reaching the sensor field
of view even if the ground reflectance is zero. This offset
observed on a dark pixel is subtracted from each pixel to give
the radiance at ground.
The term \ — sp takes into account the multiple scattering
from the surrounding area. For a non-uniform surface the target
reflectance p has to replaced by an average reflectance p of
the surrounding area (Tanre et al., 1981). For a darker (brighter)
surrounding area this leads to a lower (higher) at-sensor
radiance (adjacency effect, Dave 1980).
L m ~ Lo +
pSTdo W Jup
71
(l-sp)
(4)
The reflectance then calculates as
Simple Dark Pixel Subtraction: The original method as
described above was proposed by (Chavez, 1975) for Landsat
images. Here we assume a scan angle dependent offset and
therefore investigate column specific histograms. The
correction is done for each band separately.
Modified Chavez Method: In some cases where the image
content was not a statistical mixture, an overcorrection was
observed for the red and NIR bands (Chavez, 1988). Therefore
Chavez proposed a prediction scheme which uses a X' K rule for
the atmospherically scattered radiance. The exponent k ranges
from 4 for a clear Rayleigh-type atmosphere to 0.5 for a very
hazy atmosphere. Since the blue band offset shows the largest
atmospheric effect this is supposed to be the most accurate
value. The calibrated radiance value of this offset allows to
decide the k value. The larger the offset the hazier the
atmosphere. The k decision rule has to be flying height
dependent. With the X' K rule the offset values for the green, red
P
ffn, A>)(1_^)
ST T
*“* x down ± up
(5)
If we know p this takes up the form of an affine function of
the measured radiance L m with correction constants A and B.
p = AL m +B
(6)
Actually p is an integral of the reflectances weighted by the
distance from the target and depending on the view angle and
on the Rayleigh and aerosol contributions to the transmittance.
(Richter, 1996) gives an effective range of 500 m to 1000 m for
airborne images, and for flying heights H less than 1 km, the
effective range is H/2. Calculating the integral causes an