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