The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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angle 0i . This ô 0 is used to calculate L 0 , T down , T up , and s for all 
image locations. 
L o =L o (b,-h,,0 r ,0 l ,S l) ,h,H) (15) 
Town — Tdown (16) 
T r -W-d„0„S t ) (17) 
s = s(e l —e 6 ,S 0 ,h,H) (18) 
The parameters (ai...a 4 , b^.-by, Ci...e 6 , d!...d 3 , e!...e 6 ) were 
determined separately for each band using a multilinear 
regression with simulated atmospheric data. The data were 
calculated in a range of 500 m to 9000 m for the flying height 
over ground, 0 m to 6000 m for the ground elevation, 7 km to 
100 km for the visibility, 0° to 60° for the sun zenith angle, and 
0° to 35° for the view zenith angle. 
Figure (2) shows the linear correlation coefficients r 2 for the 
different quantities. Due to the large number of parameters we 
obtain a very high correlation above 0.992. The decrease in 
correlation for s in the NIR band is of no significance, since the 
s-dependence is a second order effect. 
deltaO 
-- L0 
s 
Tdown 
— -Tup 
wavelength [nm] 
Figure 2. Correlation coefficients for the parametrised 
quantities 80, L0, Tdown, Tup, and s for the ADS40 bands B, 
G, R, NIR. 
Model sensitivity: Neglecting the multiple reflection term sp in 
eqn. (5) the error in reflectance Ap caused by the path radiance 
uncertainty AL 0 is 
Ap = fT-AL <> 
dU 
7T 
T T s 
1 down x up 
AA, 
(19) 
So in order to keep the output reflectance error small the path 
radiance error has to be kept as small as possible. This requires 
a careful selection of the dark pixel. Eqn. (19) also shows that 
the absolute reflectance error becomes larger for smaller 
transmission, i.e. for a hazy atmosphere. 
3. BIDIRECTIONAL EFFECTS 
As already presented in (Beisl, 2004) the Walthall model 
(Walthall et al., 1985, Nilson and Kuusk, 1989), which is 
extended by a hot spot term D, can be used for correcting the 
bidirectional effects. Eqn. (20) is a linear function of its free 
parameters and can be easily inverted using a least squares 
regression. 
p(O i ,e r ,(p) = 
a Of Of + b (Of + Of ) + cO i 0 r cos cp + dD + e 
(20) 
where p = reflectance factor 
dj = incident illumination zenith angle 
6 r = reflection view zenith angle 
(p = relative azimuth angle 
D = hot spot term 
a, b, c, d, e = free parameters 
D = -^tan 2 0 X + tan 2 0 X - 2 tan 0 { tan 0 T cos cp (21) 
The samples for model inversion can be retrieved by calculating 
column averages of the total image as described in (Beisl, 2004), 
since a column in a line scanner image represents a line of 
constant view angle. The relative shape of the modelling is then 
used for a multiplicative correction. 
For a good inversion quality, i.e. for all images matching 
together in the mosaic, it is recommended to merge the statistics 
from each image together and perform a simultaneous 
correction (Beisl, 2002). This will also improve the correction 
of images with inhomogeneous statistics. 
4. DATA AND RESULTS 
In order to verify the two new atmospheric correction 
algorithms (Angstrom method and Modified Song-Lu-Wesely 
Method) ground reflectance measurements have been carried 
out in the center area of the test flight region. The test flight 
pattern was a double cross strip at two different flying heights 
(1500 m and 2500 m above ground). In total four image blocks 
with four different atmospheres (visibility 10 km, 20 km, 30 km, 
and 40 km) were tested in the same area. 
Figures 3 and 5 show the correction results for two different 
horizontal visibilities (10 km and 20 km) which is an empirical 
measure for the aerosol content. The uncorrected pseudo 
reflectance shows a blue hue due to Rayleigh scattering. The 
modified Song-Lu-Wesely method and the Angstrom method 
correct this phenomenon, the latter works slightly stronger. It 
can also be seen that a BRDF correction is still necessary to 
homogenize the image. 
Figures 4 and 6 show a grass target observed from two 
directions and two flying heights on two days with different 
visibilities. Already the pseudo reflectance shows a stable 
reflectance result. The modified Song-Lu-Wesely method and 
the Angstrom method correct the blue hue and give a more 
accurate value for the NIR reflectance. 
For an asphalt target (reflectance -0.15, not shown here) the 
results of pseudo reflectance, modified Song-Lu-Wesely 
method and the Angstrom method are also constant with flying 
height, visibility and flight direction. The discrepancy from the 
measured ground reflectance is at most 0.03. The blue hue is 
removed and the NIR value is unchanged. 
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