163 
At = 
i 
1 
[arc sin C - y - W - 6Wt ] 
6W o i 
Next with the exact value of viewing time t^ 
for the point M^, it is possible to calculate 
the osculatory parameters (p,R,I,W,e x ,e y ) and 
the shuttle coordinates X and S'. 
Referring again to Figure 1, we can then write 
the following vector equation in a non-inertial 
(terrestrial) reference system: 
SMi = OMi - OS 
which is equivalent to the vector slant range that 
one can rewrite in terms of elements of Figure 3 
as follows: 
r= xi - fx(t ± ) - tiVe] 
Normalizing the vector s’, one obtains 
s = IIsit *u which gives the direction cosine of the 
line SM^. One can obtain a more accurate value 
of the scalar slant range directly from the image 
data, so that only the orientation u of the vector 
slant range need be kept from 3. By combining 
these two parts, image scalar(s) and vector(H), a 
refined value is obtained for Is: 
Snew = s TT 
Referring to Figure 1, note that the local 
incidence angle 0^ is the angle between the two 
lines M^S and OM-^. The coordinates for the 
three points S, Mj[ and 0 (intersection of the 
first normal and the Z axis) are known and allow 
one to compute the direction cosine (l,m,n) of 
each line. Thus, the local incidence angle 0 L 
is given by: 
cos©l = 1}I2 + m^n^ + n i n 2 
The advantage to use the image slant range module 
in the calculation of the new shuttle position at 
time t^ has been shown when comparing both slant 
range values as obtained from image and from orbit 
calculations. In fact, such a comparison has 
shown an average difference of 613 metres (based 
on a twenty point dataset). A second calculation 
on the same dataset but with a second initial 
shuttle position (modified with only one 
checkpoint for image slant range value), has shown 
the average difference reduced to approximately 50 
metres. This second approach has been finally 
preferred due to the consistency of both measures 
of slant range. 
2.2 Image resampling and filtering 
The rectification of raw SIR-B images into the 
intermediate level was achieved by using a 
polynomial fit between GCP locations obtained from 
raw image (but with a modified pixel location 
which excludes terrain parallax effect from the 
model) and those extracted from topographic maps. 
Using respectively 14 and 13 GCPs for the 29 and 
53 degree SIR-B dataset, a quadratic polynomial 
regression was found to best fit the 
transformation with few independent check points 
(see Table 1). The residuals obtained for each 
image and for both sets of GCPs (test and model 
points) were always less than 37.5 metres (1.5 
pixel) in either line or pixel direction. These 
results are in agreement with those published by 
Welch and Ehlers in 1985. 
Table 1. Quadratic polynomial fit residuals for 
SIR-B image rectification at the intermediate 
level. 
Incidence Residuals On Test On All Points 
Angle RMS (Pixel Points (Model & Test) 
Unit): (Total) (Total) 
29° 
Pixel 
1.49(5) 
1.44(19) 
Line 
1.28 
1.22 
53° 
Pixel 
1.30(3) 
1.28(16) 
Line 
1.44 
1.43 
The SIR-B images were then resampled into a 
rotated UTM intermediate grid defined also at 25 
metre pixel size. A 50 degree UTM rotation was 
applied in order to minimize the differences in 
geometry between the raw and the intermediate 
level products. Figure 4 shows both resampled 
images which cover an area 56.75 km long by 
15.125 km. These images have also been 
radiometrically corrected by applying a 3 by 3 
pixel window filter (Lee, 1981) in order to reduce 
the speckle effect (which was found to be 
necessary at the digital stereo matching level). 
Figure 4. SIR-B images (29° left, 53° right) 
processed at intermediate level.