Juergen Oberst 
  
A first attempt was made to measure the stars' positions manually. This was accomplished using an appropriate tiepoint 
program which allowed us to make the line/sample measurements at sub-pixel level. Stars seen in the in images were 
correlated with known stars by comparison with charts and catalogs. 
Next, the star identifications and position measurements were made automatically. For this purpose, an image area mi 
having the size, for example, of i=20 x j=20 pixels around some "pilot" star was extracted and placed into a mask. 
Subsequently, the entire image was scanned for windows wij, to match this particular pattern. A star identification was 
considered to be acceptable, when the cross correlation coefficient c, given by the expression c = cp / Ve / Ver, 
exceeded a fixed value, e.g. 0.5, for a given window wjj of the image. cp, c], and cp were then computed by 
multiplication of corresponding DN values of the windows mij and wjj (from which the mean DN values for the 
respective windows was subtracted) and by summations over all lines and samples, i,j: 
co = à wij * mij (4a) 
€1 = mij * mij (4b) 
c2 = 2 Wij * wij (4c) 
The correlation coefficients c for each window position were stored in data arrays, in which the position of the star was 
determined by searching for local maxima. The coordinates of this maximum were determined with subpixel accuracy. 
From the right ascension and declination of the stars in the catalog, we computed the expected line/sample coordinates 
of these stars using the nominal pointing data available for each image. These were compared with the star positions 
from the automated star search. Normally, 50-80% of the stars in the chart, falling within the area of the respective 
image, were successfully correlated with stars in the images. 
In the following, the precise positions of the stars were compared with the catalog. A least-squares program was 
developed to determine the camera focal length and the precise pointing of the image in terms of boresight right 
ascension, declination, and twist on the basis of the identified stars. The nominal image pointing parameters were used 
as a first guess to start the iterations. The 1- o value of the residuals of the star positions after these fits are shown in 
Table 4. While 6 — 1.07 pixels, on average, for the manual fits (second column), this value is effectively reduced to 
G =0.75 for the automated matching (third column). The large o (^1) for some of the manual measurements is 
probably due to misidentifications of stars. When the identification of stars is correct, the accuracy of the 
measurements is typically on the same order as that of the automated matching. When distinct signatures of smeared 
stars are available, the automated matching is clearly superior to the manual measurements (see image starcl131, Fig. 
4). In cases of very heavy smear, however, in which star signatures overlap, the automated matching failed. 
5.2 Distortion Model 
The residuals were then examined for image distortion (see Fig. 6, left) and subjected to the laboratory distortion 
function (eqs. 1-3). The residuals are reduced from 6 = 0.79 to 6 = 0.617 (39.1%), a quite moderate improvement (Fig. 
6, right). Alternatively, the laboratory function (Table 3) was used to correct the raw line/sample star positions using 
equations (1-3); then the fitting was repeated. The residuals after the fit are reduced to an average of 6 = 0.47 pixels, 
with some images showing residuals of as small as 6 = 0.32 (Table 4, rightmost column). This indicates that the 
characteristic distortion pattern found during the calibration on the ground can still be identified in the in-flight images; 
but obviously; the random noise in the star position measurements is large for some of the images. The camera focal 
length was found to be: f = 685.24 +/- 0.29 mm (mean of all fits), a value which has a higher uncertainy and which is 
slightly smaller than the laboratory value of 686.55 +/- 0.05. Both focal lengths are clearly above the nominal value of 
677 mm. 
In the next step, an attempt was made to determine a new distortion model from the in-flight data to identify possible 
changes in the camera geometric properties after spacecraft launch. All residuals after the individual fits were 
combined and new polynomial coefficients was fitted, as was done for the laboratory images. The initial residuals with 
G — 0.791 were reduced to 6 = 0.525 after the fit. Thus, the laboratory model accounts for 56% of the scatter in the 
data. Although this new model seems to be a better fit than the laboratory model, tests suggest that the two sets of 
coefficients probably differ only because of the random errors in the data. Random errors in the line/sample position 
measurements are clearly larger than in the calibration images (6 = 0.354). 
  
226 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
Ta 
Im: 
Fil 
sta: 
sta: 
sta 
stai 
sta 
sta 
sta 
sta 
stai 
nav 
nav 
nav 
nav 
nav 
nav 
nav 
nav 
nav 
nav 
*%)