) m 
5 
^bje) 
of plate 
300 
»rdinates of these 
»ints (sides and dia- 
l each length consi- 
luations. One set is 
onals. The measu - 
possible, the eli - 
>0) independently - 
Lis least squares ad- 
on each end of the 
of these pointings 
length measure - 
l a <j of + 0. 6 fx at 
ith this method ha - 
ve given results for the two grids which agree in the individual coordinates to better than 1. 0 
micron. Using the arithmetic means values of these individual calibrations, it is believed that 
the coordinates of the 25 points on each of the grids are determined with a sigma smaller than 
1 micron. Most of the comparators used in the satellite triangulation program have been cali 
brated using these grids. 
Based on extensive tests, the accuracy of the coordinate measuring process for a star 
image, using the arithmetic mean of 2 sets of 4 measurements each, is 1 1. 0 to - 1.5 [x (one 
sigma level), including identification (setting) and comparator errors. The mean error of unit 
weight, after adjustment, for a single camera orientation is presently t 2. 3 to 2. 7 [X . This dis 
crepancy between measurement accuracy and final results clearly indicates the need for some 
more sophistication in the mathematical model which simulates the process of exposing the pho 
tograph. If 150 star positions are measured, the error contributed by the orientation of a sin 
gle ray within the bundle ranges from a minimum of t 0. "3 at the center of the plate, to maxi 
mum 0. "5 at a point 6 cm from the center of the plate *. 
The standard deviation for a double setting of an individual satellite image is t 2 mi 
crons. It is justified to assume that the orbit of an artificial satellite during the short period 
of observation (at most 2 minutes), because of its dynamic characteristics, is a curve which 
is smoother in nature than can be reconstructed from the corresponding plate measurements. 
Consequently, a high-order polynominal (mostly 4th or 5th order) can be applied to smooth the 
random errors of the satellite imagery which result from the measuring process and the shim 
mer effect. Due to extremely high timing accuracy (± 40 micro seconds), the recording of indi 
vidual satellite images at equal intervals can be considered flawless. It is possible, therefore, 
as an independent operation, to smooth the x and the y coordinate measurements using a power 
series of time. The necessary least-squares fit is accomplished after the raw data (compara - 
tor measurements) are corrected for lens distortion, refraction and phase of illumination. This 
phase depends on the size and shape of the sunilluminated object and the relative geometry bet 
ween sun, satellite and photogrammetric tracking station. In the case of a spherical-shaped 
balloon, the significance of this correction is to refer the ultimately computed satellite direc 
tions to the center of the satellite, in order to provide, from all tracking stations, geometri 
cally consistent data for the spatial triangulation. There is a slight difference in the mathema 
tical formulation for this correction, depending on whether the surface of the satellite produces 
a moon or planet-like reflection, or whether the surface acts more like a mirror providing a 
high-light point as a source of reflection. 
During the least squares fit it is necessary to assign specific weights to the coordina 
tes of the individual satellite images in accordance with their location on the photograph. 
Numerous results from such curve fits have been obtained which show a typical stan 
dard deviation of + 3. 3 fx for a single satellite image (compare fig. 2). Making allowance for a 
standard deviation of t 2.0 ^ for the measurements of the jmage coordinates, a contribution of 
! 2. 5 , or, with f = 300 mm, about * 2 seconds of arc, results from the shimmer effect. This 
result is in agreement with independent quantitative studies of this phenomenon. 
Finally, a set of fictitious plate coordinates is computed using the coefficients of the 
least squares-fitted polynominal. This approach can be considered as a data compression pro 
cess whereby the coordinate measurements of 500 to 600 satellite images are combined into a 
single set of fictitious x, y coordinates. The instant of time used to compute these coordinates 
is chosen so that the fictitious satellite image is as close to the center of the photogram as pos 
sible. Perhaps the greatest significance is that this procedure allows us to synchronize the va 
rious tracking stations by applying small time correction to compensate for any asynchroniza - 
tion of the chopping shutter between different tracking cameras. In addition, this step makes it 
possible to correct for the difference in travel time of light signals from the satellite to diffe 
rent tracking station. 
* 
Compare diagram on precedent page 
- 47 -