Typically, a pinhole in the focal plane of a large aperture and 
long focal length collimator served as an artificial star. The 
star intensity and its spectral distribution was adjustable by 
appropriate filters in the illumination optics. The emerging 
light from the collimator is a plane wavefront illuminating 
in parallel all entrance apertures of the MOMS-2P optics 
module. Each lens forms an image of the artificial star on 
the CCD-arrays in the corresponding focal planes. By direct 
read-out of the CCD-response using the nominal signal pro- 
cessing electronics, an end-to-end performance of the system 
is obtained. Therefore, this approach takes into account all 
possible sources of deterioration in the entire chain, namely 
the residual aberrations of the optics, the focus and align- 
ment condition, the detector response and detector internal 
cross-talk, and finally the quantization and noise effects of the 
signal processing electronics. The principle test setup which 
is used for all subsequent measurements is given in Figure 3. 
  
   
  
  
  
  
Turn Table 8 
P un 
/ \ [Ea TEUER 3 a. AR em 
x 2 se 1 \ -— i 
f S \ RNIT \ Illumination 
/ E SL Cassegrain \ Optics 
/ 2 Stereo 2 | [QR Collimator | 
| m — \ N e Ba 
| 3 IMS ] ——R— M—Ó—Ó 
| = | E al 
w | Ó— | 
| = MSI] | Tete = 
119 | (artifical star, ete) 
LEES —_— 
esti? Collimator Support m 
Turn Table o 
| | 
Optical Bench | 
i lm te i 
  
ee EA 
Figure 3: Principle test setup for calibration of MOMS-2P 
optics module 
Geometrical Alignment And Calibration: The geometri- 
cal correlation is obtained by measuring the gravity center of 
the star image intensity distribution in relation to a precisely 
known angle in the object space of the sensor. Assuming a 
distortion free optics (which has been ensured by the theoret- 
ical design and high precision manufacturing and assembling 
at the manufacturer), the relation between a position z, y at 
the CCD and the corresponding object angles a, 3 is: 
tan(a) = T and  tan(8) — A (1) 
with: 
FL = Focal Length of the system, including detector 
z,y = Coordinates at detector 
a,f = Angles in object space 
Thus, if the optics module is stimulated at a certain angle 
o, B, the deviation of the measured spot image gravity cen- 
ter from the nominal position z, y can be obtained. Inversely, 
if a large number of data pairs x, y vs. «, is measured, an 
average value for the system focal length FL can be deduced, 
which is listed in Table 1 for each channel. FL shall be iden- 
tical for all channels respectively in a defined relationship to 
each other (i.e. relation 1:3 between the nadir high resolution 
(HR) stereo channel and the other channels). 
For the geometric measurements, the gravity center of the 
star image has been centered on about 15 pixels per CCD- 
array in an approximate 400 pixel interval. For these pix- 
els the z,y, a, 3 data set has been recorded. To increase 
92 
the measurement accuracy and to eliminate systematic er- 
rors caused by the turn table axis geometry, four data sets 
per CCD-array have been recorded. Data sets 1 and 3 were 
measured in normal position, data sets 2 and 4 in reverse 
position, i.e. MOMS-2P is rotated 180° around both the hor- 
izontal and the vertical turn table axis. The mean value of the 
measure in normal and reverse position is free of systematic 
errors, e.g. the deviation of horizontal and vertical turn table 
axis from 90° (see section 2.3). Thus, the geometry of each 
CCD-array is defined by 15 data points times 4 data sets = 
60 data points. This “raw” data set has been further refined 
by interpolation into a finer equidistantly spaced interval of 
200 pixels per sensor. Special precautions on the selection 
of the appropriate interpolation algorithm were necessary to 
preserve the shape of the data set and to avoid “overshoot- 
ing" effects at the upper and lower limits of the sensor. After 
several tests, the Akima interpolation turned out to be the 
optimum without deteriorating the raw data by more than 
0.1 pixel. Note: The interpolation can be avoided by directly 
measuring a 200 pixel interval. However, the measurement 
of a single pixel to the desired sub-pixel accuracy is a time 
consuming process involving many iteration steps in the turn 
table control. Although the measurement process was au- 
tomated by computer, a single CCD-array measurement (15 
data points) lasted several hours. Thus, simply to achieve an 
economic calibration procedure, the 400 pixel interval with 
subsequent interpolation was decided. 
2.2 Calibration Equipment 
In order to fulfill the alignment and calibration task, the on- 
ground equipment has been specifically designed with the fol- 
lowing performance figures: 
Collimator The collimator is an on-axis "Cassegrain" tele- 
scope inversely used. It provides a usable aperture of 650 mm 
to illuminate all lenses simultaneously. The focal length is 
7.8 m which allows relatively large dimensions for the object 
structures (pinhole diameter) and thus, reduces tolerances. 
The wavefront quality over the full aperture is better A/8 
peak to valley. Taking into account that each lens of the 
MOMS-2P optics module uses only a small fraction of the 
full aperture, the residual measurement error introduced by 
the collimator is < * of a pixel which is negligible compared 
to other error sources in the test setup. 
A crucial point is the perfect collimation (i.e. the artificial 
star is virtually at infinity), since it determines then the final 
resolution (modulation transfer function, MTF) of the over- 
all system. The "infinity" condition of the test equipment 
is referred to a precision flat of same size as the collima- 
tor aperture and two independent focusing principles ( "Knife 
Edge" test and Point Spread Function PSF in autocollima- 
tion). This approach has been selected to avoid systematic 
errors (Hubble effect!). 
Angular Reference (Two-Axis Turn Table) The angular 
reference to obtain the object angles o, is provided by a 
high precision two-axis turn table with precision encoders 
(Heidenhain ROD 800). The minimum resolvable angle is 
0.36", accounting to 1/7 pixel measurement error of the HR 
CCD-array. This is probably the worst figure in the overall 
error budget, but it must be noted that this encoder accuracy 
was the best available on the market at the time of the design 
of the instrument and the test facilities. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996 
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