A faint point source located in a region with strong and highly
structured cirrus background shall be
observed at 60
and 100. As a single chopped
observation with one or two reference positions does not allow a
reliable background determination mapping with the C100 array
is mandatory. At 100 the Airy disc nearly covers the whole
C100 array.
To get sufficient sky coverage for background subtraction a 4 x 5
raster with an oversampling factor of 2/3 in Z direction is chosen.
Thus, the separation of the raster points in Y direction is 92
and
in Z direction 69, respectively. Note that the map is measured in
one filter
first, and then repeated in the second filter. The sampling procedure is
illustrated in Fig. 17.
NUMBER OF RASTER LEGS: 5
OVERSAMPLING FACTOR: 2/3
NUMBER OF RASTER POINTS IN Y: 4
The estimated fluxes are:
at 60
:
EXPECTED SOURCE FLUX: 0.088 
UNCERTAINTY IN SOURCE FLUX: 0.2
MAXIMUM BACKGROUND FLUX: 15.6 
at 100:
EXPECTED SOURCE FLUX: 0.08
UNCERTAINTY IN SOURCE FLUX: 0.2
MAXIMUM BACKGROUND FLUX: 10.5
Calculation of the power incident on the detector for each wavelength range:
For each filter the constants C1 and 
are taken from
Tab. 10 and 4, respectively.
The resulting power on the detector is (Equ. 6):
at 60 
m : 
at 100 m : 
Calculation of the noise terms:
For each filter C2, C3 and 
are taken from Tab. 10
and 9, respectively. At 60m the noise terms are:
(see Equ. 9)
(see Equ. 11)
(see Equ. 12)
The total noise at 60 is (Equ. 8):
.
Similarly the total noise at 100 is:
.
With an integration time of 32 sec at each sky position the S/N ratio becomes:
at 60m : 
at 100m : 
For the integration time at each chopper position the integration time of 32 sec is divided by the repetition factor of 26, leading to an integration time of 1.2 sec per chopper position. The next higher integer is 2 sec.
The map is obtained with 20 individual spacecraft raster pointings. At each spacecraft pointing a total of 13 positions is measured with the chopper (cf. Tab. 11 and Fig. 17). With an integration time of 2 sec for each chopper position the total integration time for the complete map in two filters is 2 sec x 13 chopper steps x 20 spacecraft raster positions x 2 filters = 1040 sec.
The integration time of 2 sec at each chopper position is significantly shorter than the 32 sec recommended as a minimum value for staring observations. Since each celestial position in the inner part of the map is observed 26 times (cf. Tab. 12, coverage factor), and the length of the area sampled by one chopper sweep is comparable to the size of the Airy disc, in general no large flux differences should occur, and therefore no large drift effects should be expected. Since memory effects depend on the time spent on a bright source the quick sampling with the chopper minimises these memory effects.
The times needed for the spacecraft micro-slews between the individual
spacecraft raster positions are calculated with the formulae given
in the ISO Observer's Manual. For the slews of 69 in Z direction the
time required for one slew is 7 sec. As 5 positions have to be measured in
Z direction, 4 such slews are required. Thus, 4 x 7 sec = 28 sec are
necessary for these slews.
The time for one slew of 92 in Y direction is 8 sec.
Since 4 positions have to be measured, 3 slews
are necessary for each raster leg. 5 individual raster legs are
required for the map, leading to 8 sec x 3 x 5 = 120 sec total slewing
time in Y direction. The resulting total amount of time for
slewing to all the individual spacecraft raster positions is thus 148 sec.
For mapping in 2 filters this time has to be doubled since the whole
mapping is performed filter by filter. Before starting the observation
with the second
filter the spacecraft must slew back to the starting point of the map
which needs another 37 sec. Thus, the total slewing time
is 333 sec.
The following overheads have to be added:
time for target acquisition and slewing : 180 sec
time for initial instrument set-up : 15 sec
time for FCS exposures (2 for each filter): 64 sec
time for wheel positioning (2 wheels) : 20 sec
time for stabilization of heated detectors : 270 sec
time for spacecraft micro-slews (see above): 333 sec
The total observing time is: 1922sec.
