Worked Example

In a point-like object which is surrounded by a compact nebula, the amount of radiation emitted by the dust and its radial distribution shall be measured at 20m.

The following series of one small and four large apertures is selected: 18, 23, 52, 79, and 120. The diffraction limited apperture at is the 18 one.

EXPECTED SOURCE FLUX : 245.0
EXTENDED COMPONENT : 5 % = 0.05
UNCERTAINTY IN SOURCE FLUX : 20.0
MAXIMUM BACKGROUND FLUX : 1.0

The flux from the extended component is:

.

The individual noise terms are calculated with Eqs. 18 to 22.

With the 18 aperture only the point-source is measured. Note that (see Tab. 2)

Representative of the larger apertures the NEPs are calculated only for the 120 aperture. Here .

and are derived from Eqs. 16 and 17, respectively:

An on-source integration time of 64sec per aperture setting is selected, yielding a S/N ratio for the central point-source between 2400 and 2800. The S/N ratio for the extended component is calculated with Equ. 15.

.

Since the central point-source is rather bright the observation is performed in staring mode. For background determination a second (preferantially concatenated) observation with this same AOT should be performed, which is not counted in the following observing time calculation. The observation for background determination should be performed before the on-source observation.

The total observing time is calculated as follows:

5 apertures 64 sec : 320 sec
time for target acquisition and slewing : 180 sec
time for instrument set-up : 15 sec
time for FCS exposure : 16 sec
time for wheel positioning (1 filter + 4 apertures): 50 sec
time for stabilization of heated detectors : 90 sec

This yields a total of 671sec for the multi-aperture measurement on the target. For the concatenated background observation 511sec have to be added (in the concatenated observation the target acquisition time is reduced from 180sec to 20sec; see ISO Observer's Manual).