Worked Examples

  PHT03

A point source, which was only marginally detected by IRAS, shall be studied in the four bands at 11.5, 25, 60 and 100m. The largest aperture, 180, is selected such that no flux is cut off at the longest wavelength (diffraction). The background level at the source position is comparable to the expected source flux, so rectangular chopping observations are chosen. Due to the aperture size selected the chopper throw has to be 180. Since there is no other source close to the target no avoidance region is specified.

The fluxes at 25, 60 and 100 m are extrapolated from the IRAS fluxes and the spectral information of the target at other wavelengths. Since it is an extrapolation, the uncertainties rise with wavelength. The estimates for the maximum background fluxes are derived from the IRAS sky flux maps.

The aim of this observation is the detection of the target in the IRAS bands, with a S/N ratio of 5 or better. Therefore, short integration times of are selected.

The estimated fluxes are:

at 11.5 m:
EXPECTED SOURCE FLUX : 2.53
UNCERTAINTY IN SOURCE FLUX : 0.5
MAXIMUM BACKGROUND FLUX : 21.34
at 25m:
EXPECTED SOURCE FLUX : 0.63
UNCERTAINTY IN SOURCE FLUX : 0.5
MAXIMUM BACKGROUND FLUX : 47.72
at 60 m:
EXPECTED SOURCE FLUX : 0.1
UNCERTAINTY IN SOURCE FLUX : 0.7
MAXIMUM BACKGROUND FLUX : 13.34
at 100 m:
EXPECTED SOURCE FLUX : 0.04
UNCERTAINTY IN SOURCE FLUX : 0.4
MAXIMUM BACKGROUND FLUX : 8.0

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 2, respectively. The resulting power on the detector is (Eq. 6):

at 11.5 m :
at 25m :
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 11.5 m:
(see Equ. 9)
(see Equ. 11)
(see Equ. 12)

Then the total noise is (see Equ. 8):

Similarly the total noise for the other filters is:

at 25m :
at 60m :
at 100m :

With an on-source integration time of 32 sec the S/N values for each filter are:

at 11.5m :
at 25m :
at 60m :
at 100m :

Since the observation is chopped, for each filter 32 sec will be spent on-source and the same amount of time on the off-source position. The exposure time per filter is thus 64 sec, and for all 4 filters it is 256 sec.

The following overheads have to be added for this observation:

time for target acquisition and slewing : 180 sec
time for instrument set-up : 15 sec
time for FCS exposures (3 detectors) : 48 sec
time for wheel positioning (4 filters + 1 aperture): 50 sec
time for stabilization of heated detectors (1 detector): 90 sec

Note that the overhead for heating stabilization is only added once since the non-heated P1 detector is used, and the heating of P2 is performed during the measurements with P1. The P1 measurements comprise the exposure time in the 11.5 filter (64 sec), the instrument set-up (15 sec), one FCS exposure (16 sec), and the positioning of 1 filter and 1 aperture (20 sec). The sum of 115 sec completely covers the 90 sec heating stabilization time of P2 (cf. Sect. 6.3).

The total observing time is approximately 639 sec.

PHT05

The absolute sky surface brightness level at 60 m shall be measured towards a single position in the galactic plane. Therefore, PHT05 is used with an aperture of 99.

The fluxes are:

EXPECTED SOURCE FLUX : 40.0
UNCERTAINTY IN SOURCE FLUX : 4.0
MAXIMUM BACKGROUND FLUX : 0.0

For this observation a MAXIMUM BACKGROUND FLUX has not been specified since the background itself is the target of the observation. The Zodiacal Light contribution is contained in the EXPECTED SOURCE FLUX.

The power on the detector and the noise terms are calculated similar to the example for PHT03, but here for the 99 aperture and an extended source. Since the aim is to measure the background level very accurately, a S/N ratio of more than 100 should be achieved.

The total noise is dominated by the photon noise of the source:

For the integration time Eq. 7 yields less than a second. However, for reasons mentioned in Section 2.8 concerning detector drifts the minimum of 32 sec integration should be used, in particular since the accuracy of the flux level has to be rather high. With 32 sec the S/N ratio is:

.

Since the same amount of time is also spent measuring the flux level of the FCS the exposure time is 64 sec. Furthermore, the following overheads have to be added:

time for target acquisition and slewing : 180 sec
time for instrument set-up : 15 sec
time for wheel positioning (1 filter + 1 aperture): 20 sec
time for stabilization of heated detectors : 90 sec

The total observing time for this observation is approximately 369 sec.