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### Applying the radiometer formula

Since we use the chopper wheel method for calibration, it is convenient to write the radiometer equation in units of , the `antenna temperature corrected for rear spillover losses and atmospheric attenuation'. The r.m.s. noise fluctuation is then:

• We call integration time (in seconds) the sum of the integration times ON the source and on the OFF position. This time does not take into account additional times due to telescope movement and data handling. For standard observations, the same amount of time is spent on the source and on a reference field (the raster mode can be different).

• B is the channel width (Hz) of an individual backend channel. Note that this is not the same as the channel spacing. The `channel' width should be taken at maximum equal to half the linewidth, or equal to 50 MHz, whichever is the smallest (weak lines broader than 50 MHz, in fact, are more difficult to detect than 50 MHz-wide lines).

• is the system temperature (K) (see below)

• For position- or beam- switched observations the factor K equals 2 and takes into account that half of is spent on the source itself and that a substraction ON-OFF will be made. For frequency switched observations K equals since all the time is spent on the source. The factor f is 1.15 for the autocorrelator, 1.0 for the filterbank (see above). The factor is due to losses in the dichroic mirror.

The system temperature (in the scale) is calculated by OBS via

``` with  the mean physical atmospheric temperature (see [2])
¯ , and

with 		 the zenith opacity in the signal sideband 		 ,

the airmass 		 ,

the sideband gain ratio (see Table 2)

the sky brightness temperature 		 ,

the mean physical atmospheric temperature (see [2])		 ,

the ambient temperature 		 , and

the receiver temperature (see Table 2) 		 .

```

Zenith opacities are strongly correlated with the most important atmospheric absorbant, water; the relevant parameter is the amount of precipitable water vapour (pwv --see [2],[3]). For 20% of the time during winter (summer) the pwv is below 2 mm (4 mm). The `average' pwv is below 4 mm during the winter regime and below 7 mm during the summer regime (see e.g. IRAM technical reports [2],[4]). Zenith opacities for typical winter and summer conditions are given in Table 3.

Table:   Zenith opacities for typical weather conditions at selected frequencies

Note that January and February are dedicated in principle to 0.8 mm and bolometer observations. Especially during this period the night-time opacities are better than the day-time opacities.

Table 4 gives examples of the rms noise after 10 minutes of total integration time (ON + OFF position). To calculate the system temperature some typical values were chosen: Elevation , gain ratio between 0.001 and 1 (depending on receiver and frequency), forward efficiency , cabin temperature K, mean atmospheric temperature = 250 K.

Table:   Examples of rms noise values after 10 minutes of integration (assuming )

Next: Application of the Up: Example of calculation Previous: Example of calculation

Robert Lucas
Thu Mar 9 12:14:01 MET 1995