Correcting the Temperature Scale

The most important part of the data reduction is to ensure that the temperature scale of the observations is as accurate as possible. If the received antenna temperature is T$_{\rm A}$ then the aim is to correct this to yield the true temperature of the source T$_{\rm r}$. The first step is to correct for atmospheric absorption and the efficiency of the telescope. The telescope efficiency is a fixed parameter that takes into account things like the amount of radiation absorbed by the wind shield and how reflective the dish is. The sky correction varies with elevation since clearly signal from a source at the zenith will have to pass through less atmosphere than a source that is low on the horizon. If $\tau$ is the optical depth of the atmosphere at the zenith then at a lower elevation the absorption will be given by $e^{\tau M}$ where $M$ is the airmass (which will be unity at the zenith). Both of these corrections, generally denoted by $\eta_{\rm SKY}$ and $\eta_{\rm TEL}$, are applied automatically by the telescope software. The temperature scale after these corrections is referred to as T $^*_{\rm A}$.  

Another correction that needs to be made is to correct for scattering from the secondary support structure onto the telescope, this is the forward spillover and scattering efficiency, denoted by $\eta_{\rm fss}$and is around 0.7 to 0.8 depending on frequency for the JCMT. This correction yields the international accepted T $^*_{\rm r}$ scale which should be the same for all equivalent telescopes. The only remaining correction is due to the source-beam coupling efficiency, $\eta_{\rm c}$ which is a measure of the size of the source compared to the beam size. If the source is of comparable size or larger than the beam size then $\eta_{\rm c} \approx 1$ whereas if it is an unresolved point source $\eta_{\rm c} < 1$.

It is important to apply all these corrections to the telescope data as the simulated data produced by the modelling programs described later all assume a perfect telescope with no atmosphere.