Evaluating thus requires to determine both and .
Assuming the receiver temperature is known, the noise power received on the
sky is given by
In case of a double side-band receiver and single side-band signal,
is a sum of the contribution of the two receiver bands weighted
by the sideband gain ratio (gain in the image band divided by gain in the
To determine the opacity , the trick is to model the atmospheric emission to derive the transmission. There is some hope that it can work (at least in reasonably good conditions) because the transmission is dominated by a few constituants, among which only the water vapor varies significantly with time. Hence, if the atmosphere can be modelled by a small number of layers, it is possible to derive the transmission from the emission. The atmospheric model used (ATM, J. Cernicharo) is derived from a ``Standard atmosphere'' and the knowledge of the Atmospheric pressure and outside Temperature (and the altitude of the site). Together with the season in the year, these parameters give a good approximation of the physical temperature of the absorbing layers. By a minimization routine, with the amount of precipitable water vapor in millimeters as variable, the best model fitting the measured is found. Then, for each band (signal and image), the total zenith opacities are computed by summing the opacities due to Oxygen and Water, with a small empirical correction factor for other minor constituents.
The zenith opacities are used together with the elevation (number of air
masses) to compute , the SSB scaling factor