Evaluating thus requires to determine both and .
Assuming the receiver temperature is known, the noise power received on the
sky is given by

(7) |

(8) |

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
signal band).

(9) |

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

(10) |