10.2.3 Relative errors or errors on T_cal^L/T_cal^U

Following Eq.10.5, the side band ratio will be affected by the following term:

$$T = \frac{e^{(\Delta(\tau^L-\tau^U))}}{\sin (Elevation)}$$ (10.12)

where $\Delta(\tau^L-\tau^U)$ is the error on the sideband zenith opacity difference. This difference is maximum at frequencies corresponding to a wing of an atmospheric line, for example when observing around 115 GHz, near the O₂ line at 118 GHz. As example, taking the frequencies of 112 and 115 GHz for a source at 20^o in elevation and a zenith opacity difference $(\tau^L-\tau^U)=0.150$, an error of 0.030 on this difference (coming from $A_\nu$) will give an error of less than 1% on the gain G^UL. Moreover errors on Oxygen lines are very unlikely because the content in Oxygen in the atmosphere is relatively well known and only varying with the altitude of the site.

At the same frequencies, an error of 5mm (which would be enormous) on the water vapor content will only induce an error of 1% on the gain. Around such low frequency and for small frequency offsets, the water absorption is essentially achromatic. Improper calibration of the water vapor fluctuations will then result in even smaller errors since this is a random effect.