10.2.2 Absolute errors on T_cal due to instrumental parameters

The equations above show that T_cal is also dependent of the instrumental parameters T_rec, $\eta_f$ and T_load. These parameters can also lead to errors on T_cal. Derivatives of the appropriate equations are given in the IRAM report ``Amplitude Calibration''. Applying these equations and taking T_atm=240 K, T_load=290 K and T_emi=50 K, the possible resulting errors are given in the table 10.1.

 

Table 10.1: Percentage error on amplitude scale introduced by erroneous input parameters.

Item	Tcab	Trec	$\eta_f$
Typical Error	2 K	10 K	0.01
Induced variation (in %)	0.7	0.3	1.3

 

As a consequence, the most critical parameter of the calibration is the Forward Efficiency $\eta_f$. This parameter is a function of frequency, because of optics surface accuracy, but also of the receiver illumination. If $\eta_f$ is underestimated, T_sky is underestimated and you may obtain anomalously low water vapor content, and vice-versa.

The sideband gain ratio G^UL is also a critical parameter. G^UL is not only a scaling factor (see Eq.10.5), but is also involved in the derivation of the atmospheric model since the contributions from the atmosphere in image and signal bands are considered. This effect is important only if the opacities in both bands are significantly different, as for the J=1-0 line of CO.

Eq.10.5 shows that as soon as the receivers are tuned in single side band ( G^UL<10^-2 or rejection >20dB), the effect on T_cal^L is insignificant. Errors can be significant when the tuning is double-side band with values of G^UL around $\sim 0.8-0.2$. For example, when the emissivity of the sky is the same in both bands ( T_sky^U=T_sky^L), the derivative of Eq.10.8 shows that an error of 0.1 on G^UL=0.5 leads to $\frac{\Delta T_{cal}}{T_{cal}}\simeq \frac{dG^{UL}}{1+G^{UL}} \sim 6.5\%$.

However, this problem is only relevant to single-dish observations and cannot happen in interferometry because as soon as three antennas are working, G^UL can be accurately measured (see Chapter 7). At Bure the accuracy on G^UL is better than about 1 % and the system is stable on scale of several hours.