The equations above show that Tcal is also dependent of the instrumental
parameters Trec, and Tload. These parameters can also lead to
errors on Tcal. Derivatives of the appropriate equations are given in the IRAM
report ``Amplitude Calibration''. Applying these equations and taking
Tatm=240 K,
Tload=290 K and
Temi=50 K, the possible resulting errors
are given in the table 10.1.
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As a consequence, the most critical parameter of the calibration is the Forward
Efficiency . This parameter is a function of frequency, because of optics
surface accuracy, but also of the receiver illumination. If
is
underestimated, Tsky is underestimated and you may obtain anomalously low water
vapor content, and vice-versa.
The sideband gain ratio GUL is also a critical parameter. GUL 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
(
GUL<10-2 or rejection >20dB), the effect on TcalL is insignificant.
Errors can be significant when the tuning is double-side band with values of
GUL around
. For example, when the emissivity of the sky is the
same in both bands (
TskyU=TskyL), the derivative of Eq.10.8 shows
that an error of 0.1 on
GUL=0.5 leads to
.
However, this problem is only relevant to single-dish observations and cannot happen in interferometry because as soon as three antennas are working, GUL can be accurately measured (see Chapter 7). At Bure the accuracy on GUL is better than about 1 % and the system is stable on scale of several hours.