10.2 Single-dish Calibration of the Amplitude

This calibration is done automatically and in real-time but it can be redone a posteriori if one or several parameters are wrong using the CLIC command ATMOSPHERE. However, for 99 % of the projects, the single-dish calibration is correct. Moreover, we will see in this section that in most cases, even with erroneous calibration parameters, it is almost impossible to do an error larger than $\sim 5\%$.

For details about the properties of the atmosphere, the reader has to refer to the lecture by M.Bremer (Chapter 9) while the transmission of the atmosphere at mm wavelengths is described in the lecture of M.Guélin (Chapter 8). Most of this lecture is extracted from the documentation ``Amplitude Calibration'' by S.Guilloteau for single-dish telescope and from [Guilloteau et al 1993].

Since all this part of the calibration is purely antenna dependent and in order to simplify the equations, the subscript _i will be systematically ignored. In the same spirit, the equations will be expressed in T_A^* scale taking $\eta_f = \eta_B$.

The atmospheric absorption (e.g. for the Lower side-band T_cal^L) can be expressed by

$$T_{cal}^L = \frac{(T_{load}(1+G^{UL})-T_{emi}^L-G^{UL}T_{emi}^U)} {e^{-\tau^L/\sin(Elevation)}}$$ (10.5)

where T_load is the hot load and T_emi^L and T_emi^U are the noise temperature received from the sky in the lower an upper sidebands respectively (for the IRAM interferometer, the difference in frequency between the upper and lower sidebands is $\sim3$ GHz).

The system temperature T_sys is given by:

$$T_{sys}^L = T_{cal}^L\times \frac{M_{atm}}{M_{load}-M_{cold}}$$ (10.6)

The main goal of the single-dish calibration is to measure T_cal (hence T_sys) as accurately as possible.

At Bure, during an atmospheric calibration, the measured quantities are:

• Phase 1, M_atm: the power received from the sky
• Phase 2, M_load: the power received from the hot load
• (Phase 3), M_cold: the power received from the cold load

T_rec, the noise temperature of the receiver, is deduced from the measurements on the hot and cold loads at the beginning of each project and regularly checked. The receiver sideband ratio G^UL is also measured at the beginning of each project (see R.Lucas lecture 7). T_emi, the effective temperature seen by the antenna, is given by

$$T_{emi} =\frac{(T_{load}+T_{rec})*M_{atm}}{M_{load}}-T_{rec}$$ (10.7)

Moreover, T_emi which is measured on the bandwidth of the receiver, can be expressed as the sum of T_emi^L and T_emi^U (a similar expression exists for T_sky):

$$T_{emi}= \frac{T_{emi}^L+T_{emi}^U*G^{UL}}{1+G^{UL}}$$ (10.8)

T_emi is directly linked to the sky temperature emissivity (or brightness temperature) T_sky by:

$$T_{sky} = \frac{T_{emi}- (1-\eta_f)\times T_{cab}}{\eta_f}$$ (10.9)

were T_cab is the physical temperature inside the cabin and $\eta_f$, the forward efficiency, which are both known (or measurable) quantities.

Our calibration system provides then a direct measurement of T_emi and hence of T_sky, which is deduced from quantities accurately measured. Hence, in Eq.10.5 the only unknown parameter remains $\tau^L$, the opacity of the atmosphere at zenith, which is iteratively computed together with T_atm the physical atmospheric temperature of the absorbing layers. This calculation is performed by the atmospheric transmission model ATM (see Chapter 8) and the documentation ``Amplitude Calibration'').

The opacity $\tau^L$ (or more generally $\tau_\nu$) comes from two terms:

$$\tau_\nu = A_\nu + B_\nu \times w$$ (10.10)

$A_\nu$ and $B_\nu$ are the respective contributions to O₂ and H₂O, the water vapor content w is then adjusted with T_atm by the model ATM to match the measured T_sky. The ATM model works as long as the hypothesis done on the structure of the atmosphere in plane-parallel layers is justified, as it is usually the case for standard weather conditions.