Partial Beam Coverage

This scheme has been implemented on Plateau de Bure, where the dynamic range of the detectors is relatively small (only 2 between optimum sensitivity and saturation). The only change from the standard equations presented before is the introduction of the “beam filling factor” or “calibration efficiency” $C_{eff}$ in the output on the chopper (from Eq. (1-2))

  $$Mean\_load / K = Trec + C_{eff} * T_{load} + (1-C_{eff}) * T_{emi}$$ (17)

Algebra similar to that already exposed yields

  $$Tcal = C_{eff} * \frac{(T_{load} - T_{emi}) * (1. + Gain\_i)} {B_s * e^{-Tau\_s * Air\_mass}}$$ (18)

just correcting $Tcal$ by an additional $C_{eff}$ scaling factor.

In TREC mode, the sky emission is derived by

  $$T_{emi} = \frac{(T_{load} + Trec) * Mean\_atm * C_{eff}} {Mean\_load - (1-C_{eff})*Mean\_atm} - Trec$$ (19)

and in AUTO mode, the receiver temperature may be derived by

  $$Trec = \frac{C_{eff} * Mean\_atm * T_{load} - (Mean\_load - (1-C_{eff}) * Mean\_atm) * T\_emi}{Mean\_load - Mean\_atm}$$ (20)