Basic Equations

The CALIBRATION procedure goal is to convert backend counts into intrinsic surface brightness or flux density of the source. This conversion can be divided formally in two steps: correction for individual backend channel gains and receiver bandpass, and correction for atmospheric absorption and antenna gain.

Apart from putting the telescope into orbit, there is hardly any hardware fix which may help overcome the atmospheric absorption perfectly. Hence, the correction of atmospheric effects is difficult. The goal is to estimate properly the noise contribution from the atmosphere and the atmospheric transmission. OBS uses the standard chopper wheel technique to calibrate the backends and receiver gains.

This technique assumes the detector (receiver + IF cables + backend) is linear. Thus the detector counts, $Mean\_*$, are related to ``effective temperatures'' by

$$Mean\_load / K = Trec + T_{load}$$ (1)

when looking at any given load at a known (effective) temperature T_load. Trec is the receiver noise temperature. On the sky,

$$Mean\_atm / K = Trec + T_{emi}$$ (2)

When looking at source of brightness T_B, one obtains

$$Mean\_source / K = Trec + T_{emi} + B_s * e^{-\tau} * T_B$$ (3)

where B_S is the appropriate antenna to source coupling factor, $\tau$ the atmospheric optical depth. Thus T_B can be derived from the counts introducing the ``calibration temperature'' Tcal with

$$T_B = Tcal * \frac {(Mean\_source-Mean\_atm)}{(Mean\_load-Mean\_atm)}$$ (4)

and, in this simple case, Tcal would be given by

$$Tcal = (T_{load} - T_{emi}) \frac {e^{\tau}}{B_s}$$ (5)

The basic equations presented above assume a pure single-sideband reception (or pure double-sideband on a continuum source). The system noise temperature is given by

$$Tsys = \frac{Tcal * Mean\_atm}{Mean\_load - Mean\_atm}$$ (6)