Monitoring the atmospheric emission

The radiation temperature ¹ of the atmosphere $T_{\rm EM}$ is determined by using the usual ``chopper wheel'' calibration technique: one compares the emission of the atmosphere, to both an ambient load of radiation temperature $T_{\rm CHOP}$ (the absorbing table that is switched in to the beam), and a cold load of radiation temperature $T_{\rm COLD}$ (an absorber in the receiver dewars towards which the beam is redirected by switching in a corner mirror).

The three measurements give ($T_{\rm AMB}$ is the temperature in the receiver cabin and $\eta_{\rm F}$ the forward efficiency):

$$\mbox{$C_{\rm SKY}$}= K (\mbox{$T_{\rm R}$}+ (1-\mbox{$\eta_{... ...\mbox{$T_{\rm AMB}$}+\mbox{$\eta_{\rm F}$}\mbox{$T_{\rm EM}$})$$

$$\mbox{$C_{\rm CHOP}$}= K (\mbox{$T_{\rm R}$}+ \mbox{$T_{\rm CHOP}$})$$

$$\mbox{$C_{\rm COLD}$}= K (\mbox{$T_{\rm R}$}+ \mbox{$T_{\rm COLD}$})$$

These measurements are combined to give $T_{\rm R}$ and $T_{\rm EM}$. Actually $T_{\rm R}$ is quite stable and we can avoid too frequent cold load measurements by assuming $T_{\rm R}$ constant.

The system noise of the atmospheric monitor is given by:

$$\mbox{$T_{\rm SYS}$}= \frac{\mbox{$T_{\rm R}$}+ (1 - \mbox{$... ...eta_{\rm F}$}}+\mbox{$T_{\rm EM}$}= \mbox{$T_{\rm LOSS}$}+ tem$$

Note that this is different from the usual formula for the system temperature, since our reference plane is below the atmosphere, not above.

Thus a variation $\Delta \mbox{$T_{\rm EM}$}$ of atmospheric emission leads to a variation $\Delta P$ of the total power $P$, given by:

$$\Delta P/P = (\Delta \mbox{$T_{\rm EM}$}+ \Delta\mbox{$T_{\rm LOSS}$})/ \mbox{$T_{\rm SYS}$}$$

where we allowed for a change in $T_{\rm LOSS}$ due to a variety of possible causes: variations in receiver noise, ambient temperature, forward efficiency (or ground noise).