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System temperature

We start by deriving the sky temperature with:

$\displaystyle T_{sky} = \left(T_{hot}+T_{rec}\right)\frac{P_{sky}}{P_{hot}}-T_{rec}-T_{spill}$ (52)

Estimating $ T_{spill}$ requires knowledge of the forward efficiency $ \eta_f$ . It is also used to compute the sky emission $ T_{emi}$ :

$\displaystyle T_{emi} = \frac{T_{sky}}{\eta_f}$ (53)

The water vapor content variable of an atmospheric model predicting sky brightness ( $ T_{emi,s}^{atm}$ and $ T_{emi,i}^{atm}$ ) and opacity ( $ \tau_{atm,s}$ and $ \tau_{atm,i}$ ) in the signal and image sideband is then varied in order to minimize the following quantity:

$\displaystyle T_{emi} - \frac{T_{emi,s}^{atm}+g_{im}T_{emi,i}^{atm}}{1+g_{im}}$ (54)

The system temperatures for the signal $ T_{sys,s}$ and image $ T_{sys,i}$ sidebands are then computed as follows:
$\displaystyle T_{sys,s} = \frac{e^{\tau_s}\left(T_{hot}-T_{sky}-T_{spill}\right)(1+g_{im})}{\eta_f}\frac{P_{sky}}{P_{hot}-P_{sky}}$     (55)
$\displaystyle T_{sys,i} = \frac{e^{\tau_i}\left(T_{hot}-T_{sky}-T_{spill}\right)(1+\frac{1}{g_{im}})}{\eta_f}\frac{P_{sky}}{P_{hot}-P_{sky}}$     (56)

where:

$\displaystyle T_{sky}+T_{spill} = (1-\eta_f) \left(\frac{T_{emi,s}^{atm}+g_{im}T_{emi,i}^{atm}}{1+g_{im}} \right)+\eta_f T_{ground}$ (57)


next up previous contents index
Next: Scaling of data Up: Atmosphere Previous: Receiver temperature   Contents   Index
Gildas manager 2022-01-17