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Measurements

Assume we have a system that measures the total power $ P$ received at the output terminal and that input power is measured in temperature scale $ T$ (see eq. 2) with an unknown gain ($ K_{p}$ ) i.e. we have:

$\displaystyle P = K_{p} T$ (44)

Similarly, let's assume that the autocorrelations are on a power scale with a gain $ K_{c}$ , different from $ K_{p}$ , but the same for auto- and cross- correlations (this point is checked with measurement on a noise source, which is fully correlated for different antennas, so that autocorrelations match the crosscorrelation amplitudes). Then we have:

$\displaystyle \widetilde{A_{ij}} = K_p T_{ij}$ (45)

where $ T_{ij}$ is the source power at the input port.

In using the chopper wheel method, we place loads with known effective temperature in front of the receiver. For NOEMA, one uses a hot load made of absorber which is at the temperature of the receiver cabin and a cold load located inside the cryostat on the 15K stage ; regular observations are made on the sky:

$\displaystyle P_{hot}$ $\displaystyle =$ $\displaystyle K_p \left(T_{hot}+T_{rec}\right)$ (46)
$\displaystyle P_{cold}$ $\displaystyle =$ $\displaystyle K_p \left(T_{cold}+T_{rec}\right)$ (47)
$\displaystyle P_{sky}$ $\displaystyle =$ $\displaystyle K_p \left(T_{sky}+T_{spill}+T_{rec} + T_a \right)$ (48)
$\displaystyle C_{ii}$ $\displaystyle =$ $\displaystyle K_c \left(T_{sky}+T_{spill}+T_{rec} + T_a \right)$ (49)
$\displaystyle \vert C_{ij}\vert$ $\displaystyle =$ $\displaystyle K_c T_a$ (50)

The difference between the cross-correlation amplitudes $ \vert C_{ij}\vert$ and the autocorrelations $ C_{ii}$ is that the "noise" (i.e. $ T_{sky}+T_{spill}+T_{rec}$ ) is uncorrelated between different antennas and vanishes from the cross-products.


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