7.2.4 Side band calibration

A millimeter-wave interferometer can be used to record separately the signal in both sidebands of the first LO (see Chapter 5). If the first mixer does not attenuate the image side band, then it is useful to average both side bands for increased continuum sensitivity, both for detecting weaker astronomical sources and increasing the SNR for calibration.

However the relative phases of the two sidebands can be arbitrary (particularly at Plateau de Bure where the IF frequency is variable since the LO2 changes in frequency in parallel with the LO1). This relative phase must be calibrated out. This it is done by measuring the phases of the upper and lower sidebands on the passband calibrator observation. These values can be used later to correct each side band phase to compensate for their phase difference.

During the passband calibration one calculates:

$$e^{i\phi_U} = \frac{\int{\ensuremath{\widetilde{V}} _{ij,USB}... ...rt\int{\ensuremath{\widetilde{V}} _{ij,USB}(\nu,t) d\nu}\vert}$$ (7.18)

and

$$e^{i\phi_L} = \frac{\int{\ensuremath{\widetilde{V}} _{ij,LSB}... ...rt\int{\ensuremath{\widetilde{V}} _{ij,LSB}(\nu,t) d\nu}\vert}$$ (7.19)

Then at any time the double side band visibility is:

$$\ensuremath{\widetilde{V}} _{ij,DSB}(\nu,t) = e^{-i\phi_U} \e... ...nu,t)+e^{-i\phi_L} \ensuremath{\widetilde{V}} _{ij,LSB}(\nu,t)$$ (7.20)

As a result the two terms on the right hand side have zero phase at the time of the pass band calibration and they keep the same phase during the whole observing session.

At observing time, offsets on the first and second LOs can be introduced so that both $\phi_U$ and $\phi_L$ are very close to zero when a project is done. This actually done at Plateau de Bure, at the same time when the side band gain ratio is measured (see Chapter 10).