5.3.1 Fringe rate method

One might choose to drop the phase rotation on the second LO and let the fringes drift at their natural fringe rates. These rates are opposed in sign for the USB and LSB, and they might be separated electronically. However the natural fringe rate sometimes goes to zero (when the angular distance between source and baseline direction is minimum or maximum), and at least in these cases the method would fail.

It would be more practical to offset the LO1 and LO2 phase rates $\dot{\ensuremath{\varphi_\mathrm{\scriptscriptstyle 1}} }$ and $\dot{\ensuremath{\varphi_\mathrm{\scriptscriptstyle 2}} }$ from their nominal values by the same amount . If the offsets have the same sign, they will compensate for the USB and offset the fringe rate by $2 \ensuremath{\omega_\mathrm{\scriptscriptstyle OFF}}$ in the LSB. If is large enough, the LSB signal will be cancelled. Note that offsetting $\dot{\ensuremath{\varphi_\mathrm{\scriptscriptstyle 1}} }$ by a fixed amount is equivalent to offsetting the LO1 frequency.

This is a simple method to reject the unwanted side band. Note that the associated noise is not rejected.