Phase-stabilised operation of PRIMA

Measurements of the atmospherically induced phase perturbations can be made on a bright star ( $\theta\left ( t \right )$ in Equations 12 and 14) and then the optical path length from the both stars can be physically adjusted (typically using movable mirrors) to remove the term $\theta\left ( t \right )$ from the phase perturbations from both stars. For star (SeS) we get:

$$C_{SeS}' = C_{SeS}\exp\left (i\Delta \theta\left ( t \right )\right )$$ (15)

In the isoplanatic regime, $\left < \left \vert\Delta\theta\left ( t \right )\right \vert^{2}\right >_{t} <1$ so the fringes on star (SeS) will remain stable to within $\sim1$ radian over long periods of time. This means that the fringe signal for star (SeS) can be integrated on the detector over many atmospheric coherence times. In practice the maximum integration time in the infrared is limited by detector saturation from the thermal background, but the S/N for fringe measurements on the faint star (SeS) will be a few times larger than for the non phase-stabilised case discussed in Section 2.2.3.

In this mode of operation, $C_{PS}'C_{SeS}'^{*}$ can be calculated in the same way as in Section 2.2.3, providing information about the angular separation of the stars. Note that the phase of $C_{PS}'C_{SeS}'^{*}$ (the astrometric phase) is only a useful parameter when the S/N ratio of $C_{PS}'C_{SeS}'^{*}$ is greater than unity, so that for faint (SeS) stars $C_{PS}'C_{SeS}'^{*}$ must be integrated as a complex number until the S/N ratio is greater than one before the astrometric phase is calculated. This has important implications for the software running the PRIMA FSUs.