Narrow angle astrometry

The aim of the PRIMA astrometry program is to accurately measure the angular separation of stars which have small angular separations. This is possible using an interferometer as the atmosphere applies similar perturbations to both stars when the angular separation is small. For example the first star (PS) could have a correlated flux $C_{PS}$ and atmospheric phase perturbation $\theta\left ( t \right )$ and the second star (SeS) a correlated flux $C_{SeS}$ and atmospheric phase perturbation $\theta\left ( t \right )+\Delta \theta\left ( t \right )$, giving atmospherically perturbed correlated fluxes of:

$$C_{PS}'\left ( t \right ) = C_{PS}A_{PS}\left ( t \right )\exp\left (i\theta\left ( t \right )\right )$$ (11)

$$C_{SeS}'\left ( t \right ) = C_{SeS}A_{SeS}\left ( t \right )\exp\left (i\left [\theta\left ( t \right )+\Delta \theta\left ( t \right )\right ]\right )$$ (12)

Note that $\Delta\theta\left ( t \right )$ fluctuates randomly with zero mean. If the variance over time of $\Delta\theta$, $\left < \left \vert\Delta\theta\left ( t \right )\right \vert^{2}\right >_{t} <1$ we are said to be in the isoplanatic regime (where the fringe differential phase is small). The mean difference in the phase of the correlated fluxes for the two stars is then related directly to the astrometric separation of the stars.

There are two general approaches to long baseline interferometry which I will call phase stabilised interferometery and non-phase stabilised interferometery.