Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors

The requirements on station-keeping for constellations of free-flying collectors coupled as (future) imaging arrays in space for astrophysics applications are discussed. The typical knowledge precision required in the plane of the array depends on the angular size of the targets of interest; it is generally at a level of tens of centimeters for typical stellar targets, becoming of order centimeters only for the widest attainable fields of view. In the "piston" direction, perpendicular to the array, the typical knowledge precision required depends on the bandwidth of the signal, and is at a level of tens of wavelengths for narrow approx. 1% signal bands, becoming of order one wavelength only for the broadest bandwidths expected to be useful. The significance of this result is that, at this level of precision, it may be possible to provide the necessary knowledge of array geometry without the use of signal photons, thereby allowing observations of faint targets. "Closure-phase" imaging is a technique which has been very successfully applied to surmount instabilities owing to equipment and to the atmosphere, and which appears to be directly applicable to space imaging arrays where station-keeping drifts play the same role as (slow) atmospheric and equipment instabilities.