Visibility Study in a Chief-Deputy Formation for CMB Polarization Missions

Scientific instruments on board satellites are becoming increasingly sensitive, making it imperative to submit these instruments to a thorough calibration. In-flight calibration could be largely improved by using an ancillary microsatellite flying in formation with the main satellite and emitting a well-defined and known reference signal. Due to the main satellite attitude motion, the calibration satellite and therefore, its calibration signal, will only enter the instrument FoV (Field of View) at certain instants. It is not intuitive how frequently and during how much time this will happen, or how this depends on the scan strategy. In the present work, the available time for calibration and its characteristics in terms of total, mean, and maximum duration are studied, deriving analytical expressions for these quantities. These expressions are validated numerically and allow us to assess the impact of different scan strategies and to evaluate the most suitable region to locate the calibration satellite. The focal plane of the instrument is also modelled to evaluate the calibration process at detector level, calculating the number of detectors viewed and the direction of the polarized signal that they received. For this last analysis, only numerical methods have been employed. The tools are finally used in a case study in order to show how they can be employed to test, evaluate, and optimize scanning strategies and relative positions. The tools presented in this work can be easily adapted to evaluate more generally the characteristics of the observation of each point in the sky for a given scan strategy and instrument FoV.