The Locus Algorithm I: A technique for identifying optimised pointings for differential photometry

Studies of the photometric variability of astronomical sources from ground-based telescopes must overcome atmospheric extinction effects. Differential photometry by reference to an ensemble of reference stars which closely match the target in terms of magnitude and colour can mitigate these effects. This Paper describes the design, implementation and operation of a new algorithm, The Locus Algorithm; which enables optimised differential photometry. The Algorithm is intended to identify, for a given target and observational parameters, the Field of View (FoV) which includes the target and the maximum number of reference stars similar to the target. A collection of objects from a catalogue (e.g. SDSS) is filtered to identify candidate reference stars and determine a rating for each which quantifies its similarity to the target. The algorithm works by defining a locus of points around each candidate reference star, upon which the FoV can be centred and include the reference at the edge of the FoV. The Points of Intersection (PoI) between these loci are identified and a score for each PoI is calculated. The PoI with the highest score is output as the optimum pointing. The steps of the algorithm are precisely defined in this paper. The application of The Locus Algorithm to a sample target, SDSS1237680117417115655, from the Sloan Digital Sky Survey is described in detail. The algorithm has been defined here and implemented in software which is available online. The algorithm has also been used to generate catalogues of pointings to optimise Quasar variability studies and to generate catalogues of optimised pointings in the search for Exoplanets via the transit method.