Fibre assignment in next-generation wide-field spectrographs

We present an optimized algorithm for assigning fibres to targets in next-generation fibre-fed multi-object spectrographs. The method, which we have called the draining algorithm, ensures that the maximum number of targets in a given target field is observed in the first few tiles. Using randomly distributed targets and mock galaxy catalogues, we have estimated that the gain provided by the draining algorithm, compared to a random assignment, can be as much as 2 per cent for the first tiles. For a survey such as the Baryon Oscillation Spectroscopic Survey (BigBOSS), this would imply saving for observation several hundred thousand objects or, alternatively, reducing the covered area in ∼350 deg2. An important advantage of this method is that the fibre collision problem can be solved easily and in an optimal way. We also discuss the additional optimizations of the fibre-positioning process. In particular, we show that if we allow for the rotation of the focal plane, we can improve the efficiency of the process by ∼3.5–4.5 per cent, even if only small adjustments are permitted (up to 2°). For instruments that allow large rotations of the focal plane, the expected gain increases to ∼5–6 per cent. Therefore, these results strongly support the use of focal plane rotation in future spectrographs, as far as the efficiency of the fibre-positioning process is concerned. Finally, we discuss the implications of our optimizations and provide some basic hints for an optimal survey strategy, based on the number of targets per positioner.