An Efficient Targeting Strategy for Multiobject Spectrograph Surveys: the Sloan Digital Sky Survey ``Tiling'' Algorithm

Large surveys using multiobject spectrographs require automated methods for deciding how to efficiently point observations and how to assign targets to each pointing. The Sloan Digital Sky Survey (SDSS) will observe around 10⁶ spectra from targets distributed over an area of about 10,000 deg², using a multiobject fiber spectrograph that can simultaneously observe 640 objects in a circular field of view (referred to as a ``tile'') 1.49d in radius. No two fibers can be placed closer than 55" during the same observation; multiple targets closer than this distance are said to ``collide.'' We present here a method of allocating fibers to desired targets given a set of tile centers that includes the effects of collisions and that is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering of the sky with equally spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally spaced distribution that provides more uniform completeness. For the SDSS sample, we can attain a sampling rate of greater than 92% for all targets, and greater than 99% for the set of targets that do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets). The methods used here may prove useful to those planning other large surveys.