Seeing-limited Imaging Sky Surveys—Small versus Large Telescopes

Typically large telescope construction and operation costs scale up faster than their collecting area. This slows scientific progress, making it expensive and complicated to increase telescope size. We review the argument that a metric that represents the capability of an imaging survey telescopes, and that captures a wide range of science objectives, is the telescope grasp—the amount of volume of space in which a standard candle is detectable per unit time. We show that in a homogeneous Euclidean universe, and in the background-noise dominated limit, the grasp is: ${ \mathcal G }\propto {\rm{\Omega }}{A}_{\mathrm{eff}}^{3/4}{\sigma }^{-3/2}{t}_{{\rm{E}}}^{3/4}/({t}_{{\rm{E}}}+{t}_{{\rm{D}}})$ , where Ω is the telescope field of view, A_eff is the effective collecting area of the telescope, σ is the instrumental or atmospheric seeing or the pixel-size, whichever dominates, t_E is the exposure time, and t_D is the dead time. In this case, the optimal exposure time is three times the dead time. We also introduce a related metric we call the information-content grasp, which summarizes the variance of all sources observed by the telescope per unit time. We show that, in the background-noise dominated regime, the information-content grasp scales like the grasp. For seeing-dominated sky surveys, in terms of grasp, étendue, or collecting-area optimization, recent technological advancements make it more cost effective to construct multiple small telescopes rather than a single large telescope with a similar grasp or étendue. Among these key advancements are the availability of large-format back-side illuminated CMOS detectors with ≲4 μm pixels, well suited to sample standard seeing conditions given typical focal lengths of small fast telescopes. We also discuss the possible use of multiple small telescopes for spectroscopy and intensity interferometers. We argue that if all the obstacles to implementing cost-effective wide-field imaging and multi-object spectrographs using multiple small telescopes are removed, then the motivation to build new single large-aperture (≳1 m) visible-light telescopes which are seeing-dominated, will be weakened. These ideas have led to the concept of the, currently under construction, Large-Array Survey Telescope.