Telescope arrays for wide-field sky surveys. A technical assessment and a cost model

ABSTRACT In this study we tackled a proxy approach to wide-field large monolithic telescopes in terms of composite assembly of smaller instruments. As a conveniently ‘fast’ f-number is the ultimate parameter to efficiently carry out inspection of large portions of sky, we show that a telescope array can provide a cost-effective solution, as a factor of $\sqrt N $ reduced f-number can be achieved when combining N (similar) telescopes, each of diameter darray, to synthesize an equivalent monolithic diameter ${D}_{\rm{mono}} = \sqrt N {d}_{\rm {array}}$. A cost model is developed, in this regard, by comparing the COTS figures for telescopes up to a metric size as supplied by primary international manufacturers. If a standard cost versus diameter relationship is assumed, in the form C∝Dn, then data indicate that n = 2.5 ± 0.4. In addition, a more realistic multiparametric dependence is assumed, including the f-number, in the form $C \propto {( {{{{D}^3} {/ {\vphantom {{{D}^3} f}}} f}} )}^m$, with m = 0.70 ± 0.08. This eventually leads us to estimate that cost of the optical tube assembly (OTA) for commercial telescopes scales as C∝D2.10 ± 0.24f−0.70 ± 0.08. Even considering the supplementary addition of CCD/CMOS detectors for a telescope array, a general saving scheme confirms that any array solution with N ≥ 4 telescopes, each with a diameter in excess to 30–40 cm, could be a competitive alternative to a bigger monolithic instrument of metric class (or larger), mainly aimed at wide-field surveys.