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 √N reduced f-number can be achieved when combining N (similar) telescopes, each of diameter d_array, to synthesize an equivalent monolithic diameter D_mono=√N × d_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 vs. diameter relationship is assumed, in the form C∝Dⁿ, then data indicate that n=2.5±0.4. In addition, a more realistic multi-parametric dependence is assumed, including the f-number, in the form C∝(D³/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∝D^2.10±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.

(Upper panel): cost vs. telescope aperture scaling relationship for a few primary manufacturers in the European market, as labelled in the plot. The value of index "n" of the fitting power law (C∝Dⁿ) is reported in the legend.
(Lower panel): same, as derived from the Ackermann et al. (2015) compilation, mainly aimed at the US market.

An illustrative sketch of the sagittal depth and other reference parameters of eq. (13) to assess the geometry of the telescope primary mirror.

Cost vs. SD² scaling relationship for the few primary manufacturers taken as a reference, as labelled in the plot. The SD² parameter is a measure of the departure from the initial flat surface of the mirror blank, to be accounted along the optical manufacturing process, according to the targeted f-number of the telescope. The value of index "m", according to eq. (16), is reported in the legend.