Why Thirty Meters?
The diameter of the primary mirror (M1) is a key design choice – it drives the size and complexity of almost every other observatory system. From a science perspective, we know that the observations limited by atmospheric turbulence improve in sensitivity as diameter squared (D2). Furthermore, AO systems allow us to remove much of the effects of turbulence, achieve diffraction-limited imaging, and gain an improvement of D4. Hence, science gain motivates the largest diameter enabled by technology and cost.
Technologically, large M1 diameters are enabled by using the precision-controlled, segmented mirror techniques pioneered with great success by the W. M. Keck Observatory. The TMT M1 design team includes many of the key developers of the Keck system.
In principle, arbitrarily large mirrors are possible. However, our analysis of AO technology development over the next ten years with respect to our detailed science goals suggests that D = 30 meters occupies an attractive and achievable scientific “sweet spot” at near-infrared wavelengths.
Obviously, cost also limits M1 diameter – how does financial pressure affect choice of aperture size? Prior to the design of the Keck telescopes, ground-based optical-IR telescope costs scaled roughly as D2.7, reflecting the nearly volumetric dependence of observatory cost on aperture. The advent of thinner primary mirrors with shorter focal lengths, as in the Keck design, reduced this relationship to an estimated D2; i.e., varying as the area of the aperture. A detailed cost study of key TMT design parameters (aperture, segment count, segment size, segment thickness, and enclosure diameter) for several hundred estimated elements in TMT concluded that TMT costs should scale as approximately D1.15 relative to the Keck capital investment. Thus, we conclude that the TMT design represents an improved cost scaling and that the proposed 30 meter diameter of TMT represents a good value relative to the extraordinary science reach.