Scale effects in active optics of large segmented mirrors

This paper is concerned with the extrapolation of the active optics of current 10-m class telescopes (Keck, VLT) to the next generation of 30–40 m Extremely Large Telescopes (ELT), and future, even larger ones. It describes how the various factors affecting the structural response and the control–structure interaction are influenced by the size of the telescope. Using the scaling laws for the natural frequencies and the structural response on the one hand, and the control requirements on the other hand, the paper shows how orders of magnitude can be estimated without resorting to complicated analysis. One especially important aspect for larger telescopes is that the joint increase of the control bandwidth and the reduction of their resonance frequencies will make them substantially more sensitive to control–structure interaction than smaller ones.