Estimation of normalized point-source sensitivity of segment surface specifications for extremely large telescopes.

We present a method which estimates the normalized point-source sensitivity (PSSN) of a segmented telescope when only information from a single segment surface is known. The estimation principle is based on a statistical approach with an assumption that all segment surfaces have the same power spectral density (PSD) as the given segment surface. As presented in this paper, the PSSN based on this statistical approach represents a worst-case scenario among statistical random realizations of telescopes when all segment surfaces have the same PSD. Therefore, this method, which we call the vendor table, is expected to be useful for individual segment specification such as the segment polishing specification. The specification based on the vendor table can be directly related to a science metric such as PSSN and provides the mirror vendors significant flexibility by specifying a single overall PSSN value for them to meet. We build a vendor table for the Thirty Meter Telescope (TMT) and test it using multiple mirror samples from various mirror vendors to prove its practical utility. Accordingly, TMT has a plan to adopt this vendor table for its M1 segment final mirror polishing requirement.