Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation

Starting from the successful Keck telescope design, we construct and analyze the control matrix for the active control system of the primary mirror of a generalized segmented-mirror telescope, with up to 1000 segments and including an alternative sensor geometry to the one used at Keck. In particular we examine the noise propagation of the matrix and its consequences for both seeing-limited and diffraction-limited observations. The associated problem of optical alignment of such a primary mirror is also analyzed in terms of the distinct but related matrices that govern this latter problem.