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Tolerancing the fabrication errors of static optical elements for ELT-size wide-field AO systems

Advanced wide-field AO systems, such as Multi-Conjugate AO (MCAO) systems often require many static optical elements (mirror and lenses) in addition to the active ones (deformable mirrors). These static elements induce additional wave-front errors due to random fabrication errors such as polishing errors. For ELT-size AO systems, these optical elements can be very large, and thus their cost and availability critically depends on how of much fabrication error can be tolerated. Therefore, a rigorous tolerance analysis is absolutely critical. Requirements can, in principle be relaxed, on account that fabrication errors with spatial scales larger than the inter-actuator spacing of the deformable mirrors (DMs) can be corrected. However, this process is significantly complicated by the fact that these optical elements are often conjugated far away from the DMs, and therefore DM correction cannot be achieved over a wide field of view (FOV). In this paper, we present our tolerance analysis in the context of NFIRAOS, the first-light MCAO system for the Thirty Meter Telescope. We start from two top-level error budgets: the “on-axis” error budget, which specifies the acceptable residual wave-front error in the narrow 17”x17” science FOV; and the “off-axis” error budget, which specifies the acceptable residual wave-front error at the edge of the 2’ diameter technical FOV. The former directly relates to science image quality, whereas the latter directly relates to sky coverage. For different assumptions on the spatial power spectrum of the polishing errors, we derive the requirements on each optical element in NFIRAOS using a Monte-Carlo analysis of the predicted off-axis performance of the system with on axis AO correction.