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We consider high-resolution optical modeling of the Thirty Meter Telescope for the purpose of error budget and instrumentation trades utilizing the Modeling and Analysis for Controlled Optical Systems tool. Using this ray-trace and diffraction model we have simulated the TMT optical errors related to multiple effects including segment alignment and phasing, segment surface figures, temperature, and gravity. We have then modeled the effects of each TMT optical error in terms of the Point Source Sensitivity (a multiplicative image plane metric) for a seeing limited case and an adaptive optics corrected case (for the NFIRAOS). This modeling provides the information necessary to rapidly conduct design trades with respect to the planned telescope instrumentation and to optimize the telescope error budget.

The primary mirror control system (M1CS) keeps the 492 segments of the Thirty Meter Telescope primary mirror aligned in the presence of disturbances. A global position control loop uses feedback from inter-segment edge sensors to three actuators behind each segment that control segment piston, tip and tilt. If soft force actuators are used (e.g. voice-coil), then in addition to the global position loop there will be a local servo loop to provide stiffness. While the M1 control system at Keck compensates only for slow disturbances such as gravity and thermal variations, the M1CS for TMT will need to provide some compensation for higher frequency wind disturbances in order to meet stringent error budget targets. An analysis of expected high-wavenumber wind forces on M1 suggests that a 1Hz control bandwidth is required for the global feedback of segment edge-sensorbased position information in order to minimize high spatial frequency segment response for both seeing-limited and adaptive optics performance. A much higher bandwidth is required from the local servo loop to provide adequate stiffness to wind or acoustic disturbances. A related paper presents the control designs for the local actuator servo loops. The disturbance rejection requirements would not be difficult to achieve for a single segment, but the structural coupling between segments mounted on a flexible mirror cell results in controlstructure interaction (CSI) that limits the achievable bandwidth. Using a combination of simplified modeling to build intuition and the full telescope finite element model for verification, we present designs and analysis for both the local servo loop and global loop demonstrating sufficient bandwidth and resulting wind-disturbance rejection despite the presence of CSI.

We investigate a new metric, Normalized Point Source Sensitivity (PSSN), for characterizing the seeing limited performance of the Thirty Meter Telescope. As the PSSN metric is directly related to the photometric error of background limited observations, it truly represents the efficiency loss in telescope observing time. The PSSN metric properly accounts for the optical consequences of wavefront spatial frequency distributions due to different error sources, which makes it superior to traditional metrics such as the 80% encircled energy diameter. We analytically show that multiplication of individual PSSN values due to individual errors is a good approximation for the total PSSN when various errors are considered simultaneously. We also numerically confirm this feature for Zernike aberrations, as well as for the numerous error sources considered in the TMT error budget using a ray optics simulator, Modeling and Analysis for Controlled Optical Systems. We also discuss other pertinent features of the PSSN including its relations to Zernike aberration and RMS wavefront error.

Modeling, Systems Engineering, and Project Management for Astronomy II, Orlando, FL, USA, Series: Proceedings of SPIE; no. 6271