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We present an estimate of the optical performance of the Thirty Meter Telescope (TMT) after execution of the full telescope alignment plan. The TMT alignment is performed by the Global Metrology System (GMS) and the Alignment and Phasing System (APS). The GMS first measures the locations of the telescope optics and instruments as a function of elevation angle. These initial measurements will be used to adjust the optics positions and build initial elevation look-up tables. Then the telescope is aligned using starlight as the input for the APS at multiple elevation angles. APS measurements are used to refine the telescope alignment to build elevation and temperature dependent look-up tables. Due to the number of degrees of freedom in the telescope (over 10,000), the ability of the primary mirror to correct aberrations on other optics, the tight optical performance requirements and the multiple instrument locations, it is challenging to develop, test and validate these alignment procedures. In this paper, we consider several GMS and APS operational scenarios. We apply the alignment procedures to the model-generated TMT, which consists of various quasi-static errors such as polishing errors, passive supports errors, thermal and gravity deformations and installation position errors. Using an integrated optical model and Monte-Carlo framework, we evaluate the TMT's aligned states using optical performance metrics at multiple instrument and field of view locations. The optical performance metrics include the Normalized Point Source Sensitivity (PSSN), RMS wavefront error before and after Adaptive Optics (AO) correction, pupil position change, and plate scale distortion.

We have developed an integrated optical model of the semi-static performance of the Thirty Meter Telescope. The model includes surface and rigid body errors of all telescope optics as well as a model of the Alignment and Phasing System Shack-Hartmann wavefront sensors and control algorithms. This integrated model allows for simulation of the correction of the telescope wavefront, including optical errors on the secondary and tertiary mirrors, using the primary mirror segment active degrees of freedom. This model provides the estimate of the predicted telescope performance for system engineering and error budget development. In this paper we present updated performance values for the TMT static optical errors in terms of Normalized Point Source Sensitivity and RMS wavefront error after Adaptive Optics correction. As an example of a system level trade, we present the results from an analysis optimizing the number of Shack-Hartmann lenslets per segment. We trade the number of lenslet rings over each primary mirror segment against the telescope performance metrics of PSSN and RMS wavefront error.

This paper provides an overview of the various image quality metrics used in astronomical imaging and explains in details a new metric, the Normalized Point Source Sensitivity. It is based on the Equivalent Noise Area concept, an extension of the EE80% metric and is intuitively linked to the required science integration time. As it was proved in recent studies, the PSSN metric properly accounts for image degradation due to the spatial frequency content of a given telescope aberration and the effects of various errors can be multiplicatively combined, like those expressed in Central Intensity Ratio. Extensions of the metric for off-axis imaging and throughput degradation are presented. Wavelength and spatial frequency dependence of PSSN are discussed. While the proper calculation of the PSSN metric requires the precise knowledge of the PSF of both the optics and atmosphere, there is a straightforward approximation linking PSSN to the Zernike decomposition of the OPD. Besides the summary of various aspects of the Point Source Sensitivity, the paper provides many numerical examples derived for the Thirty Meter Telescope.

We evaluate how well the performance of the Thirty Meter Telescope (TMT) can be maintained against thermally induced errors during a night of observation. We first demonstrate that using look-up-table style correction for TMT thermal errors is unlikely to meet the required optical performance specifications. Therefore, we primarily investigate the use of a Shack-Hartmann Wavefront Sensor (SH WFS) to sense and correct the low spatial frequency errors induced by the dynamic thermal environment. Given a basic SH WFS design, we position single or multiple sensors within the telescope field of view and assess telescope performance using the JPL optical ray tracing tool MACOS for wavefront simulation. Performance for each error source, wavefront sensing configuration, and control scheme is evaluated using wavefront error, plate scale, pupil motion, pointing error, and the Point Source Sensitivity (PSSN) as metrics. This study provides insight into optimizing the active optics control methodology for TMT in conjunction with the Alignment and Phasing System (APS) and primary mirror control system (M1CS).

We investigate a new metric, the normalized point source sensitivity (PSSN), for characterizing the seeing-limited performance of large telescopes. As the PSSN metric is directly related to the photometric error of background limited observations, it represents the efficiency loss in telescope observing time. The PSSN metric properly accounts for the optical consequences of wave front spatial frequency distributions due to different error sources, which differentiates from traditional metrics such as the 80% encircled energy diameter and the central intensity ratio. 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 error budget of the Thirty Meter Telescope (TMT) using a ray optics simulator. Additionally, we discuss other pertinent features of the PSSN, including its relations to Zernike aberration, RMS wave front error, and central intensity ratio.

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.

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.

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.

We have investigated two approximation methods for estimating the normalized point source sensitivity (PSSN), which is a recently developed optical performance metric for telescopes. One is an approximation based on the power spectral density (PSD) of the wavefront error. The other is the root-square-sum of the wavefront slope. We call these approximations β approximation and SlopeRMS approximation, respectively. Our analysis shows that for the Thirty Meter Telescope (TMT), the uncertainty of the β approximation is less than 1×10(-3) if the PSSN is better than 0.95, assuming the input PSD estimation is accurate. In addition, we find that the SlopeRMS approximation is a simple method for estimating the worst-case PSSN value in the specific situation when the PSSN is dominated by low-frequency aberrations. Therefore, the SlopeRMS approximation is expected to be useful for specifying a mirror surface for mirror vendors. Accordingly, TMT has a plan to adopt the SlopeRMS approximation for its M2 and M3 polishing specification.