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The fundamental developmental issue facing the next generation of X-ray astronomical telescopes is the manufacturability, assembly, and structural robustness of the grazing incidence optics. Combining the high angular resolution requirements with large effective areas and physical launch vehicle restrictions leads to very thin shelled optics that must remain very stable. Meeting these stability requirements while also surviving launch and space environments presents a significant engineering challenge. Over the last few years, the Next Generation X-ray Optics (NGXO) team at NASA Goddard has been developing thin segmented silicon optics that are assembled into both modules and meta-shells, which show great promise in meeting these challenges. This paper summarizes the analytical approaches, as well as the environmental tests, used to assess such assemblies. Many parameters in the design space of the assembly have been assessed and optimized using Finite Element (FE) models and ray trace algorithms. The results of these analyses have helped shape reasonable and justifiable error budgets, as well as guide the team's decision making in both near and long term processes. The structural integrity of an assembly has been assessed both with testing and FE models. Preliminary strength testing has been conducted on the basic components used in the assembly.

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in highenergy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton.The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

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