Comparative opto-mechanical assessment of various lightweighting patterns for a 352-mm aluminum alloy Ritchey–Chrétien telescope primary mirror

Résumé fourni par la source

Direct comparison of lightweight mirror architectures is complicated when designs differ in retained mass, obscuring the independent influence of topology on opto-mechanical performance. We present a rigorous comparative assessment of three lightweighting topology families—hexagonal honeycomb (HXH), radial spiderweb (RSW), and diamond hierarchical honeycomb (DHH) —evaluated under a strictly mass-matched design framework. Four geometric variants were developed for each topology, yielding 12 primary mirror configurations for a 352-mm aluminum alloy Ritchey–Chrétien telescope, all constrained to 4.195 kg ±1%, representing more than 59% mass reduction relative to the equivalent solid mirror (10.437 kg). Finite element analyses were performed under axial gravity, lateral gravity, and uniform polishing-pressure loading conditions, complemented by modal analysis. Optical performance was quantified using rigid-body-motion-corrected peak-to-valley and root mean square (RMS) surface errors, with residual deformation fields further characterized through Zernike polynomial decomposition into 36 Noll-indexed terms. The results demonstrate that lightweighting topology significantly governs structural, optical, and dynamic performance independently of mirror mass. The RSW topology achieved the highest global stiffness and dynamic stability, producing the lowest gravity-induced RMS surface error of 22.36 nm and the highest first natural frequency of 971.64 Hz. The HXH topology exhibited the lowest global stiffness, with gravity-induced RMS errors reaching up to 32.50 nm and fundamental frequencies as low as 844.69 Hz. The DHH topology demonstrated superior local face-sheet support, achieving the lowest maximum optical surface displacement under polishing-pressure loading. Zernike decomposition revealed distinct topology-dependent aberration signatures, with trefoil dominating under axial gravity loading and astigmatism under lateral gravity loading. These findings establish quantitative opto-mechanical trade-offs among the three topology families and confirm that mass-matched evaluation provides a rigorous framework for isolating topology-dependent performance in lightweight telescope mirror design.

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