This paper presents the design and optimization of a composite flexible support structure aimed at addressing the challenges associated with maintaining the positional accuracy and surface integrity of large-aperture cryogenic infrared lenses with long focal lengths. The primary objective of the structure is to maintain precise lens alignment while preserving the surface shape under operational conditions. The design complexities and underlying principles of the flexible support structure are systematically explored. A mechanical model of the flexible support structure was derived based on its structural characteristics, and the equilibrium equation was established to ensure the lens meets thermal deformation requirements in various directions. Optimization of key design parameters was conducted for a lens operating at 200 K, measuring 304 mm × 230 mm. The gravitational deformation of the optimized lens exhibited a root mean square (RMS) surface accuracy of 7.72 nm in the X direction, 7.08 nm in the Y direction, and 9.60 nm in the Z direction for lens surface 1. For lens surface 2, RMS values were 8.62 nm in the X direction, 8.41 nm in the Y direction, and 9.64 nm in the Z direction. At 200 K and lower temperatures, the RMS values of lens surfaces 1 and 2 were 2.41 nm and 2.74 nm, respectively, with a first-order mode frequency of 143.37 Hz.
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