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ZERODUR is a well-recognized glass-ceramic known for its excellent dimensional stability under varying temperatures, making it ideal for optical elements. This material is used extensively for lightweight components, including mirrors for space telescopes and parts for space instrumentation and industrial applications.

Regarding the center thickness relative to the diameter for ZERODUR mirrors used in Cassegrain telescopes for space applications, the typical aspect ratio of 6:1 (diameter to thickness) serves as a general guideline. However, several factors should be considered for space applications:

1. Thermal Stability: Space environments subject mirrors to significant temperature variations. Proper thickness is essential to manage thermal deformation and maintain optical accuracy. You can use the STAR module of OpticStudio to simulate and analyze the thermal stability of your mirror design, providing valuable insights into how temperature changes might affect performance. To understand more about thermal and structural deformation, you can refer to the article on the KBA about the STAR Module:  :OpticStudio STAR Module - Data import and analysis tutorial – Knowledgebase (zemax.com) 

2. Mechanical Support: The thickness affects the mirror's structural integrity. In space, the design must balance robustness to withstand launch stresses and operational conditions while preventing deformation.

3. Optical Performance: To avoid optical distortion, the thickness must be optimized to preserve the desired focal length and image quality without introducing aberrations.

Additionally, due to the manufacturing process, ZERODUR mirrors may exhibit surface defects such as microcracks or scratches, which are typically identified using mechanical profilometers. To ensure lightweight ratios and precise size control for space applications, finite element analysis, including structural and thermal calculations, is crucial for the mirror assembly.

While the 6:1 aspect ratio provides a useful starting point, precise design requirements will depend on the specific mission and telescope configuration. Detailed analysis and simulations, such as those provided by the STAR module in Optic Studio, will offer more tailored guidelines.