Equivalent analytical calculation of the temperature field of the lightweighted primary mirror for large-aperture telescope

The thermal loads of ambient temperature and solar radiation around the telescope directly influence the temperature distribution within the primary mirror for a large-aperture telescope. Based on the unsteady heat conduction and boundary condition in the cylindrical coordinate system, the analytical temperature field for the primary mirror is calculated by separation of variables and Greens function method. To verify the theoretical model, the temperature distribution of a 2.8 m aperture solid mirror is calculated by the analytical solution. The calculated radial temperature distribution at the optical surface is in good agreement with those of FEA method, which reveal that the analytical solution can well reflect temperature distribution at the optical surface. A lightweighted mirror is equivalent to a thin mirror without ribs in the thermal analysis. The FEA analysis is conducted with both the mirror models, which verifies the validity of the equivalent model. The equivalent analytical calculation results of the temperature field for the lightweighted primary mirror have a significant reference value in the early design of the primary mirror for a large-aperture telescope.