Fig. 1. Diagram of X-ray telescope system components and heat transfer model

Fig. 2. Lens parameters （lens thickness δ， diameter D， contact heat transfer coefficient G₀）

Fig. 3. Analysis of focused lens heat transfer factor and expected value of spoke thermal compensation （G_r is the radiative heat transfer factor G4 1，G5 1 between the lens and the radial environment T_r， and G_d is the radiative heat transfer factor G6 1，G7 1 between the axial environment T_d）

Fig. 4. Spoke area heat exchanger grid division

Fig. 5. Analysis flow of the optimal design method for the first type of heater

Fig. 6. Curve of variation of surrogate value with the number of regions （at k=4， the surrogate value is minimized to 0.283 4）

Fig. 7. Assembly status of two types of heaters on a focusing mirror hub

Fig. 8. Schematic diagram of the overall distribution of the two types of heaters （a-1 to a-16 for type I heaters， b-1 to b-16 for type II heaters）

Fig. 9. Distribution of thermocouples on the lens

Fig. 10. Results of lens temperature test