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Bonding Effect Analysis of the Primary Mirror of an Experimental Telescope with Reverse Engineering of Finite Element Method Yi-Kai Huang 1 and Po-Hsuan Huang 2 1 Research Assistant, 2 Principal Engineer, System Engineering Division, National Space Organization, National Applied Research Laboratories, 8F, 9 Prosperity 1st Road, Hsinchu Science Park, Hsinchu, Taiwan A. Abstract In this paper, a reverse engineering method was adopt to the finite element and wavefront error analysis of the primary mirror of a small space telescope experimental model. The experimental space telescope with 280mm diameter primary mirror has been assembled and aligned in 2011, but the measured system optical performance and wavefront error did not achieve the goal. In order to find out the root causes, static structure finite element analysis (FEA) has been applied to analyze the structure model of the primary mirror assembly. We established the corresponding model and boundary condition setup for several assuming effects which may cause deformation of the primary mirror have been proposed, such as gravity effect, adhesive effect, flexures bonding effect, thermal expansion effect, etc. Now a new assumption of the flexures bonding effect is proposed, and we adopt reverse engineering to verify this effect. Besides, the numerical wavefront error and Zernike polynomials will be calculated by opto‐mechanical analysis software. B. System Architecture Types of Telescopes Ritchey‐Chrétien Cassegrain Effective Focal Length 1400 mm Diameter of Primary Mirror 280 mm Materials Mirror (M1 & M2) Zerodur ® Iso‐Static Mount (ISM) 304 Stainless Steel Main Plate Aluminum Alloy M2 Supporting Ring Aluminum Alloy Struts Carbon‐Fiber‐Reinforced Polymer Table 1. System architecture of ExM100 telescope Figure 1. System architecture of ExM100 telescope. System architecture of M1 Assembly: The supporting system of primary mirror during ISM bonding is illustrated in Figure 2(a). Before three ISMs were bonded to the primary mirror, the mirror was supported by three metallic hemisphere supporting structures from backside as shown in Figure 2(b). Then, three metallic hemisphere supporting structures would be released from the primary mirror after finishing ISM bonding procedure. Figure 2. Supporting system of ExM100 primary mirror during ISM bonding. (a) Supporting system architecture (b) Hemisphere supporting structure C. Finite Element Analysis with Reverse Engineering 1. Reverse Engineering Method Process: Figure 3. Reverse engineering method flow chart. Figure 4. CAD model of primary mirror with adhesive, ISM and supporting system. (a) Stage 1 (b) Stage 2 Figure 5. Deformation of primary mirror with gravity effect along Z‐axis. (a) Isometric view (b) Bottom view Figure 6. Deformation of primary mirror (a) Deformed CAD Model from FEA 1 (b) Gravity effect along ‐Y‐axis. 3. FEA 2: Gravity Effect Along ‐Y‐axis with Three ISMs Support Figure 7. WFE map of primary mirror surface with gravity effect along ‐Y‐axis. (a) Analyzed WFE map of primary mirror (b) Measured WFE map of primary mirror Term Aberration Name Analyzed WFE Measured WFE PV 2.11E‐01 1.55E‐00 RMS 5.05E‐02 2.86E‐01 4 Astigmatism‐x ‐1.07E‐01 5.20E‐01 6 Astigmatism‐y ‐1.00E‐05 ‐2.83E‐02 7 Trefoil‐x ‐1.00E‐05 2.10E‐02 8 Coma‐x ‐1.00E‐05 1.09E‐01 9 Coma‐y ‐1.06E‐02 ‐7.51E‐02 10 Trefoil‐y 1.00E‐05 3.19E‐01 11 Tetrafoil‐x ‐3.00E‐03 ‐4.08E‐02 12 Astigmatism‐x ‐1.48E‐02 1.23E‐01 Unit: λ (λ=632.8 nm) Table 1. Zernike polynomials of primary mirror surface with gravity effect along ‐Y‐axis. D. Optical Analsys of WFE map of primary mirror Figure 7(a) shows the analyzed WFE map of primary mirror which was caused by the superposition of gravity effect along Z‐axis and ‐Y‐axis. Figure 7(b) shows the measured WFE map of primary mirror. The measured WFE PV is 1.55 λ and the WFE RMS is 0.29 λ (λ=632.8 nm), respectively. Supporting Pad Supporting Pad Adhesive Adhesive (a) (b) ISM 2. FEA 1: Gravity Effect Along Z‐axis with Three Points Support (a) (b) (a) (b) E. Conclusion According to the Zernike polynomials value of Table 1, both of the analyzed and measured result obtain primary aberration such as Astigmatism‐x, Coma‐y, and Tetrafoil‐x. However, the analyzed result of reverse engineering method presents quite different pattern from the measured WFE map because of term 10 trefoil‐y. Which means, there could be other reasons cause the trefoil‐y aberration. In conclusion, the new assumption of the flexures bonding effect is reasonable according to the similarity between measured WFE and analyzed WFE. Despite this, in order to improve the simulation accuracy, the shrinkage of structural adhesive should be considered. Therefore, the method of structural adhesive analysis should be refined in our future work. M1 M2 Mainplate ISM Adhesive ISM
