Keywords

1 Introduction

With the deepening and expansion of the application of space remote sensing, the aperture of space telescopes continues to grow. The aperture of space telescopes ranges from 2.4 m of the Hubble, 3.5 m of the Herschel, to 6.5 m of the JWST [1], presenting a growing trend to reach the maximum launch capacity. Launch safety and in-orbit performance stability of such a large aperture mirror is one of the key factors related to the success or failure of the whole space telescope mission. As the tie between the mirror and the main structure of the space telescope, the support structure is one of the most prominent links that affect the precision and stability of the mirror. Several main support forms of large aperture mirror are compared and the key technologies and development of mirror support design are discussed in this paper.

2 Main Supporting Forms of Large Aperture Mirror

The large aperture mirror usually adopts back support form, which is tested, installed and emitted in the vertical state of optical axis, The main forms are three-point support, hexapod support and whiffle-tree support.

Three-point support is directly based on the principle that three points determine a plane, while the three points can be actual or virtual. For the circular plate mirror with radius of R, which is equal thickness without holes, the theoretical analysis shows that the optimal positions of the three points are arranged uniformly on the circle with radius of 0.645R. For rectangular mirror, the positions of the support points are influenced by geometric parameters such as the aspect ratio. The main mirror of the famous Hubble telescope takes this support form and the three back support points are distributed in the positions shown in Fig. 1. There are two ball hinges and a flexible lever for kinematic support in each support structure [3].

Fig. 1.
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The 3 supporting points on the rear of HST primary mirror

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The hexapod support is composed of six rods, usually in the configuration of three bipod structures, which is fixed to the back or side of the mirror. There are two work condition, upright use and inverted use. Figure 2(a) shows the upright use condition with three support points on the mirror rear, and Fig. 2(b) shows the inverted use condition with six support points on the mirror rear. The instantaneous pivot of each bipod support structure is its virtual pivot position, and the whole hexapod support system is similar to a Stewart parallel mechanism. The sensitivity of the mirror position to the length of each rod can be obtained by the Jacob matrix analysis which is a function of the azimuth of the support rod. Flexible structures are often designed at both ends of each rod, so that they have high axial stiffness and low lateral stiffness. The results show that the flexible support structure of bipod can effectively reduce the influence of external dynamic load on the mirror while keeping good thermal stability of the mirror [4].

Fig. 2.
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Examples of hexapod support

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Hexapod support is the most widely used support form of space mirror at present. The primary mirrors of space telescopes such as Herschel, SPICA, SNAP, ALADIN, WorldView-4 are designed with hexapod support. The Interface Region Imaging Spectrograph (IRIS) launched in 2013 by NASA, which carries a high-resolution ultraviolet camera, has nine mirrors mounted by hexapod support, as shown in Fig. 3, maintaining the surface accuracy better than 1 nm for different sub-aperture of 8–15 mm [5]. It is necessary to point out that in the application of large aperture space mirror, auxiliary support is usually set in addition to hexapod support to meet the requirements of the launching mechanical environment.

Fig. 3.
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The IRIS mirrors

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Whiffle-tree support is a support system developed on the basis of three-point positioning principle [6]. Three support points are expanded to a multiple of 2 or 3 through different kinds of hinges, beams and tripods. Due to the problems of gap control, preventing cold welding, friction uncertainty and so on, flexure hinges are used to replace the mechanical hinges in space applications. Figure 4 shows several examples of whiffle-tree system of different number of points. In 1945, Hindle described an installation technology named after his name, and introduced in detail the multi-point mechanical support system of 9 points or 18 points, which is similar to the whiffle-tree structure proposed by Thomas Grubb in principle.

Fig. 4.
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The many whiffle-tree configurations

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Because the mirror aperture of space telescope was relatively small and the lightweight ratio was low, the demand of the application of whiffle-tree multi-point support was small. Therefore, the application of whiffle-tree structure is mainly concentrated in the project of ground-based astronomical telescope, such as the TMT and E-ELT [7, 8]. With the aperture of space mirror increasing gradually, the application of the whiffle-tree structure in the aerospace project is also increasing step by step. The typical case is the primary mirror of the Stratospheric Observatory for Infrared Astronomy (SOFIA), which was mounted with a combination of 6 points bipod support on the side and 18 points whiffle-tree support on the back to keep the surface shape accuracy in the mechanical environment such as gravity, overload and so on.

The three kinds of supports are extended on the basis of the three-point positioning principle, so the number of support points can be summarized as 3 × 2m × 3n. With the increase of the number of support points, the surface figure of the mirror under gravity is improved, and the applicability to the aperture and stiffness of mirror is enhanced in turn. On the other hand, the complexity of support structure is also increased, which leads to the increase of design difficulty, especially the adaptability to forced displacement and thermal load will also be affected. From the point of view of resistance to mechanical environment, three-point support and hexapod support usually need auxiliary support during launch. Therefore, whiffle-tree support has stronger applicability to space-based large aperture mirrors.

3 Key Techniques of Large Aperture Mirror Support

3.1 Optimization of the Support Points

In general, the more the number of support points, the better the quality of surface figure of mirror under gravity, and the higher the stiffness of the support structure, but at the same time it will result in an increase of the design difficulty and the total mass. Therefore, the principle of determining the number of support points is that the number is as small as possible on the condition of meeting the requirements of mounting, system testing, transport, launch and on-orbit work, etc. For the space mirror, the number and position of the support points are affected by the curvature radius, lightweight configuration and other parameters, so it is usually combined with the mirror’s design to carry out the optimization design at component level. A popular method at present is the automatic multi-disciplinary optimization on the basis of parametric model [10,11,12,13].

3.2 Structure Athermal Design Technology

For space telescopes, on the one hand, the thermal control measures are limited by the technical level and the resources of the satellite, so the working environment of the mirror is bound to temperature fluctuation. On the other hand, the mirror cell mostly are made of several different materials, and the coefficient of thermal expansion (CTE) of the mirror, the support structure and the adhesive connected to each other are different. The mirror and the whole telescope are sensitive to the thermal deformation, which may lead to a significant decline in performance. Therefore, the thermal stability must be taken into account in the design of large aperture mirror support and the athermal design should be carried out.

The thermal stability of the support structure is designed based on the thermal compensation principle, and reasonable geometric configuration is developed for the difference of the CTEs, so that the thermal deformation of each part is coordinated with each other and the key geometric parameter is maintained. Figure 5 shows a typical application of the principle of thermal compensation which is similar to a Hooke’s compensated pendulum [14], in which the four sides of a rhombus are of the same material and the diagonal in the middle are made of another material with different CTE. If the rhombus side length, angle and CTE are properly configured, the pendulum position can always maintain a high degree of stability under the condition of temperature changing. For the more complex thermal environment, the support structure can achieve stability by increasing the variety of materials and thermal compensation elements [15, 16].

Fig. 5.
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Hooke’s compensated pendulum

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3.3 Un-stressed Assembly

Due to the dimension error and geometric error of the parts machining, the mirror components will deform during the assembly process, which will affect the optical performance of the mirror. The main measures to reduce assembly stress are the adhesive.

The adhesive is usually of low elasticity modulus and used to replace the bolts and other connections, which can avoid the hard contact between mirror and support structure, make the stress distribution uniform and reduce the influence of the surface machining error of parts. However, during the curing process from liquid state to glass state, the adhesive layer will produce volume shrinkage and internal stresses. Therefore, the selection and the parameters design of adhesive layer should not only meet the requirements of strength, but also control the effect of curing shrinkage. The shrinkage during late curing should be minimized, and not to cure for a long time at ambient temperature [17,18,19]. Some measures can be taken to decrease the curing stress, such as reducing the stiffness of the support structure in the adhesive area, controlling the adhesive area of both the total component and single block, and cleaning the spilled bond. Flexure hinge is an important link for mirror support to realize kinematic support and reduce the influence of friction. The ideal kinematic support can make the mechanical state of mirror unaffected by the elastic deformation of the surrounding environment. Therefore, the flexure hinge is of great significance to the realization of stress-free assembly. In addition, the multistep nonlinear analysis can be used to simulate the variation of the loads, connection states and boundary conditions sequentially to evaluate the stress effect in the assembly process [20].

4 Conclusions

This study proposes a discussion about the support form and the key technologies of large aperture space mirror. After years of relevant technologies development, the conditions for the project of large aperture space telescope in China have come to be mature. With another upsurge of international space exploration, many countries have proposed plans to build large aperture space telescopes and we believe that will derive the development of technology in related fields and promote space science status of China.