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Abstract
We propose analysis methods for mirror bonding. The functional relationship between the shrinkage of the adhesive layer and the shape accuracy of the mirror is established numerically. By designing the structural form of the optical mounting and setting an appropriate stiffness ratio between the mirror and bonding position of the optical mounting, the theoretical surface shape accuracy change can be determined. Accordingly, the mirror is bonded, and the surface shape accuracy of the mirror after bonding is found to be 0.020λ. This approach is useful in mirror design applications that require rapid preparation and accuracy control.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In aerial imaging equipment, the material used in the mirror is usually silicon carbide or mono-crystalline silicon, which exhibit remarkable environmental adaptability and high optical surface accuracy [1]. To improve the quality of the equipment and obtain higher-resolution images, rapid manufacturing processes, higher surface shape accuracy, and lower mirror volume and weight are required. Ultrathin and lightweight mirrors are becoming increasingly important in various applications, including the fast steering mirror (FSM). The design of the mirror optical mounts is extremely important because of their effect on the stability of the mirror [2]. The optical mount usually includes both mechanical and bonding connections. However, as materials such as silicon carbide and mono-crystalline silicon cannot be directly connected to the load-bearing structure, the mechanical connection utilizes a fastening method such as end rings. Moreover, the optical mounts must have the same thermal expansion coefficient as the mirror, and the mirror assembly requires remarkable environmental adaptability. When the thermal expansion coefficients of the base material and the mirror material differ, the temperature change has a significant influence on the surface shape accuracy [3].
In contrast to mechanical connections, the adhesive bonding method can reduce the weight and complexity of the connection. The bonding operation is simple; at the same time, the influence of the support structure on the surface shape of the mirror can be reduced. However, bonding without distorting the figure of the mirror is a challenge in the preparation process. The curing process of the adhesive layer usually affects the surface accuracy [4]. Extensive research has been carried out to reduce the influence of bonding on the mirror. Roulet proposed a deformable alumina and titanium mirror with an embedded actuator support system, fabricated by three-dimensional (3D) printing, to minimize errors caused by the bonding interfaces during mirror assembly [5]. However, in most cases, processing the mirror and optical mount separately, and bonding them together is necessary. Optical mounts are often made of metal. Elucidating the nature of the mirror adhesive is the only way to improve the bonding process [6].
Optical epoxy adhesives are generally used to bond optical components because of their high bonding strength, acid and alkali resistance, room temperature curing, and low curing shrinkage properties [7,8]. During the curing process, the volume shrinkage of the adhesive layer is an important property of the optical epoxy adhesive [9]. Although the volume shrinkage only ranges from 0.3–3.7%, the instability of this adhesive would affect the surface accuracy of the lightweight mirror [10]. Shrinkage during curing usually causes stress. If the shrinkage occurs rapidly, the stress is usually greater. Research on the bonding of mirrors has been conducted in the field of optical support. Zuo and Chen bonded a 2 mm ultrathin mirror shell, determined the effect of the glue curing time on the surface shape accuracy through experiments, and simulated the stress of the bonding layer on the mirror [11]. For the curing and shrinking process of mirrors, the equivalent linear expansion coefficient method can be used to simulate and analyze the effect of the bonding layer on the surface shape [12]. However, this method should determine the optical mount structure based on experience, and then determine the rationality of the structure based on the results of the surface shape accuracy measurements. Where experience is insufficient, it may be necessary to iterate the simulation process to determine a reasonable optical mount structure. In addition, the simulation model of the bonding layer needs to be established during the simulation process, which increases the number of simulation calculations and prolongs the design time.
In this study, realization methods and analysis elements for the micro-stress bonding of mirrors were developed. Firstly, a cantilever-type glue flexure structure was designed for the optical mount. Then, simplifying the analysis of the mirror-bonding process made it possible to quickly evaluate the influence of the bonding shrinkage on the surface accuracy of the mirror. Thus, the bonding deformation distribution relationship was analyzed, and unit deformation and unit force methods developed. The unit deformation method can be used to obtain the influence function of the adhesive layer shrinkage on the mirror surface; this can be used to obtain the stiffness ratio between the mirror and the optical mount. The influence of the stiffness of the optical mount on the surface accuracy of the mirror was established, and this influenced the design of the optical mount. This study evaluates the changes in the surface accuracy of the mirror after bonding and aims to reduce the design cycle time. The process route for the adhesive bonding of the mirror can thus be optimized, avoiding multiple optical processing points. Related theoretical research can be applied to the design of the mirror support structure, including evaluating the influence of installation stress on the shape accuracy of the mirror.
2. Theory
In the traditional mirror preparation process, bonding is usually an intermediate process [13]. Optical and bonding processing of the mirror often needs to be carried out in two different institutions or by different manufacturers. After bonding, the mirror needs to be optically processed until it meets the optical surface shape accuracy requirements, before it is coated. This prolongs the manufacturing cycle. The realization of micro-stress bonding of the mirror can position bonding as the last preparation step, preventing mutual coordination in the preparation process, and substantially reducing the processing cycle.
It is very important to determine the bonding quality of the mirror as it determines its ultimate stability. The shrinkage of the adhesive layer during the bonding process can be theoretically analyzed. The aim of bonding theory analyses is to determine the optical mount structure and improve the bonding quality with the surface shape accuracy of the mirror bonded being the constraint [14]. The requirements for supporting structures result in low surface figure error, sufficient tilt stability, and low displacement error [15]. The optical mount can be designed with a flexure structure to ensure the surface shape accuracy of the mirror after bonding. Including a flexible link in the supporting structure can effectively improve the surface accuracy of the mirror assembly, while the structural rigidity of the mirror can still be guaranteed in a vibrating environment. Ryaboy discussed the bonding problem for mirrors, derived the analytical equations of thermal stress and deformation caused by continuous bonding, three-point bonding, and planar bonding around the periphery, and analyzed them using a finite element model [16]. The deformation of the peripheral continuous bonding and the surrounding three-point bonding are inferred to be similar. It provides the relevant theoretical basis for the realization of a flexible structure. The flexible structure based on multi-point bonding is the focus of the design, and it is often an iterative process. The rapid design of the optical mount structure is essential to reducing the design time of the mirror. An illustration of the whole assembly under consideration is shown in Fig. 1.
2.1 Key points of mirror bonding
Mirror bonding is an important step in mirror preparation. The following three key points must be considered in the design of the mirror:
- 1. Mirror-bonding area strength: After determining the mirror structure according to the optical index, the bonding area of the mirror determines the bonding strength. A smaller bonding area will affect the stability of the mirror in a mechanical environment, and a larger bonding area will generate greater stresses, which affect the surface accuracy of the mirror after bonding.
- 2. Surface shape accuracy of the mirror after bonding: The curing shrinkage of the adhesive layer produces shrinkage stress, which often affects the surface shape of the mirror. Normally, after the mirror is bonded, the surface of the mirror is reprocessed until the final surface shape requirement is reached. Then, the optical coating is applied. In some situations, for example, when the surface of the mirror needs to be coated with a high-reflection (HR) film, the traditional process may not be followed. This is because the deposition temperature (or post-deposition annealing temperature) of the HR film is relatively high [17,18], often reaching 150 °C or higher. The maximum safety temperature of the general optical epoxy resin adhesive is 80 °C, which affects the stability of the adhesive. Therefore, the bonding process must be carried out after completing the preparation of the mirror. In these situations, the success of the mirror preparation is dependent on adherence of the surface shape accuracy after bonding to the optical index design requirement.
- 3. Structural rigidity of the mirror assembly: The bonding stress caused by the curing and shrinkage of the adhesive layer is related to the structure of different mirror optical mounts. To meet the surface shape accuracy requirements of the mirror after bonding, the optical mount of the mirror is usually designed with a flexible structure. The rigidity of the flexible structure determines the pointing accuracy and dynamic performance of the mirror.
The design and analysis route of the mirror-bonding proposed in this study is shown in Fig. 2. According to the design input requirements, the analysis process of the mirror-bonding process needs to be determined. Then, the design elements in the design process are clarified. Finally, the theoretical design or simulation results that meet the indicators are determined. Design elements are design parameters that must be considered in the analysis of mirror bonding. The rationality of the structure is determined by evaluating the surface shape accuracy of the mirror after bonding, and the micro-stress bonding of the mirror can be conceptualized.
Analysis of the bonding process can be performed through a combination of theoretical calculations and simulation analysis. The influence of the shrinkage stress of the adhesive layer on the surface accuracy of the mirror can be reduced by the following two actions:
- 1. Reducing the bonding area of the mirror assembly.
- 2. Structurally optimizing the design of the optical mount.
2.2 Adhesive layer strength
The bonding strength of the mirror is related to the bonding area, which is determined by the structure of the mirror. Therefore, before the bonding analysis of the mirror, the structure of the mirror must be determined. The diameter-to-thickness ratio of the mirror determines the lightweight nature of the mirror, and the structural design is based on this. The theoretical formula for the mirror surface deflection $\delta$ [19] is given by:
where $\rho$ is the density of the optical component, R is the radius of the optical component, E is the elastic modulus of the optical component, t is the thickness of the optical component, and v is the poisson ratio of the optical component.During the curing and shrinking process, the size of the adhesive varies with the size of the bonding area; hence, the bonding area should be appropriate for this condition. A reasonable bonding area can minimize the bonding stress and improve the bonding strength of the adhesive layer. When the mirror assembly is bonded and assembled, the minimum bonding area ${S_{\min }}$ can be obtained using the following formula:·
where M is the weight of the optical component; a is the acceleration factor under the worst conditions; ${f_s}$ is the safety factor, usually 2–4; and J is the shear strength or tensile strength of the bonding.The bonding area of the mirror must be larger than the minimum bonding area, thus Eq. (2) can be used to confirm the bonding parameters of the mirror.
2.3 Surface influence function
After determining the bonding area of the mirror, the optical mount structure can be determined through a theoretical analysis of the bonding. A gap is designed between the mirror and the optical mount; the adhesive layer fills the gap size. To reduce the influence of temperature on the curing process of the adhesive layer, the entire process occurs at normal temperature. Therefore, the main factor that affects the surface shape change of the mirror after bonding is the shrinkage of the adhesive layer.
When calculating the influence of bonding stress on the deformation of the mirror surface through finite element analysis, if the deformation tolerance is exceeded, the design must be changed and a new finite element analysis model built. This is a time-consuming process and usually does not result in an optimal solution. The change in bonding stress can be linked to the deformation of the mirror surface. The mirror adhesive layer can be regarded as a free expansion layer in the normal direction of the mirror. Therefore, the direction of the main deformation is radial. The maximum deformation, ${\mathrm{\delta }_{\max }}$, of the mirror is given by
The force and moment acting on the mirror mounting surface have a linear relationship with the surface shape change of the mirror [20]. For the respective support positions, the unit deformation method is utilized to perform the finite element simulation and calculate the influence function of the deformation of the adhesive layer on the change of the mirror surface. For the influence function, ${Z_r}$, the unit is dimensionless. Owing to the small deformation size of the mirror, the unit deformation ${\mathrm{\delta }_r}$ of the bonded position of the selected mirror becomes 1 nm. The influence function is related to factors including the bonding area of the mirror, the ratio of the diameter to the thickness of the mirror, and the size of the supporting position of the mirror. It can be determined after the mirror structure has been determined using finite element analysis.
2.4 Stiffness ratio
We adopt a radial flexure-bonded cell structure for the optical mount of the mirror [21]. The flexure design reduces the bond and optical stresses and the distortion with varying temperature.
For the mirror, the tensile force generated by the curing and shrinkage of the adhesive layer on the mirror is F. The bonded position of the mirror is a cylindrical structure. As the amount of change is very small, the amount of change of the mirror remains in the linear elastic range. The deformation ${\mathrm{\delta }_1}$ is related to the stiffness of the stressed part of the mirror. The deformation ${\mathrm{\delta }_\textrm{1}}$ at the interface of the mirror and the optical mount is
where F is the contact force between the adhesive layer and the mirror and ${K_{mirror}}$ is the stiffness of the mirror.For the central single-point supporting mirror, according to Eq. (3), the deformation of the mirror surface is proportional to the deformation ${\mathrm{\delta }_1}$ at the bonding structure of the mirror, and the influencing function value is ${Z_1}$.
where ${\mathrm{\delta }_1}$ is the radial unit deformation and ${Z_1}$ is the influence function.For the optical mount, the tensile force generated by the curing of the adhesive layer on the optical mount is also F. According to Hooke's law, the deformation at the bonded structure of the optical mount is
where ${K_{mount}}$ is the stiffness of the optical mount.During the curing process of the adhesive layer, the interaction forces between the adhesive layer and the mirror, and that between the adhesive layer and the optical mount, resist the shrinkage of the adhesive layer. Therefore, the deformation of the adhesive layer caused by the interaction force is
where ${K_{adhesive}}$ is the stiffness of the adhesive.When the adhesive layer is cured, the adhesive layer is in a stable state. At this time, the theoretical shrinkage value of the adhesive layer is the sum of the mirror, optical mount, and change value of the adhesive layer. When the gap size is l, the shrinkage size of the adhesive layer can be calculated using the following formula:
Therefore, by considering the deformation ${\mathrm{\delta }_{mirror}}$ at the bonding structure of the mirror as a constraint, the relationship between the optical mount rigidity and the optical mount can be established using the following equation:
The curing of an adhesive layer is a complex process. During the curing process of the adhesive layer, the physical properties of the adhesive layer are constantly changing, causing the interaction force F to change concurrently. It is difficult to make more accurate theoretical calculations and develop simulation analyses for the curing process of the adhesive layer. Therefore, the structure of the optical mount can be calculated more rapidly by simplifying the parameters of the shrinkage process of the adhesive layer. By assuming that the adhesive layer is an absolute rigid body during the curing process and that no internal stress is generated, ${K_{adhesive}}$ becomes infinite, and the theoretical size change of the adhesive layer curing shrinkage becomes the sum of the size changes of the reflective mirror and the optical mount. At this time, the influence of the adhesive layer parameters on the shape of the mirror can be ignored. This is summarized in the following formula:
The reason for this assumption is that the aforementioned dimensional change value is the theoretical maximum. In real-life situations, the adhesive layer will not be an absolute rigid body; hence, the size change of the mirror and the optical mount will be smaller than the aforementioned change value. In addition, the maximum value of the change in the shape of the mirror is calculated by setting the safety factor at the same time. The calculation formula is determined as follows:
The aforementioned formula shows that the stiffness ratio between the bonding position of the mirror and that of the optical mount is an important design parameter. The stiffness ratio determines the amount of deformation in the mirror. From Eqs. (4) and (6), the stiffness ratio is equal to the inverse ratio of the deformation of the bonding position:
The stiffness is determined by the specific structure and material properties. The structure of the mirror and the optical mount may be extremely complicated, and it is difficult to evaluate the rigidity ratio between the bonding position of the mirror and the bonding position of the optical mount through theoretical formulas. The stiffness ratio of the two can be calculated faster by finite element analysis. This can be carried out using the unit force method. The unit uniform force is applied to the bonding position of the mirror and the optical mount, and the deformation of the two is calculated. The stiffness ratio is the inverse ratio of the amount of deformation. This method simulates and analyzes the mirror and the optical mount separately and does not need to consider the adhesive layer, which greatly reduces the design difficulty and design cycle time.
The selection of the stiffness ratio must be suitable. When the mirror structure is determined, the greater the stiffness ratio, the smaller is the maximum value of the mirror surface shape change. Correspondingly, the stiffness of the optical mount is worse than that of the mirror. When the stiffness of the optical mount is below a certain level, it affects the mechanical properties of the entire assembly. Therefore, after determining the flexible structural parameters of the optical mount, it is necessary to further calculate the mechanical properties of the entire assembly. Modal analysis is an effective method for studying the dynamic characteristics of components; it involves the application of system identification methods in the field of engineering vibration. Modes are inherent characteristics of the mechanical structural parts. Each mode has a characteristic mode shape and damping ratio. If the natural frequency of the component is the same or close to the input frequency of the system, it will cause resonance and affect the dynamic characteristics of the system. The modal simulation analysis of the mirror assembly can be used to determine whether the index requirements have been met.
3. Materials and methods
3.1 Design input
Before the bonding analysis starts, the design input indicators must be clarified. After arranging the related optical indicators, the main technical indicators are listed in Table 1. The size of the mirror needs to be larger than the clear aperture, and the natural frequency of the mirror must be greater than three times the bandwidth of the control system.
Table 1. Mirror Optical Index Requirements
3.2 Parameters calculation of adhesive layer area
When the optical aperture, φ, was 54 mm and a folding mirror was placed at 45°, the effective beam size was 54 mm × 76 mm. On one side in the long axis direction, 4 mm was reserved, on one side in the short axis direction, 6 mm was reserved, and the mirror surface size was 66 mm × 84 mm. The mirror was octagonal, and the envelope size was approximately 88 mm, with a central support. The mirror was manufactured using SiC; invar alloy 4J32 was used to manufacture the optical mount, which had a coefficient of thermal expansion similar to that of the mirror.
According to the requirements of the optical index, the mirror surface shape accuracy (RMS) was less than 1/40 λ (λ = 632.8 nm). From Eq. (1), the thickness of the mirror surface (t > 1.82 mm) could be calculated. Considering the machinability of the mirror and the theoretical calculation error, the thickness of the mirror surface could be regarded as 3.5 mm, and the mirror diameter–thickness ratio was approximately equal to 25.1. The total thickness of the mirror was 9.2 mm. The mirror weight was reduced by this structural arrangement; the structural parameters of the mirror are listed in Table 2.
Table 2. Mirror Structural Parameters
The mirror was bonded with epoxy resin adhesive. The epoxy adhesive used was GHJ-01(Z) optical epoxy adhesive, which is a two-part adhesive. The significant part is a mixture of a near colorless low-molecular weight bisphenol A epoxy resin and a bifunctional epoxy diluent. The second part is a curing agent: a colorless to light color low viscosity hexamethylene diamine adduct. The tensile strength of the optical epoxy adhesive after bonding is approximately 14 MPa. Under the 40 g acceleration mechanical condition and where the safety factor is 4, the minimum bonding area of the mirror was calculated by Eq. (2) to be 80 mm2. The mirror was bonded to eight areas on the outer ring. The diameter of the bonding position was 45 mm, and the corresponding angle value of each bonding area was 25°. This meant that the required height of the bonding area exceeded 1.02 mm. Considering the operability of the bonding process and the unevenness of the adhesive layer, the bonding height required to meet the bonding strength requirements was determined to be 3 mm. The whole assembly was shown in Fig. 3.
3.3 Optical mount design and analysis
After the mirror structure was determined, a finite element simulation of the mirror was performed using the unit deformation method. The mirror utilized a central support structure, and the bonded area consisted of eight areas evenly distributed on the outer side of the back of the mirror. The project team used Hypermesh (Altair, Inc.) and MATLAB (MathWorks, Inc.) software for co-simulation. A unit deformation of 1 nm in the radial direction was applied to the bonding area of the mirror. As shown in Fig. 4, the amount of deformation was extracted from the surface of the mirror, and the number of nodes used was 5609. The root mean square (RMS) value of the mirror shape accuracy calculated was 0.365 nm by fitting the Zernike polynomial; hence, the value of the influence function ${Z_r}$ was 0.365.
Fig. 4. Mirror shape accuracy under unit deformation: (a) Finite element model of the mirror; (b) Surface shape simulation results.
The bonding strength of the adhesive decreased as the thickness of the adhesive layer increased. According to the temperature stress-free calculation formula, the thickness of the glue layer was 0.012 mm. The temperature stress-free calculation formula [22] is as follows:
where ${r_0}$ is radius of the mirror bonding position, ${\alpha _c}$ is the thermal expansion coefficient of the optical mount, ${\alpha _0}$ is the thermal expansion coefficient of the mirror, and ${\alpha _b}$ is the thermal expansion coefficient of the adhesive.Therefore, in the theoretical calculation, the radial theoretical gap between the mirror and optical mount was 0.012 mm. The line shrinkage rate of the epoxy adhesive was 3%, the maximum change value of the mirror shape constraint was 1 nm (RMS), and the safety factor was 4, which could be obtained using Eq. (11); the stiffness ratio was required to be larger than 415.2.
First, the unit force analysis method was adopted for the mirror. As shown in Fig. 5, under the action of unit force, the deformation of the bonding position of the mirror was 0.5 nm. Using Eq. (12), the deformation of the optical mount should have exceeded 207.6 nm. Considering the processing technology and dimensional accuracy, the size of the flexible structure of the optical mount should not have been less than 1 mm. When also considering the size of the flexible structure of the optical mount (1.2 mm), the deformation of the optical mount was 615.5 nm under the action of a unit force, which not only meets the stiffness ratio requirements, but also has good processing technology. Through iterative calculations, the theoretical change in the surface shape of the mirror was determined to be 0.427 nm.
Fig. 5. Deformation under unit force analysis: (a) Deformation of the mirror under a unit force; (b) Deformation of the optical mount under a unit force.
3.4 Modal analysis
The low-order modes directly reflected the stiffness characteristics of the mirror assembly. The modal analysis results of the mirror assembly are presented in Table 3. The fundamental frequency of the mirror assembly was 2234.2 Hz, which is three times greater than the control system bandwidth of the assembly at 200 Hz. The rigidity of the mirror assembly meets the requirements, and excess resonance through the material can be avoided.
Table 3. Mirror Modal Simulation
Through theoretical calculation and simulation analysis, the structure of the mirror and optical mount can be determined as shown in Fig. 6.
4. Results
The mirror underwent rough processing, modification, polishing, and various other processes in sequence. When the surface shape of the mirror was processed within 1/50 λ (RMS), the bonding process could be initiated. The surface shape of the mirror before bonding is shown in Fig. 7, where the surface shape accuracy is 0.019 λ (RMS).
Pre-treatment of the mirror bonding and the bonding operation are also very important to ensure the accuracy of the mirror surface. The mirror-bonding process was as follows.
- (1) All mechanical structural parts needed to be ultrasonically cleaned, and the bonding position of the mirror and the optical mount were wiped with optical absorbent cotton dipped in a mixture of 40% alcohol and 60% ether until the surface of the absorbent cotton was free of stains.
- (2) The optical mounting base was fixed on the tooling to ensure the relative position of the mirror and the optical mounting base during bonding.
- (3) The optical epoxy adhesive was evenly coated on the optical mounting seat, and then placed into the mounting hole on the back of the mirror. The optical mount was gently rotated to remove air bubbles in the adhesive layer and make the adhesive layer more evenly distributed. After it felt smoother, the mirror was left to stand; the curing process was thus initiated. Because dust and other impurities mixed into the adhesive layer affect the properties of the adhesive layer, the entire bonding process needs to be carried out in a dust-free environment. The curing state of the mirror is shown in Fig. 8.
After curing at 20°C±2°C for at least 7 days, the assembly was subjected to high- and low-temperature cycle tests to achieve sufficient curing of the adhesive layer and reduce the residual stress in the curing process of the adhesive layer. The upper and lower limits of the test temperature aimed to exceed the working temperature of the mirror by 5 °C. As the working environment temperature of the mirror ranges from −40 °C–55 °C, the test temperature is −45 °C–60 °C. The conditions of a high- and low-temperature cycle are shown in Fig. 9; three high- and low-temperature cycles were performed.
The accuracy of the surface shape of the mirror was tested. As shown in Fig. 10, the surface shape accuracy distribution of the mirror was 0.020 λ after bonding, which met the optical index requirements. After the thermal cycle test, it was returned to room temperature. The surface shape accuracy of the mirror was 0.020 λ. There was no obvious change in the surface quality, which met the basic requirements of environment adaptability.
5. Summary
In this study, based on the requirement for the rapid production of the mirror, a mirror-bonding analysis method was developed to reduce the manufacturing cycle time. The developed method could be used to enable bonding after the preparation of the mirror is completed; it meets the requirements of the optical index design. This paper introduced the key design elements in the mirror-bonding process and evaluated the effect of the curing shrinkage of the adhesive on the change in the accuracy of the mirror surface. The developed method reasonably simplifies the bonding analysis process. Specifically, the unit force method is used to determine the stiffness ratio of the bonded position of the mirror and the optical mount. Then, the structural parameters of the mirror are determined. The combination of theoretical and simulation analyses minimizes the curing shrinkage stress of the adhesive layer, which is conducive to the realization of a low-stress mirror assembly. The test results showed that the surface accuracy of the mirror before and after bonding was 0.019λ and 0.020λ, respectively, which meets the basic requirements of photoelectric load. It also exhibited remarkable stability after cycling in high- and low-temperature environments. The method developed in this study provides guidance for the design process of mirror bonding and a reference for the realization of the micro-stress bonding of the mirror. This approach is useful in mirror design applications that require rapid preparation and surface shape accuracy control.
Funding
Key Laboratory of Airborne Optical Imaging and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (HCKF-201912HJ03).
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. L. Yi, X. Zhang, H. Hu, Z. Zhang, and D. Xue, “Comprehensive study of the rapid stressed mirror polishing method for off-axis aspheric SiC thin-plate mirrors,” Opt. Express 28(22), 32802–32818 (2020). [CrossRef]
2. Y. Wang, P. Wang, and Z. Liu, “Research and design of kinematic support flexibility for metal mirror,” Optik 241, 166386 (2021). [CrossRef]
3. M. A. Kahan, M. B. Levine-West, and C. Y. Chan, “Optimum design and experimental verification of glue bonding area and thickness for an eight-inch reflective mirror,” Proc. SPIE 9953, 99530J (2016). [CrossRef]
4. K. W. Chan, J. R. Mazzarella, T. T. Saha, W. W. Zhang, M. P. Biskach, A. Numata, R. E. Riveros, R. S. McClelland, and P. M. Solly, “Recent advances in the alignment of silicon mirrors for high-resolution x-ray optics,” Proc. SPIE 11119, 10 (2019). [CrossRef]
5. W. W. Zhang, K. D. Allgood, M. Biskach, K. W. Chan, M. Hlinka, J. D. Kearney, J. R. Mazzarella, R. S. McClelland, A. Numata, R. E. Riveros, and T. T. Saha, “High-resolution, lightweight, and low-cost x-ray optics for the Lynx observatory,” J. Astron. Telesc. Inst. Syst. 5(2), 1 (2019). [CrossRef]
6. A. Invernizzi, A. Lefevre, P. Wuillaume, E. Harel, R. Cluzel, R. Geyl, R. Mercier-Ythier, M. Cayrel, C. Haupt, C. A. Hauck, and M. Muller, “ELT secondary mirror manufacturing progress at Safran Reosc,” Proc. SPIE 11451, 10 (2020). [CrossRef]
7. Z. D. Fan, Y. Dai, C. Guan, G. Tie, and J. Liu, “Effect of the adhesive layer on the unimorph deformable mirror,” Optik 160, 77–85 (2018). [CrossRef]
8. K. W. Chan, J. R. Mazzarella, T. T. Saha, E. Harel, R. Cluzel, R. Geyl, R. Mercier-Ythier, M. Cayrel, C. Haupt, C. A. Hauck, and M. Muller, “Alignment and bonding of silicon mirrors for high-resolution astronomical x-ray optics,” Proc. SPIE 10699, 141 (2018). [CrossRef]
9. J. D. Vreugd, K. Jansen, L. J. Ernst, and J. A. C. M. Pijnenburg, “Modelling of viscoelastic properties of a curing adhesive,” Mater. Charact. 57, 241–251 (2007). [CrossRef]
10. O. Vlasenko, A. Zverev, and M. Sachkov, “Using the DP-190 glue for adhesive attachment of a large space mirror and its rim,” Proc. SPIE 9151, 91513I (2014). [CrossRef]
11. H. Zuo and K. Chen, “Mechanical analysis on the influence of the bonding process on the ultra-thin mirror shell,” Proc. SPIE 10700, 136 (2018). [CrossRef]
12. L. Sun, L. Li, S. Li, Q. Zhao, J. Sun, J. Q. Wu, and B. L. Hu, “Curing shrinkage stress and deformation analysis of adhesive bonding large aperture mirror,” Proc. SPIE 10837, 25 (2019). [CrossRef]
13. Z. Dong, A. Jiang, Y. Dai, and J. Xue, “Space-qualified fast steering mirror for an image stabilization system of space astronomical telescopes,” Appl. Opt. 57(31), 9307–9315 (2018). [CrossRef]
14. W. W. Zhang, M. P. Biskach, V. T. Bly, J. M. Carter, K. W. Chan, J. A. Gaskin, M. Hong, B. R. Hohl, W. D. Jones, J. J. Kolodziejczak, and L. D. Kolos, “Affordable and lightweight high-resolution x-ray optics for astronomical missions,” Proc. SPIE 9144, 914415 (2014). [CrossRef]
15. F. N. Yu and S. Y. Xu, “Support structure and optical alignment technology of large-aperture secondary mirror measured by back transmission method,” Optik 207, 164274 (2020). [CrossRef]
16. V. M. Ryaboy, “Analysis of thermal stress and deformation in elastically bonded optics,” Proc. SPIE 6665, 66650K (2007). [CrossRef]
17. J. Dong, J. Fan, S. Mao, Y. Lan, Y. Zou, H. Wang, J. Zhang, and X. Ma, “Effect of annealing on the damage threshold and optical properties of HfO2/Ta2O5/SiO2 high-reflection film,” Chin. Opt. Lett. 17(11), 113101 (2019). [CrossRef]
18. J. Bellum, E. Field, D. Kletecka, and F. Long, “Reactive ion-assisted deposition of e-beam evaporated titanium for high refractive index TiO2 layers and laser damage resistant, broad bandwidth, high-reflection coatings,” Appl. Opt. 53(4), A205–211 (2014). [CrossRef]
19. P. R. Yoder Jr, “Opto-mechanical Systems Design,” (CRC University, 2005).
20. D. Vukobratovich and P. Coronato, “Unit moment analysis as a guide to mirror mount design,” Proc. SPIE 9573, 95730R (2015). [CrossRef]
21. J. G. Daly and M. D. Hawk, “Adhesive bonds for optics: analysis and trade-offs,” Proc. SPIE 10371, 1 (2017). [CrossRef]
22. C. L. Monti, “Athermal bonded mounts: incorporating aspect ratio into a closed-form solution,” Proc. SPIE 6665, 666503 (2007). [CrossRef]
