Objective The imaging quality of compound eye optical system is affected by many factors, such as material performance changes, processing and adjustment errors, optical and mechanical structure deformation and so on. As a key integrated component in the compound eye optical system, the dimensional accuracy of the spherical cover determines the positioning accuracy between the relay cylinders and the spherical lens. Generally, considering the weight reduction of the overall system, there is a preference for thinning its wall thickness. However, when the wall thickness is thinned to a certain extent, the thermal deformation of the spherical cover structure increases due to ambient temperature fluctuations, and its impact on the image quality of the compound eye system can not be ignored. In the process of optical system design, usually based on the designer's experience and processing level, using the method of tolerance analysis, by observing the sensitive items and pass rate to realize the performance stability prediction of optical system before actual processing is not perfect. In aerospace and missile guidance, the use of digital photography combined with sensors can also achieve high-precision monitoring of thermal deformation, but it requires actual sampling, which cannot achieve the purpose of pre manufacturing prediction. It is hoped that the basic strategies and findings of this study can help to predict the stability of the same type of compound eye optical system and provide an effective reference for the structural design of the spherical cover.

Methods A 3×3 array compound eye optical system is designed by using Zemax software, which is mainly composed of spherical concentric objective lens system and relay system(Fig.1). Because the light from the spherical concentric objective lens is a concentric beam, the influence of thermal deformation is small. In the rear relay camera array, if the optical axis of the sub camera is not concentric, the imaging quality will be seriously affected. Therefore, the spherical cover, a thin-walled structure with high accuracy requirements, is selected as the research object of thermal deformation. Based on the structural parameters, the spherical cover model is established in Solidworks and imported into Hypermesh for structural mesh generation (Fig.4). Imported into ANSYS Workbench, the position information and deformation data of the key nodes on the edge of the mounting hole on the spherical cover are extracted through the finite element steady state thermal structure coupling analysis, and the thermal deformation data is obtained through data processing, which is converted into the error of the corresponding optical system and inversely returned to the structure of the optical system, so as to realize the simulation of the impact of the thermal deformation of the structure on the imaging quality of the system.

Results and Discussions A method is proposed to predict the influence of thermal deformation of spherical cover structure caused by ambient temperature change on the imaging quality of compound eye optical system. The MTF of the single channel of the designed compound eye optical system is higher than 0.4 at the spatial frequency of 100 lp/mm, the maximum distortion of the system is 0.309%, and the wavefront aberrations of different wavelengths and fields of view are less than 0.25 λ (RMS), meeting the requirements of general imaging system(Fig.2). The position information and deformation data of the key nodes at the edge of the mounting hole on the spherical cover are extracted by ANSYS Workbench (Fig.9), and the thermal deformation of the spherical cover in a stable temperature environment (30-100 ℃) is simulated. The thermal deformation is converted into the corresponding optical system error and introduced into the initial compound eye optical system structure to realize the secondary evaluation of the system performance (Fig.8), which provides an effective reference for the structural design of the spherical cover.

Conclusions The thermal deformation of the spherical cover is converted into the error of the corresponding optical system and introduced into the compound eye optical system structure. The results show that the thermal deformation of the spherical cover will lead to the maximum deformation of 0.424 mm (Fig.5) and the tilt error of −0.367°-0.270° along the axis of the relay sub camera, and the tilt error is the key factor affecting the image quality of the compound eye optical system. The thermal expansion of the structure mainly presents a "bulge" shape, and the closer to the center (except for the central hole position), the greater the tilt error, resulting in a more significant decline in image quality. The application ambient temperature of the designed compound eye optical system should not be greater than 70 ℃.