The internal orientation elements of a spaceborne camera are a key factor affecting the remote sensing accuracy, and precise calibration is required before the launch into orbit. During the imaging of a spaceborne camera in orbit, due to disturbances such as satellite temperature changes, deformation of optomechanical structures such as mirrors can occur to result in changes in internal orientation elements. However, there is currently little research on the analysis and testing techniques for on-orbit changes of orientation elements within spaceborne cameras. The optomechanical integration simulation technology has been widely applied to the performance analysis of spaceborne cameras, and some scholars have already applied it to the stability analysis of internal elements in cameras. Meanwhile, there is no research on the variation of internal orientation elements caused by temperature changes in camera calibration on the ground. Therefore, we study the change mechanism of internal orientation elements caused by optical component deformation, and provide optomechanical integration analysis and ground testing methods for evaluating the stability of internal orientation elements in orbit. Additionally, the accuracy of the proposed method by comparing simulation and experimental results is further demonstrated.

We propose a method for evaluating the stability of spaceborne cameras’ interior orientation elements, which includes integrated analysis and experiments. The finite element method is often adopted for thermal elastic analysis of optomechanical systems. The deformation of the finite element node after thermal elastic deformation will include both rigid displacement of the optical element and surface high-order deformation. The high-order deformation affects the surface shape accuracy of the mirror, while the rigid displacement will affect the line of sight. Firstly, based on the principle of the changes in the cameras’ internal orientation elements caused by the rigid body displacement of the mirrors, a mathematical model is built for the relationship between rigid body displacement and internal orientation elements. Then, the thermal elasticity analysis of the spaceborne camera is carried out by adopting the optomechanical thermal integrated analysis method, and the rigid body displacement under elastic deformation is extracted based on the best-fit method. Finally, in response to the testing requirements of internal orientation calibration under different temperatures, an experimental platform is established and the internal orientation elements are calibrated at different camera temperatures.

The spaceborne camera undergoes thermal elastic deformation when the temperature rises by 3 ℃ (Fig. 4). Based on the best-fit method, the rigid body displacement of various optical surfaces caused by thermal elastic deformation is further extracted (Tables 1 and 2). The variation in internal orientation elements after rigid body displacement of optical components is obtained by optomechanical integration simulation analysis (Table 3). In the ground experiments, internal orientation element calibration on the spaceborne camera is performed at temperatures of 20, 23, and 26 ℃ respectively (Fig. 6), with the results of internal orientation elements recorded in Table 4 and statistical analysis of changes in internal orientation elements caused by temperature differences of 3 ℃ shown in Table 5. Results show that the error between the simulation and experimental results of the camera’s internal orientation elements at different temperatures is within 0.1 pixel (Tables 3 and 5), which verifies the proposed integrated analysis method and experimental technology. The change in internal orientation elements of the camera under a temperature change of 3 ℃ is less than 0.3 pixel, further demonstrating the camera’s sound stability.

The proposed simulation and experimental analysis methods can effectively evaluate the stability of the camera’s internal orientation elements in temperature conditions, thereby fully verifying the stability of the camera’s internal orientation elements during the design and ground testing stages. The analysis of the internal orientation elements in traditional cameras mainly relies on software analysis, and only simulates and tests the stability of the internal orientation elements, with a lack of ground test verification methods and verification of simulation accuracy. Our study is based on the mechanism of temperature-induced changes in internal orientation elements. It builds not only an integrated simulation platform, but also a calibration testing platform for the cameras’ internal orientation elements including camera temperature control. On the one hand, it provides a systematic verification method for subsequent scholars to carry out related studies via simulation and ground testing. On the other hand, the calculation accuracy of simulation compared to calibration experiments is obtained to provide support for simulation analysis technology. After simulation and experimentation, the stability of the internal orientation elements of the spaceborne camera in a uniform temperature field of 3 ℃ is within 0.3 pixel, indicating sound thermal stability. Additionally, the simulation and experimental results of optomechanical integration show that the calculation error of the variation in internal orientation elements is within 0.1 pixel, which proves that the proposed simulation and experimental method has sound analysis and measurement accuracy.