Analysis and compensation of the influence of chromatic aberration on the imaging model parameters of star sensors

Objective Star sensors serve as crucial tools for providing high-precision three-axis attitude information for various spacecraft, relying on stars as their reference points. To ensure the accuracy of star sensor attitude measurements, calibration is essential to obtain precise imaging model parameter values. However, stars can be divided into different spectral types, each representing unique radiation characteristics. Current laboratory calibration methods commonly employ a single spectral band to simulate star imaging for parameter calibration, neglecting the spectral diversity of stars. Due to the disparity between the energy distribution of the single spectral band and the actual stellar spectral distribution, chromatic aberration leads to differences between the model parameter values obtained using the existing single spectral band calibration and the true values, thereby impacting on the accuracy of star sensor attitude measurement. Since complete elimination of lens chromatic aberration is unfeasible, this paper proposes a parameter compensation method for star sensor imaging models based on the spectral characteristics of stars. This approach aims to improve the accuracy of model parameters and reduce the impact of chromatic aberration on star vector measurement, thus improving the measurement accuracy of star sensors. Methods The article first establishes a star sensor imaging model under spectral differences, and further analyses how chromatic aberration affects the imaging model parameters for stars of varying spectral types. These analyses reveal that different spectral types of stars correspond to distinct imaging model parameters. Based on the established model mentioned and the theoretical analysis above, the article abandons the original method of simulating stellar imaging with a single wavelength. Instead, it proposes using three typical spectral bands to simulate stellar imaging, and calculate the imaging positions of stars with different spectral types using information from these three spectral bands. By collecting calibration dates using the calibration system, as depicted in Fig. 6, optimization methods are used to calibrate the imaging model parameters of stars with different spectral types. With this calibration result, the imaging model parameters of stars with different spectral types can be compensated after the star has been identified, thereby improving the accuracy of imaging model parameters. Results and Discussions Using the calibration method proposed in the paper, the imaging model parameters corresponding to different spectral types of stars are acquired and presented in Fig.7-9. Building upon these findings, the paper employs the calibration results to compensate for the imaging parameters of identified stars. The experiment demonstrates that the proposed compensation method can effectively reduce the error in measured star angular distance, with detailed comparison results illustrated in Fig.12. Compared to the angular distance measured by existing parameters calibrated using a single spectral band, the root mean square error of star angle distance measured by this compensation method is reduced by 40.81%. Unlike existing methods that rely solely on a single spectral band to simulate stellar imaging, the proposed method offers a more realistic simulation of stars of different spectral types under chromatic aberration. Consequently, it yields more accurate imaging model parameters for stars of varying spectral types, thereby reducing the impact of chromatic aberration on the measurement error of star angular distance. Conclusions This paper begins by acknowledging the differences in the spectral energy distribution among stars of various spectral types, as well as the inherent vertical chromatic aberration in transmission lenses. It proceeds to model and analyze how chromatic aberration affects the imaging model parameters for stars with different spectral types. Furthermore, it introduces a parameter compensation method and validates its effectiveness through field experiments. The findings of this study offer valuable insights and novel research avenues for enhancing the measurement accuracy of star sensors. Future research can explore the use of more spectral bands to simulate stellar imaging, thereby further improving the accuracy of model parameters. © 2024 Chinese Society of Astronautics. All rights reserved.