Centroiding Error Modeling and Code Optimization for Restored Star Images Using Coded Exposure in High-Dynamic Conditions

Under high-dynamic conditions, star sensors often capture images with low signal-to-noise ratio (SNR). Image restoration can mitigate energy dispersion from star trailing, but it is inherently ill-posed with conventional exposure. Coded exposure, with its reversible blur kernel, preserves more information and enables higher-quality star image restoration. However, existing studies focus on the restoration process but cannot quantitatively analyze centroiding accuracy in restored star images. To analyze the centroiding accuracy, this paper establishes a full-link model including the imaging and restoration process of coded-exposure star sensors based on Fourier optics, and provides a spatial-frequency domain representation of restored star points. A centroiding error model is derived and its influencing factors are analyzed. Based on the error model, a code optimization strategy for high-dynamic star image restoration is proposed to further improve centroiding accuracy. Experimental results show strong consistency with the proposed centroiding error model. Under high-dynamic conditions (SNR = 2∼3), the optimized code reduces centroiding error by 12.7% compared to Raskar’s optimal code. Compared with the commonly used Richardson–Lucy restoration algorithm, the deconvolution restoration algorithm employed in this paper achieves lower centroiding error with only 1/25 of the computation time.