Defocus estimation for star sensors based on closed energy contours

This paper presents a novel, to our knowledge, defocus estimation method for star sensors, leveraging the equivalent radius R₈₀ of the 80%-energy closed contour in conjunction with pixel-phase compensation. In contrast to existing approaches, the proposed method operates on a single isolated-star-spot image and circumvents the need for complex parametric reconstruction of the point-spread function. The processing pipeline comprises background subtraction, noise suppression, centroid estimation, and pixel-phase compensation, followed by subpixel interpolation and threshold-based searching to extract the largest connected region that encloses approximately 80% of the total spot energy. The radius of an equal-area circle is then adopted as R₈₀, and a quadratic calibration model is established to relate R₈₀ to the axial defocus. Experiments conducted over a defocus range from -0.46875 to 0.46875 µm confirm that R₈₀ varies quadratically with defocus. Notably, pixel-phase compensation reduces the mean standard deviation of R₈₀ from 0.0426 to 0.0214 pixels, yielding a 49.8% improvement in repeatability. On independently acquired test images, the mean absolute bias of the seven position-wise mean estimates is 0.0092 µm. Owing to its single-image requirement and avoidance of iterative PSF fitting, the method is particularly well suited for practical focal-plane alignment and on-orbit image-quality assessment in star sensor systems.