Desensitization optimization method for a space camera with a tiltable secondary mirror based on the nodal aberration theory

During in-orbit imaging, space cameras are susceptible to platform vibrations, leading to image blur and target positioning deviations. To achieve high-precision image stabilization, catadioptric optical systems often employ tilt control of the secondary mirror (SM) to compensate for image motion. However, SM tilt introduces additional aberrations that degrade the imaging quality. Based on the nodal aberration theory (NAT), this study systematically derives analytical expressions for the sensitivity of astigmatism and coma to SM tilt, constructs a desensitization evaluation function with the root mean square of sensitivity as the objective, and proposes a desensitization optimization method for space cameras with a tiltable secondary mirror. Validation via optical design case studies demonstrates that under SM tilt conditions of ±0.05^∘, the proposed method significantly enhances the modulation transfer function (MTF) values at the Nyquist frequency and improves image quality across the entire field of view while also strengthening the system's tolerance performance. The imaging performance across all aspects surpasses that achieved by both conventional methods and SAB optimization. The results indicate that the proposed method effectively enhances the imaging stability of space cameras in disturbed environments while maintaining structural rationality.