Simultaneous Compensation for Perturbed Dual-Channel Telescopes Based on Nodal Aberration Theory

Active compensation for perturbed space telescopes is an effective means of improving the image quality. In common-aperture dual-channel telescopes, compensation can only be achieved by adjusting a shared secondary mirror (SM), making it difficult to balance the inconsistent misalignment aberrations between the channels. To address this issue, an analytic method for simultaneous compensation of dual-channel aberrations is proposed. Based on the improved Nodal Aberration Theory (NAT), the analytic solution for the common compensation position of the SM is derived by establishing a geometric balance between the aberration field nodes in the image planes of the two channels. On this basis, the theoretical conditions required for the consistency of the optimal compensation positions in the dual channels are also presented. The robustness of the method is validated through Monte Carlo simulations under conditions of random noise and surface figure errors. The results show that the average RMS wavefront error (WFE) of each channel is reduced to less than λ/16 (λ = 632.8 nm) after compensation under various misalignment conditions. Compared with the traditional Sensitivity Matrix Method (SMM), the proposed method exhibits superior compensation accuracy and decoupling capability in correcting dual-channel aberrations, thereby significantly improving the optical performance of the system.