Double Zernike polynomial-based desensitization design method for off-axis optical systems

High-performance off-axis optical systems require not only excellent nominal performance but also strong robustness against alignment tolerances. However, in conventional desensitization procedures for off-axis systems, the lack of an efficient full-field wavefront representation and sensitivity evaluation framework limits the design efficiency. In this work, a practical desensitization design method is developed by integrating the double Zernike (DZ) polynomial with nodal aberration sensitivity (NAS). The double Zernike expansion is introduced as the full-field representation of the optical path difference (OPD) to address the lack of field dependence in Zernike polynomials. The DZ coefficient matrix is determined through discrete orthogonality and Gaussian quadrature (GQ) with specific sampling conditions in both the field and pupil domains. Based on the DZ coefficient matrix, the full-field wavefront representation is incorporated into an NAS-guided sensitivity evaluation. The full-field wavefront reconstruction capability of DZ polynomials is validated in a TMA (three-mirror anastigmat) system. The DZ-based aberration model is then incorporated into a sensitivity-guided desensitization optimization of an off-axis four-mirror telescope for gravitational-wave detection. Under the same alignment tolerances, the maximum full-field RMS wavefront error of the optimized design at the 90% cumulative probability level is reduced from 0.0843λ to 0.0324λ (λ = 1064 nm). These results demonstrate the effectiveness of the proposed method for full-field wavefront reconstruction and robust design of complex off-axis optical systems.