Aberration field distribution characterization and tolerance analysis based on nodal aberration theory

Tolerance analysis is a critical bridge between optical design, manufacturing, and system alignment. The numerical evaluation metrics used in traditional methods can reflect the overall image quality but are insufficient to reveal the specific composition and distribution characteristics of the residual aberrations. In high-precision and complex optical systems, these metrics obscure the intrinsic relationship between system tolerance and imaging quality, thus limiting their analytical capability. To address this issue, an analytical expression for the wavefront aberration of the complex freeform optical system under tolerance perturbations is derived based on nodal aberration theory (NAT) and double Zernike (DZ) polynomials. An aberration field distribution model is then constructed using the derived expression. A freeform off-axis three-mirror system is used to validate the proposed model. By comparing the full-field displays (FFDs) of aberrations obtained from the model with those derived from real ray tracing, the similarity exceeds 0.8, which validates the proposed model. On this basis, a tolerance analysis method based on aberration field distribution is proposed. This method provides theoretical support for deeply understanding the mechanism of tolerance perturbations on aberration characteristics and addresses the limitation of current commercial software in performing full-field tolerance analysis for specific aberrations.