Optimization method for off-axis reflective optical systems based on linear astigmatism control

A full-field astigmatism characterization and optimization method based on Legendre polynomial expansion is proposed to address the difficulty of directly constraining linear astigmatism in off-axis reflective optical systems. In this method, the full-field astigmatism distribution is treated as a function of field coordinates and decomposed using orthogonal Legendre polynomials. The first-order expansion coefficients are used to characterize the linear astigmatism component, thereby establishing a quantitative metric for linear astigmatism evaluation. By integrating the ZOS-API with a user-defined operand (UDOC) in ZEMAX, direct constraint and optimization of linear astigmatism are achieved. An off-axis three-mirror system is used as a design example to validate the proposed method. The results show that the linear astigmatism coefficient is reduced from 0.024967 to 0.008183, a reduction of 67.22%, while both the spot diagrams and the modulation transfer function (MTF) are significantly improved. The proposed method effectively suppresses linear astigmatism in off-axis reflective optical systems and provides what we believe to be a new approach for their optimization design.