Approximate analytic astigmatism of unit-magnification multipass system.

We develop a way to estimate the approximate analytic astigmatism with a high accuracy for any unit-magnification multipass system (UMS). The coaxial optical transmission model for UMS is simplified based on the system's features. Furthermore, astigmatism is derived as a distinct form of vector addition and, thus, feasible analytic astigmatism can be obtained. The effectiveness of our method is verified by simulations for a Bernstein-Herzberg White cell. In our cases, the relative error of optimization for astigmatism correction by our method is smaller than 5 per thousand, which is only one-tenth of that by Kohn's method. Our method significantly improves the efficiency for astigmatism correction, and further benefits the optical design of a UMS.