Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

The application of freeform elements in optical systems increases the number of variables available for correction. This creates the potential to design compact systems with excellent imaging performance. However, it is non-trivial to determine which configuration of the system to choose and where to place the freeform element to obtain the best design. The knowledge of aberration distribution in the system is very helpful in answering these questions. In the following paper, we analyze Zernike surface contributions to the total wave aberration in non-symmetric freeform mirror systems using the method introduced in [J. Opt. Soc. Am. A 34, 1856 (2017). We demonstrate the benefits of the proposed method in determining effective location of the freeform element and in finding critical differences between possible configurations. By analyzing surface contributions to the total wave aberration characterized by Zernike fringe coefficients, it is possible to find solutions corrected for aberrations of orders higher than the order of coefficients used for freeform sag contribution described with the same Zernike polynomial set