Tang, Z.Z.TangGross, H.H.Gross2022-05-062022-05-062021https://publica.fraunhofer.de/handle/publica/41613110.1364/OE.4398622-s2.0-85119444189The imaging performance evaluation of symmetry-free optical systems is of great importance during the correction process of optical design. However, due to the complexity and limitations of the available tools, the higher-order aberrations in the system cannot be well analyzed and are hard to control. In this paper, the theoretical background and the mathematical approach of a quantitative analysis method for surface-decomposed transverse aberration in the symmetry-free systems are introduced. With the mixed ray-tracing calculation in both real and paraxial cases, the implementations of full-order intrinsic/induced aberration, as well as the surface-additive Zernike coefficient fitting method are demonstrated. The applications of this method help assess the correction performance considering the relatively critical surfaces in an arbitrary off-axis system. The reliability and the accuracy of the method will be evaluated in part II with a test system. And as an illustration of the practical usage of the method for optical design, the corresponding applications on a group of lithographic systems will also be demonstrated.enaberrationoptical system620621journal article