Higher-order aberration and sensitivity analysis of symmetry-free optical systems

Due to the symmetry-free structure of off-axis systems, the aberration analysis based on a paraxial reference is not valid anymore. To solve this problem, a higher-order aberration analysis tool is developed based on the mixed ray-tracing method. The essential concept of the analysis tool is a mixture of the real and paraxial ray trace to obtain the surface-decomposed aberrations. In a symmetry-free system, the generalized paraxial ray-tracing is realized with the parabasal matrices, deduced from the real optical axis ray of the system together with the parabasal rays. The tool allows for the calculation of the surface-resolved full-order intrinsic/induced aberrations. Furthermore, a surface-additive Zernike coefficient fitting method is proposed, based on the full-order aberrations. This method is useful for the comprehensive aberration analysis of the systems suffering from strong induced effects. It can be also applied for sensitivity evaluation of the surfaces in the system from the manufacturing viewpoint. The limitations of the method lie in the numerical calculation, which limits the visualization of the relationship between the system structure and matrices.