Analytical aberration theory for plane-symmetric optical systems and its application in distortion analysis of spectrometers

Based on a generalization of paraxial optics and wavefront aberration expansion, we derive the aberration coefficients of main aberration types (i.e., third-group aberrations) in plane-symmetric systems. The derivation removes approximations used in prior work and includes contributions from freeform surfaces and induced aberrations to reach formulas of aberration coefficients that are widely applicable to plane-symmetric systems. The analytical formulas of aberration coefficients provide a good prediction of aberrations in an optical system based on the arrangement and shapes of optical surfaces without real raytracing. When applied to the analysis of distortion in freeform spectrometers, the theory predicts distortion behavior consistent with results simulated from real raytracing. The formulas of aberration coefficients also provide useful insights on aberration balancing between surfaces and between intrinsic and induced aberrations.