Seidel primary ray aberration coefficients for objects placed at finite and infinite distances

In a recent study, the present group proposed a methodology for determining the Seidel primary aberration coefficients in terms of the polar coordinates of the source ray for an object placed at a finite distance from the entrance pupil [P. D. Lin and R. B. Johns, Opt. Express27, 19712 (2019)]. However, that model will be failed for an object placed at infinity. It is also found that all existing works in the optics field use in-plane coordinates of the entrance pupil (i.e., X_a and y_a) to investigate the aberration coefficients. Accordingly, the present study revisits the problem once again using a Taylor series expansion of a ray in terms of the object height h₀ and coordinates [x_ay_a]^T. In the proposed methodology, the independent variables of the optical system are identified and the intercept coordinates of the skew ray on the image plane are then expanded with respect to these variables. It is shown that the expressions of the Seidel primary aberration coefficients are very concise and the corresponding numerical results are in good agreement with those obtained from Zemax simulations. Notably, the method proposed in this study is also valid for objects lying at infinity provided that the collimated rays emerging from the object are incident on the entrance pupil. Moreover, the methodology can also be extended to have the numerical values of the higher-order ray aberration coefficients for axis-symmetrical systems.