While in OSCAR, the function Add_Astigmatism() can add an extra sagitta distortion with a Zernike polynomial over a certain diameter, it is not always practical. Sometimes, it is simpler to define a surface with two perpendicular radii of curvature R_x and R_Y.
The solution described here was given to me by Jean-Yves Vinet (a big thank from all the OSCAR users). A 3D ellipsoid in a general manner could be defined as the surface following this equation:
Isolating the z coordinate, the above equation could be written as:
For a surface tangential to the plan z = 0, we take:
In case of astigmatic mirror with R_x and R_y, we can set: