Lie algebraic approach to the problem of computing the third-order aberrations of optical systems

The seidel third-order aberration coefficients of a thick lens imaging system are derived analytically with the aid of Lie algebra and optical symplectic map.We have shown that the expressions obtained in this paper are general and applicable to analyzing aberrations of the conventional optical imaging systems such as thin lens,concave(or convex)-planar lens and spherical lens etc.By a suitable choice of geometrical parameters.