It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations

The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has form, $$ W({h}_0,\rho,\phi )=\sum_{j=0}^{\propto } \sum_{p=0}^{\propto \sum_{m=0}^{\propto {C}_{\left(2j+m\right)\left(2p+m\right)m}({h}_0{)}^{2j+m}(\rho {)}^{2p+m}(\mathrm{cos}\phi {)}^m where j , p and m are non-negative integers, ρ ϕ polar coordinates pupil, h 0 is object height. However, one non-zero component (i.e., C 133 3 cos ) missing from this when image plane not Gaussian plane. This implies that a sufficient condition only, rather than necessary condition, since it cannot guarantee all components can be found. Accordingly, paper presents new method determining any order. results show three six secondary tertiary aberrations, respectively, in existing literature.