## Appendix A  
For an optical system with \(n\) surfaces, when the surface \(k\) is tilted, the aberration field decenter vector of before the the surface \(k\) is 0, and the surface \(k\) and the subsequent \(j\) surfaces have the aberration field decenter vector that is not 0. The aspheric aberration field decenter vector of surface \(k\) is 0, so the aberration field decenter vector of surface \(k\) is equal to spherical aberration field decenter vector, as follows [19]:  
\[\overset{\rightarrow}{\sigma}_{k}=\frac{\overset{\rightarrow}{T_{k}}}{ \overset{\rightarrow}{i_{k}}} \tag{1}\]  
\(\overset{\rightarrow}{T_{k}}\) is the tilt vector of surface \(k\), and \(\overset{\rightarrow}{i_{k}}\) is the chief ray incident angle of surface \(k\). The aberration field decenter vectors of \(j\) surfaces behind surface \(k\) can be obtained through optical axis ray (OAR) tracing. When j surfaces are all spherical, the aberration field decenter vector of surface \(j\) is as follows [19]:  
\[\overset{\rightarrow}{\sigma}_{j}=\frac{\overset{\rightarrow}{T_{k}}}{\overset{ i_{j}}{i_{j}}}\big{(}i_{j}\cdot\overline{y}_{k}-\overset{i_{j}}{i_{j}}\cdot y_  
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