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为了克服非球面（特别是高次非球面）光学系统自动设计中的严重困难，我们运用辛卜森数值积分及若干数学处理建造了一种全新的优化指标——辛卜森指标。为减少实际追迹光线的计算量并同时满足辛卜森积分对等距节点上函数值的要求，采用拉格郎日插值方法计算若干非常规抽样光线对应的垂轴像差近似值。事实证明，辛卜森指标的引用可以迅速改善很差的初始结构，大大减少优化过程中的慢收敛、发散、震荡或“无解”，实现快速而稳定的优化；将它用于预优化过程，可以为后续自动设计提供优异的“雏型”结构，还可从纯球面系统入手，自动设计出理想的非球面系统；利用它还可自动确定各非球面参数的合理的增量
In order to overcome the serious difficulties in the automatic design of aspheric (especially high-order aspheric) optical systems, we built a new index of optimization, the Simpson index, by using Simpson numerical integration and several mathematical treatments. In order to reduce the computational complexity of tracing light and meet the requirements of the function value of equidistant nodes by using SABO integrals, Lagrangian interpolation method is used to calculate the vertical axis aberration approximation of some unconventional sampled rays. It turns out that references to the Simpson Index can quickly improve poor initial structures, greatly reduce slow convergence, divergence, turbulence, or “no solution” in the optimization process to achieve fast and stable optimization; use it for the pre-optimization process , Can provide excellent “prototype” structure for subsequent automatic design, but also start from the pure spherical system, automatically design the ideal aspheric system; use it to automatically determine the reasonable increment of each aspherical parameter