Takaki Nick, Bauer Aaron, Rolland Jannick P
Appl Opt. 2018 Dec 10;57(35):10348-10354. doi: 10.1364/AO.57.010348.
Orthogonal polynomials offer useful mathematical properties for describing freeform optical surfaces. Their advantages are best leveraged by understanding the interactions between variables such as tip and tilt, base sphere and conic variables, and packaging variables that define the problem of design for manufacture. These interactions can cause degeneracy, which can complicate the interpretation of design specifications in manufacturing and, consequently, negatively impact the cost of fabrication and assembly. Optimization constraints to break degeneracy during design are also discussed.
正交多项式为描述自由曲面光学表面提供了有用的数学特性。通过理解诸如倾斜和俯仰、基础球面和圆锥变量以及定义制造设计问题的封装变量等变量之间的相互作用，可以最好地利用它们的优势。这些相互作用可能导致简并，这会使制造中设计规范的解释变得复杂，从而对制造和组装成本产生负面影响。还讨论了在设计过程中打破简并的优化约束。
