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引用次数: 0
摘要
虽然二阶表面分析,主要是平均功率和柱面图,通常用于描述渐进加法镜片(PAL)表面的特征,但最近有人提出,三阶变化也可能与渐进加法镜片的光学和视觉性能有关。本文提出了一种三阶平滑度量及其相关的黎曼距离,以进一步表征 PAL 的表面光学性能。这些指标可作为经典指标的补充评分工具,特别是用于分析远、近、中间和混合区之间的过渡区域。本文提供了计算这些指标的方法。这种三阶平滑度量还能对 PAL 主曲线进行正式定义,即嵌入 PAL 表面的曲线,该曲线能使连接远近参考点的线径积分最小化,并采用三阶平滑度量加权。最后,本文介绍了一种利用平集大地程序计算此类主曲线的综合方法。所有这些想法都将通过几个真实的 PAL 曲面付诸实践。
Third-order smoothness metric to characterize progressive addition lenses
Although second-order surface analyses, mainly mean power and cylinder maps, are commonly used to characterize the progressive addition lens (PAL) surface, recently it has been suggested that third-order variations may also have relevancy in PAL optical and visual performance. This paper proposes a third-order smoothness metric, and its associated Riemannian distance, to further characterize PAL’s surface optical performance. These metrics can provide a complementary scoring tool to those classical ones, particularly, to analyze the transition zones between far, near, intermediate, and blending zones. A method to compute these metrics is provided. This third-order smoothness metric also enables a formal definition of the PAL principal curve, namely, the curve embedded in the PAL surface, that minimizes the line path integral joining the far and near reference points weighted by the third-order smoothness metric. Finally, the paper describes a comprehensive methodology to compute such principal curves using a level-set geodesic procedure. All these ideas are put into practice with several real PAL surfaces.