Jester Philipp, Menke Christoph, Urban Karsten
Corporate Research and Technology, Carl Zeiss AG, Carl-Zeiss-Strasse 22, 73447 Oberkochen, Germany.
Appl Opt. 2011 Feb 20;50(6):822-8. doi: 10.1364/AO.50.000822.
We introduce a representation of aspheric surfaces that is based on a B-spline quasi-interpolation scheme. The scheme is implemented in a ray trace algorithm, and bounds on the approximation error are established. Examples for the reproduction of aspheric surfaces in polynomial description and the ray tracing accuracy are presented. The proposed approach allows the specification of local and global structures and the efficient treatment of measured surface data. The representation gives access to a wavelet analysis, offering extended possibilities for the tolerance analysis of optical systems containing aspheric elements.
我们介绍一种基于B样条准插值方案的非球面表示方法。该方案在光线追踪算法中得以实现，并确定了近似误差的界限。文中给出了多项式描述下非球面再现的示例以及光线追踪精度。所提出的方法允许指定局部和全局结构，并能有效处理测量得到的表面数据。这种表示方法可用于小波分析，为包含非球面元件的光学系统的公差分析提供了更多可能性。
