Wilson Randall H, Brost Randy C, Strip David R, Sudol Ronald J, Youngworth Richard N, McLaughlin Paul O
Production Systems Engineering Technology Division, Eastman Kodak Company, 2901 Juan Tabo NE, Suite 210, Albuquerque, New Mexico 87112-1881, USA.
Appl Opt. 2004 Jan 1;43(1):57-66. doi: 10.1364/ao.43.000057.
Optical designs often specify both surface form and centering (tilt and lateral displacement) tolerances on aspheric surfaces. In contrast to spherical surfaces, form and centering errors are coupled for aspheric surfaces. Current standards do not specify how to interpret such tolerances, and in particular they do not define the position of an aspheric surface that has form errors. The straightforward definition that uses the best-fit surface position that minimizes rms error has subtle problems. The best-fit surface position for aspheric surfaces is influenced by power error and can be highly sensitive to surface form errors when the derivative of aspheric departure is small. We analyze the conditions under which form and centering tolerances may be considered compatible when the best-fit surface-position definition is used. We propose alternative definitions of surface position that do not suffer from the same problems and consider their consequences for optical design and metrology.
光学设计通常会规定非球面表面的表面形状和定心（倾斜和横向位移）公差。与球面不同，非球面的形状和定心误差是相互关联的。现行标准未规定如何解释此类公差，尤其是未定义存在形状误差的非球面表面的位置。使用使均方根误差最小化的最佳拟合表面位置的直接定义存在一些微妙问题。非球面表面的最佳拟合表面位置受光焦度误差影响，并且当非球面偏差的导数较小时，可能对表面形状误差高度敏感。我们分析了在使用最佳拟合表面位置定义时，形状公差和定心公差可被视为兼容的条件。我们提出了不会出现同样问题的表面位置替代定义，并考虑了它们对光学设计和计量学的影响。
