线性化拟合高次非球面

High-order Aspheric Surface Fitting Based on Linear Match

在光学非球面镜制造过程中,由于诸工艺参数的影响,能否保证非球面方程各个系数的精度是一个重要问题.为利用非球面检测数据拟合非球面方程,将常见的高次非球面方程进行归类:抛物线型,W型和M型,并提出相应类型下高次非球面方程的线性化方法,由此转化为线性化最小二乘问题.经过实例验证,该方法对抛物线型的拟合精度高达1μm,W和M型的拟合精度高达10μm.该方法操作简单,不需要初值,可靠性高,可以达到较好的拟合效果.

In order to make sure of the accuracy of high - order aspheric equations coefficients which are affected by many processing parameters in the manufacture, a surface fitting method based on linear match was presented. According to the measured data, high - order aspheric equations can be classified into three types： parabola type, W type and M type. And corresponding linearization method was proposed. Then the problem was transferred into linear least square fitting. After example validating, the precision of parabola type was in the or- der of 1 μm, while those of W type and M type are 10μm. Satisfied fitting features and reliable results can be ob- tained by this simple method without initial value.