基于迭代算法的两平板互检求解方法

提出了一种基于两平板绝对检验的迭代面形恢复算法。算法基于两平板互检方法，通过分别翻转和旋转其中一块平板，获得4次两两测量结果。对测量得到的4个结果数据进行翻转和旋转逆操作，直接推导出三个面形与测量结果及相互之间的关系公式。设置初始面形，逐次迭代逼近4次测量结果。实验表明，该方法仅需要50次以内迭代，即可得到偏差小于0.1 nm均方根值的绝对面形。详细分析了实验过程中的各项误差来源，并对每项误差进行了定量计算，获得总的测量误差为1.417 nm。

Abstract

A method for reconstruction surfaces map on iterative algorithm is presented. According to flipping and rotationg one of the two plates, four measurements are generated. The formulas are directly derived from four measurements that require rotation or flipping operations. Three trial surfaces are initialized, then the new surfaces are calculated according to the formulas. The trial surfaces are replaced by the new surfaces. The experiment shows that this method can achieve a deviation of 0.1 nm, which only requires no more than 50 iterations．And the error sources are analyzed in detail. The total measuring error of this method is 1.417 nm.

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基于迭代算法的两平板互检求解方法

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