基于扩展平均的多步相移算法及误差抑制特性比较

Multi-step Phase-shifting Algorithm Based on Extended Averaging Technique and its Error Suppression Characteristics Comparison

为满足移相干涉测量中纳米甚至亚纳米高准确度检测要求,需采用对误差敏感度更低的相移算法.基于扩展平均技术,在传统4步和3步算法的基础上分别推导了A类和B类5~13步相移算法公式,以5、6、7和13步算法为例,通过仿真及数值计算,比较了两类算法对相移器移相误差及CCD非线性误差的抑制特性.结果表明：同类算法下,步数越多的算法,对这两项误差的抑制效果越好,但达到一定步数后对测量的影响可以忽略;B类算法具有增强的移相误差抑制能力,在相移不准情况下可优先选用B类算法;A类算法对CCD非线性误差几乎完全免疫,而B类算法受一定CCD非线性误差影响,但对大多数高准确度CCD来说,其在常规检测中的影响可以忽略;由相移噪音引入的随机性测量误差的极大值要略大于相移噪音本身,且不同算法对相移噪音的抑制效果差别不大,因此相移噪音对测量的影响不可忽略.文中给出了不同误差影响下各算法引入波面检测误差的比较数据,研究结果可为实际干涉测量中最适相移算法的使用和选用提供理论指导及数据参考.

In order to meet the requirements of nano or even hypo-nano measurement accuracy in phaseshifting interferometry,multi-step phase-shifting algorithms with lower sensitivity to errors are needed. Based on traditional 4and 3steps algorithms,class A and class B of 5to 13steps phase-shifting algorithms were deduced based on extended averaging technique.Take 5,6,7and 13steps algorithms as example,suppression characteristics of algorithms to PZT phase shift error and CCD non-linearity error were compared through simulation and numerical calculation.The results show that the error suppression effect to above two error sources becomes better with the increasing of its steps,but when the steps reach a certain number,the values of errors are insignificant for the measurement.Class B algorithms have enhanced phase shift error suppression effect,and as for large phase shift error,class B algorithms are preferred.Class A algorithms are almost completely immune to 2nd order CCD non-linearity error,class B algorithms have some sensitivity to this error,but the influence are very small for most high accuracy CCD in common measurement.Also,the phase noise should not be neglected in measurement,and maximum value of PV wavefront measurement error caused by phase shift noise is larger than the noise itself in many times calculation.Wavefront errors of different algorithms caused by different errors were acquired,and the research can provide favorable reference for the using or choosing of suitable phaseshifting algorithm in actual interferometry.