相移相位测量的全息再现算法及测量误差分析

用全息原理和方法研究相移相位测量,得到了N步整周期相移再现物光波复振幅同步叠加函数(N步相移函数),同时提出一种新的相移相位测量误差分析和最大误差估计方法。N步相移干涉图是以理想平行光为参考光的无衍射同轴全息图,将其与对应的相移参考光相乘后求和得到N步相移函数;在理想情况下,这是一种复振幅分离、测量和物光波复振幅函数同步叠加方法,存在误差时计算出的相位是最小二乘方法的最佳期望结果。利用N步相移函数得到的N 1步相移函数,说明非理想N步相移函数是理想N步相移函数与误差函数之和,可以把相位型误差转化为与振幅和强度相对误差同等的误差来对待,降低了相位测量中误差估计的难度,给出了N步相移算法最大误差的估计方法和公式。

Holographic Reconstructing Algorithm and Its Error Analysis about Phase-Shifting Phase Measurement

Phase-shifting phase measurement is studied according to the holographic principle and method,a function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period is proposed,and N-step phase-shifting function is for short.Meanwhile,a novel error analysis and maximum error evaluation method for phase-shifting phase measurement is presented.In N-step phase-shifting phase measurement,the interferograms are seen as a series of in-line holograms without diffraction and the reference beam is an ideal parallel-plane wave.So the N-step phase-shifting function can be obtained by summing after multiplying the interferogram by the original reference wave.In the ideal condition,the proposed method is a kind of synchronous superposition algorithm in which the complex amplitude is separated,measured and superposed.When error exists in measurement,the result from N-shifting function is the optimal expected value of the least-squares fitting algorithm.In the above method,N 1-step phase-shifting function can be obtained from N-step phase-shifting function,indicating that the N-step phase-shifting function can be separated into two parts: the ideal N-step phase-shifting function and its errors.The phase-shifting errors in N-step phase-shifting phase measurement can be treated as same as the errors of amplitude and intensity under understanding of N 1-step phase-shifting function.The difficulties of the error evaluation in phase-shifting phase measurement are depressed by this error evaluation method.Meanwhile the maximum error evaluation method of phase-shifting phase measurement and its formula are proposed.