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。

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.