%A LU Xiaoxu, ZHONG Liyun, ZHANG Yimo
%T The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement
%0 Journal Article
%D 2007
%J Front. Electr. Electron. Eng.
%J Frontiers of Electrical and Electronic Engineering
%@ 2095-2732
%R 10.1007/s11460-007-0054-3
%P 293-297
%V 2
%N 3
%U {https://journal.hep.com.cn/fee/EN/10.1007/s11460-007-0054-3
%8 2007-09-05
%X Phase-shifting measurement and its error estimation method were studied according to the holographic principle. A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period (*N*-step phase-shifting function for short) was proposed. In *N*-step phase-shifting measurement, the interferograms are seen as a series of in-line holograms and the reference beam is an ideal parallel-plane wave. So the *N*-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave. In ideal conditions, 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 of the *N*-step phase-shifting function is the optimal expected value of the least-squares fitting method. In the above method, the *N*+1-step phase-shifting function can be obtained from the *N*-step phase-shifting function. It shows 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*-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the *N*+1-step phase-shifting function. The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error estimation method. Meanwhile, the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.