The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement

Abstract

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.