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

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 holo-grams 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 synchro-nous superposition algorithm in which the complex ampli-tude 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 esti-mation method.Meanwhile,the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.

Development of surface reconstruction algorithms for optical interferometric measurement

Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing.A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications,but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy,speed,robustness,and dynamic range,especially in on-line or on-machine conditions.This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements.Principles,configurations,and applications of typical optical interferometers with different capabilities and limitations are presented.Theoretical background and recent advances of fringe analysis algorithms,including coherence peak sensing and phase-shifting algorithm,are summarized.The new developments in measurement accuracy and repeatability,noise resistance,self-calibration ability,and computational efficiency are discussed.This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement.To address these challenges,advanced techniques in image stitching,on-machine measurement,intelligent sampling,parallel computing,and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.