To realize separation and phase demodulation of superimposed interference intensity signals in multi-surface interferometry measurements,a frequency-corrected-based multi-surface wavelength-shift-ing interferometry algorithm is proposed,which can realize the simultaneous reconstruction of the surface shapes of the measured transparent plates.The wavelength-shifting interferometry technique can enable each interference harmonic to feature different phase-shifting values according to the corresponding opti-cal path difference(OPD),which provides the basis for the separation and phase demodulation of each signal.In existing multi-surface measurement techniques,the harmonic frequencies are often roughly es-timated from information such as the cavity length and optical thickness of the measured plates,but the estimation accuracy is low and cannot cope with phase-shifting errors.Therefore,this paper realizes the accurate extraction of each interference harmonic frequency by multi-point averaging and frequency cor-rection,which can effectively eliminate the influence of abnormal value and additive Gaussian noise(AGN)on the frequency solution accuracy,and can demodulate each harmonic phase simultaneously only by the weighting operation between interferograms.The comparative analysis and experimental results verify the reliability of the proposed algorithm.
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