Random two-frame phase-shifting interferometry via minimization of coefficient of variation

Random two-frame phase-shifting interferometry (PSI) is an advanced technique to retrieve the phase information from as few as two interferograms with unknown phase steps. Because of the advantages of no requirement for accurate phase shifters and much less time for data acquisition and processing, random two-frame PSI is attracting more and more interest in fast and high-precision optical metrology. However, reconstructing the phase from only two interferograms is challenging because it is an ill-posed problem in essence, especially when the phase step is unknown. Although some solutions have been proposed for this problem to date, most of them require complicated preprocessing or special usage preconditions for interferograms to be demodulated. In this letter, we developed an elegant phase reconstruction method for random two-frame PSI, which is much different from frameworks of existing methods. In the proposed approach, the phase of random two-frame PSI can be accurately reconstructed using the phase step value which minimizes the coefficient of variation (CV) of the modulation term of interferograms. Sufficient numerical simulations and experimental data demonstrate the high accuracy and high efficiency of this CV minimization (CVM) method. Moreover, its performance is not limited by the number of fringes in interferograms, in contrast to existing state-of-the-art approaches. We anticipate extensive applications of the CVM method in random two-frame PSI in the future.