Real-time measurements of phase steps out-of-range (0, 2π) by a dynamic self-calibrating generalized phase-shifting algorithm

摘要

Recently, a method for measuring phase steps in real-time from a dynamic interferogram within the range (0, 2 pi) has been presented. It was named Dynamic Volume Enclosed by a Surface (DVES) method and was built on a very well known algorithm of type self-calibrating generalized phase-shifting interferometry relied on geometric concept of volume enclosed by a surface (VES), which is enough fast, and accurate. DVES is validated by the properties and conditions given by VES, so a measurement within the range (0, 2 pi) is accepted, and out-of-range is rejected. In this manuscript, we restructure the DVES method to be able of measuring in real-time phase steps out-of-range (0, 2 pi) rad, which is the best of our contributions. Besides, the VES conditions are dropped, except at t = 0 when the system is calibrated, and the VES properties are synthesized mathematically to only a control signal, and two equations to correct the measured phase steps automatically when necessary. Finally, an unwrapping algorithm is applied to obtain a continuous curve. It makes the present proposal a very efficient method for real-time measurements without limitations in the phase-steps. The viability of our proposal is done with a numerical simulation, and the verification is carried out by retrieving experimentally a continuous curve of phase steps from a slide respecting to its rotation angle.