Time-directional filtering of wrapped phase for observing transient phenomena with parallel phase-shifting interferometry

Recent development of parallel phase-shifting interferometry (PPSI) enables accurate measurement of time-varying phase maps. By combining a high-speed camera with PPSI, it became possible to observe not only time-varying but also fast phenomena including fluid flow and sound in air. In such observation, one has to remove static phase (time-invariant or slowly-varying phase unrelated to the phenomena of interest) from the observed phase maps. Ordinarily, a signal processing method for eliminating the static phase is utilized after phase unwrapping to avoid the 2π discontinuity which can be a source of error. In this paper, it is shown that such phase unwrapping is not necessary for the high-speed observation, and a time-directional filtering method is proposed for removing the static phase directly from the wrapped phase without performing phase unwrapping. In addition, experimental results of simultaneously visualizing flow and sound with 42 000 fps are shown to illustrate how the time-directional filtering changes the appearance. A MATLAB code is included within the paper (also in https://goo.gl/N4wzdp) for aiding the understanding of the proposed method.