Full-field vibration amplitude recovery from high-resolution time-averaged speckle interferograms and digital holograms by regional inverting of the Bessel function

High-resolution time-averaged speckle interferometry and quasi-binary electronic speckle interferometry are two methods used in mechanical vibration measurement. The first method is used to increase the spatial resolution of time–average patterns. Detecting with subpixel resolution the minima of the Bessel-type fringes becomes thus possible. The second method is used to obtain a high contrast of the fringe pattern and a measurement range doubled with respect to that of traditional time–average holography. Quasi-binary fringes are loci of constant sign of the Bessel function modulating the object image. The two methods are closely related and based on a common principle. The objectives of the paper are to extend these methods to Fresnel digital holography and to propose a new data processing algorithm, allowing using the time–average hologram for calculating the unwrapped vibration-related phase map. The phase is calculated by local inversion of the Bessel function. Quantitative data processing is possible for both undersampled and oversampled fringe patterns. Only the basic holographic equipment is used, without any stroboscopic or modulating devices.