Vibration amplitude field estimation based on high-resolution time-averaged interferograms

Abstract

High-resolution time-averaged interferograms are obtained, in speckle interferometry or in digital holography, by using the orthogonal components of the hologram of the vibrating object and those of the object in a reference position. By using a procedure equivalent to the synchronous detection, one may obtain not only a high-resolution time-averaged fringe pattern but also a quasi-binary interferogram. The two fields are closely related to each other and present the interest of a significant phase noise reduction. In high-resolution time-averaged fringe patterns the center of dark fringes may be obtained with subpixel accuracy. Among the possible applications one is particularly interesting: the estimation of the complete vibration-related phase field, a result equivalent to phase unwrapping. The phase estimation is done solely on the basis of a single fringe pattern, whos fringe locus is the usual Bessel function. It is based on the local inversion of the Bessel function inside each of the different regions where this function is invertible, regions delimited by known phase values, corresponding to the successive extrema and zeros of the Bessel function. The implementation of the method is illustrated with a practical example. The results are discussed and compared with those obtained by stroboscopic digital holography and by reference phase modulation in speckle interferometry. A discussion tries to show the advantages and limitations of the method, as well as possible future developments.