Hilbert-Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects

The Hilbert-Huang transform working principle is used to develop advanced single-frame and two-frame Bessel fringe pattern generation and demodulation algorithms especially tailored to enhance full-field vibration studies using time-averaged interferometry. The Bessel fringe pattern, named as the Besselogram, is understood as calculated amplitude modulation/contrast variation map of the time-averaged interferogram intensity distribution. Proposed Besselogram processing techniques are computationally fast and robust to fringe pattern imperfections and environmental disturbances encountered in interferometric studies of vibrating micro-objects. The advanced fast adaptive bidimensional empirical mode decomposition scheme is employed to filter interferograms, Bessel fringes and their phase maps. Reported Bessel fringe pattern analysis method possesses unique ability to determine both vibration phase and amplitude distribution maps from a single time-averaged interferogram. Comprehensive numerical simulations corroborate advantageous features of proposed methods. Experimental evaluation performed for two resonant modes of a silicon micro-membrane is enclosed for completeness of the analysis.