Fourier transform method and temporal phase in order to measure frequency, amplitude, and surface profile of a low-frequency vibrating cantilever

A novel method of phase differences extraction is applied in order to study vibrations on a homogenous cantilever. It is achieved considering fringe patterns with carrier frequency and slow varying respect to the time. The technique is based on the Fourier-transform method and by the quotient of the two adjacent frames of the patterns. Fringe pattern is obtained by fringe projection on a fixed end homogenous cantilever, undergoing harmonic vibration. With this technique, we can obtain profiles of different vibrating modes of the cantilever for frequencies less than that of the camera frame rate (33.3 ms). In this communication theoretical analysis and experimental profile modes are shown.