Fourier transform and temporal phase shifting methods to measure vibration frequency of a cantilever without out-of-plane conversion

Abstract

It is well known that interferometric techniques used to measure the modal parameters of vibrating objects require the conversion of phase values to out‐of‐plane values. This task is not simple and often only an approximation is available. In this work, an oscillation frequency measurement is proposed using interferometric techniques without applying out‐of‐plane conversion. In this technique a binary pattern is projected on a cantilever surface and a mathematical model based in interferometry of phase extraction is used for obtaining phase differences of two consecutive frames, captured while the cantilever is vibrating in a natural mode. A projected binary pattern on a cantilever surface is considered as an interferometric pattern with a carrier frequency, which is introduced by the grating period. The deformations of the projected grating period are considered as the desired phase in an interferometric pattern. Period deformations contain information about oscillations and therefore, about modal shape ...