Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects

A method of holographic vibration analysis is presented that permits the extraction of vibration amplitudes by means of measurements from a photodiode-array camera from time-average hologram reconstructions, concomitant (real-time) hologram interferometry, or a speckle interferometer with an electronic holography readout system. A sinusoidal phase modulation is introduced into one of the beams of the hologram interferometer to offset the argument of the Bessel-function fringes. Irradiance values from time-average interferograms with zero, plus, and minus offsets can be processed numerically by a method analogous to that used for cosine fringes from a phase-step interferometer. This permits the evaluation of vibration amplitudes with the same facilities used for static displacements. The mathematical theory of this process is presented.