We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences. The analysis leads to a thorough investigation of the effect of the width of the sensor, the surface of pixels, the numerical focusing, and the aberrations of the reference wave, as well as to an explicit formulation of the Shannon theorem for digital holography. Experimental illustrations confirm the proposed theoretical analysis.

We demonstrate that it is possible to study the modal structures of a vibrating object with digitally recorded holograms by use of the time-averaging principle. We investigate the numerical reconstruction from a theoretical point of view, and we show that the numerically reconstructed object from a digital hologram is modulated by the zeroth-order Bessel function. Results of experiments in time-averaged digital holography are presented.

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts. Experiment results are presented in the case of a loudspeaker under a sinusoidal excitation; digital and analogical holography are also compared.

A setup that permits full-field vibration amplitude and phase retrieval with digital Fresnel holography is presented. Full reconstruction of the vibration is achieved with a three-step stroboscopic holographic recording, and an extraction algorithm is proposed. The finite temporal width of the illuminating light is considered in an investigation of the distortion of the measured amplitude and phase. In particular, a theoretical analysis is proposed and compared with numerical simulations that show good agreement. Experimental results are presented for a loudspeaker under sinusoidal excitation; the mean quadratic velocity extracted from amplitude evaluation under two different measuring conditions is presented. Comparison with time averaging validates the full-field vibrometer.

Opportunities for full field 2D amplitude and phase vibration analysis are presented. It is demonstrated that it is possible to simultaneously encode-decode 2D the amplitude and phase of harmonic mechanical vibrations. The process allows the determination of in plane and out of plane vibration components when the object is under a pure sinusoidal excitation. The principle is based on spatial multiplexing in digital Fresnel holography. Experimental results are presented in the case of an industrial application.