Pascal Picart

General theoretical formulation of image formation in digital Fresnel holography

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.

Time-averaged digital holography

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.

Digital three-color holographic interferometry for flow analysis

A digital three-color holographic interferometer was designed to analyze the variations in refractive index induced by a candle flame. Color holograms are generated and recorded with a three layer photodiode stack sensor allowing a simultaneous recording with a high spatial resolution. Phase maps are calculated using Fourier transform and spectral filtering is applied to eliminate parasitic diffraction orders. Then, the contribution along each color is obtained with the simultaneous three wavelength measurement. Results in the case of the candle flame are presented. Zero order fringe, meaning zero optical path difference, can be easily extracted from the experimental data, either by considering a modeled colored fringe pattern or the wrapped phases along the three wavelengths.

Some opportunities for vibration analysis with time averaging in digital Fresnel holography

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.

Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification

We present a numerical method for reconstructing large objects using a convolution method with an adjustable magnification. The method is based on the image locations and magnification relations of holography when the illuminating beam is a spherical wavefront. A modified version of the angular spectrum transfer function is proposed that allows the filtering in the spatial frequency spectrum. Experimental results confirm the suitability of the proposed method.

Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms

We present an all-numeric multiplexing/demultiplexing technique for digitally recorded holograms that allow the simultaneous determination of the in-plane and the out-of-plane components of the displacement vector of an object submitted to some loading. The twin-sensitivity measurement is obtained from two different illumination directions that give two sensitivity vectors. The spatial multiplexing is achieved by an incoherent mixing of two duplets of coherent waves that produce holograms carried with orthogonal polarized reference waves. The spatial demultiplexing uses the autocorrelation function of the multiplexed holograms as a position estimator. The estimator then enables the determination of the pixel-to-pixel correspondence between the holograms for the double component determination. Results of the experiment are presented.

High-resolution digital two-color holographic metrology.

An algorithm designed for digital color holography is presented. It is based on a filter bank allowing full object reconstruction with a pixel pitch being invariant along each wavelength. Its application to high-resolution simultaneous two-wavelength metrology is described.

Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry

This Letter presents a method for real-time 3D measurements based on three-color digital holographic interferometry. The optical setup is considerably simplified, since the reference beams are combined into a unique beam. A convolution algorithm allows the three monochrome images to be superposed to provide simultaneous full-field 3D measurements. Experimental results confirm the suitability of the proposed method.

Full-field vibrometry with digital Fresnel holography

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.

2D full field vibration analysis with multiplexed digital holograms

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.