Denis Lebrun

Application of wavelet transform to hologram analysis: three-dimensional location of particles

The wavelet analysis provides an efficient tool in numerous signal-processing problems and has been implemented in optical processing techniques, such as in-line holography. When the diffraction pattern recorded on a hologram is analyzed by means of a wavelet transform, the 3-D location of small particles can be determined very accurately. The diffraction process can, in fact, be interpreted as a convolution with a family of wavelet functions, or, merely, as a wavelet transform. The scale parameter of the wavelet family is related to the axial distance z that the wave propagates. The original field is then reconstructed by searching for the optimum value of the scale parameter which produces a maximum of the wavelet transform modulus. The technique proposed is implemented and experimental results are presented.

Application of in-line digital holography to multiple plane velocimetry

We present the preliminary results of a digital holographic system that can determine the two-dimensional velocity vector fields in several slices of a sample volume. A CCD camera directly records the diffraction patterns of small particles illuminated by a double-pulse laser diode. In fact, the diffraction can be interpreted as a convolution with a wavelet family of functions. The scale parameter a is related to the distance z between a particle and the CCD camera. Then, the intensity distributions in a plane located at a distance z are reconstructed by computing the wavelet components for the corresponding scale parameter a. Afterwards, a particle image velocimetry algorithm is applied to the numerically reconstructed pair of images. The feasibility of this technique is demonstrated for two simulated displacements.

Digital in-line holography for three-dimensional?two-components particle tracking velocimetry

We have used a digital in-line holography system with numerical reconstruction to determine 2D velocity fields in several slices of a sample volume. This system records directly on a charge-coupled device (CCD) camera the diffraction patterns of small particles illuminated by a double-pulse laser diode. The numerical reconstruction is based on the wavelet transformation method. A slice is reconstructed by computing the wavelet components for different scale parameters. These parameters are related to the axial distance between a particle and the CCD camera. The particle images are identified and localized by analysing the maximum of the wavelet transform modulus and the width of the particle image (L50). Afterwards, a point-matching algorithm is applied to the set pairs containing the particles. This step is followed by velocity vector extraction. The details of the velocity extraction and the data processing method are presented and the simulations and experimental results are discussed.

Application of multiple exposure digital in-line holography to particle tracking in a Bénard–von Kármán vortex flow

Digital in-line holography is applied to studying the trajectories of individual water droplets in airflow. In order to track the particles, multiple exposure holography is performed using a modulated laser diode emitting at the wavelength of 635 nm and a lens-less CCD camera. This method leads to an accuracy better than 100 µm on the axial location. A study of the signal-to-noise ratio of such holograms shows that the number of exposures must be limited. Preliminary tests of this method are carried out in a Benard–von Karman street first characterized by laser Doppler velocimetry and hot wire anemometry. An example of a trajectory of a water droplet obtained in this flow at Reynolds number Re = 63 and Strouhal number St = 0.13 shows that digital holography is a promising method to extract the trajectories of droplets in laminar or turbulent flows.

Hologram reconstruction by use of optical wavelet transform

High-speed in-line holography is used to visualize the trajectories of glass fibers being drawn out in a turbulent flame. To improve the signal-to-noise ratio, the images are not observed by a conventional reconstruction setup, but the holographic plate is placed directly on the input plane of a wavelet-transform optical system. This processing system is based on a VanderLugt correlator with inclusion of an electrically addressed spatial light modulator. The shape of the matched filters is deduced by successive rotation and dilatation operations of wavelet functions in the Fourier domain. We estimate the three-dimensional location of a fiber element and its orientation by searching for the daughter wavelet that yields the maximum intensity on the output plane of the correlator, which also contains the reconstructed image. The results are compared with those obtained by conventional optical reconstruction. The signal-to-noise ratios of the images observed on the output plane are improved. Moreover, it is shown that the axis coordinate accuracy is improved to Dz = +/-50 microm, instead of +/-0.5 mm for holographic reconstruction.

Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter

Abstract In-line holograms of glass fibers are digitally recorded during the manufacturing fiberization process. The numerical reconstruction is realized by a wavelet based method. We show that the recording–reconstruction process can be interpreted as a linear shift invariant system with a Gaussian point-spread function. A demonstration is proposed and the result is illustrated by numerical simulations. This new interpretation is of a great interest because a reconstructed image can be viewed as a convolution operation of the object function with a predefined point-spread function which is not dependent on the recording axial distance. Experimental results are provided for the diameter measurement of glass fibers.

Size measurement of bubbles in a cavitation tunnel by digital in-line holography

Digital in-line holography (DIH) with a divergent beam is used to measure size and concentration of cavitation bubbles (6-100 μm) in hydrodynamic facilities. A sampling probe is directly inserted in the cavitation tunnel, and the holograms of the bubbles are recorded through a transparent test section specially designed for DIH measurements. The recording beam coming from a fiber-coupled laser diode illuminates the sample volume, and holograms are recorded by a CMOS camera. From each hologram, the sampling volume can be reconstructed slice by slice by applying a wavelet-based reconstruction method. Because of the geometry of the recording beam, a magnification ratio must be introduced for recovering the 3D location and size of each bubble. The method used for processing holograms recorded in such a configuration is presented. Then, statistical results obtained from 5000 holograms recorded under different pressures in the cavitation tunnel are compared and discussed.

Digital phase contrast with the fractional Fourier transform

A new method of digital phase contrast based on fractional-order Fourier reconstruction is proposed. We show that the diffraction patterns produced by pure phase objects exhibit linear chirp functions that can be advantageously processed using the fractional Fourier transform. The optimal fractional orders lead to the longitudinal location of the phase object, while the analysis of the reconstructed pattern leads to its diameter and to the value of the phase shift. Simulations and experimental results are given. The configuration tested in this paper is a very general Gaussian illumination.

Digital in-line particle holography: twin-image suppression using sparse blind source separation

We propose a robust autofocus method for reconstructing digital holograms and twin-image removal based on blind source separation approach. The method is made up of two components: an efficient quincunx lifting scheme based on wavelet packet transform, whose role is to maximize a sharpness metric related to the sparseness of the input holograms, and a geometric unmixing algorithm, which achieves the separation task. Experimental results confirm the ability of sparse blind source separation to discard the unwanted twin-image from in-line digital holograms of particles.

Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements

Far-field diffraction patterns of a glass cylinder are spatially sampled with a photodiode array. Three photometric signal processing methods are discussed. The first one is based on the analysis of fringes in the central lobe. It can be used for diameter monitoring, but not for a wide range of diameter measurements. The second method consists of best-fitting between the theoretical model of the irradiance distribution in the central fringe and the corresponding experimental data. The accuracy of this method (±1 μm, in the range 10 to 50 μm) is improved by introducing the optical transfer function (OTF) of the photosensitive area into the calculation. The third method uses a reliable estimation of the intensity at the center and the half-width of the central fringe in order to resolve the inverse problem by Newtons method. This method can be used for realtime measurements but must be improved by statistical approaches.