Sébastien Coëtmellec

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.

Digital in-line holography: influence of the shadow density on particle field extraction

We have used a digital in-line holography system with numerical reconstruction for 3D particle field extraction. In this system the diffraction patterns (holograms) are directly recorded on a charge-coupled device (CCD) camera. The numerical reconstruction is based on the wavelet transformation method. A sample volume 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 analyzing the maximum of the wavelet transform modulus and the equivalent diameter of the particle image. The general process for the 3D particle location and data processing method are presented. As in classical holography we found that the signal to noise ratio depends only on the shadow density. Nevertheless, we show that both the volume depth and the shadow density affect the percentage of extracted particles.

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.

Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography

We demonstrate that the fractional-order Fourier transformation is a suitable method to analyze the diffraction patterns of particle field holograms. This method permits reconstruction of in-line digital holograms beyond the Fraunhofer condition (d2/lambdaz approximately/= 10). We show that the diameter of spherical particles is measured with good accuracy. Simulation and experimental results are presented.

Digital in-line holography in thick optical systems: application to visualization in pipes

We apply digital in-line holography to image opaque objects through a thick plano-concave pipe. Opaque fibers and opaque particles are considered. Analytical expression of the intensity distribution in the CCD sensor plane is derived using a generalized Fresnel transform. The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models. Holograms obtained with a 12 mm thick plano-concave pipe are then reconstructed using a fractional Fourier transform. This method allows us to get rid of astigmatism. Numerical and experimental results are presented.

Micropipe flow visualization using digital in-line holographic microscopy

Digital in-line holography is used to visualize particle motion within a cylindrical micropipe. Analytical expression of the intensity distribution recorded in the CCD sensor plane is derived using the generalized Huygens-Fresnel integral associated with the ABCD matrices formalism. Holograms obtained in a 100microm in diameter micropipe are then reconstructed using fractional Fourier transformation. Astigmatism brought by the cylindrical micropipe is finally used to select a three dimensional region of interest in the microflow and thus to improve axial localization of objects located within a micropipe. Experimental results are presented and a short movie showing particle motion within a micropipe is given.

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.

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform

We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.

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.

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.