Loïc Méès

Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz-Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.

Scattering of laser pulses (plane wave and focused Gaussian beam) by spheres

The scattering of laser pulses (in the femtosecond-picosecond range) by large spheres is investigated. We call a sphere large when its diameter is larger than the length associated with the pulse duration, allowing one to observe the temporal separation of scattering modes including surface waves.

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.

Time gate, optical layout, and wavelength effects on ballistic imaging

A method to distinguish a hidden object from a perturbing environment is to use an ultrashort femtosecond pulse of light and a time-resolved detection. To separate ballistic light containing information on a hidden object from multiscattered light coming from the surrounding environment that scrambles the signal, an optical Kerr gate can be used. It consists of a carbon disulfide (CS(2)) cell in which birefringence is optically induced. An imaging beam passes through the studied medium while a pump pulse is used to open the gate. The time-delayed scattered light is excluded from measurements by the gate, and the multiple-scattering scrambling effect is reduced. In previous works, the two beams had the same wavelength. We propose a new two-color experimental setup for ballistic imaging in which a second harmonic is generated and used for the image, while the fundamental is used for gate switching. This setup allows one to obtain better resolution by using a spectral filtering to eliminate noise from the pump pulse, instead of a spatial filtering. This new setup is suitable for use in ballistic imaging of dense sprays, multidiffusive, and large enough to show scattered light time delays greater than the gate duration (tau=1.3 ps).

Resonant spectra of a deformed spherical microcavity

We rigorously compute the resonance spectrum for a deformed spherical microcavity illuminated by plane waves. Particular attention is paid to the shift of resonances due to small departures from sphericity, which includes a discussion on the behavior of individual scattering coefficients. These results are obtained for deformed microcavities that are large with respect to the wavelength of the incident wave.

Cylindrical localized approximation to speed up computations for Gaussian beams in the generalized Lorenz–Mie theory for cylinders, with arbitrary location and orientation of the scatterer

A cylindrical localized approximation to speed up numerical computations in generalized Lorenz-Mie theory for cylinders, in a special case of perpendicular illumination, was recently introduced and rigorously justified. We generalize this approximation to the case when the cylinder is arbitrarily located and arbitrarily oriented in a Gaussian beam.

Long time exposure digital in-line holography for 3-D particle trajectography

One advantage of digital in-line holography is the ability for a user to know the 3-D location of a moving particle recorded at a given time. When the time exposure is much larger than the time required for grabbing the particle image at a given location, the diffraction pattern is spread along the trajectory of this particle. This can be seen as a convolution between the diffraction pattern and a blurring function resulting from the motion of the particle during the camera exposure. This article shows that the reconstruction of holograms recorded under such conditions exhibit traces that could be processed for extracting 3D trajectories.

Localized approximation for Gaussian beams in elliptical cylinder coordinates

We establish a localized approximation to evaluate the beam-shape coefficients of a Gaussian beam in elliptical cylinder coordinates. As for the case of spherical coordinates and of circular cylinder coordinates, this approximation provides an efficient way to speed up computations within the framework of a generalized Lorenz-Mie theory for elliptical cylinders.

Improvement of the size estimation of 3D tracked droplets using digital in-line holography with joint estimation reconstruction

Digital holography is a valuable tool for three-dimensional information extraction. Among existing configurations, the originally proposed setup (i.e. Gabor, or in-line holography), is reasonably immune to variations in the experimental environment making it a method of choice for studies of fluid dynamics. Nevertheless, standard hologram reconstruction techniques, based on numerical light back-propagation are prone to artifacts such as twin images or aliases that limit both the quality and quantity of information extracted from the acquired holograms. To get round this issue, the hologram reconstruction as a parametric inverse problem has been shown to accurately estimate 3D positions and the size of seeding particles directly from the hologram. To push the bounds of accuracy on size estimation still further, we propose to fully exploit the information redundancy of a hologram video sequence using joint estimation reconstruction. Applying this approach in a bench-top experiment, we show that it led to a relative accuracy of 0.13 % (for a 30 µm diameter droplet) for droplet size estimation, and a tracking accuracy of σ x × σ y × σ z = 0.15 × 0.15 × 1 pixels.

Quantitative phase retrieval reconstruction from in-line hologram using a new proximal operator: application to microscopy of bacteria and tracking of droplets

Phase retrieval reconstruction is a central problem in digital holography, with various applications in microscopy, biomedical imaging, fluid mechanics. In an in-line configuration, the particular difficulty is the non-linear relation between the object phase and the recorded intensity of the holograms, leading to high indeterminations in the reconstructed phase. Thus, only efficient constraints and a priori information, combined with a finer model taking into account the non-linear behaviour of image formation, will allow to get a relevant and quantitative phase reconstruction. Inverse problems approaches are well suited to address these issues, only requiring a direct model of image formation and allowing the injection of priors and constraints on the objects to reconstruct, and hence offer good warranties on the optimality of the expected solution. In this context, following our previous works in digital in-line holography, we propose a regularized reconstruction method that includes several physicallygrounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation of micrometric objects on reconstructions of in-line holograms simulated with advanced models using Mie theory. Then we discuss the quality of reconstructions from experimental inline holograms obtained from two different applications of in-line digital holography: tracking of an evaporating droplet (size~100μm) and microscopy of bacterias (size~1μm). The reconstruction algorithm and the results presented in this proceeding have been initially published in [Jolivet et al., 2018].1