Fabrice Onofri

Electromagnetic scattering from a multilayered sphere located in an arbitrary beam

A solution is given for the problem of scattering of an arbitrary shaped beam by a multilayered sphere. Starting from Bromwich potentials and using the appropriate boundary conditions, we give expressions for the external and the internal fields. It is shown that the scattering coefficients can be generated from those established for a plane-wave illumination. Some numerical results that describe the scattering patterns and the radiation-pressure behavior when an incident Gaussian beam or a plane wave impinges on a multilayered sphere are presented.

Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle

A vectorial complex ray model is introduced to describe the scattering of a smooth surface object of arbitrary shape. In this model, all waves are considered as vectorial complex rays of four parameters: amplitude, phase, direction of propagation, and polarization. The ray direction and the wave divergence/convergence after each interaction of the wave with a dioptric surface as well as the phase shifts of each ray are determined by the vector Snell law and the wavefront equation according to the curvatures of the surfaces. The total scattered field is the superposition of the complex amplitude of all orders of the rays emergent from the object. Thanks to the simple representation of the wave, this model is very suitable for the description of the interaction of an arbitrary wave with an object of smooth surface and complex shape. The application of the model to two-dimensional scattering of a plane wave by a spheroid particle is presented as a demonstration.

Critical angle refractometry and sizing of bubble clouds.

The principle of the critical angle refractometry and sizing technique is extended to characterize the size distribution and the mean refractive index of clouds of bubbles. For a log-normal bubble-size distribution, simulations show that the mean size, the relative width of the size distribution, and the mean refractive index of the bubbles have a particular and easily identified influence on the critical scattering patterns. Preliminary experimental results on air bubble/water flows clearly demonstrate the potential and robustness of this new technique for bubbly flow characterization.

Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects

We report experimental investigations on the influence of various optical effects on the far-field scattering pattern produced by a cloud of optical bubbles near the critical scattering angle. Among the effects considered, there is the change of the relative refractive index of the bubbles (gas bubbles or some liquid-liquid droplets), the influence of intensity gradients induced by the laser beam intensity profile and by the spatial filtering of the collection optics, the coherent and multiple scattering effects occurring for densely packed bubbles, and the tilt angle of spheroidal optical bubbles. The results obtained herein are thought to be fundamental for the development of future works to model these effects and for the extension of the range of applicability of an inverse technique (referenced herein as the critical angle refractometry and sizing technique), which is used to determine the size distribution and composition of bubbly flows.

Size, velocity, and concentration in suspension measurements of spherical droplets and cylindrical jets.

The principle of an optical technique for simultaneous velocity, size, and concentration in suspension measurements of spherical droplets and cylindrical jets is proposed. This technique is based on phase Doppler anemometry working in the dual burst technique configuration. The particle size and velocity are deduced from the reflected signal phase and frequency, whereas the amplitude ratio between the refracted and the reflected signals is used for measuring the concentration of small scatterers inside the particles. Numerical simulations, based on geometrical optics and a Monte Carlo model, and an experimental validation test on cylindrical jets made of various suspensions, are used to validate the principle of the proposed technique. It is believed that this new technique could be useful in investigating processes in which liquid suspensions are sprayed for surface coating, drying, or combustion applications.

Critical Angle Refractometry for Simultaneous Measurement of Particles in Flow: Size and Relative Refractive Index

The principle of the optical technique critical angle refractometry, used to determine the size and refractive index of spherical particles (with relative refractive index below unity) in liquid flows, was investigated. This technique is based on the observation of the particle scattering pattern around the critical angle. Similarly to the recent technique developed for rainbow scattering pattern analysis for droplet temperature and size measurements, it is shown that the relative particle refractive index (mr<1) and size can be determined from the position of the primary diffraction fringe and from the angular spacing between two fringes. Explicit equations for refractive index and particle size measurement were derived from the first-order term of the physical optics approximation. An experimental validation test and numerical computations based on the Lorenz-Mie theory were used to validate the principle of the proposed technique and to estimate its sensitivity, which was shown to be of the same order as that of the rainbow technique. This technique is considered to be useful for various applications in liquid multiphase flows where the particles size and material are to be characterized.

Experimental validation of the vectorial complex ray model on the inter-caustics scattering of oblate droplets

We report the first experimental validation of the Vectorial Complex Ray Model (VCRM) using the scattering patterns of large oblate droplets trapped in an acoustic field. The two principal radii and refractive index of the droplets are retrieved with a minimization method that involves VCRM predictions and experimental light scattering patterns. The latter are recorded in the droplet equatorial plane between the primary rainbow region and the associated hyperbolic-umbilic diffraction catastrophe. The results demonstrate that the VCRM can predict the fine and coarse stuctures of scattering patterns with good precision, opening up perspectives for the characterization of large non-spherical particles.

Measurement of bubbles by Phase Doppler technique and trajectory ambiguity

That paper is devoted to the analysis of the importance of the finite size of the laser beam on the quality of bubble measurements by a Phase Doppler Anemometer (PDA) (trajectory ambiguity or Gaussian beam effect). Detection at 30 ° and 70° are studied for a standard PDA, a non-standard PDA and dual burst configurations. The possibility to sort bubbles and perfectly reflecting particles is discussed.

Three interfering beams in laser Doppler velocimetry for particle position and microflow velocity profile measurements

It is proposed to use three interfering and coplanar laser beams to form the probe volume of laser Doppler systems. This allows us to obtain, for each particle crossing this probe volume, a Doppler signal whose frequency amplitude spectrum exhibits two characteristic peaks. Electromagnetic calculations and experimental validations clearly demonstrate that we can estimate simultaneously, from the analysis of these two frequency peaks, the particle position along the optical axis and one velocity component. This technique is expected to have great potentialities for velocity profile measurements in microfluidic or boundary layer flows, as well as for the sizing of spherical particles.

Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.