Fabrice Onofri

The near-periodic structures of highly symmetric, non-absorbing particle holograms significantly limit the robustness and efficiency of conventional inverse methods. A physically grounded iterative inverse approach is introduced to address the abundance of secondary minima of cost functions and the resulting parameter dependencies. Accelerated scattering computations based on hybrid and asymptotic models are used rather than the full Lorenz–Mie theory. Particular emphasis is placed on determining the refractive index (linked to the particle composition), a parameter often neglected despite its central importance. The ranges of particle–photosensor distances, particle diameters, and refractive indices over which reliable parameter recovery can be achieved are delineated. Finally, a numerical analysis of synthetic holograms is used to quantify the expected root-mean-square error (RMSE) on the retrieved parameters, revealing a marked increase in precision with both decreasing photosensor–particle distance and particle-to-medium refractive index contrast.

This work explores the possibility of using cylindrical lenses in digital in-line holography to reduce particle hologram imprint and cross-interference on the camera sensor. Experimental results on sprayed and levitated droplets, together with simulations using Rayleigh–Sommerfeld integrals and ABCD analysis, confirm the feasibility of this compression method for spherical particles. However, it turns out that, when using a back-propagation method to reconstruct the particle field, reducing the fill rate of the camera sensor does not in itself improve the quality of the particle field reconstruction. It is the asymmetric magnification of the optical system that enables this improvement, transforming the twin particle problem into a two half-twin particle problem. The latter have a less impact on the reconstruction process, allowing the statistics to be improved. This advantage increases with the magnification factor of the optical system. The authors believe that this optical method could be even more interesting for parametric inversion methods used for full volumetric reconstruction of particle fields.

First, we construct a faster approximation of the Lorenz-Mie theory (LMT) that is valid in both the near and far fields and for all scattering directions. Inspired by the Fresnel diffraction and the localization principle, it uses new approximations of spherical Hankel functions. It is much more accurate than the usual far-field approximation of the LMT, with a similar computational time. It can be applied directly to coated and multilayered spheres, and is most likely generalizable to shaped electromagnetic and acoustic beams. Secondly, we restrict the previous approximation to the near-forward scattering and develop a new formulation of diffraction for spheres, which we call the Lorenz-Mie-Fresnel (LMF) diffraction. Similar in aspect to the Fresnel diffraction, it is more accurate and discrete, though not necessarily faster. Finally, we derive the Fresnel diffraction by a disk from the LMT series using a discrete-to-continuous approximation, thereby establishing the connection between these two century-old theories.

Anomalous reflection and tunneling contributions of the high-frequency forward light scattering by non-absorbing spheres are modeled by the scalar diffraction of two complex annuli—one for TM and TE polarizations. Their complex radii, which depend on the refractive indices and particle size, are derived from the complex angular momentum (CAM) method, thus suggesting possible extensions to non-electromagnetic scattering. Coupled with the diffraction of a disk, and a geometrical optics approximation (GOA) for the refractive contributions, we propose an accurate hybrid model that requires one to two orders of magnitude less computational time than the Lorenz–Mie theory (LMT) in the near field, a crucial improvement for, e.g., inverse methods.

The rainbow patterns of oblate spheroidal drops have been observed in experiments nearly forty years ago [ Nature 312, 529 (1984)10.1038/312529a0 ]. However, the prediction for those complex patterns has been a challenge for conventional light scattering models. The vectorial complex ray model (VCRM) allows to account for the direction, the polarization, the phase, the amplitude and the wavefront curvature of waves and provides a powerful tool for the study of the light/electromagnetic wave interaction with a homogeneous object of any shape with smooth surface. In [ Opt. Lett. 46, 4585 (2021)10.1364/OL.434149 ], the authors have reported an important breakthrough of VCRM for the three-dimensional scattering (VCRM3D) and the simulated rainbow patterns of oblate drops. The present paper is devoted to the detailed description of the numerical implementation allowing the simulation of the 3D scattering field by a nonspherical particle. Its ability to predict both the fine and coarse intensity structures of the rainbows and the near-backward scattering patterns of spheroids is demonstrated. This work opens perspectives for exploring the 3D scattering characteristics of large objects with any smooth shape and developing relevant optical techniques for particle characterization.

The analysis of nano- and microparticle suspensions with micro systems affords improved space–time yields, selectivity, reaction residence times and conversions capabilities. These capabilities are of primary importance in various fields of research and industry. The few microfluidic lab-on-a-chip approaches that have been developed are essentially designed to analyse fluid phases or involve the use of benchtop particle sizing instruments. We report a novel microscale approach to characterize the particle size distribution and absolute concentration of colloidal suspensions. The method is based on a photonic lab-on-a-chip with three scale-specific detection channels to record simultaneous light extinction spectra. Experiments carried out on particle standards with sizes ranging from 30 nm to 0.5 µm and volume concentrations of 1 to 1000ppm, clearly demonstrate the value and potential of the proposed method.

The scattering patterns near the primary rainbow of oblate drops are simulated by extending the vectorial complex ray model (VCRM) [ Opt. Lett. 36, 370 (2011)OPLEDP 0146-9592 10.1364/OL.36.000370 ] to three-dimensional (3D) calculations. With the curvature of a wavefront as an intrinsic property of a ray, this advanced ray model permits, in principle, to predict the amplitudes and phases of all emergent rays with a rigorous algebraic formalism. This Letter reports a breakthrough of VCRM for 3D scattering with a line-by-line triangulation interpolation algorithm allowing to calculate the total complex amplitude of a scattered field. This makes possible to simulate not only the skeleton (geometrical rainbow angles, hyperbolic–umbilic caustics), but also the coarse (Airy bows, lattice) and fine (ripple fringes) structures of the generalized rainbow patterns (GRPs) of oblate drops. The simulated results are found qualitatively and quantitatively in good agreement with experimental scattering patterns for drops of different aspect ratios. The physical interpretation of the GRPs is also given. This work opens up prominent perspectives for simulating and understanding the 3D scattering of large particles of any shape with a smooth surface by VCRM.