Pablo Cobelli

Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry

The measurement of an objects shape using projected fringe patterns needs a relation between the measured phase and the objects height. Among various methods, the Fourier transform profilometry proposed by Takeda and Mutoh [Appl. Opt.22, 3977-3982 (1983)] is widely used in the literature. Rajoub et al. have shown that the reference relation given by Takeda is erroneous [J. Opt. A. Pure Appl. Opt.9, 66-75 (2007)]. This paper follows from Rajoubs study. Our results for the phase agree with Rajoubs results for both parallel- and crossed-optical-axes geometries and for either collimated or noncollimated projection. Our two main results are: (i) we show experimental evidence of the error in Takedas formula and (ii) we explain the error in Takedas derivation and we show that Rajoubs argument concerning Takedas error is not correct.

Experimental study on water-wave trapped modes

We present an experimental study on the trapped modes occurring around a vertical surface-piercing circular cylinder of radius a placed symmetrically between the parallel walls of a long but finite water waveguide of width 2 d . A wavemaker placed near the entrance of the waveguide is used to force an asymmetric perturbation into the guide, and the free-surface deformation field is measured using a global single-shot optical profilometric technique. In this configuration, several values of the aspect ratio a / d were explored for a range of driving frequencies below the waveguides cutoff. Decomposition of the obtained fields in harmonics of the driving frequency allowed for the isolation of the linear contribution, which was subsequently separated according to the symmetries of the problem. For each of the aspect ratios considered, the spatial structure of the trapped mode was obtained and compared to the theoretical predictions given by a multipole expansion method. The waveguide–obstacle system was further characterized in terms of reflection and transmission coefficients, which led to the construction of resonance curves showing the presence of one or two trapped modes (depending on the value of a / d ), a result that is consistent with the theoretical predictions available in the literature. The frequency dependency of the trapped modes with the geometrical parameter a / d was determined from these curves and successfully compared to the theoretical predictions available within the frame of linear wave theory.

Experimental observation of trapped modes in a water wave channel

The fluid around a free surface piercing circular cylinder in a long narrow wave tank can exhibit a local oscillation that does not propagate down the channel but is confined to the vicinity of the cylinder. This is a manifestation of the so-called trapped modes, bound states in the continuum occurring in many situations in physics. In this letter, using Fourier Transform Profilometry, fully space time resolved measurements for the free surface deformation are obtained. The scattering characteristics of the cylinder and consequently the behavior of the trapped-mode frequency are determined.

Supershear Rayleigh waves at a soft interface.

We report on the experimental observation of waves at a liquid foam surface propagating faster than the bulk shear waves. The existence of such waves has long been debated, but the recent observation of supershear events in a geophysical context has inspired us to search for their existence in a model viscoelastic system. An optimized fast profilometry technique allows us to observe on a liquid foam surface the waves triggered by the impact of a projectile. At high impact velocity, we show that the expected subshear Rayleigh waves are accompanied by faster surface waves that can be identified as supershear Rayleigh waves.