deletions | additions       diff --git a/emailpolgraslandmong.tex b/emailpolgraslandmong.tex  index 46b0ab1..e4721b9 100644  --- a/emailpolgraslandmong.tex  +++ b/emailpolgraslandmong.tex 
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When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation leads to an increase of the local temperature. There is consequently a local dilatation, and the resulting displacement can propagate as elastic waves. Elastic waves can be separated in two components in a bulk: compression waves, corresponding to a curl-free propagation; and shear waves, corresponding to a divergence-free propagation. propagation \cite{aki2002quantitative}.  This phenomenon has been notably observed in metals. Measuring the compression and shear waves can be used as a method of inspection to reveal potential cracks in the solid. In a medical context, induction of compression wave has been studied for the last twenty years, with the development of photoacoustic imaging. In this technique, a laser beam is absorbed by the tissue, which induces local displacements. These displacements can propagate as compression waves which are acquired by acoustic transducers. Time of flight measurements allows then to find the source of the waves. The optical absorption coefficient of the tissue depends on the optical wavelength, so different structures can be observed by tuning properly the laser wavelength. For example, oxygenated and de-oxygenated haemoglobin can be discriminated in this way. The frequency of the elastic waves used in photoacoustic imaging are typically of a few megahertz. At this frequency, only compression waves can propagate, as shear waves at a frequency of a few megahertz are quickly attenuated, typically over a few microns in soft tissues. 
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The Z axis is defined here as the laser beam axis, and the ultrasound probe is in the XZ plane, as illustrated by Figure \ref{Figure1}.  In this experiment, we used first a 4x8x8 cm$^3$ water-based phantom made from 5\% polyvinyl alcohol, 0.1 \% black graphite powder and 1\% salt. Three A  freezing/thawing cycles were cycle was  applied to stiffen the material to a value of 15$\pm$5 kPa  \cite{17375819}. The laser beam was emitted by a Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France), which produced a 200 mJ, 5 mm in diameter Q-switched pulse at a central wavelength of 532 nm during 10 ns. The absorption of the laser beam by the medium led to a local increase of temperature. The resulting temperature distribution equation in a semi-infinite space with a boundary plane at $z=0$ is given by $\nabla^2 T - \frac{1}{\kappa} \frac{\partial T}{\partial t} = - \frac{A}{K}$, where $T$ is the temperature distribution, $A$ the heat produced per unit volume per unit time and $K$ and $\kappa$ are respectively the thermal conductivity and diffusivity \cite{ready2012effects}. 
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In both cases, the absorption of the laser by the phantom leads to a local displacement which can propagate as elastic wave in the medium. To observe the elastic wave, the medium was scanned with a 5 MHz ultrasonic probe made of 128 elements and a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was used in ultrafast mode \cite{bercoff2004supersonic}, acquiring 1000 ultrasound frames per second. Due to the presence of graphite particles, the medium presented a speckle pattern on the ultrasound image. Tracking the speckle spots with an optical flow technique (Lucas-Kanade method) allowed to compute one component of the displacement in the medium (``Z-displacement'' or ``Y-displacement''). The laser beam was triggered 10 ms after the beginning of the ultrasound acquisition.