deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index f0ab91a..2a13a5f 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
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When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation increases the local temperature. This leads to a local dilatation due to thermal expansion, 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 \cite{landau1986theory}. This phenomenon has been notably observed in metals. Compression and shear waves induced by laser are even used as a method of inspection to reveal potential cracks in solids.  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 \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. 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. We hypothesized in this study that applying a laser beam in a soft tissue can induce shear waves. This has an increasing interest in medical imaging, with the development for the last two decades of shear wave elastography methods \cite{krouskop1987pulsed}, \cite{ophir1991elastography}, \cite{muthupillai1995magnetic}. This term covers the techniques used to measure or map the elastic properties of biological tissues. The shear modulus, directly proportional to Young's modulus in soft tissues, varies of several orders of magnitude in human body. This parameter can be measured by using shear wave. A shear wave propagates indeed in an organ at a speed proportional to the square root of the shear modulus, so measuring the speed throughout the organ allows to compute its shear modulus \cite{sandrin2002shear}. Shear wave elastography techniques have been successfully applied in several organs such as the liver \cite{sandrin2003transient}, the breast \cite{goddi2012breast}, \cite{sinkus2005viscoelastic}, the prostate \cite{cochlin2002elastography}, \cite{souchon2003visualisation} and the eye cornea \cite{tanter2009high}. 
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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 (\textit{Z-displacement} or \textit{Y-displacement}). The laser beam was triggered 10 ms after the beginning of the ultrasound acquisition.