deletions | additions       diff --git a/Dependance with beam power.tex b/Dependance with beam power.tex  index 52bb281..7903cbd 100644  --- a/Dependance with beam power.tex  +++ b/Dependance with beam power.tex 
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%Shear wave amplitude has been shown to be linearly dependent on laser beam power in thermoelastic and ablative regime. However, at higher amplitude (about 10$^9$ W.cm$^{-2}$ in metals \cite{scruby1990laser}), a plasma occurs and lead to a non-linear amplitude of the displacement with laser energy.  The dependence of the generated shear wave amplitude with laser energy has been was then  investigated by increasing the laser beam energy from 10 to 200 mJ. To decrease noise influence, increase the signal-to-noise ratio,  amplitude have been averaged over four experiments for each energy level. Successive energy levels were randomly chosen to avoid any time-related bias and impact location was changed after each laser emission  to avoid any potential  local degradation of the medium. Shear wave amplitude were measured between 0 and 10 mm of the medium surface, an arbitrary location where shear waves had high amplitudes. Resulting measurements are illustrated in Figure \ref{Figure4}-(A). A linear dependence is observed, with a threshold at low amplitude due to ambient noise. The sample was then replaced by a similar phantom except that cellulose particles were used instead of graphite particles: thus, the phantom presented a weak optical absorption but a comparable speckle pattern. A black disk of variable diameter was painted on a surface of the phantom at the laser beam impact location, to control the absorption area. Paint thickness was higher than 500 $\mu$m.  The amplitude of the induced shear waves versus black disk diameter in the second phantom is illustrated in Fig. \ref{Figure3}-(B). We observe a linear relationship between shear wave amplitude and black disk diameter, with a correlation coefficient of 0.9281. In both series of experiments (20 plus 23 measurements), we measured shear wave frequency of 500 $\pm$ 100 Hz.