deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index 38bb7e0..cd0d248 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
...
The Z axis is defined here as the laser beam axis, and the ultrasound imaging plane is in the YZ plane, as illustrated by Figure \ref{Figure1}.  In this experiment, we used first a 4x8x8 cm$^3$ tissue-mimicking phantom made of water and of  5\% polyvinyl alcohol, 0.1 \% black graphite powder and 1\% salt. A freezing/thawing 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. We assume that the reflection of the laser is negligible, as the medium was black, and we also suppose a one-dimensional heating - radial heat flow is consequently neglected, as the laser size (5 mm in diameter) is quite large compared to the characteristic heat flow distance () or the thermal diffusion length in the material (a few tens of micrometers). The laser was absorbed in the medium with an exponential decay of the optical intensity $I$ along medium depth $r$\cite{scruby1990laser}:  \begin{equation} 
...