\section{Introduction}
-%% blabla +
+Cantilevers are used inside atomic force microscope which provides high
+resolution images of surfaces. Several technics have been used to measure the
+displacement of cantilevers in litterature. For example, it is possible to
+determine accurately the deflection with different mechanisms.
+In~\cite{CantiPiezzo01}, authors used piezoresistor integrated into the
+cantilever. Nevertheless this approach suffers from the complexity of the
+microfabrication process needed to implement the sensor in the cantilever.
+In~\cite{CantiCapacitive03}, authors have presented an cantilever mechanism
+based on capacitive sensing. This kind of technic also involves to instrument
+the cantiliver which result in a complex fabrication process.
+
+In this paper our attention is focused on a method based on interferometry to
+measure cantilevers' displacements. In this method cantilevers are illuminated
+by an optic source. The interferometry produces fringes on each cantilevers
+which enables to compute the cantilever displacement. In order to analyze the
+fringes a high speed camera is used. Images need to be processed quickly and
+then a estimation method is required to determine the displacement of each
+cantilever. In~\cite{AFMCSEM11}, the authors have used an algorithm based on
+spline to estimate the cantilevers' positions.
+%%RAPH : ce qui est génant c'est qu'ils ne parlent pas de spline dans ce papier...
+ The overall process gives
+accurate results but all the computation are performed on a standard computer
+using labview. Consequently, the main drawback of this implementation is that
+the computer is a bootleneck in the overall process. In this paper we propose to
+use a method based on least square and to implement all the computation on a
+FGPA.
+
+The remainder of the paper is organized as follows. Section~\ref{sec:measure}
+describes more precisely the measurement process. Our solution based on the
+least square method and the implementation on FPGA is presented in
+Section~\ref{sec:solus}. Experimentations are described in
+Section~\ref{sec:results}. Finally a conclusion and some perspectives are
+presented.
+
+
+
%% quelques ref commentées sur les calculs basés sur l'interférométrie
\section{Measurement principles}
\label{sec:measure}
+In order to develop simple, cost effective and user-friendly cantilever arrays,
+authors of ~\cite{AFMCSEM11} have developped a system based of
+interferometry. In opposition to other optical based systems, using a laser beam
+deflection scheme and sentitive to the angular displacement of the cantilever,
+interferometry is sensitive to the optical path difference induced by the
+vertical displacement of the cantilever.
+%%RAPH : est ce qu'on pique une image? génant ou non?
+The system build by authors of~\cite{AFMCSEM11} has been developped based on a
+Linnick interferomter~\cite{Sinclair:05}. A laser beam is first split (by the
+splitter) into a reference beam and a sample beam that reachs the cantilever
+array. In order to be able to move the cantilever array, it is mounted on a
+translation and rotational stage with five degrees of freedom. The optical
+system is also fixed to the stage. Thus, the cantilever array is centered in the
+optical system which can be adjusted accurately. The beam illuminates the array
+by a microscope objective and the light reflects on the cantilevers. Likewise
+the reference beam reflects on a movable mirror. A CMOS camera chip records the
+reference and sample beams which are recombined in the beam splitter and the
+interferogram. At the beginning of each experiment, the movable mirror is fitted
+manually in order to align the interferometric fringes approximately parallel to
+the cantilevers. When cantilevers move due to the surface, the bending of
+cantilevers produce movements in the fringes that can be detected with the CMOS
+camera. Finally the fringes need to be analyzed. In~\cite{AFMCSEM11}, the
+authors used a LabView program to compute the cantilevers' movements from the
+fringes.
+
+
+
+
+
+
+
\subsection{Architecture}
\label{sec:archi}
%% description de l'architecture générale de l'acquisition d'images
\subsubsection{Comparison}
-\subsection{VDHL design paradigms}
+\subsection{VHDL design paradigms}
-\subsection{VDHL implementation}
+\subsection{VHDL implementation}
\section{Experimental results}
\label{sec:results}
