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 optic interferometer~\cite{CantiOptic89},
-pizeoresistor~\cite{CantiPiezzo01} or capacitive
-sensing~\cite{CantiCapacitive03}.
-%% blabla +
+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}
