ispell

[dmems12.git] / dmems12.tex

diff --git a/dmems12.tex b/dmems12.tex
index 10db6244de9d66bf5861f7f42700d7a49ee986ba..1dd3b4a2de6c5480ecc61bfad98723515cbf48d5 100644 (file)
--- a/dmems12.tex
+++ b/dmems12.tex
@@ -63,7 +63,16 @@
 
 \begin{abstract}
 
 
 \begin{abstract}
 

-  
+  Atomic force microscope (AFM) provides high resolution images of
+  surfaces. We focus our attention on an interferometry method to
+  estimate the cantilevers deflection.  The initial method was based
+  on splines to determine the phase of interference fringes, and thus
+  the deflection. Computations were performed on a PC with LabView.
+  In this paper, we propose a new approach based on the least square
+  methods and its implementation that we developed on a FPGA, using
+  the pipelining technique. Simulations and real tests showed us that
+  this implementation is very efficient and should allow us to control
+  a cantilevers array in real time.

 
 
 \end{abstract}
 
 
 \end{abstract}


@@ -78,15 +87,15 @@ FPGA, cantilever, interferometry.
 \section{Introduction}
 
 Cantilevers  are  used  inside  atomic  force  microscope (AFM) which  provides  high
 \section{Introduction}
 
 Cantilevers  are  used  inside  atomic  force  microscope (AFM) 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
+resolution images of  surfaces.  Several techniques have been  used to measure the
+displacement  of cantilevers  in literature.   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
 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.
+based on  capacitive sensing. This kind  of technique also  involves to instrument
+the cantilever 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
 
 In this  paper our attention is focused  on a method based  on interferometry to
 measure cantilevers' displacements.  In  this method cantilevers are illuminated


@@ -100,8 +109,8 @@ spline to estimate the cantilevers' positions.
 The overall process gives accurate results but all the computations
 are performed on a standard computer using LabView.  Consequently, the
 main drawback of this implementation is that the computer is a
 The overall process gives accurate results but all the computations
 are performed on a standard computer using LabView.  Consequently, the
 main drawback of this implementation is that the computer is a

-bootleneck. In this paper we propose to use a method based on least
-square and to implement all the computation on a FGPA.
+bottleneck. In this paper we propose to use a method based on least
+square and to implement all the computation on a FPGA.

 
 The remainder  of the paper  is organized as  follows. Section~\ref{sec:measure}
 describes  more precisely  the measurement  process. Our  solution based  on the
 
 The remainder  of the paper  is organized as  follows. Section~\ref{sec:measure}
 describes  more precisely  the measurement  process. Our  solution based  on the


@@ -124,16 +133,16 @@ presented.
 %% qu'elle est.
 
 In order to develop simple,  cost effective and user-friendly cantilever arrays,
 %% qu'elle est.
 
 In order to develop simple,  cost effective and user-friendly cantilever arrays,

-authors   of    ~\cite{AFMCSEM11}   have   developped   a    system   based   of
+authors   of    ~\cite{AFMCSEM11}   have   developed   a    system   based   of

 interferometry. In opposition to other optical based systems, using a laser beam
 interferometry. In opposition to other optical based systems, using a laser beam

-deflection scheme and  sentitive to the angular displacement  of the cantilever,
+deflection scheme and  sensitive to the angular displacement  of the cantilever,

 interferometry  is sensitive  to  the  optical path  difference  induced by  the
 vertical displacement of the cantilever.
 
 The system build by these authors is based on a Linnick
 interferometry  is sensitive  to  the  optical path  difference  induced by  the
 vertical displacement of the cantilever.
 
 The system build by these authors is based on a Linnick

-interferomter~\cite{Sinclair:05}.  It is illustrated in
+interferometer~\cite{Sinclair:05}.  It is illustrated in

 Figure~\ref{fig:AFM}.  A laser diode is first split (by the splitter)
 Figure~\ref{fig:AFM}.  A laser diode is first split (by the splitter)

-into a reference beam and a sample beam that reachs the cantilever
+into a reference beam and a sample beam that reaches the cantilever

 array.  In order to be able to move the cantilever array, it is
 mounted on a translation and rotational hexapod stage with five
 degrees of freedom. The optical system is also fixed to the stage.
 array.  In order to be able to move the cantilever array, it is
 mounted on a translation and rotational hexapod stage with five
 degrees of freedom. The optical system is also fixed to the stage.


@@ -199,7 +208,7 @@ I(x) = ax+b+A.cos(2\pi f.x + \theta)
 where $x$ is the position of a pixel in its associated segment.
 
 The global method consists in two main sequences. The first one aims
 where $x$ is the position of a pixel in its associated segment.
 
 The global method consists in two main sequences. The first one aims

-to determin the frequency $f$ of each profile with an algorithm based
+to determine the frequency $f$ of each profile with an algorithm based

 on spline interpolation (see section \ref{algo-spline}). It also
 computes the coefficient used for unwrapping the phase. The second one
 is the acquisition loop, while which images are taken at regular time
 on spline interpolation (see section \ref{algo-spline}). It also
 computes the coefficient used for unwrapping the phase. The second one
 is the acquisition loop, while which images are taken at regular time


@@ -231,7 +240,7 @@ that computing the deflection of a single
 cantilever should take less than 25$\mu$s, thus 12.5$\mu$s by phase.\\
 
 In fact, this timing is a very hard constraint. Let consider a very
 cantilever should take less than 25$\mu$s, thus 12.5$\mu$s by phase.\\
 
 In fact, this timing is a very hard constraint. Let consider a very

-small programm that initializes twenty million of doubles in memory
+small program that initializes twenty million of doubles in memory

 and then does 1000000 cumulated sums on 20 contiguous values
 (experimental profiles have about this size). On an intel Core 2 Duo
 E6650 at 2.33GHz, this program reaches an average of 155Mflops. 
 and then does 1000000 cumulated sums on 20 contiguous values
 (experimental profiles have about this size). On an intel Core 2 Duo
 E6650 at 2.33GHz, this program reaches an average of 155Mflops. 


@@ -304,17 +313,17 @@ available  and  must  be  done  by   configuring  a  set  of  CLBs.  Since  this
 configuration  is not  obvious at  all, it  can be  done via  a  framework, like
 ISE~\cite{ISE}. Such  a software  can synthetize a  design written in  a hardware
 description language  (HDL), map it onto  CLBs, place/route them  for a specific
 configuration  is not  obvious at  all, it  can be  done via  a  framework, like
 ISE~\cite{ISE}. Such  a software  can synthetize a  design written in  a hardware
 description language  (HDL), map it onto  CLBs, place/route them  for a specific

-FPGA, and finally  produce a bitstream that is used to  configre the FPGA. Thus,
-from  the developper  point of  view,  the main  difficulty is  to translate  an
+FPGA, and finally  produce a bitstream that is used to  configure the FPGA. Thus,
+from  the developer  point of  view,  the main  difficulty is  to translate  an

 algorithm in HDL code, taking  account FPGA resources and constraints like clock
 signals and I/O values that drive the FPGA.
 
 Indeed, HDL programming is very different from classic languages like
 C. A program can be seen as a state-machine, manipulating signals that
 evolve from state to state. By the way, HDL instructions can execute
 algorithm in HDL code, taking  account FPGA resources and constraints like clock
 signals and I/O values that drive the FPGA.
 
 Indeed, HDL programming is very different from classic languages like
 C. A program can be seen as a state-machine, manipulating signals that
 evolve from state to state. By the way, HDL instructions can execute

-concurrently. Basic logic operations are used to agregate signals to
+concurrently. Basic logic operations are used to aggregate signals to

 produce new states and assign it to another signal. States are mainly
 produce new states and assign it to another signal. States are mainly

-expressed as arrays of bits. Fortunaltely, libraries propose some
+expressed as arrays of bits. Fortunately, libraries propose some

 higher levels representations like signed integers, and arithmetic
 operations.
 
 higher levels representations like signed integers, and arithmetic
 operations.
 


@@ -333,7 +342,7 @@ pipelines in order to handle multiple data streams.
 
 \subsection{The board}
 
 
 \subsection{The board}
 

-The board we use is designed by the Armadeus compagny, under the name
+The board we use is designed by the Armadeus company, under the name

 SP Vision. It consists in a development board hosting a i.MX27 ARM
 processor (from Freescale). The board includes all classical
 connectors: USB, Ethernet, ... A Flash memory contains a Linux kernel
 SP Vision. It consists in a development board hosting a i.MX27 ARM
 processor (from Freescale). The board includes all classical
 connectors: USB, Ethernet, ... A Flash memory contains a Linux kernel


@@ -372,8 +381,8 @@ intensity in gray levels. Let call $I(x)$ the intensity of profile in $x
 \in [0,M[$. 
 
 At first, only $M$ values of $I$ are known, for $x = 0, 1,
 \in [0,M[$. 
 
 At first, only $M$ values of $I$ are known, for $x = 0, 1,

-\ldots,M-1$. A normalisation allows to scale known intensities into
-$[-1,1]$. We compute splines that fit at best these normalised
+\ldots,M-1$. A normalization allows to scale known intensities into
+$[-1,1]$. We compute splines that fit at best these normalized

 intensities. Splines are used to interpolate $N = k\times M$ points
 (typically $k=4$ is sufficient), within $[0,M[$. Let call $x^s$ the
 coordinates of these $N$ points and $I^s$ their intensities.
 intensities. Splines are used to interpolate $N = k\times M$ points
 (typically $k=4$ is sufficient), within $[0,M[$. Let call $x^s$ the
 coordinates of these $N$ points and $I^s$ their intensities.


@@ -407,7 +416,7 @@ determine these four parameters. Since it is an iterative process
 ending with a convergence criterion, it is obvious that it is not
 particularly adapted to our design goals.
 
 ending with a convergence criterion, it is obvious that it is not
 particularly adapted to our design goals.
 

-Fortunatly, it is quite simple to reduce the number of parameters to
+Fortunately, it is quite simple to reduce the number of parameters to

 only $\theta$. Let $x^p$ be the coordinates of pixels in a segment of
 size $M$. Thus, $x^p = 0, 1, \ldots, M-1$. Let $I(x^p)$ be their
 intensity. Firstly, we "remove" the slope by computing:
 only $\theta$. Let $x^p$ be the coordinates of pixels in a segment of
 size $M$. Thus, $x^p = 0, 1, \ldots, M-1$. Let $I(x^p)$ be their
 intensity. Firstly, we "remove" the slope by computing:


@@ -551,7 +560,7 @@ Finally, the whole summarizes in an algorithm (called LSQ in the following) in t
 
 We compared the two algorithms on the base of three criteria:
 \begin{itemize}
 
 We compared the two algorithms on the base of three criteria:
 \begin{itemize}

-\item precision of results on a cosinus profile, distorted with noise,
+\item precision of results on a cosines profile, distorted with noise,

 \item number of operations,
 \item complexity to implement an FPGA version.
 \end{itemize}
 \item number of operations,
 \item complexity to implement an FPGA version.
 \end{itemize}


@@ -593,13 +602,13 @@ Table \ref{tab:algo_prec} gives the maximum and average error for the two algori
   30 & 17.06 & 2.6 & 13.94 & 2.45 \\ \hline
 
 \end{tabular}
   30 & 17.06 & 2.6 & 13.94 & 2.45 \\ \hline
 
 \end{tabular}

-\caption{Error (in \%) for cosinus profiles, with noise.}
+\caption{Error (in \%) for cosines profiles, with noise.}

 \label{tab:algo_prec}
 \end{center}
 \end{table}
 
 These results show that the two algorithms are very close, with a
 \label{tab:algo_prec}
 \end{center}
 \end{table}
 
 These results show that the two algorithms are very close, with a

-slight advantage for LSQ. Furthemore, both behave very well against
+slight advantage for LSQ. Furthermore, both behave very well against

 noise. Assuming the experimental ratio of 50 (see above), an error of
 1 percent on phase correspond to an error of 0.5nm on the lever
 deflection, which is very close to the best precision.
 noise. Assuming the experimental ratio of 50 (see above), an error of
 1 percent on phase correspond to an error of 0.5nm on the lever
 deflection, which is very close to the best precision.


@@ -610,7 +619,7 @@ profiles. Nevertheless, we can see on figure \ref{fig:noise20} the
 profile with $N=10$ that leads to the biggest error. It is a bit
 distorted, with pikes and straight/rounded portions, and relatively
 close to most of that come from experiments. Figure \ref{fig:noise60}
 profile with $N=10$ that leads to the biggest error. It is a bit
 distorted, with pikes and straight/rounded portions, and relatively
 close to most of that come from experiments. Figure \ref{fig:noise60}

-shows a sample of worst profile for $N=30$. It is completly distorted,
+shows a sample of worst profile for $N=30$. It is completely distorted,

 largely beyond the worst experimental ones. 
 
 \begin{figure}[ht]
 largely beyond the worst experimental ones. 
 
 \begin{figure}[ht]


@@ -657,12 +666,12 @@ problem:  DSP48 take  inputs of  18  bits maximum.  For larger  multiplications,
 several DSP must be combined, increasing the latency.
 
 Nevertheless, the hardest constraint does not come from the FPGA characteristics
 several DSP must be combined, increasing the latency.
 
 Nevertheless, the hardest constraint does not come from the FPGA characteristics

-but from the algorithms. Their VHDL  implentation will be efficient only if they
+but from the algorithms. Their VHDL  implementation will be efficient only if they

 can be fully (or near) pipelined. By the way, the choice is quickly done: only a
 small  part of  SPL  can be.   Indeed,  the computation  of spline  coefficients
 implies to solve  a tridiagonal system $A.m =  b$. Values in $A$ and  $b$ can be
 computed from  incoming pixels intensity  but after, the back-solve  starts with
 can be fully (or near) pipelined. By the way, the choice is quickly done: only a
 small  part of  SPL  can be.   Indeed,  the computation  of spline  coefficients
 implies to solve  a tridiagonal system $A.m =  b$. Values in $A$ and  $b$ can be
 computed from  incoming pixels intensity  but after, the back-solve  starts with

-the  lastest  values,  which  breaks  the  pipeline.  Moreover,  SPL  relies  on
+the  latest  values,  which  breaks  the  pipeline.  Moreover,  SPL  relies  on

 interpolating far more points than profile size. Thus, the end of SPL works on a
 larger amount of data than the beginning, which also breaks the pipeline.
 
 interpolating far more points than profile size. Thus, the end of SPL works on a
 larger amount of data than the beginning, which also breaks the pipeline.
 


@@ -689,27 +698,19 @@ will include real experiments in the final version of this paper.
 
 \subsection{VHDL implementation}
 
 
 \subsection{VHDL implementation}
 

-
-
-% - ecriture d'un code en C avec integer
-% - calcul de la taille max en bit de chaque variable en fonction de la quantization.
-% - tests de quantization : équilibre entre précision et contraintes FPGA
-% - en parallèle : simulink et VHDL à la main
-
-

 From the LSQ algorithm, we have written a C program that uses only
 integer values. We use a very simple quantization by multiplying
 double precision values by a power of two, keeping the integer
 part. For example, all values stored in lut$_s$, lut$_c$, $\ldots$ are
 From the LSQ algorithm, we have written a C program that uses only
 integer values. We use a very simple quantization by multiplying
 double precision values by a power of two, keeping the integer
 part. For example, all values stored in lut$_s$, lut$_c$, $\ldots$ are

-scaled by 1024.  Since LSQ also computes average, variance, ... to
-remove the slope, the result of implied euclidian divisions may be
+scaled by 1024. Since LSQ also computes average, variance, ... to
+remove the slope, the result of implied Euclidean divisions may be

 relatively wrong. To avoid that, we also scale the pixel intensities
 relatively wrong. To avoid that, we also scale the pixel intensities

-by a power of two. Futhermore, assuming $nb_s$ is fixed, these
-divisions have a knonw denominator. Thus, they can be replaced by
+by a power of two. Furthermore, assuming $nb_s$ is fixed, these
+divisions have a known denominator. Thus, they can be replaced by

 their multiplication/shift counterpart. Finally, all other
 multiplications or divisions by a power of two have been replaced by
 left or right bit shifts. By the way, the code only contains
 their multiplication/shift counterpart. Finally, all other
 multiplications or divisions by a power of two have been replaced by
 left or right bit shifts. By the way, the code only contains

-additions, substractions and multiplications of signed integers, which
+additions, subtractions and multiplications of signed integers, which

 is perfectly adapted to FGPAs.
 
 As said above, hardware constraints have a great influence on the VHDL
 is perfectly adapted to FGPAs.
 
 As said above, hardware constraints have a great influence on the VHDL


@@ -736,24 +737,40 @@ that.
 
 \subsection{Simulation}
 
 
 \subsection{Simulation}
 

-Currently, we have only simulated our VHDL codes with GHDL and GTKWave (two free
-tools with linux).  Both approaches led to correct results.  At the beginning of
-our simulations, our  pipiline could compute a new phase each  33 cycles and the
-length of the  pipeline was equal to  95 cycles.  When we tried  to generate the
-corresponding bitsream  with ISE environment  we had many problems  because many
-stages required  more than the  10$n$s required by  the clock frequency.   So we
-needed to decompose  some part of the  pipeline in order to add  some cycles and
-simplify some parts between a clock top.
-% ghdl + gtkwave
-% au mieux : une phase tous les 33 cycles, latence de 95 cycles.
-% mais routage/placement impossible.
+Before experimental tests on the board, we simulated our two VHDL
+codes with GHDL and GTKWave (two free tools with linux). For that, we
+build a testbench based on profiles taken from experimentations and
+compare the results to values given by the SPL algorithm. Both
+versions lead to correct results.
+
+Our first code were highly optimized : the pipeline could compute a
+new phase each 33 cycles and its latency was equal to 95 cycles. Since
+the Spartan6 is clocked at 100MHz, it implies that estimating the
+deflection of 100 cantilevers would take about $(95 + 200\times 33).10
+= 66.95\mu$s, i.e. nearly 15000 estimations by second.
+

 \subsection{Bitstream creation}
 
 \subsection{Bitstream creation}
 

-Currently both  approaches provide synthesable  bitstreams with ISE.   We expect
-that the  pipeline will  have a latency  of 112  cycles, i.e. 1.12$\mu$s  and it
-could accept new profiles of pixel each 48 cycles, i.e. 480$n$s.
+In order to test our code on the SP Vision board, the design was
+extended with a component that keeps profiles in RAM, flushes them in
+the phase computation component and stores its output in another
+RAM. We also added a wishbone : a component that can "drive" signals
+to communicate between i.MX and others components. It is mainly used
+to start to flush profiles and to retrieve the computed phases in RAM.
+
+Unfortunately, the first designs could not be placed and route with ISE
+on the Spartan6 with a 100MHz clock. The main problems came from
+routing values from RAMs to DSPs and obtaining a result under 10ns. By
+the way, we needed to decompose some parts of the pipeline, which adds
+some cycles. For example, some delays have been introduced between
+RAMs output and DSPs. Finally, we obtained a bitstream that has a
+latency of 112 cycles and computes a new phase every 40 cycles. For
+100 cantilevers, it takes $(112 + 200\times 40).10 = 81.12\mu$s to
+compute their deflection.
+
+This bitstream has been successfully tested on the board TODAY ! YEAAHHHHH
+

 
 

-% pas fait mais prévision d'une sortie tous les 480ns avec une latence de 1120

 
 \label{sec:results}
 
 
 \label{sec:results}
 


@@ -761,7 +778,18 @@ could accept new profiles of pixel each 48 cycles, i.e. 480$n$s.
 
 
 \section{Conclusion and perspectives}
 
 
 \section{Conclusion and perspectives}

-
+In this paper we have presented a new method to estimate the
+cantilevers deflection in an AFM.  This method is based on least
+square methods.  We have used quantization to produce an algorithm
+based exclusively on integer values, which is adapted to a FPGA
+implementation. We obtained a precision on results similar to the
+initial version based on splines.  Our solution has been implemented
+with a pipeline technique.  Consequently, it enables to handle a new
+profile image very quickly. Currently we have performed simulations
+and real tests on a Spartan6 FPGA.
+
+In future work,  we plan to study  the quantization. Then we want  to couple our
+algorithm with a high speed camera and we plan to control the whole AFM system.

 
 \bibliographystyle{plain}
 \bibliography{biblio}
 
 \bibliographystyle{plain}
 \bibliography{biblio}