X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/dmems12.git/blobdiff_plain/8d8c7405f943188a7b597675cc8a23e95430b6d7..85ccdc9bbf8d6b30f5737245a16d277a7713908c:/dmems12.tex?ds=inline diff --git a/dmems12.tex b/dmems12.tex index 701ce92..c5ee6cf 100644 --- a/dmems12.tex +++ b/dmems12.tex @@ -44,7 +44,7 @@ -\title{Using FPGAs for high speed and real time cantilever deflection estimation} +\title{A new approach based on least square methods to estimate in real time cantilevers deflection with a FPGA} \author{\IEEEauthorblockN{Raphaël Couturier\IEEEauthorrefmark{1}, Stéphane Domas\IEEEauthorrefmark{1}, Gwenhaël Goavec-Merou\IEEEauthorrefmark{2} and Michel Lenczner\IEEEauthorrefmark{2}} \IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, DISC, University of Franche-Comte, Belfort, France\\ \{raphael.couturier,stephane.domas\}@univ-fcomte.fr} @@ -63,7 +63,15 @@ \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. This method was based on the spline method to interpolate the +deflection and the computations were performed on a PC with LabView. In this +paper, we propose a new method based on the least square method and we present +the implementation that we developped on a FPGA. Our method can be pipelined on +a FPGA in order to manipulate image profiles very quickly. Simulations and real +tests we have performed showed us that this implementation is very efficient and +should allow us to control of a cantilevers array in real time. \end{abstract} @@ -90,19 +98,18 @@ 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 +by an optic source. The interferometry produces fringes on each cantilever 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 +cantilever. In~\cite{AFMCSEM11}, authors have used an algorithm based on spline to estimate the cantilevers' positions. - 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 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. The remainder of the paper is organized as follows. Section~\ref{sec:measure} describes more precisely the measurement process. Our solution based on the @@ -118,13 +125,6 @@ presented. \section{Measurement principles} \label{sec:measure} - - - - - - - \subsection{Architecture} \label{sec:archi} %% description de l'architecture générale de l'acquisition d'images @@ -138,24 +138,26 @@ 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. -The system build by authors of~\cite{AFMCSEM11} has been developped based on a -Linnick interferomter~\cite{Sinclair:05}. It is illustrated in -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 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. 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. +The system build by these authors is based on a Linnick +interferomter~\cite{Sinclair:05}. It is illustrated in +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 +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. +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}, authors used a LabView program to +compute the cantilevers' deflections from the fringes. \begin{figure} \begin{center} @@ -171,21 +173,29 @@ cantilevers' movements from the fringes. \subsection{Cantilever deflection estimation} \label{sec:deflest} -As shown on image \ref{img:img-xp}, each cantilever is covered by -interferometric fringes. The fringes will distort when cantilevers are -deflected. Estimating the deflection is done by computing this -distortion. For that, (ref A. Meister + M Favre) proposed a method -based on computing the phase of the fringes, at the base of each -cantilever, near the tip, and on the base of the array. They assume -that a linear relation binds these phases, which can be use to -"unwrap" the phase at the tip and to determine the deflection.\\ - -More precisely, segment of pixels are extracted from images taken by a -high-speed camera. These segments are large enough to cover several -interferometric fringes and are placed at the base and near the tip of -the cantilevers. They are called base profile and tip profile in the -following. Furthermore, a reference profile is taken on the base of -the cantilever array. +\begin{figure} +\begin{center} +\includegraphics[width=\columnwidth]{lever-xp} +\end{center} +\caption{Portion of an image picked by the camera} +\label{fig:img-xp} +\end{figure} + +As shown on image \ref{fig:img-xp}, each cantilever is covered by +several interferometric fringes. The fringes will distort when +cantilevers are deflected. Estimating the deflection is done by +computing this distortion. For that, authors of \cite{AFMCSEM11} +proposed a method based on computing the phase of the fringes, at the +base of each cantilever, near the tip, and on the base of the +array. They assume that a linear relation binds these phases, which +can be use to "unwrap" the phase at the tip and to determine the deflection.\\ + +More precisely, segment of pixels are extracted from images taken by +the camera. These segments are large enough to cover several +interferometric fringes. As said above, they are placed at the base +and near the tip of the cantilevers. They are called base profile and +tip profile in the following. Furthermore, a reference profile is +taken on the base of the cantilever array. The pixels intensity $I$ (in gray level) of each profile is modelized by: @@ -289,25 +299,23 @@ computation, we give some general information about FPGAs and the board we use. \subsection{FPGAs} -A field-programmable gate array (FPGA) is an integrated circuit -designed to be configured by the customer. FGPAs are composed of -programmable logic components, called configurable logic blocks -(CLB). These blocks mainly contains look-up tables (LUT), flip/flops -(F/F) and latches, organized in one or more slices connected -together. Each CLB can be configured to perform simple (AND, XOR, ...) -or complex combinational functions. They are interconnected by -reconfigurable links. Modern FPGAs contain memory elements and -multipliers which enable to simplify the design and to increase the -performance. Nevertheless, all other complex operations, like -division, trigonometric functions, $\ldots$ are not 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. Such a -software can synthetize a design written in an 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 algorithm in HDL code, taking account FPGA resources -and constraints like clock signals and I/O values that drive the FPGA. +A field-programmable gate array (FPGA) is an integrated circuit designed to be +configured by the customer. FGPAs are composed of programmable logic components, +called configurable logic blocks (CLB). These blocks mainly contains look-up +tables (LUT), flip/flops (F/F) and latches, organized in one or more slices +connected together. Each CLB can be configured to perform simple (AND, XOR, ...) +or complex combinational functions. They are interconnected by reconfigurable +links. Modern FPGAs contain memory elements and multipliers which enable to +simplify the design and to increase the performance. Nevertheless, all other +complex operations, like division, trigonometric functions, $\ldots$ are not +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 +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 +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 @@ -346,10 +354,11 @@ that communicate between i.MX and Spartan6, using Spartan3 as a tunnel. By default, the WEIM interface provides a clock signal at 100MHz that is connected to dedicated FPGA pins. -The Spartan6 is an LX100 version. It has 15822 slices, equivalent to -101261 logic cells. There are 268 internal block RAM of 18Kbits, and -180 dedicated multiply-adders (named DSP48), which is largely enough -for our project. +The Spartan6 is an LX100 version. It has 15822 slices, each slice +containing 4 LUTs and 8 flip/flops. It is equivalent to 101261 logic +cells. There are 268 internal block RAM of 18Kbits, and 180 dedicated +multiply-adders (named DSP48), which is largely enough for our +project. Some I/O pins of Spartan6 are connected to two $2\times 17$ headers that can be used as user wants. For the project, they will be @@ -364,18 +373,18 @@ phase. The second one, detailed in this article, is based on a classical least square method but suppose that frequency is already known. -\subsubsection{Spline algorithm} +\subsubsection{Spline algorithm (SPL)} \label{sec:algo-spline} Let consider a profile $P$, that is a segment of $M$ pixels with an 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 $x = 0, 1, \ldots,M-1$. A -normalisation allows to scale known intensities into $[-1,1]$. We compute -splines that fit at best these normalised intensities. Splines (SPL in the -following) 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. +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 +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. In order to have the frequency, the mean line $a.x+b$ (see equation \ref{equ:profile}) of $I^s$ is computed. Finding intersections of $I^s$ and this line allow to obtain @@ -396,7 +405,7 @@ Two things can be noticed: computation of $\theta$. \end{itemize} -\subsubsection{Least square algorithm} +\subsubsection{Least square algorithm (LSQ)} Assuming that we compute the phase during the acquisition loop, equation \ref{equ:profile} has only 4 parameters: $a, b, A$, and @@ -462,7 +471,7 @@ computed. \end{itemize} Finally, the whole summarizes in an algorithm (called LSQ in the following) in two parts, one before and one during the acquisition loop: -\begin{algorithm}[h] +\begin{algorithm}[htbp] \caption{LSQ algorithm - before acquisition loop.} \label{alg:lsq-before} @@ -483,7 +492,7 @@ Finally, the whole summarizes in an algorithm (called LSQ in the following) in t } \end{algorithm} -\begin{algorithm}[ht] +\begin{algorithm}[htbp] \caption{LSQ algorithm - during acquisition loop.} \label{alg:lsq-during} @@ -643,42 +652,36 @@ an FPGA implementation: it mainly depends on the type of operations and their ordering. The final decision is thus driven by the third criterion.\\ -The Spartan 6 used in our architecture has hard constraint: it has no -built-in floating point units. Obviously, it is possible to use some -existing "black-boxes" for double precision operations. But they have -a quite long latency. It is much simpler to exclusively use integers, -with a quantization of all double precision values. Obviously, this -quantization should not decrease too much the precision of -results. Furthermore, it should not lead to a design with a huge -latency because of operations that could not complete during a single -or few clock cycles. Divisions are in this case and, moreover, they -need an varying number of clock cycles to complete. Even -multiplications can be a 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 but from the algorithms. Their VHDL implentation 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 -the lastest 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. - -LSQ has not this problem: all parts except the dichotomial search -work on the same amount of data, i.e. the profile size. Furthermore, -LSQ needs less operations than SPL, implying a smaller output -latency. Consequently, it is the best candidate for phase -computation. Nevertheless, obtaining a fully pipelined version -supposes that operations of different parts complete in a single clock -cycle. It is the case for simulations but it completely fails when -mapping and routing the design on the Spartan6. By the way, -extra-latency is generated and there must be idle times between two -profiles entering into the pipeline. +The Spartan 6 used in our architecture has a hard constraint: it has no built-in +floating point units. Obviously, it is possible to use some existing +"black-boxes" for double precision operations. But they have a quite long +latency. It is much simpler to exclusively use integers, with a quantization of +all double precision values. Obviously, this quantization should not decrease +too much the precision of results. Furthermore, it should not lead to a design +with a huge latency because of operations that could not complete during a +single or few clock cycles. Divisions are in this case and, moreover, they need +a varying number of clock cycles to complete. Even multiplications can be a +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 +but from the algorithms. Their VHDL implentation 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 +the lastest 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. + +LSQ has not this problem: all parts except the dichotomial search work on the +same amount of data, i.e. the profile size. Furthermore, LSQ needs less +operations than SPL, implying a smaller output latency. Consequently, it is the +best candidate for phase computation. Nevertheless, obtaining a fully pipelined +version supposes that operations of different parts complete in a single clock +cycle. It is the case for simulations but it completely fails when mapping and +routing the design on the Spartan6. By the way, extra-latency is generated and +there must be idle times between two profiles entering into the pipeline. %%Before obtaining the least bitstream, the crucial question is: how to %%translate the C code the LSQ into VHDL ? @@ -688,20 +691,76 @@ profiles entering into the pipeline. \section{Experimental tests} +In this section we explain what we have done yet. Until now, we could not perform +real experiments since we just have received the FGPA board. Nevertheless, we +will include real experiments in the final version of this paper. + \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 +scaled by 1024. Since LSQ also computes average, variance, ... to +remove the slope, the result of implied euclidian divisions may be +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 +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 +is perfectly adapted to FGPAs. + +As said above, hardware constraints have a great influence on the VHDL +implementation. Consequently, we searched the maximum value of each +variable as a function of the different scale factors and the size of +profiles, which gives their maximum size in bits. That size determines +the maximum scale factors that allow to use the least possible RAMs +and DSPs. Actually, we implemented our algorithm with this maximum +size but current works study the impact of quantization on the results +precision and design complexity. We have compared the result of the +LSQ version using integers and doubles and observed that the precision +of both were similar. + +Then we built two versions of VHDL codes: one directly by hand coding +and the other with Matlab using the Simulink HDL coder +feature~\cite{HDLCoder}. Although the approach is completely different +we obtained VHDL codes that are quite comparable. Each approach has +advantages and drawbacks. Roughly speaking, hand coding provides +beautiful and much better structured code while Simulink allows to +produce a code faster. In terms of throughput and latency, +simulations shows that the two approaches are close with a slight +advantage for hand coding. We hope that real experiments will confirm +that. + \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. \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. + % pas fait mais prévision d'une sortie tous les 480ns avec une latence de 1120 \label{sec:results} @@ -710,7 +769,16 @@ profiles entering into the pipeline. \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 +studied the quantization of this algorithm and have implemented it on a +FPGA. Our method gives comparable results compared to the initial version based +on splines. Our solution has been be 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 want to couple our algorithm with a high speed camera +and we plan to control the whole AFM system. \bibliographystyle{plain} \bibliography{biblio}