Julien Bert
email: jbert@ens2m.fr

Sounkalo Dembélé
email: sdembele@ens2m.fr

Nadine Lefort-Piat

Performing Weak Calibration at the Microscale, Application to Micromanipulation

We improve and adjust usual weak calibration techniques to the case of stereo video microscopes : Harris detector using a simplex optimization method for feature points detection, a "cha" window based ZNSSD correlation for points matching. Images of a pattern made with a water drop covered with nickel fillings are used. The result is validated by constructing 3D view of a micromanipulation work field.

I. Introduction

Micromanipulation is the manipulation of parts at the microscale, i.e. in the range from 1 µm to 1 mm, for assembly, sorting or testing. In addition to biomicroparts like cells and pollen seeds, artificial microparts are chemically or mechanically synthetized, or micromachined. Classical examples of the first and second types are respectively grains of powder like drugs or cosmetics, and optomechatronic components like balls, pegs, pins, threads, membranes, lenses, shutters and fibres. In some cases these microparts define final products (MEMS), otherwise they must be assembly to lead to the final products. For that purpose some automated microassembly systems have been developed by [START_REF] Yang | A surpervisory waferlevel 3d microassembly system for hybrid mems fabrication[END_REF], [START_REF] Matsumoto | Development of mems component assembly machine -application of robotics technology to micromechatronics[END_REF], [START_REF] Popa | Micro and mesoscale robotic assembly[END_REF] and [START_REF] Sun | Task-reconfigurable system for mems assembly[END_REF]. From those results it can be noticed that a microimaging system is always required, and the most used is the photon microscope connected to a camera. The images and their processing and analysis allow the task of surveillance, system control or microparts recognition. The drawback of above imager is the fact that the depthof-field is very short and the field of view is very narrow.

Since many years computer vision deals with the problem of using multiple view imaging systems. Those systems increase the robustness of the information of the work field. Recently the photon video microscope is equipped with two optic paths. This stereo video microscope perceives the work field with two different angles of view, left and right, like human vision. That microimaging system opens new perspectives for micromanipulation and it main application: microassembly. But the following usual algorithms must be restricted according to the drawbacks of that kind of image source as pointed out above: epipolar rectification, dense stereo correspondence, 3D reconstruction, 3D visual servoing, depth-estimation... Each method requires at least a weak calibration, which corresponds to the estimation of the relative geometry between the two views. Usually at the macro scale it is easy to perform weak calibration: two images of calibration pattern (like a chess board) is required. After the stereo views is obtained, feature are detected in every view and matched, then the calibration parameters are estimated [START_REF] Genc | Weak calibration and image-based rendering algorithms[END_REF]. But at the micro scale it is difficult to find a calibration pattern with the good characteristics: the latter must contain random pattern over a 3D surface. Then, the corresponding images exhibit speckle and depth information.

In this paper we propose a solution to the problem of weak calibration of two views micro imaging system. We mention the geometry of two views in section 2. We develop in section 3 the stages of our approach: feature detection with a modified Harris detector, improved feature matching, calibration parameters estimation. We apply our algorithm to a commercial stereo video microscope (LEICA MZ16 A). For that purpose an intelligent pattern is made with a water drop recover of nickel filings.

II. GEOMETRY OF TWO VIEWS

Fig. 1 shows the projective model of two views imaging system (stereo vision system). The points O and O ′ are respectively the optic center of the left and right images sources, then the line [OO ′ ] is the baseline of the stereo vision system. The projection of O in the view ψ ′ defines the epipole v ′ , the projection of O ′ in the view ψ It has been shown [START_REF] Faugeras | The Geometry of Multiple Images[END_REF], [START_REF] Hartley | Multiple View Geometry[END_REF] that the point p of ψ and its correspondence p ′ of ψ ′ are linked by the epipolar constraint :

p ′T F p = 0 ( 1
)
where F is called the fundamental matrix and is of dimensions 3 × 3 and rank 2. F corresponds to a projective morphism between ψ and ψ ′ , its depends on the epipole v ′ , and the homography A between the two views. The computation of F is known as the weak calibration of the corresponding stereovision system i.e. the recovery of the relative geometry of the system since it allows the determination of the epipoles. The estimation of F is an important step in rendering techniques: 2D or 3D view synthesis. The weak calibration stages developed in the paper are: feature points detection in the two views (of a calibration pattern) with a modified Harris detector, feature points matching with an improved windowed correlation and F estimation.

III. The calibration Stages

A. Feature points detection by a simplex Harris detector

The first corners detector algorithm was published by Moravec [START_REF] Moravec | Towards automatic visual obstacle avoidance[END_REF]. Today, there are several corners detectors in the literature, but only two are more popular, Susan [START_REF] Smith | Susan -a new approach to low level image processing[END_REF] and Harris [START_REF] Harris | A combined corner and edge detector[END_REF]. Ref. [START_REF] Schmid | Comparing and evaluating interest points[END_REF] shows that Harris detector is the most robust according to illumination changes. This is why, Harris detector is often used for feature point detection. It is based on an auto-correlation function since the latter puts in light the intensity changes:

E(u, v) = x y W (x, y) [I (x + u, y + v) -I (x, y)] 2 (2)
where [u, v] is the displacement of W (x, y), the window of auto-correlation (rectangular i.e. constant or gaussian) and I the intensity of the image. By considering a small shift the bilinear approximation M of E can be written:

M = x y W (x, y) I 2 x I x I y I x I y I 2 y ( 3
)
where I x and I y are the derivative functions defines by:

I x = ∂I(x,y) ∂x I y = ∂I(x,y) ∂y (4)
For every pixel of the image the detector response is:

R = det M -k (trace M ) 2 (5)
det M = λ 1 λ 2 and trace M = λ 1 + λ 2 with λ 1 and λ 2 the eigenvalues of M . The value of k is constant and is empirically defined to 0.04 × 10 -6 in our experiments. According to the detector response and the eigenvalues, it is possible to determine if the region of the window is a corner (R > 0), an edge (R < 0) or a flat (R ∼ 0) Fig. 2.

Usually the number of detected corners, N cd, for condition R > 0, is too important. In order to adjust that number, a threshold t is empirically defined and the corners N cd is determined by the condition R > t:

N cd = f (R(t)) (6)
Let us consider the stereo images from Tsukuba data base (Fig. 3). For t = 0, Ncd is respectively 672 points and 689 points for the left and right images, for t = 0.1 it becomes 59 points and 61 points. But in F estimation (and others parameters estimation like the collineation matrix) the same number of corners are required in both images. We propose a modification of Harris detector in order to define a priori the number of corners N c * to detect. The problem is to find the value t * of t that gives the desired number of corners N c * i.e. to resolve:

N c * -f (R(t)) = 0 (7)
This is an optimization problem that can be solved using a Nelder-Mead simplex method [START_REF] Nelder | A simplex method for function minimization[END_REF]. That method compares the values of the objective function with zero and does not require the use of any derivatives. A simplex in Rn is a set of n + 1 points that do not lie in a hyperplane. For example a triangle is a simplex of 2 dimensions. In the Nelder-Mead method, the simplex can vary in shape from iteration to iteration following reflect, expand, contract and shrink. The corner response for the image is calculated once. While N c * -N cd is different with zero, the simplex modifies the threshold t (Fig. 4).

B. Feature points matching by a X-ZNSSD

The matching between left and right features is performed with a zero-mean normalized sum of squared differences (ZNSSD) correlation since the latter is robust than the former SSD correlation. Its consists of the definition of the correlation window, the computation of the correlation function (also called criterion) around the features and the selection of the features corresponding to the maximum of that criterion (maximum of likelihood). According to the window, the SSD algorithm is more or less robust. Multiple window (multiple asymmetric windows from [START_REF] Fusiello | Symmetric stereo with multiple windowing[END_REF]) or multiple recursive window (recursive adaptive size multi-windowing from [START_REF] -Y. Chan | Dense stereo correspondence based on recursive adaptive size multiwindowing[END_REF]) are used to improve the robustness. Refer to [START_REF] Aschwanden | Experimental results from a comparative study on correlation-type registration algorithms[END_REF] for the comparative study.

We use a non recursive multiple window that gives best results. It can be expressed as followed:

W X = W odd k .X k∆x,k∆y (x, y) (8)
k is an integer. ∆x and ∆y are respectively x and y spaced intervals. W k is a window based on W defined as followed: where f w (x, y) is a continuous function (rectangular window) and X ("cha") the 2D function of Dirac comb. The latter corresponds to the product of two Dirac comb:

W = f w (x, y).X ∆x,∆y (x, y) (9)
X ∆x,△y (x, y) = X ∆x (x).X ∆y (y) = +∞ m=-∞ δ (x -m∆x) . +∞ n=-∞ δ (y -n∆y) (10)
Odd and the scale factor k are defined as followed: The Zero-mean Normalized Sum of Squared Differences (ZNSSD) criterion is defined by:

W odd k x = k × |W | x -mod 3 (k × |W | x ) W odd k y = k × |W | y -mod 3 (k × |W | y ) (11
c x,y = - i,j [(I(x+i,y+j)-Ī)-(I ′ (x ′ +i,y ′ +j)-Ī′ )] 2 i,j [I(x+i,y+j)-Ī] 2 i,j [I ′ (x ′ +i,y ′ +j)-Ī′ ] 2 (12)
where Ī and Ī′ is the mean of images I and I ′ respectively. In usual approach each left feature is compared with all the right features. The right feature for which the minimum value of the criterion is obtained corresponds to the maximum likelihood between left one and right one. Then that approach is slow. In order to increase the speed of the process we used a method based on relaxation technique [START_REF] Zhang | A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[END_REF] with only the neighbor constraint. Each feature p of the left image I is projected without any transformation in the right image I ′ and the euclidean distance between p and every p ′ of I ′ is computed (Fig. 6):

dist E (p; p ′ ) = (y ′ -y) 2 + (x ′ -x) 2 (13)
The criterion is computed only for a predefined neighborhood: a number of points p ′ in a given radius around p. A point p ′ that matched a point p is removed from I ′ : a unique correspondence is guaranteed for each point p. Finally we obtain two sets matches points that allows the estimation of the fundamental matrix.

In order to compare the performance of rectangular window based matching and cha window based matching, we overlay a regular grid of points in both Tsukuba's images. And we perform a dual matching: forward matching that leads to the correspondence of every left point in the right view and backward matching by calculating the correspondence of that point in the left view. Then the euclidian distance between original and estimated point is calculated. We apply this approach to the images from Tsukuba. Fig. 7 shows the evolution of the mean error of matching according to the size of correlation window. The cha window based approach is the best whatever the window size. For example, a window of 21×21 pixels leads to an error of 6.86 pixels for the rectangular window and 0.67 pixel for the cha one that corresponds to a decrease of 90.2% of the former error. The mean value of best matching is 56.7%.

C. Estimation of Fundamental Matrix

The fundamental matrix is computing by the normalized eight-point algorithm introduced by Longuet-Higgins [START_REF] Longuet-Higgins | A computer algorithm for reconstruction a scene from two projections[END_REF] and finalized by Hartley [START_REF] Hartley | In defense of the eight-point algorithm[END_REF]. To estimate the matrix F at least height points correspondences are required. The first stage is a normalization of every point of both images. The normalization is a transformation with a translation and an isotropic scaling so that the centroid of the reference points is at the origin of the coordinate and the euclidian distance of the points from the origin is equal to √ 2. We get two sets of normalized points, and the fundamental matrix is defined by the equation:

p′T F p = 0 ( 14
)
where p′ = [x ′ , ŷ′ , 1] T and p = [x, ŷ, 1] T are the rectified point. It can be written as:

x′ ŷ′ 1   f 1 1 f 1 2 f 1 3 f 2 1 f 2 2 f 2 3 f 3 1 f 3 2 f 3 3     x ŷ 1   = 0 (15)
if that equation is expanded it becomes:

x′ x f 1 1 + x′ ŷ f 1 2 + x′ f 1 3 + ŷ′ x f 2 1 + ŷ′ ŷ f 2 2 +ŷ ′ f 2 3 + x f 3 1 + ŷ f 3 2 + f 3 3 = 0 ( 16
)
that result can be written as:

A f = 0 ( 17
)
with f the vector made up of the entries of F and A defines linear equations, by the set of n matches point, of the form:

   x′ 1 x1 x′ 1 ŷ1 x′ 1 ŷ′ 1 x1 ŷ′ 1 ŷ1 ŷ′ 1 x1 ŷ1
A = U A Σ A V T A (19)
where the last column of V T A corresponds to the vector f i.e. the entries of the fundamental matrix F . The property of F is that it is singular, thus the rank of F should be two than F can be written:

F = U F Σ F V T F ( 20
)
where Σ F = diag(σ 1 , σ 2 , σ 3 ). To constraints F to have a rank of two it is composed by the elements of SVD( F ) with the constraint value σ 3 = 0:

F = U F [diag(σ 1 , σ 2 , 0)]V T F (21)
Finally the fundamental matrix F is denormalized by the inverse transformation of points (translation and isotropic scaling) that corresponds to the original matching p ↔ p ′ . We used the RAndom SAmple Consensus algorithm (RANSAC) exposed in [START_REF] Fischler | Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography[END_REF]. This algorithm removes the outliers from the model F .

IV. Application

We apply ours algorithms to a commercial stereo video microscope (LEICA MZ16 A) with a magnification from 0.1x to 2x. Two different optical paths of the light lead to two views of the scene recorded in two cameras. The system is dedicated to the surveillance and control of a microassembly station. Part of 400µm × 400µm × 4µm etched in silicon wafer have to be assembled to form 3D products.

A. Pattern Calibration

Weak calibration is achieved from stereo views of a calibration pattern. The latter must satisfy:

• the pattern must be textured, the matching is based on correlation technique, without texture the matching is impossible,

• the texture must be not repetitive because of the ambiguity during the matching,

• the feature points must be at several depths (not at the same plane), for the good estimation of the fundamental matrix. Then in the macro scale two perpendicular chess boards are used. At the micro scale the realization of that kind of pattern is a great challenge. Then we use a water drop recover by nickel filings. Fig. 8 shows different water drops, the diameter is of 1.5mm for the big and 500µm for the small. That pattern leads to well textured images with feature points at different depths.

B. Simplex Harris detector

One specificity of the photonic micro-imager [START_REF] Yang | Optomechatronic design of microassembly systems for manufacturing hybrid microsystem[END_REF] is the small depth-of-field, then an image is sharp only for objects inside the depth-of-field. The size of the calibration pattern is larger than the depth-of-field of the stereo video microscope. In this case Harris detector gives features only in the area of the image which is in focus. To obtain features of the pattern at many levels, we must move the depth-of-field along the pattern and extract features. We acquire a stack image at different levels to cover the entire depth of the pattern. The features are computed for every stack view and at the end gathered to form a unique set of feature points. Fig. 9 shows three stack images of the calibration pattern. We define for each stack a set value of 200 features in simplex Harris detector. For each stack the detector finds respectively a threshold of t = 0.0666, t = 0.0444 and t = 0.0385. Finally we obtain a set of 600 points for different depths of the scene (Fig. 9).

C. X-ZNSSD Matching

We apply the X-ZNSSD and the rectangular ZNSSD to the views of the micro-pattern presented Fig. 9. We calculate the mean error of matching according to the window size. The result is shown Fig. 10.

For high window sizes (superior to 15 pixels) the methods are equivalent: the errors of matching are quite identical. But for lower window sizes cha window is better. A 9 × 9 pixels size leads to an error of 128.8 pixels for the rectangular window and 67.6 pixels for cha window: a decrease of 47.5%. The mean diminution is 21.4%.

D. Surface Reconstruction

Fundamental matrix F describes the relative geometry between both image sources. One interest of F is the fact it allows the performing of fast dense correspondence of the epipolar lines between two views [START_REF] Zhang | A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[END_REF]. The latter allows the estimation of the disparity δ(p, p ′ ) i.e. the displacement (in pixel) between every couple of feature points (p, p ′ ):

δ(p, p ′ ) = dist E (p, p ′ ) ( 22
)
with dist E the Euclidian distance. The disparity means the relative depth between the points according to the imaging system and can be rendered in 3D. After been calibrated by the approach exposed above we recorded a pair of image from the LEICA video microscope and reconstructed using the method from [START_REF] Fleig | Surface reconstruction of the surgical field from stereoscopic microscope views in neurosurgery[END_REF] a 3D view of the work field. It represents a microgripper tips manipulating microparts (Fig. 11).

V. CONCLUSION

We have succinctly mentioned the geometry of two views and exposed a best approach to perform weak calibration of that kind of imaging system at the micro scale. That process consists of a feature points detection using a Harris detector, a ZNSSD matching of feature points and the fundamental matrix estimation. We improve above techniques to adjust them to the views from stereo video microscopes. Harris detector is modified by integrating an optimization method based on simplex (simplex Harris detector) in order to guaranty a priori the number of feature points to detect since the same number is required for both views. The modification of the ZNSSD concerns the correlation window: it is discretized by a 2D Dirac combs (X-ZNSSD). It is more robust and accurate than usual rectangular window based approach.

We also define a calibration pattern made with a water drop recovered by nickel fillings. It satisfies all the constraints of a good calibration pattern. By stacking and gathering the views we overcome the depth-of-field limitation of the stereo micro imager (LEICA MZ16 A) and get enough feature points at enough level to perform the calibration of the system. That result was used to achieve 3D view of a micromanipulation scene. That is very useful, it is can be used in surveillance or control of the micromanipulation.

Future work will deal with the fabrication of a stable calibrated pattern since water drop is good but it evaporate after a short time and it size cannot be controlled. Our intention is to used microtechnology by etching textured shapes in a silicon wafer.

Fig. 1 .

 1 Fig. 1. Epipolar geometry.

Fig. 2 .

 2 Fig. 2. Definition of a corner, an edge or a flat according to the detector response (R) and the eigenvalues (λ 1 , λ 2 ).

Fig. 3 .

 3 Fig. 3. The Tsukuba stereo images (384 × 288 pixels) is used as a benchmark.

Fig. 4 .

 4 Fig. 4. The scheme of the Harris simplex. Where N c * is the number of corners desired and N c d the number of corners detected.

Fig. 5 .

 5 Fig. 5. Left, the classical rectangular window correlation. Right, the cha window correlation with k = 2.

Fig. 6 .

 6 Fig. 6. Process of the closer neighbor method.

  ) with | * | x and | * | y the cardinal along x and y respectively and mod n ( * ) the modulo. We represent in Fig. 5 the rectangular window and the cha window. The two windows perform the correlation with the same time whatever the value of k since they have the same number of pixels (|W | = |W X |).

Fig. 7 .

 7 Fig.7. Mean error matching on Tsukuba images: mean errors of matching (2500 features) according to the size of window for the rectangular and cha window.

Fig. 8 .

 8 Fig. 8. Example of our micro calibration pattern for the stereomicroscope.

Fig. 9 .

 9 Fig. 9. Feature points detected at different levels, and afterwards assembled (lower right).

Fig. 10 .

 10 Fig.10. Mean error matching on images of the micro-pattern: mean error of matching (2500 features) according to the size of window for the rectangular and cha window.

Fig. 11 .

 11 Fig. 11.Top, the stereo images of microgripper. Bottom, the surface reconstruction.


A Cherry

J Abadie

E Piat

Microforce sensor for microbiological applications based on a floating-magnetic principle

In this paper, we present the design of a new magnetic nano and microforce sensor for microbiological applications. The sensing part of the sensor presents a naturally stable six degrees of freedom equilibrium state using the combination of upthrust buoyancy and magnetic force. The sensor allows force measurement without deformation of the sensing element using a feedback control loop and is able to measure the components, in the horizontal plan, of the external force applied. The measurement range varies between around ± 100 µN with a resolution of 20 nN and a linear output. The mechanical stiffness of the passive system is about 0.018 N.m -1 (same order of magnitude than an AFM micro-cantilever). A complete static study and experimental validation of the used principle are presented in this paper.

I. INTRODUCTION

Recently, microscale sensing and manipulation have become a challenging issue mainly in micro-assembly of hybrid microsystems and biomanipulation. In fact, the potential applications are vast. In this context, many tools have been developped to visualize the micro world, but unfortunately it is not the same with regard to measurements of micro object mechanical parameters or concerning the forces applied on it.

In the field of single cell micromanipulation, the handling of individual cells is still often solved manually by human operators without force sensing. These tasks require long hours of practice and in spite of individual training, the failure rate remains very high. In fact, the high degree of accuracy needed for tools positioning and the weakness of the mechanical efforts involved in these tasks make them very difficult to achieve. It is important to notice that these forces are included in the micro Newton scale. Such small forces provide a difficult challenge for designing sensors that can output measurements with high resolution and high accuracy.

Such force measurements appear also useful in the field of the micro assembly. When manipulating micro objects, especially delicate structures, pure position control is usually not adequate or sufficient to ensure successful operation and prevent damage to the objects. Force control is often needed in order to achieve better manipulation results. Our objective is to improve the communication between the operator and the micro world by including new This work was not supported by any organization A. Cherry, J. Abadie and E. Piat are with Laboratoire d'Automatique de Besanc ¸on -UMR CNRS 6596 -ENSMM, France Emmanuel.piat@ens2m.fr ways of interaction such as for instance the possibility of feeling efforts.

Forces sensing is strongly related to the measurement of displacement or deformation of an elastic structure. The deformation is either detected by measuring the change in some material properties (electrical resistance, capacitance etc. . . ), or directly measured by optical devices. The applied force is directly calculated using the structure stiffness which is established after calibration with a known force. A short selection of nano and microforce sensors based on this principle is described below. A 3D micromanipulation system was developed by [START_REF] Arai | 3d micromanipulation system under microscope[END_REF]. This system allows to control the interface forces in contacttype micromanipulations between objects and effector, using a multi-axial force sensor built with strain gauges. The force sensing is based on the piezoresistivity effect which has a good linearity in some conditions. This type of sensor must be calibrated before each measurement because of the plastic deformation. The size of the gauge must also be adapted to the sensing structure dimensions. In the case of microstructures, the gauge fabrication becomes difficult to achieve.

Sun introduced a design of a planar capacitive force sensor with 6 degrees of freedom used to characterize Mouse Zona Pellucida and quantify its mechanical property differences before and after fertilization [START_REF] Sun | Mechanical property characterization of mouse zona pellucida[END_REF]. This capacitive sensor is able to resolve normal forces applied to a cell as well as tangential forces generated by improperly aligned cell probes. However this design is fabricated using MEMS technology and can not measure constant forces.

Li designed a highly sensitive 1-D and 2-D sensor system for applications in micro-assembly and bio-manipulation using an in situ PVDF (polyvinylidene fluoride) piezoelectric sensor [START_REF] Li | Novel micro gripping, probing and sensing devices for single-cell surgery[END_REF]. The sensor system has a resolution in the range of sub-micronewton. The charge developed across the plate is linearly proportional to the applied pressure and thickness but decrease with time when a non-varying load is applied.

Girot and Rougeot used a system based on atomic force microscope (AFM) to analyze the contact forces and remote forces at a microscopic scale within the framework of micromanipulation [START_REF] Rougeot | Forces analysis for micromanipulation[END_REF], [START_REF] Girot | Towards a non-destructive in vitro biomechanical characterization[END_REF]. The sensing element is a microcantilever with a stiffness K = 0.03N/m. The applied force is proportional to the micro-cantilever deflection. The drawback of this technic is that it's a global quantification of force without indication of the measurement direction and thus the type of solicitation.

Other type of microforce sensors based on AFM used a carbon nanotube (CNT) probe, calibrated by the electromechanical resonance [START_REF] Arai | Pico-newton order force measurement using a calibrated carbon nanotube probe by electrmechanical resonance[END_REF]. The CNT is attached to the AFM cantilever by an electron-beam-induced deposition (EBID).

The sensor is able to measure the contact forces in piconewton order resolution by measuring the deformation of the CNT probe from FE-SEM images.

All the systems described before are monolithics. In the case of micromecanisms constituted by several assembled parts, friction prohibits correct force measurement in the microworld. One way to avoid friction problem, is to use levitation methods in these devices.

Our laboratory developed a microforce sensor based on magnetic levitation in entirely passive configuration using diamagnetic and magnetic materials [START_REF] Boukallel | Passive diamagnetic levitation: theoretical foundations and application to the design of a micro-nano force sensor[END_REF], [START_REF] Boukallel | Microrobots for in vitro fertilization applications[END_REF], [START_REF] Boukallel | Levitated micro-nano force sensor using diamagnetic levitation[END_REF]. The levitating part (see figures 1 and 2) is used as a one direction force sensing device. The displacement of this device, when an external force is applied on it, is measured using a laser beam and is proportional to this force. The absence of friction associated with a low stiffness (K = 0.021 N/m) makes the sensor highly sensitive. The only problem of this configuration is the weight limitation of the levitating part (less than 200 milligrams). Because passive levitation is naturally stable and seems a very efficient and low cost principle to measure microforces, we decided to carry on the work initiated by [START_REF] Boukallel | Passive diamagnetic levitation: theoretical foundations and application to the design of a micro-nano force sensor[END_REF] substituting diamagnetic levitation by a floating principle in order to suppress the weight limitation. The part used as the force sensing device is also naturally stable with 6 degrees of freedom (proof not included in this paper). This paper presents the description of this new micro forces sensor which is totally compatible with biological materials. Both static and dynamic studies are presented with a 1D model and model identification is explained. As this paper is focused mainly on the sensor design and not its complete 3D dynamic model, only a simplified 1D model is detailed here. Moreover, as the sensor allows measurements of forces without any displacement of the sensible part, we briefly present the design used to make possible the feedback control loop. The sensing element is a triangular platform suspended by 3 small buoyancy tanks L 1 , L 2 and L 3 and presents a naturally stable six degrees of freedom equilibrium state (see figure 3). Thus, the sensing device is the entire platform on which the object to be manipulated is locked. Each buoyancy tank is formed by 2 fixed cubic magnets M 1 (5x5mm) and a cylindrical moving magnet M 2 placed at the corner of the triangular platform, inside a float. The magnets M 1 are placed such that their north and south poles are in opposite directions. The distance between the 2 magnets M 1 influences the value of magnetic forces applied on the floating magnets M 2 . The magnets M 1 and M 2 are made of NdFeB and the three floating magnets M 2 have a radius of 2mm and a thickness of 2.5mm. The platform mass is supported against gravity by the combined upthrust buoyancy of the three floats. Thus, the platform weight is not an issue for this sensor. Magnetic forces of magnets M 1 provide stability of platform in the plane (xOy). The upthrust buoyancy provide the stability along z axis. The platform position is measured with three laser interferometers. In this case, an external force applied on the floating platform can be deduced according to its magnetic stiffness and displacement measured by the laser sensor.

II. SENSOR CONFIGURATION

In all next sections of this paper, the study will be only focused on one of three buoyancy tanks L 1 , L 2 and L 3 . The same study is also valid for the two other buoyancy tanks.

III. STATIC STUDY

In this section, the principle of force measurements according to x, y and z directions is presented. Concerning the module L 1 , at the equilibrium state position four external forces described below are applied on the floating magnet M 2 (see figure 4). The top magnet M 1 applies an attractive force, called F att , on M 2 . The lower magnet M 1 applies also an attractive force called F att on M 2 obtained symmetrically to the plan (xOy). We note F mag the vectorial sum of F att and F att . The third force is the upthrust buoyancy called F b applied by the water at the centre of gravity G of the float along z. We will also suppose that G is the centre of gravity of magnet M 2 . The fourth force P , also acting along z, is the total weight of the float. When an unknown external force F ext is applied at the centre of gravity G of M 2 , the new stable equilibrium state is obtained applying the principle of static at the float centre of gravity G(x G , y G , z G ):

F mag + F ext + P + F b = 0 (1)
Because F b and P are the largest forces (several orders of magnitude) compared to the other microforces, it is possible to consider that F ext is applied only in the (xOy) plan. Thus, F b compensates P and we can write

F ext = F mag .
The determination of the external force F ext in the plane (xOy) is conditioned by the determination of the magnetic force applied on G. The determination of F mag is possible knowing the position of the floating magnet M 2 .

A. Evaluation of F mag

The magnetic field produced at a point M by a permanent magnet modelled by a surface distribution of loads is given by the following equation [START_REF] Bancel | Three-dimensional analytical optimization of permanent magnets alternated structure[END_REF]:

B mag (M ) = S + J 4π AM | AM | dS + + S - -J 4π BM | AM | dS - (2)
The determination of the field components B x (M ), B y (M ) and B z (M ) at the point M can be done by the integration of the equation (2) along x, y and z. The magnetic force applied on the magnet M 2 is given by the following equation :

F mag = V m 2 • ∇ B mag (M ) • dv (3)
where B mag (M ) is the field produced by both magnets M 1 at a point M inside the magnet M 2 . V is the volume of magnet M 2 and m 2 its magnetization. This magnétisation is about 8.89 × 10 4 A • m -1 . Figure 5 presents the evaluation of the magnetic force along x such that F y mag and F z mag equal to zero. This curve allowed us to calculate the magnetic stiffness K x m = dF x /dx of our passive floating system at any float position. On this curve we note a particular point S which corresponds to the equilibrium of the float when F ext =0. The cartesian coordinates of S are x = 11.7mm, y = 0 and z = 0 according to a fixed reference axes L(x,y,z). The origin L of the fixed reference axes is located at the center of upper and lower magnets M 1 (see figure 4). One can notice that m 2 does not have an influence on S but only on K x m .

IV. SIMPLIFIED MODEL OF THE FLOAT (1D) A. Dynamic equilibrium

The dynamic equilibrium along x is given by the following equation:

F x ext + F x mag + F x f + F x p = mẍ (4)
in which F x ext is the external force applied on the floating magnet M 2 along x and F x mag is the magnetic force produced by the two permanent magnets M 1 . In case of small displacements around the point of equilibrium state S, this function is assumed linear and we can write :

F x mag = K x m • x (5)
The stiffness K x m at S is about 18.9 × 10 -3 N.m -1 .

F x f is the viscous friction force between the float and water (atmosphere influence is neglected). Like for the magnetic force, in case of small displacements we can write :

F x f = K x f • ẋ (6)
in which K x f is the friction coefficient. Finally, F x p is the total perturbation force, like capillary force (which disappears in case of symetric meniscus) and like the delayed return wave of water generated by the displacement of the float and reflected on the boards of the container.

According to a fixed reference axes with origin S, the equation ( 4) becomes :

F x ext + F x p = mẍ + K x f ẋ + K x m x (7)

B. Parameters identification of 1D model

This section is devoted to the model parameters determination. Among these parameters, the magnetic stiffness K x m is already identified knowing the magnetic force. The weight of the float m, measured with a microbalance is 5.66 × 10 -4 kg. The friction coefficient K x f , is evaluated using the free response of our system. It is obtained by pushing manually the float beyond the equilibrium point S and rapidly releasing it. These measurements were done using a laser displacement sensor which has 1µm resolution (see figure 6). The figure 7 shows the response of the experimental system and the simulation curve after the evaluation of the friction coefficient K x f (this coefficient has been set so that both curves are the closest possible). This friction coefficient is 0.8 × 10 -3 N • s • m -1 . The difference visible on the graph between the simulated and experimental curves is due to the 1-D model which doesn't represent correctly the 2D magnetic coupling on x and y axes. Perturbation forces explained before could also possibly have an unknown influence, which has to be investigated. We saw previously that force sensing is closely related to the measurement of the sensitive part displacement. This displacement can generate drawbacks in the case of high precision tasks such as biological cells micromanipulation or micro-assembling. For instance, the force sensitive part on figure 3 is the entire plateform. If this plateform moves when external forces are apply on the micro object, the microobject will also move, which can be problematic for the operator. Thus, the key idea here is to developp a device wich allows force measurements without any (or only very small) displacements of the sensitive part, thanks to an active control. The design used to make possible the feedback control loop is composed of two coils placed on both sides, above and below the floating magnet (see figure 8). In case of an external force applied to the float which tends to push it beyond the point S, the activation of coils will produce an opposed electromagnetic force F elec that will maintain the float on S. In this case, the current I in the coils is the new physical value related to the external force.

Figure 9 shows the step response for positive and negative current I. The displacement x obtained is the combination of both magnetic and electromagnetic behavior due to F mag and F elec . The response for positive and negative current is Step response for positive and negative current not the same because F mag is not symmetrical around S.

A. Evaluation of F elec

The magnetic field produced by a coil at a point M (in a cylindrical axes reference) is given by the following equations [START_REF] Jackson | Classical Electrodynamics[END_REF]:

B elec (M ) =    B r (M ) = µ0 2π IπN a 2 cosθ r 3 B θ (M ) = µ0 2π IπN a 2 sinθ r 3 B φ (M ) = 0 (8)
Fig. 10. Circular spire in which : r, θ and φ are the components of the cylindrical coordinates (see figure 10), N is the number of spires, a is the radius of the coil and I the current. These equations are valid in the case of microcoils, supposing that all spires are concentrated in the same place.

Like for magnetic force, the electromagnetic force applied to the magnet M 2 centre of gravity G is given by the following equation :

F elec = V m 2 • ∇ B elec (M ) • dv (9)
The new dynamic equilibrium along x in the presence of the two coils is given by the following equation:

F x ext + F x elec + F x p = mẍ + K x f x + xK x m ( 10
)
In this equation the electromagnetic force of two coils x axis (F x elec ) has been introduced to the equation (4).

B. Experimental validation

Thanks to the magnetic field equations of coil, We have built a complete analytical model programmed in C++ and embedded in Matlab/Simulink. This model allowed us to simulate the electromagnetic force F elec applied to the float. The figure 11 presents the evolution of this force along x in the reference axes (L, x, z). The coils axis (point B) is 5.7mm far from L. The coil used for this simulation is a circular coil of 50 spires with a radius of 1cm and a maximum current of 0.5 A. The maximum value of the electromagnetic force is produced 6mm far from the coils axis. This value is about 68 µ N for a current I equal to 0.4 A. The distance LB is choosen in order to have a maximum electromagnetic force at S (see figure 12) which gives the sensor usefull range. The figure 13 represents the evaluation of the sum of magnetic and electromagnetic forces along x for different values of I. In the final design of the sensor, this sum will have to be controlled for each float in order to maintain the platform on S. We can notice that when I is equal to zero, we have a null electromagnetic force and the curve drawn with little stars represents the magnetic force only, like on figure 5. At the point S of static equilibrium, the magnetic force is always null. On this point the maximum external force which can be measured by the device, without platform displacement, will be equal to the maximum electromagnetic force that can be generated at this point. To calculate the electrical stiffness of our configuration, we have also plot the electromagnetic force F x elec when the float is positionned on the point of stable equilibrium S (thus F mag = 0), for different values of I (see figure 14). We can see easily that the relation between I and the electromagnetic force F x elec is linear, that allowed us to write:

F x elec = K x e • i(t) (11)
Where K x e is the electrical stiffness. It's value is 1.716 × 10 -4 N.A -1 .

VI. CONCLUSION

A six degrees of freedom microforce sensor prototype was presented in this paper. The sensing part is a floating platform stabilized by a magnetic field. Compared to our previous force sensor using diamagnetic levitation this configuration hasn't weight limitation of the levitating sensing part. The sensor allows force measurements without displacement of the platform. The current I in the coils, proportional to the external force F ext , provide a linear output. The global platform mechanical stiffness K m is about 18.3 × 10 -3 N.m -1 (close to the stiffness of a classic AFM microcantilever). In this paper we have also presented a complete analytical model of one of the three buoyancy tanks. This model allowed us to simulate the electromagnetic force F elec applied to the float by the coils and the evaluation of both magnetic and electromagnetic forces for different values of I. The study of the frequency response, the perturbation forces rejection, the platform 3D modeling, the position control, the assembling and experimentation of the complete sensor is currently under development. Concerning the frequency response, this one will certainly exhibit modal resonance because of the delayed return wave of water generated by the displacement of the float.

Fig. 1 .

 1 Fig. 1. Force sensor based on passive diamagnetic levitation

Fig. 2 .

 2 Fig. 2. Levitating force sensing device

Fig. 3 .

 3 Fig. 3. Sensor configuration (two of the three buoyancy tanks are presented)

Fig. 4 .

 4 Fig. 4. Forces applied on the float

Fig. 5 .

 5 Fig. 5. Magnetic force produced by the 2 permanent magnets M 1 along x

Fig. 6 .

 6 Fig. 6. Experimental measurements of the free response

Fig. 7 .

 7 Fig. 7. float response along x

Fig. 8 .

 8 Fig. 8. Floating mechanism L 1 equipped with two coils

Fig. 9 .

 9 Fig. 9. Step response for positive and negative current

Fig. 11 .

 11 Fig. 11. Electomagnetic force produced by the two coils

Fig. 12 .

 12 Fig. 12. Optimal position of coils

Fig. 13 .

 13 Fig. 13. Evaluation of the total force along x for different I

Fig. 14 .

 14 Fig. 14. Electromagnetic force F x elec at S for different values of I


B Gkotse

M Glaser

P Jouvelot

E Matli

G Pezzullo

F Ravotti

Towards a Unified Environmental Monitoring, Control and Data Management System for Irradiation Facilities: the CERN IRRAD Use Case

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

IRRAD Tables

The IRRAD tables are used to remotely control and position samples of different types and shapes in beam. They can move along the transversal beam direction (X, Y) and rotate around it (θ).

Shuttle IRRAD-1

The IRRAD1 shuttle is a conveyer moving on a rail and it is used to remotely place small (max. 5×5cm 2 ) samples from outside to the inside of IRRAD.

Proton Irradiation Facility IRRAD

The qualification of materials, electronic components and equipment for the CERN High Energy Physics experiments and beyond requires testing against possible radiation effects. These quite complex tests are performed by specialized teams working in irradiation facilities such as IRRAD, the CERN Proton Irradiation Facility. Building upon the details of the overall irradiation control, monitoring and logistical systems of IRRAD as a use case, we introduce the motivations for and the general architecture of its new data management framework, currently under development at CERN. This infrastructure is intended to allow for the seamless and comprehensive handling of irradiation experiments in IRRAD and to help manage all aspects of the facility. Its architecture, currently focused on the specific requirements of IRRAD, is intended to be upgraded to a general framework that could be used in other irradiation facilities within the radiation effects community, as well as for other applications.

Beam Instrumentation

Irradiation System Control

IRRAD tables User interface of the IRRAD table control system

Shuttle IRRAD-1 system Shuttle Conveyer

IRRAD user interface

Administrator user interface

AD6

For monitoring the environmental conditions of the facility, IRRAD is equipped with a complete monitoring system. 500 channels are monitored for each spill:

Status panel

The data acquired are used in daily operation and displayed in dedicated status panels.

Fixed-BPM

The

IRRAD data management system development process

For this reason we propose an irradiation facility ontology

  System for Irradiation Facilities: the CERN IRRAD Use Case Blerina Gkotse, M. Glaser, Pierre Jouvelot, Emanuele Matli, Giuseppe Pezzullo, F. Ravotti To cite this version: Blerina Gkotse, M. Glaser, Pierre Jouvelot, Emanuele Matli, Giuseppe Pezzullo, et al.. Towards a Unified Environmental Monitoring, Control and Data Management System for Irradiation Facilities: the CERN IRRAD Use Case. RADECS 2017, RADiation Effects on Components and Systems, Oct 2017, Genève, Switzerland. hal-01622872

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  Testing components of the HEP experiments  Proton beam of 24 GeV/c and size of 12×12 mm 2 Spills of 400 ms every ~10 s  Proton fluence of 1×10 16 cm -2 in 14 days  Scanning samples across the beam (10×10cm 2 )  Low temperature irradiation (-25°C) survey about the irradiation facilities available worldwide we found:  Manual operations or even on paper  Autonomous operations, with specific technologies  Outdated systems  Poor or absence of data management  Lack of a common knowledge base shared among the irradiation facilities An ontology is an assembly of definitions, properties and interrelations among entities of a specific domain, in this case the irradiation facilities.

  fixed-BPM detector is composed of arrays of 4×4 mm 2 Cu pads and it is used to control the position and the alignment of the beam. When the beam impinges on the detector, the charge generated due the Secondary Electron Emission is recorded by a DAQ unit. The acquired data are then sent to a server and, after processing, they are stored in an Oracle database.The data are then visualised on a website.Mini-BPM and single-pad BPMThe mini-BPM and single-pad BPM are smaller detectors than the fixed-BPM, but of the same composition and DAQ system. They are used to align the IRRAD Tables in the beam. irradiated in 2016 and this number is increasing year by year.The amount of data to be processed (samples and users data, those described in the sections above and additional information from spectrometry and samples traceability) call for an intelligent and integrated data management system.