Guillaume Damiand
email: guillaume.damiand@liris.cnrs.fr

Alexandre Dupas
email: alexandre.dupas@gmail.com

Jacques-Olivier Lachaud
email: jacques-olivier.lachaud@univ-savoie.fr

Combining Topological Maps, Multi-Label Simple Points, and Minimum-Length Polygons for Efficient Digital Partition Model ⋆

Keywords: Topological Map, ML-Simple Point, Minimum-Length Polygon, Deformable Model, Interpixel Boundaries, Multi-Label Image

Deformable models have shown great potential for image segmentation. They include discrete models whose combinatorial formulation leads to efficient and sometimes optimal minimization algorithms. In this paper, we propose a new discrete framework to deform any partition while preserving its topology. We show how to combine the use of multilabel simple points, topological maps and minimum-length polygons in order to implement an efficient digital deformable partition model. Our experimental results illustrate the potential of our framework for segmenting images, since it allows the mixing of region-based, contour-based and regularization energies, while keeping the overall image structure.

Introduction

Energy-minimizing techniques are now widely spread approaches for segmenting images into meaningful regions. They express the problem as a balance between several energies: (i) fit-to-data: energies that express the consistency of the regions with the data, (ii) regularization: energies that enforce spatial coherence. Fit-to-data is either region-based (squared error for homogeneity) or contourbased (strong gradient). Regularization is generally enforced through boundary length penalization, sometimes curvature penalization or some a priori knowledge on the probability distribution of the partition model.

Energy minimization can be solved in the continuous world with iterative solving of partial differential equations, leading to snakes and geometric or geodesic active contours [START_REF] Kass | Snakes: Active contour models[END_REF][START_REF] Caselles | A geometric model for active contours[END_REF][START_REF] Caselles | Geodesic active contours[END_REF] and Mumford-Shah approximation [START_REF] Mumford | Optimal approximations by piecewise smooth functions and associated variational problems[END_REF][START_REF] Vese | A multiphase level set framework for image segmentation using the Mumford and Shah model[END_REF][START_REF] Pock | A convex relaxation approach for computing minimal partitions[END_REF]. Energy minimization can also be expressed in the discrete world, generally as a graph-cut problem [START_REF] Boykov | Fast approximate energy minimization via graph cuts[END_REF][START_REF] Couprie | Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest[END_REF] or a Markov Random Field (e.g., see [START_REF] Szeliski | A comparative study of energy minimization methods for markov random fields with smoothness-based priors[END_REF]). To sum up, continuous approaches achieve optimality for specific energies. Discrete approaches are close to the optimal for a wider set of energies, to the price of less pertinent regularization energies: for instance, the length of the boundary is approximated as its staircase length.

As noted by Meltzer et al. [START_REF] Meltzer | Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation[END_REF] or Szeliski et al. [START_REF] Szeliski | A comparative study of energy minimization methods for markov random fields with smoothness-based priors[END_REF], appropriate energies are more important than optimality for good segmentation results. In this paper, we therefore focus on defining an energy-minimizing framework for image segmentation that is as versatile as possible to define energies and relations between regions. We propose a purely discrete framework, which encodes both the topology and the geometry of an image partition. This digital partition is "deformable" in the sense that pixels may change their label during the minimization. The deformation is controlled so that the partition may not change topology during the deformation. This property is desirable in many image analysis applications, like segmentation with a priori knowledge on the output topology (as often in biomedical image segmentation) or atlas matching. This aspect has even been recognized by the level-set community: although the level-set principle allows arbitrary topology changes, several authors have proposed methods to reintroduce topology control in the segmentation (e.g., see [START_REF] Ségonne | Active contours under topology control -genus preserving level sets[END_REF]). This paper extends the work of [START_REF] Damiand | Fully deformable 3d digital partition model with topological control[END_REF] because our framework incorporates a new length penalizer with better regularization properties. Moreover, it combines in a single balance the energies: on one side, length penalization and alignments of boundaries with strong gradients define one energy term (in the same spirit as geodesic active contours [START_REF] Caselles | Geodesic active contours[END_REF]), on the other side region homogeneity.

Our objective is to define a digital deformable partition model. To that effect, several bottlenecks must be solved. First, we need to describe digital contours as closed paths, eventually intersecting themselves. We use interpixel topology [START_REF] Khalimsky | Computer graphics and connected topologies on finite ordered sets[END_REF] which allows to have in digital spaces good topological properties similar to the ones in continuous spaces. Second, we need to control the topology of the deformable partition. This is achieved thanks to multi-label simple points [START_REF] Dupas | Multi-label simple points definition for 3d images digital deformable model[END_REF][START_REF] Damiand | Fully deformable 3d digital partition model with topological control[END_REF]. Last, during deformations, we need a data structure to manage various queries like access to image statistics in region, estimation of the length of boundaries, etc. We use topological maps [START_REF] Damiand | Topological model for two-dimensional image representation: Definition and optimal extraction algorithm[END_REF] to describe all the cells composing the deformable partition, and all the incidence and adjacency relations between these cells. Then, we use the minimum length polygon [START_REF] Montanari | A note on minimal length polygonal approximation to a digitized contour[END_REF][START_REF] Sklansky | Minimum perimeter polygons of digitized silhouettes[END_REF][START_REF] Provençal | Two linear-time algorithms for computing the minimum length polygon of a digital contour[END_REF] criteria in order to estimate the length or evolving regions.

The paper is organized as follows. We recall the main notions of these papers in Section 2 (for further details, interested readers must refer to the original works). Then, we present the deformable process and the energies in Section 3. Illustrative experiments are given in Section 4. Future works are discussed in Section 5.

Preliminaries Notions

Pixels, Image and Regions

A pixel is an element of the discrete space N 2 . Two pixels p = (x, y) and p ′ = (x ′ , y ′ ) are 4-adjacent if |x -x ′ | + |y -y ′ | = 1. A 4-path between two pixels p and p ′ is a sequence of pixels (p = p 1 , . . . , p k = p ′ ) such that each couple of consecutive pixels are 4-adjacent. A set of pixels S is 4-connected if there is a 4-path between any couple of pixels in S having all its pixels in S.

An image is a set of pixels. In this work, we consider labeled images, i.e. images in which each pixel is associated with a label (any value). In labeled images, a region is a maximal set of 4-connected pixels. Thus, regions form a partition of the image: two different regions are disjoint, and the union of all the regions is equal to the image. Moreover, we consider a specific region R 0 , called the infinite region, which is the complementary of the image. Two regions are said 4-adjacent if there is a pixel in the first region that is 4-adjacent to a pixel in the second region.

Interpixel Topology and Cubical Complexes

In interpixel topology, we consider the cellular decomposition of the euclidean space R 2 into regular grids. Pixels are elements of dimension 2 (squares) of the decomposition, linels are elements of dimension 1 (segments) between pixels, and pointels are elements of dimension 0 (points) between linels. We call i-face an element of dimension i (see examples in Fig. 1).

For a pixel p, we note linels(p) the set of the four linels between p and its four 4-neighbors, and pointels(p) the set of the four pointels around p. For a linel l, we note pointels(l) the set of the two pointels around l. These notations are directly extended to set of elements. For example, we note pointels(L), L being a set of linels, the union of pointels(l) for all l ∈ L.

A cubical complex C is a set of pointels, linels, surfels, glued together by adjacency and incidence relations. A free pair in C is a couple (c, c ′ ) with c ∈ C being an i-face (0 ≤ i ≤ 1), c ′ ∈ C being an (i + 1)-face incident to c ′ , and such that there is no other (i + 1)-face in C distinct from c ′ incident to c. In such a case, (c, c ′ ) can be removed from C without modifying its topology. This is the basic operation used to deform a cubical complex while preserving its topology called the elementary collapse.

A cubical complex C collapses onto a second cubical complex C ′ if there is a sequence of elementary collapse transforming C into C ′ . We say that a complex Y is simple for X if Y can be "removed" from X without modifying the topology of X, and symmetrically, a complex Y ′ is add-simple for X ′ if Y ′ can be "added" into X ′ without modifying the topology of X ′ . These two notions can be defined thanks to the collapse operation (see [START_REF] Couprie | New characterizations of simple points, minimal non-simple sets and p-simple points in 2d, 3d and 4d discrete spaces[END_REF] for precise definitions, and some examples in Fig. 1).

(c) A cubical complex C ′ such that C collapses onto C ′ . (d) A cubical complex C ′′ such that C ′′ is simple for C. "Removing" C ′′ from C gives C ′ . Symmetrically, C ′′ is add-simple for C ′ and "adding" C ′′ in C ′ gives C.

Multi-label Simple Points

Given a pixel x belonging to region X, and a region R, we note l(x, R) the linels around x that "touch" R: l(x, R) = {linels l|l ∈ linels(x) and the second pixel around l belongs to R}. Similarly we note p(x, R) = {pointels p|p ∈ pointels(x) and the three pixels around p distinct from x belong to R}. The contour of x touching R, called c(x, R) is the composition of these two sets:

c(x, R) = (p(x, R), l(x, R)). We note c -(x, R) = (p -(x, R), l(x, R)), with p -(x, R) the set of pointels touching a linel in l(x, R), i.e. p -(x, R) = pointels(l(x, R)).
The frontier between two regions X and R is noted f (X, R). This is the set of all the linels between one pixel in X and one pixel in R, denoted l(X, R), plus all the pointels touching these linels p(X, R) = pointels(l(X, R)).

Definition 1 of multi-label simple points is based on the interpixel topology and the simple and add-simple notions (see examples in Fig. 2). A pixel x belonging to region X is ML-simple for region R if the flip of x in R does not modify the topology of region R (first condition of the definition), does not modify the topology of region X (second condition of the definition), and if it does not modify the different frontiers around x (last condition of the definition). For the two first conditions, a cubical complex C is said homotopic to a 1-disk if it can be collapsed onto a complex that is composed only by one linel. For the last condition, intuitively it means that two regions adjacent along one frontier before the flip are still adjacent after the flip (i.e. the frontier still exists) and that two regions not adjacent before the flip are still not adjacent after.

Definition 1 (ML-simple points). A pixel x, belonging to region X, is MLsimple for region R if: The main operation used during the deformation algorithm is the flip of a pixel x ∈ X into a given region R. This operation consists in removing x from its initial region X and adding it to region R. It has been proved in [START_REF] Dupas | Multi-label simple points definition for 3d images digital deformable model[END_REF] that if the pixel x is ML-simple point for region R, it can be flipped into region R without modifying the topology of the partition. This operation modifies regions R and X, but also some frontiers. Since pointels are deduced from linels by definition of frontiers, modifications only concern the linels of the frontiers (see example in Fig. 2):

1. c(x, R) is homotopic to a 1-disk; 2. c(x, X) is homotopic to a 1-disk;
x in R. f (X, R) = ({2, 5, 6}, {e, g}), f (X, A) = ({1, 2}, {a}), f (R, A) = ({2, 3, 4, 7}, {b, c, f }). (c) x is not a ML-simple point for R because c(x, R) = ({}, {a, b}) is not homotopic to a 1-disk. Flipping x in R modifies the topology of R. (d) x is not a ML-simple point for R because c -(x, A) = ({1, 2}, {a}) is not add-simple for f (R, A) = ({}, {}).
-l(X, R) ← l(X, R) \ l(x, R) ∪ l(x, X); -For any region O with O = X, O = R: l(X, O) ← l(X, O) \ l(x, O); -For any region O with O = X, O = R: l(R, O) ← l(R, O) ∪ l(x, O);

Minimum Length Polygon

The Minimum Length Polygon (MLP) is a classical polygonalization method of digital contours [START_REF] Montanari | A note on minimal length polygonal approximation to a digitized contour[END_REF][START_REF] Sklansky | Minimum perimeter polygons of digitized silhouettes[END_REF]. Assuming that the digital contour is the boundary of some digital object, it is the polygon with shortest perimeter, whose interior contains the centers of the pixels of the object and whose exterior contains the centers of the pixels of the background. One may also see it at the shortest closed polygonal line which stays within the strip formed by the minkowski sum of the digital contour and a centered unit square while making one loop inside it (see Fig. 3). It has been proved recently that the MLP is a good regularizer for digital active contours [START_REF] De Vieilleville | Digital Deformable Model Simulating Active Contours[END_REF]: for instance, it is a kind of convex energy in a digital space. We use the combinatorial MLP in our experiments, since it is one of the fastest method for computing it [START_REF] Provençal | Two linear-time algorithms for computing the minimum length polygon of a digital contour[END_REF].

Topological Map

Several works have proposed data structures to describe image partitions [START_REF] Fiorio | A topologically consistent representation for image analysis: the frontiers topological graph[END_REF][START_REF] Brun | Discrete maps : a framework for region segmentation algorithms[END_REF]. The common goal is to represent regions of a given partition and all the incidence and adjacency relations between regions. Structures based on combinatorial maps [START_REF] Lienhardt | N-dimensional generalized combinatorial maps and cellular quasimanifolds[END_REF] have several advantages justifying their use: they represent all the cells of the subdivision (vertices, edges and faces) and all the incidence and adjacency relations between these cells; they are defined based on a unique element called dart, simplifying their use; and they are defined in any dimension which allows extensions of this work in higher dimension.

Topological maps are an extension of combinatorial maps created to describe the whole topology of image partitions [START_REF] Damiand | Topological model for two-dimensional image representation: Definition and optimal extraction algorithm[END_REF]. A topological map is composed of a combinatorial map that describes the cells of the partition and the incidence and adjacency relations between these cells (e.g. Fig. 4(a)), plus an interpixel matrix that describes the geometry of regions (e.g. Fig. 4(b)).

The combinatorial map describes each adjacency relation between two regions by an edge composed of two darts linked together. Thus, a dart can be seen as an half-edge (for example darts 1 and 2 in Fig. 4(a)). A cycle of successive darts describes a contour of a given region (for example [START_REF] Boykov | Fast approximate energy minimization via graph cuts[END_REF][START_REF] Caselles | A geometric model for active contours[END_REF] or [START_REF] Brun | Discrete maps : a framework for region segmentation algorithms[END_REF][START_REF] Couprie | Power watersheds: A new image segmentation framework extending graph cuts, random walker and optimal spanning forest[END_REF]). In the interpixel matrix, each linel belonging to one frontier between two regions is switched on, and each pointel touching more than two linels is switched on. Other elements are switched off. Each dart knows its region, and each region knows one dart of its external contour. Moreover, each dart d is associated with a pair (pointel, linel) such that pointel corresponds to the origin of dart d, and linel is the first linel of the frontier associated with d (for example dart 1 is associated with pair (p, l)).

Deformable Model Process

To propose a new digital deformable partition model, we start by presenting the energies used and their computation algorithms. Then, we detail the main operations which are the test if a pixel is ML-simple, and the flip of a pixel. We study how to update the energies during the flip, trying to keep modifications as local as possible. Last, we give the global algorithm regrouping all these tools to minimize the energy of the digital deformable partition model.

Energies

We define the global energy of the partition as the weighted sum of two energies: E d for the energy attached to data, and E p for the energy attached to the deformable partition. In this work, we use the two following energies: contour(C) is the MLP length of contour C weighted by the pixel gradient; mse(R) is the minimum square error of region R.

These two energies can be directly computed from the topological map. For contour(C), we run through all the darts of the given contour, and for each dart we run through all its linels, providing the geometry of the contour. The corresponding MLP can be computed from this geometry in time linear in the number of linels [START_REF] Provençal | Two linear-time algorithms for computing the minimum length polygon of a digital contour[END_REF]. Then, we project each linel of the contour on the corresponding edge of the MLP. We compute the length of this projection, and multiply it by one minus the absolute difference between the two pixels around the current linel. This difference is divided by the maximal difference of the image, giving a number between 0 and 1. The value of contour(C) is simply the sum of these values for each linel of the contour. If the image is uniform, contour(C) is equal to the length of the MLP. Otherwise, contour(C) becomes smaller when it separates more contrasted pixels.

For mse(R), we run through each pixel of the image that belongs to the given region, and compute the number of pixels M 0 (R), the sum of the pixel values M 1 (R) and the sum of the pixel squared values M 2 (R). With these three values, we can directly estimate mse

(R) = 1 M0(R) (M 2 (R) -M1(R) M0(R)
). To avoid several re-computation of these values, we store them in additional elements associated with the topological map. The value of contour(C) is stored for each contour, and M 0 (R), M 1 (R) and M 2 (R) are stored for each region.

The two energies E d and E p are computed by summing up the basic energies on each element of the topological map:

E d = w R × region R mse(R) and E p = w C × contour C contour(c).
The weights w R , w C associated to both energies allow us to change the balance between the two energies.

Operations

The two main operations of the deformable process are the test if a pixel is ML-simple, and the flip of a pixel. Algorithm 1 allows to test if a given pixel is ML-simple. This algorithm follows directly Definition 1 (see [START_REF] Damiand | Fully deformable 3d digital partition model with topological control[END_REF] for more details).

Algorithm 1: isSimple(x,R)

Data: pixel x ∈ X; region R. Result: true iff x is an ML-simple point for R. if not isDisk(c(x, R)) then return f alse; if not isDisk(c(x, X)) then return f alse;

foreach region O 4-adjacent to x, O = X, O = R do P1 ← {l ∈ p(x, O)|l ∈ pointels(l(X, O) \ l(x, O))}; if not collapse(c(x, O), P1) then return f alse; P2 ← {l ∈ p(x, O)|l ∈ f (R, O)}; if not collapse(c(x, O)), P2
) then return f alse;

return true;

The two first lines of Algo. 1 correspond to the two first tests of Definition 1. Function isDisk, not given here, is simple to write since c(x, R) is restricted to a small number of cases. Indeed, c(x, R) can be empty, a cycle (i.e. a 2-disk), or made of several connected components: in these cases it is not a disk. The only other possible case is the case of the disk.

The "foreach" loop of Algo. 1 corresponds to the last condition of Definition 1; we only detail the two conditions add-simple and simple by using the definitions given in [START_REF] Couprie | New characterizations of simple points, minimal non-simple sets and p-simple points in 2d, 3d and 4d discrete spaces[END_REF]. The main principle of these definitions is to test if the given set can be collapsed onto a specific set. This is the role of function collapse not given here. In our case, the first set is c(x, O) which is bounded by the linels and pointels incident to the given pixel x. Thus, the collapse function is restricted to a small number of cases which can easily be tested.

The complexity of Algo. 1 is O(1) since each test is restricted to pointels and linels around the considered pixel, and these numbers are both bounded by 4.

Algorithm 2: flip(x,R)

Data: a pixel x ∈ X ML-simple for R. Result: flip x into region R. switch off linels in l(x, R); switch on linels in l(x, X);

foreach dart d touching x do if pointel(d) ∈ c -(x, R) then update pair(d);
The second main operation is the flip which consists in removing the given pixel x from its original region X, and add it into its new region R. To be valid, this operation requires that x is a ML-simple pixel for region R. Algorithm 2 is made of three steps. First we switch off the linels in l(x, R). Second we switch on the linels in l(x, X). Since x is flip in region R, the linels in l(x, R) become "inner linels", i.e. inside region R, while linels in l(x, X) become frontier linels between region R and X. The last step consists to update associations between darts and pairs. This updating is required when the pointel associated with a dart belongs to c -(x, R) (as in the case shown in Fig. 2(a)). In this case, the flip of x in R involves modifications of the extremities of some frontiers (in Fig. 2(a) f (X, A) = ({1, 2, 3, 4}, {a, b, c}) before the flip, and f (X, A) = ({1, 2}, {a}) after: one extremity has moved).

The complexity of Algo. 2 is also in O(1). Indeed the number of linels in l(x, R) and in l(x, X) is at most 4, and the number of darts touching pixel x is at most 12 (3 darts for each pointel around x).

Update Energies for Flip

The main operation performed during the energy minimization process consists in flipping a pixel into a given region, and then to update the different energies accordingly. A first solution is to re-compute all the energies as explained in Sect. 3.1. But this involves a considerable computation time since the flip operation is called many times. A better solution consists in updating incrementally the energies.

For mse, we know that only region X and region R are modified. Thanks to the moments stored in each region, we can directly (i.e. in O( 1)) update M 0 , M 1 and M 2 for these two regions and thus the two mse. This modification can be made in constant time without additional cost for the flip algorithm. However, the problem is more complex for contour since there is no algorithm yet able to update a MLP after the modification of one of its pixels. Thus, contour is re-computed for the two contours around the flipped pixel by using the same algorithm than for the initialization step. The improvement of this particular point is one of our future goals.

The global energy of the partition can thus be updated by subtracting original values of each energy which will be modified, and by adding the updated energy values after the flip.

Energy Minimization Algorithm

We present in Algo. 3 the global minimization algorithm taking a topological map as input, and minimizing its energy by flipping ML-simple points. The algorithm starts by an initialization step, first to compute all the energies by using the principles given in Sect. 3.1. Then, each region X is considered to find a possible flip. This is the role of the possibleFlip(X) function, which is as follows. The function runs through each linel l describing a contour of X. Linel l separates two pixels: x in X, and a second pixel in another region R. If x is ML-simple for R, then flipping x into R is a possible candidate. Then, we flip x into R and compute the difference δ between the old energy (before the flip) and the new one (after the flip). Finally, we apply the reverse flip to retrieve the initial configuration and proceed to the next linel. If δ is negative, the flip of x into R decreases the global energy. In this case, this flip (x, R) is stored in region X into a variable called candidate(X), and function possibleFlip

Experiments

In this section, we first give some deformation results on artificial image using various weights w R and w C . Then, we show how the digital deformable partition model is used to fit an initial partition with two pictures from the Berkeley Segmentation Dataset [START_REF] Martin | A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics[END_REF]. In the following, weight values w R and w C are written as the ratio w R /w C .

In Fig. 5, we deform the initial partition (Fig. 5(b)) of an image containing two regions (Fig. 5(a)). Different weights are used to illustrate how their values modify the resulting partition. If the weight of the contour energy is low (w R /w C < 1/10 3 as for example in Fig. 5(c)), the value of the region energy is greater than the value of the contour energy: the contour energy does not change the resulting partition. As the weight of the contour energy increases, the curve separating the two regions becomes straighter (Fig. 5(d)). If the weight of the region energy is set to zero, the obtained contour is nearly a straight line (Fig. 5(e)). It does not exactly match the frontiers of the initial partition: where the border crosses the curve, the gradient part of the contour energy slightly alter the shape of the border and produces some irregularities. In Fig. 6, we use the deformation process on an artificial image with five regions (Fig. 6(a)). The frontiers of the initial partition, presented in Fig. 6(b), are not aligned with the border of the different shape in the original image. The deformation process is applied with two different ratio between the energy weights. When the ratio between w R and w C is high (Fig. 6(c)), the region energy is privileged and borders follow correctly the image data. But we see that there is some artifact around the disk region: they are caused by the starting point of the different edges which do not move during the deformation process. When the ratio is lower, for instance 1/10 4 , some of the borders move correctly. However the edge separating the two darker gray region is not positioned correctly (Fig. 6(d)): the energy cost of having a curved border outweighs the gain in the region mse. Thus, the border is not able to move toward the separation of the two regions. To solve this issue, we applied a two step deformation with first a 1/1 ratio and then a 1/10 4 ratio: the produced segmentation fits correctly the image data without artifact (Fig. 6(e)). Figure 6(f) presents the partition obtained using the contour energy alone: some parts of the disk are retrieved thanks to the gradient measure used in the energy. The bottom right side of the disk is straighten to minimize the length of the contour. If we use a 2D energy based on the number of linels, similar to the one used in [START_REF] Damiand | Fully deformable 3d digital partition model with topological control[END_REF], the initial partition has already a minimal contour energy. This shows the improvement of the regularization power of the new contour energy based on the MLP and the gradient. The first real image is presented Fig. 7. Using the partition presented in Fig. 7(b), the deformation produced the partition shown in Fig. 7(c) with a 1/10 4 weight ratio. We note that the shape of the object approximate the amphora in the picture but the contours are not perfectly matched. Using the partition presented in Fig. 7(d), the result (Fig. 7(e)) also fits correctly the amphora but for instance the curved shape just up from the handles is not correctly matched due to a high MLP value. In Fig. 8, we show deformation processes applied on a picture containing two horses (Fig. 8(a)). With the initial partition, Fig. 8(b), the first deformation guided by a weight ratio of 1/10 4 fit the horses shapes (Fig. 8(c)): the legs of the small horse are segmented with the dark area of grass around. This is caused by the region energy which decreases when dark area are grouped. In Fig. 8(d), the weight ratio is 1/10 6 : the smaller horse is poorly segmented and the contour of the taller horse are approximated. We show that the contours tend to be as straight as possible: this remove thin parts of the regions.

Conclusion

In this paper, we have presented a new method of deformable digital partition. Several works have shown the interest of using deformable models for image segmentation, but to our knowledge, no work has yet be done on deforming any partition while preserving its topology. To achieve this objective, we used:

(1) topological maps to efficiently compute and store features associated with the image and the partition; (2) minimum length polygons as estimator tools; and (3) ML-simple points to guarantee the preservation of the topology.

Our experiments show the interest of this approach to deform an initial partition according to image data. We can, for instance, propose a guided segmentation tool where a user creates an initial partition that is fitted to image data using the deformation process. We can also foresee the use of the deformable partition to improve the result of segmentation algorithms according to our energies.

In future works, we will focus on improving the update of the MLP after a flip operation. The MLP is currently completely re-computed after flips, involving important computation time. This can be improved by defining dynamic MLP capable of incremental update. Another goal is to use other energies to improve our results. We can, for example, use edge-detector filters (as Canny or Marr-Hildreth detectors) instead of a simple gradient energy, or add geometrical energies on regions to take their shapes into account (for example stretching or compaction). Finally, we could consider the extension of this work in 3D. Since topological maps and ML-simple points have already been defined in 3D [START_REF] Damiand | Topological model for 3d image representation: Definition and incremental extraction algorithm[END_REF][START_REF] Damiand | Fully deformable 3d digital partition model with topological control[END_REF], we need to study the extension of MLP in higher dimension.

Fig. 1 .

 1 Fig.1. Example of interpixel topology, cubical complex and collapse. (a) A cubical complex C. Pointels are black disks (for example 1 and 5), linels are black segments (for example 2 and 4) and pixels are gray squares (for example 3 and 6). Pointel 1 is incident to linel 2 and to pixel 3. Linel 2 is incident to pixel 3. Pointels 1 and 5 are adjacent. Linels 2 and 4 are adjacent. Couple (2, 3) is a free pair. (b) Cubical complex obtained from C by the elementary collapse of free pair (2, 3). (c) A cubical complex C ′ such that C collapses onto C ′ . (d) A cubical complex C ′′ such that C ′′ is simple for C. "Removing" C ′′ from C gives C ′ . Symmetrically, C ′′ is add-simple for C ′ and "adding" C ′′ in C ′ gives C.

3 .Fig. 2 .

 32 Fig. 2. Examples of ML-simple points and non ML-simple points. (a) x is ML-simple for R. c(x, R) = ({}, {d}) and c(x, X) = ({}, {g}) are homotopic to 1-disks. c -(x, A) = ({2, 3, 4}, {b, c}) is simple for f (X, A) = ({1, 2, 3, 4}, {a, b, c}); and add-simple for f (R, A) = ({4, 7}, {f }). (b) Partition obtained from (a) after the flip of xin R. f (X, R) = ({2, 5, 6}, {e, g}), f (X, A) = ({1, 2}, {a}), f (R, A) = ({2, 3, 4, 7}, {b, c, f }). (c) x is not a ML-simple point for R because c(x, R) = ({}, {a, b}) is not homotopic to a 1-disk. Flipping x in R modifies the topology of R. (d) x is not a ML-simple point for R because c -(x, A) = ({1, 2}, {a}) is not add-simple for f (R, A) = ({}, {}).Flipping x in R modifies the adjacency between regions.

  Fig. 2. Examples of ML-simple points and non ML-simple points. (a) x is ML-simple for R. c(x, R) = ({}, {d}) and c(x, X) = ({}, {g}) are homotopic to 1-disks. c -(x, A) = ({2, 3, 4}, {b, c}) is simple for f (X, A) = ({1, 2, 3, 4}, {a, b, c}); and add-simple for f (R, A) = ({4, 7}, {f }). (b) Partition obtained from (a) after the flip of xin R. f (X, R) = ({2, 5, 6}, {e, g}), f (X, A) = ({1, 2}, {a}), f (R, A) = ({2, 3, 4, 7}, {b, c, f }). (c) x is not a ML-simple point for R because c(x, R) = ({}, {a, b}) is not homotopic to a 1-disk. Flipping x in R modifies the topology of R. (d) x is not a ML-simple point for R because c -(x, A) = ({1, 2}, {a}) is not add-simple for f (R, A) = ({}, {}).Flipping x in R modifies the adjacency between regions.

Fig. 3 .

 3 Fig. 3. Minimum Length Polygon of the digital contour C.

Fig. 4 .

 4 Fig. 4. Example of topological map. (a) Combinatorial map describing the topology of frontiers. (b) Interpixel matrix describing the geometry of frontiers.

Fig. 5 .

 5 Fig. 5. Experimentation on an artificial image with two simple regions.

Fig. 6 .

 6 Fig. 6. Deformation of an artificial image with five regions.

  (a) Image (b) Partition A (c) A 1/10 4 (d) Partition B (e) B 1/10 4

Fig. 7 .

 7 Fig. 7. Deformation of different initial partitions of a picture.

Fig. 8 .

 8 Fig. 8. Deformation of an initial partition of a picture with different weight ratio.

returns true. Otherwise, we continue to run over the linels of the contours of X. If no flip decreasing the energy is found, possibleFlip returns false.

Algorithm 3: Digital partition minimization

Data: a topological map M ; an image I. Result: minimize the energy of the digital partition. initialize all the energies of M ; S ← ∅;

At the end of the initialization loop, S contains all regions having a flip that decreases the energy. In the main loop of the algorithm, we choose a region in the set, and flip the corresponding pixel. This operation changes the geometry and the energy values of the regions X and R. Stored flips for X, R, and their adjacent regions can be invalid (for example the considered pixel is not a simple point anymore, or the flip increases the energy) and should be updated using the possibleFlip algorithm. We can then proceed with an other region of S.

The main loop finishes when the set of candidate becomes empty. In this case, the minimization process is terminated: there is no possible flip decreasing the global energy.


F Schirru

K Kisielewicz

T Nowak

B Marczewska

Single Crystal Diamond Detector for Radiotherapy

The new generation of synthetic diamonds grown as CVD single crystal on HPHT substrate offers a wide range of applications. In particular, because of the near tissue equivalence and its small size (good spatial resolution), CVD single crystal diamond finds applicability in radiotherapy as dosemeter of ionizing radiation. In the present paper we report the electrical and dosimetric properties of a new diamond detector which was fabricated at IFJ and based on single crystal detector-grade CVD diamond provided of a novel contact metallization. Diamond properties were assessed at IFJ using a Theratron 680E therapeutic 60 Co gamma rays unit and at COOK with 6 and 18 MV X-rays Varian Clinac CL2300 C/D accelerator. The new dosemeter showed high electric and dosimetric performances: low value of dark current, high current at the level of some nA during irradiation, very fast dynamic response with a rise time amounting to parts of second, good stability and repeatability of the current and linearity of the detector signal at different dose and dose rate levels typically applied in radiotherapy. Results confirm the potential applicability of diamond material as dosemeter for applications in radiotherapy.

INTRODUCTION

The fast progress in medicine and all disciplines of human health protection requires the development of new methods of dose calculation, dose delivery and dose verification. At the modern radiotherapy facilities new non-conventional and highly conformal treatments such as stereotactic treatments and intensity-modulated radiation therapy (IMRT) are routinely applied and allow us to save organs at risk delivering the dose exactly to the tumor (target area). These treatments usually involve large dose gradients and fast dose rate changes which require the development of radiation dosemeters having small active dimension (i.e. high spatial resolution) and fast dynamic response in order to follow the dose rate variation in the radiation field.

Since years diamond has been considered as a perfect candidate to work as a detector of ionizing radiation for radiotherapy due to its unique properties such as tissue-equivalence, chemical resistance, high sensitivity to radiation and radiation hardness.

At present, diamond detectors based only on natural gems and produced by the PTW Freiburg company are commercially available on the market. Different publications [1][2][3][4] can be found in literature concerning the applicability of synthetic diamond as radiation dosemeter. So far however, due to the limitations mainly imposed by the quality of the samples [5][6][7][8], there is still the lack of a real product which could equip the hospital facilities.

A considerable progress in the diamond growth was achieved recently due to the adaptation of CVD (Chemical Vapour Deposition) method to the growth of high-quality single crystal diamond films [9][10][11][12]. In this process, HPHT (High Pressure High Temperature) single crystals with a special orientation are usually used as substrate or seed. After cutting off the substrate layer and polishing the crystal surface, the free standing single crystal can be available for the experiments. Synthetic diamonds offered now on the market have sufficiently good quality to compete with the natural gems which are strongly selected from thousands. The successful construction of a detector however does not depend only on the quality of the crystals but also on the electric contacts, holders and electronic which should be properly optimized.

At IFJ we developed a new diamond dosemeter which is based on the last generation of commercial detector-grade single crystal CVD diamond (SC CVD) provided of a novel ohmic contacts. The sample was, at first, preliminary investigated at IFJ under 60 Co gamma rays beam on regard to its electrical properties i.e. dark current, dynamic response, stability and repeatability of the current signal under irradiation. Next, it was encapsulated in a solid-water plastic holder of a "finger" shape and tested at COOK under 6 and 18 MV X-rays beam as radiation dosemeter performing measurements on its sensitivity, linearity with the dose and dose rate at levels relevant for radiotherapy applications and dependence on the beam energy.

Aim of this paper is to show the potentiality of the new device for medical application in radiotherapy.

MATERIAL AND METHODS

The material considered within this work consists of one SC CVD diamond commercially obtained from the Diamond Detector Ltd. (DDL) company. The sample, labeled DD4, has dimensions of 4.7x4.7 mm 2 and is 500 µm thick. It has detector-grade quality i.e. characterized by a very low amount of Nitrogen and Boron in the order of less than 5 ppb.

The diamond sample was ordered with a novel ohmic metallization in a sandwich configuration with a central dot of 3 mm of diameter which leads to an active volume of v = 3.5•10 -3 cm 3 . The new contacts were fabricated by sputtering deposition of a diamond-like carbon (3 nm) layer followed by a layer of platinum and gold respectively 16 and 200 nm thick [13].

To test the dosimetric properties, the sample had to be properly encapsulated into a holder. Construction of the new holder was made at IFJ using a standard grade Solid Water ® GAMMEX 457 of density ρ = 1.05 g•cm -3 which does not affect the photon beam and presents nearly equivalent absorption characteristics of water over a wide range of energies relevant in clinical dosimetry. The holder has a cylindrical shape with diameter of 9 mm and 25 mm of length. To avoid the influence of the air on the detector signal, the holder cavity was properly tailored to the shape of the crystal.

Measurements of current were performed with a Keithley 6517A electrometer which served also as a voltmeter to apply the appropriate bias voltage between the electric contacts.

Irradiations were performed at IFJ using a Theratron 680E unit 60 Co gamma rays source with 1.25 MeV photon mean energy and at COOK using an X-rays linear accelerator Varian Clinac CL2300 C/D at 6 and 18 MV. Dosimetric measurements were performed at d max (depth of maximum dose) by using PMMA slabs of different thickness, area of 20x20 cm 2 and provided of drilled holes for the placement of the diamond detector itself.

Dose rate was estimated with a Markus 0.125 cm 3 ionization chamber connected to a PTW universal dosemeter T10001 while a PTW natural diamond detector served as a reference dosemeter.

RESULTS

At first, we evaluated the electrical quality of the sample DD4 by measuring its dark current as a function of the applied bias in the range ±500 V. The results presented in Fig. 1 indicate the quasi-ohmic behavior of the contacts with a dark current value below ±2 pA for a maximum applied bias of ±500 V. Measurements were performed in darkness and data reported in Fig. 1 were calculated averaging on all recorded points after stabilization of the dark current (usually half an hour). The sample shows a resistivity of 3.9•10 15 ⋅cm as deduced from the dark current measurement at +500 V.

Before evaluating other parameters, first of all we preliminary checked the current behavior of the sample under 60 Co gamma rays beam at different applied voltages. For biases > ±100 V we observed a strong instability of the current signal while for biases below such threshold the signal was found to be very stable. Also a fast dynamic response was observed in particular for -10 V. Such behavior is not clear and requires a separate study which was not performed within this work.

Fig. 2 illustrates the two minutes current response of our sample under 60 Co irradiation at dose rate of 1 Gy/min and -10 V of applied voltage. As it is possible to observe, the diamond sample shows very fast response and does not present any priming or overshoot effect which usually are present in those diamonds of poor quality. Before irradiation, the recorded dark current was I DC ~2.5•10 -13 A. After switching on the 60 Co source, the induced current reached within one second a stable value of I R ~1.27•10 -8 A leading to a high signal to noise ratio of S/N ~5.1•10 4 . When the irradiation was switched off, the current dropped, within few seconds, to the previous value of the dark current. Due to the high quality of the electric contacts, the current signal under irradiation was very stable and did not exceed the 0.5 % of variation respect its average value. These results confirm that the novel ohmic metallization composed of thin layers of diamond-like carbon, platinum and gold shows better properties compared to other kind of electric contacts as previously reported [14].

The repeatability of the current signal was checked performing five irradiations at the same operating conditions. Each cycle reported in Fig. 3 was characterized by one minute of irradiation followed by another minute of break. Taking the integral of each pulsed irradiation and averaging the values of area we found a good coefficient of repeatability of ~0.4 %.

The quality of a detector can be estimated by the knowledge of its gain factor G or charge collection efficiency. Such parameter is defined as G = I R /I P where I R is the recorded detector current and I P is the theoretical current induced by the irradiation field which is defined as:

w ev D I P / ρ = (1)
Assuming a dose rate D = 1 Gy/min, a sensitive volume of the sample of v = 3.5•10 -3 cm 3 , the density of diamond ρ = 3.5 g/cm 3 , the electronic charge e = 1.6•10 -19 C and w = 13 eV as energy required to produced an electron-hole pair in diamond, we obtain I P = 15.7 nA. Considering as previously reported I R ~1.27•10 -8 A, we obtain a gain factor of G = 0.8 which, being close to the unity, demonstrates the high quality of our SC CVD sample. To be noticed that the value of gain factor here calculated is higher than those reported in literature for commercially available natural diamonds which usually is quoted to 0.5 [15][16][17].

To have a better estimation of the time required to have complete stabilization of the current under irradiation, the electrometer was set to record the experimental data every 0.2 s. As reported in Fig. 4, the induced current reached the stabilization within one recording point i.e. within 0.2 s after switching on the 60 Co source. Such measurement clearly demonstrates the fast response of the sample DD4 and its potential applicability as radiation dosemeter in radiotherapy.

As a further step, first we developed a new radiation dosemeter by encapsulation of the SC CVD diamond sample and then we investigated the dosimetric properties of the new device to assess its suitability for radiotherapy applications.

Dose dependence of the diamond device was investigated performing irradiations with the 60 Co gamma-rays photon beam which, with its constant output guarantees more stable exposure at very low delivered doses. The detector was biased at -10 V and experimental data were collected in the dose range 0.1 -4.0 Gy at the dose rate of 2.0 Gy/min. Performing a linear fit to the experimental data reported in Fig. 5 and normalizing to the sample volume we obtain a value of sensitivity of (1.65180±0.00006)•10 -7 C•Gy -1 •mm -3 . To be noticed that data reported on Fig. 5 show a linear dependence even at low values of absorbed dose as demonstrated by analysing the derivative of the net charge. As a matter of comparison, we next evaluated the dose dependence for a PTW natural diamond. The analysis performed on the experimental data led to a sensitivity per unit of volume of (5.8540±0.0001)•10 -8 C•Gy -1 •mm -3 which is more than 2 times lower than that obtained for the new diamond dosemeter. Dose rate dependence was evaluated using the 60 Co gamma-rays photon beam, 6 and 18 MV X-rays beams as well. Measurements under 60 Co beam (Fig. 6) were performed in the dose rate range of 0.5 -2.0 Gy/min by changing the distance between the radiation source and the surface of the PMMA slab in which the diamond dosemeter was positioned. Measurements under 6 and 18 MV X-rays beams (Fig. 7) were performed in the range of dose rate 1.0 -6.0 Gy/min by changing the pulse repetition frequency of the accelerator. In this case, the distance between the source and the PMMA slab (100 cm) had to be slightly adjusted when changing the beam energy from 6 to 18 MV. Fowler's model [18] predicts a dose rate dD/dt dependence of the detector current I as:

∆ ⋅ = dt dD c I ( 2
)
where c is a constant and an exponential parameter which describes the deviation from the linearity. According to this model, is equal to 0.5 in the case of pure semiconductor with ohmic contacts and no traps. If all traps have the same capture cross section, then falls between 0.5 and 1 reaching the upper limit for a uniform or quasi-uniform trap distribution. may also exceed the unit if traps with different capture cross sections are present in the crystal [18]. Tab. 1 reports the values of the parameter calculated by fitting the experimental data with Eq. ( 2) obtained for the new diamond device and the PTW natural diamond detector. The results indicate negligible dose rate dependence for both devices in the range of dose rate investigated.

The photon energy response of the two dosemeters was the other important dosimetric property investigated in this work. It was assessed by measuring the charge sensitivity of the detectors as a function of the mean photon energy of 60 Co gamma, 6 MV and 18 MV X-rays photom beams at dose rate of 1 and 2 Gy/min. As shown in Fig. 8, the response of the diamond device was found to be almost independent on the beam energy. The sensitivity exhibited a variation in the order of the 0.2% respect its mean value which could be related to the material encapsulation of which the dosemeter is manufactured [8]. Measurements on the PTW natural diamond reported a slight dependence on the beam energy with a variation of the sensitivity in the order of 1.5% respect its mean value.

CONCLUSIONS

A new radiation dosemeter based on high quality SC CVD diamond provided of a novel ohmic metallization has been fabricated and tested in order to assess its dosimetric properties (dose response, dose rate dependence and photon energy dependence under 60 Co gamma rays and X-rays beams). Measurements were performed applying dose and dose rate levels typical for radiotherapy and the results were compared with those obtained from a commercially available PTW natural diamond. Results here reported demonstrate the potential applicability of the new device as a radiotherapy dosemeter and its dosimetric properties can be summarized as follows:

• linearity respect the absorbed dose even at low values as a consequence of its fast response (0.2 s to get the current signal stabilization under irradiation). Its sensitivity per unit of volume was found to be in the order of ~1.65•10 -7 C•Gy -1 •mm -3 more than 2 times higher than that obtained from the diamond detector PTW; • linearity respect the dose rate applied, in the range 0.5 -2.0 Gy/min for gamma rays and in the range 1.0 -6.0 Gy/min for 6 and 18 MV X-rays beams; • negligible dependence on the beam energy related to the tissue-equivalence of the encapsulation and diamond itself.

The results not only evidence the high quality of single crystal synthetic diamonds which now can be achieved by CVD techniques but also the role of the novel contact metallization which contributed positively to the quality of the current signal in terms of stability and speed response. The combination of these two aspects opens new perspectives on application of synthetic diamonds as dosemeter for radiotherapy applications. However, the reported work regarded the dosimetric properties of one particular SC CVD diamond. As a further step therefore, it would be interesting to produce a certain number of diamond dosemeter based on a batch of several crystals obtained from the same source in order to check the statistical fluctuations of repeatability of their dosimetric properties. Table 1 parameters of the diamond dosemeters DD4 and PTW under 60 Co -rays, 6 MV and 18 MV X-rays photom beams calculated by fitting the experimental data with Eq. ( 2).

FIGURESFig. 1 Fig. 2

 12 FIGURES

Fig. 3 Fig. 4

 34 Fig. 3 Signal repeatability of the sample DD4 under 60 Co irradiation at dose rate of 1 Gy/min.

Fig. 5

 5 Fig. 5 Dose response of the diamond dosemeter in the range 0.1 -4.0 Gy under 60 Co gamma rays photon beam.

Fig. 6

 6 Fig. 6 Dose rate response of the diamond dosemeter in the range 0.5 -2.0 Gy/min under 60 Co gamma rays photon beam. The device was biased at -10 V.

Fig. 7

 7 Fig. 7 Dose rate response of the diamond device in the range 1.0 -6.0 Gy/min under 6 MV X-rays photon beam. The device was biased at -10 V.

Fig. 8

 8 Fig. 8 Energy response of the diamond dosemeter evaluated for 1 and 2 Gy/min under 60 Co, 6 and 18 MV photon beams. The device was biased at -10 V. Errors (one standard deviation) correspond to the uncertainty on the dose rate estimation at different radiation fields.

Corresponding author: e-mail: F.Schirru@surrey.ac.uk, Phone: +44 01483 68

2730, Fax: +44 01483 68 6781 Confidential: not for distribution. Submitted to IOP Publishing for peer review 20 May 2010


J W Coenen

M Clever

U Samm

O Schmitz

B Schweer

S Freutel

B.Unterberg H Stoschus

B Unterberg

Charge exchange recombination spectroscopy on a

come

Introduction

In fusion experiments the properties of magnetic confinement largely depend on the impurity concentration, as well as on the plasma rotation and the radial electric field. Rotation can influence screening of external perturbations, suppress the onset of modes [8] and in case of strong rotation shear can lead to a suppression of turbulent transport. Charge exchange spectroscopy (CXRS) (cf. [39,14]) is the most successful tool for the measurement of impurity rotation and ion temperature (T i ) profiles [17,25]. The radial electric field (E r ) [24] is known to be connected to transport changes in the plasma edge, including the L-H transition( [40,35]). Knowing this, it is important to study the E r and its connection to transport and confinement. At TEXTOR two independent CXRS diagnostics are employed as is depicted in figure 1. The first makes use of a 1.2 MW Neutral Heating Beam and provides fast routine measurements of T i , v tor and n i , with a time resolution of a few milliseconds, but a poor spatial resolution of the order of 40 to 80 mm. [41] The second system, being presented here utilizes a dedicated low-power hydrogen diagnostic beam [9] allowing high spatial resolution, typically 10 to 20mm on a shot by shot basis. Typical TEXTOR plasma have a plateau phase of several seconds allowing averaging without compromising the measurement. It is used to consistently study the E r , measuring the poloidal(v pol ) and toroidal rotation(v tor ), as well as the ion temperature (T i ) and density. The E r is based on the radial force balance (Equation ( 5)). The spectroscopic measurements are used to obtain the rotation via Doppler shift spectroscopy from the spectral position with respect to an unshifted reference, while the temperature measurements are based on the broadening of the spectra. The carbon density can be calculated based on the intensity. The speciality for the v pol measurement at TEXTOR is the intrinsic calibration via opposing lines of sight, differential Doppler spectroscopy (Section 3.1). All measurements are performed on the CVI line (529 nm) CXRS line. The main focus here lies on the ability to measure E r over half the minor radius (0.5 < r/a < 1.1) consistently without any external input needed. All components of the radial force balance (cf. Equation ( 5)) can be measured simultaneously at one toroidal position of the tokamak for any heating scenario. Here the CXRS setup is presented which has been developed at TEXTOR [START_REF] Kreter | Juel-3860 of Berichte des Forschungszentrum Juelich[END_REF][START_REF] Ch | Energy Technology Edition[END_REF][START_REF] Coenen | of Energy & Environment[END_REF]. v pol , v tor , T i and n i can be measured using the hydrogen beam RuDI [26,9,30]. Systems applying similar diagnostic beams are operated TJII stellarator [4] and TCV [27,11] The paper is organized as follows. In the first part of this paper the design parameters of the complete system are given. In the second part the measurement principles for v, T, n are described, including the use of beam modulation for background substraction, the principle of differential Doppler shift spectroscopy and the methods to obtain a radial calibration (Section 3.1) via direct measurement or beam emission spectroscopy (BES). In the third and last part, an assessment of the accuracy is given as well as the principles for the error bar calculations which is followed by a consistency check on exemplary data.

Diagnostic Setup

In order to survey the challenges for accurate measurements with the CXRS diagnostic we introduce the boundary conditions set by the TEXTOR plasma and the setup itself. The resolution in v pol and v tor is required to be < 1 km/s and < 10 km/s respectively based on measurements at TEXTOR and comparable experiments [START_REF] Ch | Energy Technology Edition[END_REF]11]. A high spectral resolution instrument with a dispersion of 1pm/pixel for v pol is required. For such small bandwidth the signal intensities might be strongly interfered by photon statistics that limits the achievable spectral resolution (Section4). The used hydrogen beam delivers, in contrast to large heating NBI devices [START_REF] Busche | [END_REF], only a small equivalent current, which leads to a small emission of charge exchange light and hence making intensity one of main diagnostic challenges (cf. Section 4). The typical ion current in the source of ∼ 2 A leads to a neutral particle current of about 1.2 A at 50kV acceleration voltage, with a width (1/e) inside the vessel of 8 cm at R=1.75m (±0.5 • divergence) [START_REF] Kreter | Juel-3860 of Berichte des Forschungszentrum Juelich[END_REF].The beam modulation (10Hz) presents an easy approach to background subtraction as described in Section 3, differentiating between active charge exchange from the beam and passive charge exchange background. The low power input allows measurements during ohmic discharges without disturbing the plasma. In addition to the requirements for the rotation measurements the system should be capable of measuring the temperature over the whole temperature range accessible in the observed volume at TEXTOR 30 eV < T i < 1000 eV [38,[START_REF] Huber | [END_REF]. Another set of measurements involves the influence of the DED [16] on the magnetic topology [37,36]. To resolve this a spatial resolution between 1 and 2 cm is required. The typical averaging time for the measurement is typically 3 seconds in order to gather enough light for the high velocity resolution (cf. section 4). To assure accurate measurements the plateau of the discharge is used. The frame rate with which the data is acquired is 10 Hz due to the background subtraction sheme (cf. Section 3) based on beam modulation. Time resolved measurements (∆t =100ms) can be performed when in turn accepting larger error-bars for the measured rotation values, and thus loosing the capability of resolving changes in the v pol and the E r due to poisson statistics (cf. section 4) at low intensities. The diagnostic arrangement consists of three distinct systems, the hydrogen diagnostic beam, the toroidal and poloidal observations, including the subsequent spectrometers and camera DAQ systems. As is depicted in figure 1 the diagnostic beam is injected from the low field side of TEXTOR, while the observation systems are mounted nearly perpendicular to the direction of the beam in the poloidal and toroidal (equatorial) plane. In the following section each component shall be introduced, with a focus on the detailed description of the observation systems. Both systems cover half the minor radius of TEXTOR (0.5 < r/a < 1.1 ) allowing coverage of the plasma edge (SOL) up to the plasma core. They are optimized to deliver as much intensity as possible to minimize the effects of photon statistics on the measured quantities (cf. section 4).

Poloidal Observation System

The poloidal system observes in the poloidal plane of the tokamak vessel, as depicted in figure 1. It is equipped with a direct imaging from the vessel top and an additional bundle (3 channels) of optical fibers with a line of sight from the bottom of the vessel (opposing lines of sight) for the differential Doppler spectroscopy. Mounting a camera close to the tokamak may in future be difficult considering energetic radiation and neutrons, in case of TEXTOR however here it is a feasible way to gain intensity. Figure 2 gives an overview of the properties of this poloidal observation system. The direct imaging is optimized in two ways keeping the available hardware constraints in mind: Firstly, the direct imaging components (figure 2) relay the 270 mm observation length onto the entrance slit (h = 18mm, w = 200µm) (magnification 1:15) and subsequently through the spectrometer onto an image intensifier (fiber coupled with CCD) (25mm≡10.5mm Chip) and secondly the numerical aperture (NA) is optimized to satisfy as much as possible the limitations due to the spectrometer (NA=0.05, table 1). Details for the spectrometer and camera system are given in section 2. [START_REF] Busche | [END_REF] The distance between the RuDI beam and the first optical element (L1) is 74 cm. The in-vessel components (L1& L2) were optimized for an image NA of 0.4 [START_REF] Ch | Energy Technology Edition[END_REF] and are imaging the emission through the window onto the relay optics (L3-L5). This total setup has a length of about 216 cm. By using a direct imaging system instead of the old fiber optics based system almost an order of magnitude in intensity was gained due to improved numerical apertures. In addition a broadband anti reflection coating was applied for the range of 400 to 700 nm. The lower observation for the differential Doppler spectroscopy is located 99 cm away from the beam, with one (L4b) lens imaging the light onto the optical fibers (NA=0.4) and another one (L6) imaging the fibers onto the spectrometer slit via a small mirror. Both parts are inclined by an angle of about 11 • to the beam due to the available access points. This fact is used to perform beam emission spectroscopy (BES) to determine the radial position of the viewing lines via the Doppler shift. The radial channels can be Figure 3: Spatial resolution for the poloidal and toroidal system using a channel spacing of 1cm for the poloidal and actual viewing lines for the toroidal view. chosen depending on the experimental scenario and the intensity requirements. Since a CCD camera is used, it is possible to either readout each CCD line, hence realize a very high spatial resolution with low intensity, or combine some channels (binning) in order to have reasonable spatial resolution and a good intensity. The spatial or radial resolution is determined by the size of the observed beam volume. A channel observing 1cm of the beam will collect light from the complete volume, defined by the incident angle and the beam width. The radial resolution is in the order of 1-2 cm (cf. figure 3.

The poloidal system has a specially good resolution in the plasma edge due to the small incident angle with the beam at larger minor radius. This is of special interest for edge transport studies, as well as the measurement of the E r in the edge. The resolution plotted in figure 3 represents an evenly spaced binning of the channels. Different radial resolutions for each part of the observation volume can be achieved via CCD binning. The overlap between several channels is only resolvable by sacrificing radial resolution.

Toroidal Observation System

The toroidal observation system is mounted in the equatorial plane of the tokamak observing the hydrogen diagnostic beam via a small mirror tangentially(figure 1 &2). It consists of the collecting part (L1, L2) inside the tokamak vessel including the small mirror collecting the light from the direction of the beam, as well as a set of lenses to image onto the optical fibers (L3). The design was optimized to transfer the light to the fibers mounted at the image side. The fibers have a numerical aperture of 0.4 and a diameter of 1 mm. In contrast to the poloidal system the radial spacing is given by the size and the mounting of the optical fibers. The core of the fibers is 0.8 mm and leads to an object size of ∼14 mm (magnification 1:17.5). The radial spacing and resolution is shown in figure 3 is comparable to the typical poloidal setup. The fibers are arranged in a block of 2 × 10 fibers, giving 2 fibers per radial channel (10 total), in order to improve the intensity available for each radial channel. In contrast to the poloidal system the resolution decreases to the plasma edge. Structural constraints inside the vessel leave this as the only viable viewing option for the toroidal observation system. In front of the spectrometer the fibers form a single line are imaged onto the 250µm wide spectrometer slit using a small relay optic (cf. Section 2.3. In between the first 5 channels (10 fibers) and the last 5 channels (10 fibers) an additional fiber is supplied for the neon reference (λ=529.82 nm) produced by Geissler discharge neon lamp [33,[START_REF] Geissler | Geissler tube. Encyclopedia Britannica Online[END_REF]. All fibers are mounted in a straight brass housing, supplying accuracy and support to assure all fibers are aligned perfectly parallel to the reference channel.

Spectrometers & Camera systems

The light dispersion elements used in the actual setup are two high resolution spectrometers as described in the overview table 1. High resolution is required to resolve the particularly small poloidal velocities of order km/s. The light collecting parts are optimized for high transmission since the spectrometers themselves have got very small numerical apertures (table 1) and etendue. The values are 0.021, 0.072 for the poloidal and toroidal system, respectively. This trade off between resolution and photon statistics is the limiting factor for the capabilities of this diagnostic (Section 4). Both spectrometers are mounted in Littrow configuration with a blazed grating. Since intensity is of the essence both gratings are used near the blaze angle. The poloidal spectrometer with a focal length of 1 m and a high dispersion Echelle grating is optimized for the use at λ=529.053 nm in the 46 th order, while the toroidal spectrometer is equipped with a holographic grating an operated in the 2 nd order. Due to the high order used for the poloidal system several other lines may be visible in the observation region. A bandpass filter with a width of 2 nm is used. The poloidal spectrometer in particular is optimized for use on the CVI line but both spectrometers can cover most parts of the available spectral range (400-700nm) [START_REF] Ch | Energy Technology Edition[END_REF][START_REF] Kreter | Juel-3860 of Berichte des Forschungszentrum Juelich[END_REF]. The width of the slit of the poloidal and toroidal spectrometer is 200 µm and 250 µm, leading to an instrument function of 20 pixel and 12 pixel for the poloidal and toroidal system respectively after imaging on the subsequent cameras. The dispersion of the two spectrometers, measured with emissions from an argon (Ar I: 528.6 nm, 529.0 nm) [START_REF]Nist atomic spectra database[END_REF] and neon (Ne I: 532.1nm, 534.1nm, 534.3nm) [START_REF]Nist atomic spectra database[END_REF] reference lamp around λ=529 nm, are given in table 1. Both spectrometer systems are supplied with an image intensifier, which are tapered onto the respective cameras to increase the transmission to the chip.

Each system contains of a CCD camera system allowing frame rates up to 30 fps in full frame mode. In Section 3 the method is described to discriminate the background light from the actual active CXRS signal. Based on the beam modulation a scheme is developed for the acquisition of frames. The diagnostic beam is operated over 3s to 4s and a modulation frequency of 5 Hz with a 1:1 duty cycle. The frame rate of the camera is 10 Hz and synchronized with the frequency of the beam allowing the separate acquisition of the passive and sum of active and passive CXRS.

The toroidal system, due to the generally higher rotation velocities, can tolerate larger absolute uncertainties with respect to rotation resolution, while keeping the same relative resolution. Two rows on the chip are combined (binned) in the direction of the chip correspoding to the radial direction in the plasma. This is done to increase the read out speed. A radial channel (fiber) is typically represented by 3(6) pixel × 256 pixel, whith the carbon spectrum itself is only covering a small part in spectral direction allowing for the neon reference line (λ=529.82 nm) being displayed continuously. The whole width of the chip covers a spectral range of ∼ 4 nm (table 1), which corresponds to temperature between 20 eV and 3000 eV (Typical O(100 eV)) measured from the Doppler broadening. The spectral resolution of the spectrometer allows a Doppler shift rotation measurement between 1 km/s (0.1 pixel) and ∼ 100 km/s [15]. The situation for the poloidal spectrometer is more specialized to the needs of the measured parameters. The setup is comparable with the toroidal system with one distinct difference, due to the high spectral resolution of (1.0799 ± 0.0003) pm/pixel only a limited spectral window can be obtained across the chip. The spectral window of 1nm allows temperature measurements of up to 900 eV with a resolution well in the range of eV, taking into account only the dispersion of the spectrometer. The resolution in terms of Doppler shift measurements of the ion velocity is in the order of 0.3 pixel (statistical uncertainties) , meaning 200 m/s when considering the dispersion relation only. The radial binning, the combination of several CCD lines, is performed offline. Since the emissions are directly imaged onto the spectrometer and hence the camera chip one has complete freedom whether to analyze the whole frame line by line with a small intensity, or to choose a binning which offers more intensity. The system is able to obtain full frame images with a rate well above the beam modulation rate. The resolutions can be severely limited by the photon (Poisson) statistics which has to be taken into account for later measurements and accuracy discussions, as given in section4.

Measurement Principles

In this section the underlying measurement method is discussed. Remarks regarding correction and calibrations methods are given. In case of the presented diagnostic the Charge Exchange between Hydrogen (H) and fully ionized carbon (C) is used [17,25].

H + C 6+ → H + + C 5+ (n, l) , C 5+ (n, l) → C 5+ (n , l ) + hν (1)
For the carbon spectroscopy considered in this work the visible spectral range is used and hence the most suitable transition n → n = 8 → 7 at 529.1 nm [45] is selected. A least square minimization method is applied to find an appropriate gaussian function (fit) to the measured spectra. One of the most significant features of the charge exchange diagnostic at TEXTOR is the modulation of the utilized neutral beam. While most other CXRS diagnostics use separate viewing lines [10,24] or complex fitting methods [12,18,44] to subtract the CXRS and bremsstrahlung background from the active signal, the diagnostic presented uses frames with and without beam signal to aquire the active . The smaller ratio for the toroidal view is caused by the longer line of sight background light integration. The intensity sufficient for highly time resolved measurements can not be reached. The overall modulation is about 20% but the quality of the measurement and the spectral shape is mostly governed by the total intensity acquired through the whole discharge.

The typical time window used averaging is three seconds, giving 15 active and 15 passive frames (cf. figure 4). This means, there is a time resolution of 100 ms necessary to gather the necessary frames during the operation of the diagnostic beam, but the actual measurements are performed on a data set acquired over the whole beam period of three to four seconds for reasonably intensities. The two spectra are then used to obtain the active charge exchange spectra as shown in figure 4. The active and the passive component of the spectra can be clearly discriminated. A gaussian fit is added two show the good agreement with the expected spectral shape assuming the ideal case of a single emission line. In the case displayed the poloidal observation system was used, allowing to substantiate on the reason for the modulated beam approach. In the case of the toroidal rotation typically measured with the NBI, the active CXRS spectrum is shifted from the passive background, and hence can be more easily discriminated by a multi component gauss fit. In case of small poloidal rotation this is not the case (figure 4), there is no large shift in the spectra. In the following paragraph a short description of the available parameters is given, the rotation velocity measurements as well as the measurement of T i and n i or intensity. Peak position, width and intensity based on the gaussian fit are used. The velocity is simply deduced via the Dopplershift v ion = -c • λ 0 -λ λ 0 , where c denotes the speed of light, λ 0 the rest frame wavelength and λ the Doppler shifted λ. The ion temperature is given by spectral width of the observed emission line, assuming gaussian spectra [13]:

T [eV ] = λ F W HM λ 0 2 • mc 2 8e • ln(2) = σ s • D λ 0 2 • 1.68 • 10 8 • µ[amu]. (2)
λ F W HM gives the width of the gaussian spectrum in terms of nm while the other terms are used as conversion factors. σs is the width in pixel and D the dispersion. For the impurity density an iterative code like CHEAP [42,44] is used to solve a set of differential equations based on the measured photon flux and the known beam components. The calculation of the carbon density is done in a self consistent way, taking beam attenuation and the carbon density interdependently into account 3.1. Absolute Calibration for v pol , v tor , n i

The two observation systems utilize two distinct ways to determine the rest frame wavelength λ 0 necessary for the rotation (cf. section 3) as well as for the temperature (cf. eq.2) measurements. The poloidal system uses differential Doppler spectroscopy [START_REF] Hawkes | [END_REF], while the toroidal system relies on a neon reference line, which is observed by one of the channels imaged onto the CCD chip. Differential Doppler spectroscopy utilizes two opposing lines of sight to acquire one red shifted and one blue shifted spectrum from the same rotation. In case of the poloidal observation system, this is one channel from the top of the top and one optical fiber channel from the bottom (cf figure 2). Via this setup one obtains two spectra with distinctly the same shift in opposite directions. Both represent the rotation velocity (v pol ) with respect to the rest frame. Both spectra are fitted and the positions of λ red and λ blue are then used to calculate the position of λ 0 on the CCD chip. The mean value of the peak position corresponds to the position of λ 0 on the CCD: P os(λ 0 ) = 0.5 * (P os(λ red ) + P os(λ blue )). With sufficient photon statistics this method is accurate in the order of the velocity resolution of the spectrometer (<1 km/s) and hence the best method to assure a valid measurement of small v pol . A similar system is used at the TJII stellarator [4]. In contrast to the common use of reference lines this method presents a direct measurement of the rest frame wavelength and is hence not prone to systematic errors, compensated here by the differential approach.The main systematic errors by using a reference line are angular deviations from misaligned mounting in front of the spectrometer, causing a strong shift in rotation velocity. The toroidal observation system uses a neon reference line imaged onto the chip which is continuously emitted during the whole discharge. The line (529.82 nm) is fitted similarly to the CXRS spectra and its position used to determine the position of the rest frame wavelength. Since all fibers, including the reference channel, are mounted collectively in front of the spectrometer, the angular discrepancy is negligible. An absolute photon flux calibration for the line emission intensity measured is needed for the density calculations, it is performed using an integrating sphere in front of the observation system at the position of the neutral heating beam. This allows to measure the ratio between emitted photon flux and the counts on chip. This is then input for the CHEAP code [42,44].

Radial Calibration

There are two options for the radial calibration, the first option is to illuminate the optical fibers or the spectrometer slit, imagining them onto the position of the hydrogen beam inside of the vessel. Hence establishing a direct relation between the fiber or slit position and the radial position. This method is very accurate and typically used during opening of TEXTOR. Since a vessel opening is only performed once every year a second reliable option is needed. This option is based on the Doppler shift spectroscopy using Beam Emission Spectroscopy (BES). This method is commonly applied and results in Doppler shift spectra for each radial position, from which the radial position is deduced.

Accuracies

In this next section the accuracy and the applied uncertainty calculations for the toroidal and poloidal impurity velocity as well as for the the ion temperature are given.

Corrections regarding finite slit height [START_REF] Last | [END_REF] , Zeeman effect and Fine-structure are applied [START_REF] Ch | Energy Technology Edition[END_REF]21,[START_REF] Hey | Proc. 20th EPS Conference[END_REF] during the analysis process and thus accounted for regarding the resulting temperatures and velocities. Corrections regarding CXRS cross-sections are negligible due to the low temperatures and perpendicular viewing angle [43].

The measurement uncertainties in rotation and T i are calculated based on the uncertainty of the dispersion and the statistical uncertainty on width and position of the gaussian fit. Some of the numbers regarding the resolution have been discussed earlier (Section 2.3); with the dispersion given in table 1 the poloidal system is capable of resolving 1km/s rotation (1.6 pixel on the CCD) while 100 eV in T i are equivalent to a FWHM of 118 pixel. For the toroidal system 1km/s means 0.1 pixel and 100 eV are ∼ 7 pixel. This, with respect to the measurement accuracy, means the following: First the poloidal system is well equipped for rotation and T i measurements, but due to limitations in the intensity, is prone to errors due to poisson statistics. The smaller the intensity the more distorted the spectral shape can be influencing e.g. the subsequent position calculation. With respect to the measured quantities this means a direct impact on the accuracy. Intensity and dispersion are intertwined and both need to be optimized together in order to obtain reasonable results. High dispersion requires high intensity since less photons are accessible per pixel the higher the dispersion is set. Since we require highly accurate velocity measurements this can be quite critical, while T i is well defined within the required accuracies. For the toroidal system the situation is less This plot shows the different capabilities of the two systems and clearly shows why the poloidal system is preferred for T i ( 1 eV = 1 pixel). The uncertainties are:

σ v = c • ∆ 2 p • σ 2 D + D 2 • (σ 2 rp + σ 2 p )/λ 0 (3)
σ T = T i • (2 (σ D /D) 2 + •(σ s /σ spec ) 2 ) ( 4 )
(3) describes the calculation of the uncertainty for the velocity, taking into account the Doppler shift in terms of chip position (∆ p [pixel]), the dispersion (D[ Å/pixel]) and its uncertainty (σ D [ Å/pixel]) as well as the uncertainty on the peak position (σ p [pixel]) and the reference position (σ rp [pixel]) (both on the chip) . The gaussian fit uses as input parameters the obtained spectral data and statistical information from the data set. For the T i a similar calculation (eq.4) is performed. The dispersion as well as its uncertainty are included into the calculation as well as the spectral width (σ spec [pixel]) and its uncertainty (σ s [pixel]). From this one can deduce the typical error bars, which amount for v pol typically to σ= 0.7 km/s and for v tor σ=5 km/s. For T i it is deducible from (4) that the uncertainty scales with the temperature itself, and thus is larger in the plasma core than in the edge. The errorbar for the poloidaly measured T i lies between 2 eV and 10 eV, while the toroidally measured T i has an uncertainty of 5 to 40 eV. The present status of the diagnostic utilizes the direct imaging in order to supply as much intensity to the high dispersion spectrometer as possible. The poloidal diagnostic produces very good results with respect to the relative accuracy (0.7 km/s) which depends strongly on the intensity supplied by the observation system on top of the tokamak vessel. The reference channel (cf. figure 2)however is still transferred via fiber and those signals still suffer from small intensities. Since the spectrometer components are not in any way influenced or moved during the measurement campaign, it is assumed that the reference position is not changing from discharge to discharge. The setup is mounted without connection to the torus, thus being unaffected from vibrations. The temperature of the spectrometer as well as the camera setup is at a constant level. As mentioned above effects of e.g. magnetic fields are taken into account when performing the analysis. This allows to calculate an average reference position which is well described.The uncertainty for the average value is well below one pixel (2.41 pixel/ √ 26 = 0.47 → 0.2km/s) and small compared to the uncertainty of 0.7 km/s. Regarding the CCD and Image-intensifiers used no significant influence on the accuracy is seen or expected. The quantum efficiency of CCD and MCP are here the most significant component since impacting on the actually available intensity. However, the small original signal requires intensification via a Multi Channel Plate(MCP) thus even the 10% QE are acceptable and within industry norm. Regarding readout time and noise it can be said that compared to the 100 ms frame integration the read out time is negligible and the noise is well below the poisson levels observed. The Taper connecting MCP and CCD has a structure of 6 m and thus does not effect the resolution.

Data & First Results

An example is shown to demonstrate the capabilities of the new CXRS diagnostic with respect to the two rotational directions as well as T i and the E r measurement. The capability of TEXTOR is used adapting the toroidal plasma rotation via the net torque input from the co-current and a counter current Neutral Beam Injectors (figure 1). A series of discharges with constant input power of 1.3 MW from, a toroidal field of 2.1 T and a plasma current of 410 kA i shown. In the course of the different discharges the momentum fraction between the two tangential beams is gradually changed from full counter current (+)(#106846) via balanced beam (#106848) to full co current (-) (#106850) injection to study the behavior of plasma impurity (CVI) rotation and the measurement procedure for v pol and v tor . The TEXTOR plasma is centered around 1.75 m of the major radius with a minor radius of r = 0.46 m, locating the last closed flux surface at R ∼ 2.21 m. The first set of data presented in figure 6 shows the influence of momentum input on the toroidal rotation in TEXTOR. It is visible that the momentum input from the neutral beam accelerates the center of the plasma, causing a co-or counter-rotation, while it is also visible that even with balanced beam injection (similar for ohmic discharges) a rotation in counter direction is observed. The changes in momentum input can be observed across the whole profile except the SOL area, where the profiles are underlying a general flow into the counter direction. The profiles are fixed at the edge where the rotation is slowed down due to friction with neutral particles. The profile structure can be explained with the perpendicular viscosity, keeping the outer part connected to the innermost momentum source. The poloidal rotation shown in figure 6 shows profiles which, towards the center (r/a = 0.5 ), follow the trend of increased momentum. While the momentum input might explain those changes, the most striking observations are in the outer plasma edge: the rotation changes from the electron diamagnetic drift direction (counter +) to the ion diamagnetic drift direction (co -). Only the discharges with dominant NBI 2 injection show the strong increase in edge rotation, thus a connection with the different confinement of fast ions for the two beams can be assumed. The gradients for T i in this area are comparable (figure 7) and seem not to drive the changes. Figure 7 shows T i for all discharges discussed above. The T i is quite similar due to constand NBI power if taking into account both the radial resolution as well as the temperature uncertainty. It has be estimated from calculations [START_REF] Ongena | [END_REF] that about 8 % of the beam ions are lost via orbit losses when using NBI 2. Comparing this quantitatively with calculation is beyond the scope of this paper. This example once more stresses the value of a high resolution diagnostic focussing on the poloidal velocity resolution. The last result presented here is the E r deduced according to the radial force balance equation [7,34] given in eq.5. It is seen from [START_REF] Coenen | of Energy & Environment[END_REF], that the E r follows the contributions from v tor and v pol , dominated by v pol (cf. figures 6 and8).

E r = E r(diam.) + E r(pol) + E r(tor.) = + 1 Z i en i dp i dr -v pol B T + v tor B p (5)
p i is the pressure gradient and n i is the ion density. Z i is accounting for the impurity charge and B p,T are the respective components of the magnetic field. For circular shaped L-Mode limiter plasmas at TEXTOR with low resistivity it has been shown that the diamagnetic term can be neglected [START_REF] Coenen | D of ECA[END_REF] as found for other L-Mode plasmas [24].

Conclusion

In the course of this paper we have presented the latest status of the CXRS diagnostic on the RuDI Hydrogen Diagnostic Beam at TEXTOR. A poloidal and toroidal diagnostic is successfully integrated into the TEXTOR environment. The performance is dominated by the line intensity which can be observed.

The toroidal rotation can be measured with an accuracies of 5 km/s and the poloidal rotation is resolved well below 1 km/s (0.7km/s). The diagnostics deliver a spatially resolved measurement ∼ 1 cm of the E r with a resolution of ∼ 2 -5kV /m. This is achieved by combining the high spectral resolution of the poloidal spectrometer system, with a dispersion of (1.0799 ± 0.0003)pm/pixel and the toroidal system delivering a dispersion of 1.624 ± 0.005nm/pixel. The data presented is a good example of the capabilities of this diagnostic, showing changes of rotation from -50 km/s up to 100 km/s for the toroidal system as well as changes from -3 km/s up to 5 km/s for the poloidal rotation. T i is measured almost up to 1000eV and E r can be calculated over the whole domain accessible for this diagnostic. The system can be regularly used at TEXTOR to measure impurity (carbon) rotation and temperature on a discharge by discharge basis, meaning an integration time of about 3-4 s is needed. A method is established to consistently measure the radial electric field at one toroidal position, deriving it directly from the measured components. By using a diagnostic beam CXRS measurements are in principal feasible under all plasma conditions. Compared to other diagnostics like Doppler Reflectometry [START_REF] Conway | [END_REF] or the heavy ion beam probe [24] the advantages of this CXRS diagnostic is its high spectral and rotation resolution as well as its large coverage over half of the minor radius 0.5 < r/a < 1.1 including the whole plasma edge. This diagnostics supplies all necessary information for the radial electric field calculations and the radial force balance. No additional input parameters are needed [START_REF] Coenen | D of ECA[END_REF][START_REF] Coenen | of Energy & Environment[END_REF] the rotation as well as the pressure gradient are measured.

In order to gain more access to low intensity scenarios further improvements to the setup up are performed including actively cooled camera system removing the background noise and allowing operation during scenarios with higher radiation levels.

Figure 1 :

 1 Figure 1: (ONLINE COLOR)(left) TEXTOR(R=1.75 m r=46 cm) and diagnostics locations. (right) CXRS Diagnostic setup mounted at the Low Field Side.

Figure 2 :

 2 Figure 2: (ONLINE COLOR) Optical components, of the poloidal (Poloidal Cut) as well as the toroidal observation system and its optical elements (Top View)

Figure 4 :

 4 Figure 4: (ONLINE COLOR) (left) Intensity evolution of the CVI Line including the beam modulation (right) CXR Spectrum from the poloidal observation.

Figure 5 :

 5 Figure 5: (ONLINE COLOR)T i measured by poloidal and toroidal observation

Figure 6 :

 6 Figure 6: (ONLINE COLOR)v t or and v pol during a momentum input scan, changing the fraction between the two beam injectors, keeping the input power constant.

Figure 7 :

 7 Figure 7: (ONLINE COLOR)T i acquired with the poloidal system during a momentum scan, changing fraction between the two neutral beam injectors at constant input power.

Figure 8 :

 8 Figure 8: (ONLINE COLOR)E r during a momentum input scan, changing the momentum fraction between the two neutral beam injectors (constant input power).

Table 1 :

 1 Parameters for both, the poloidal and toroidal, observation systems

	Poloidal System	Toroidal System

Acknowledgments

This work has been performed with strong support from G. Herpers, K. von Bovert, K. Klören and D. Schüller for the technical aspects. Results are part of a finished PhD thesis at the "Heinrich-Heine-Universität, Düsseldorf". This work was partially supported by the German Research Foundation (DFG) under grant No. UN 265/1-1 and the Research Training Group GRK 1203 -Dynamics of hot plasmas.