David Tisseur

Caroline Vienne
email: caroline.vienne@cea.fr

Pierre Guérin

Angela Peterzol Parmentier

Valérie Kaftandjian

Philippe Duvauchelle

Andreas Schumm

A Modified Detectability Criterion for Conventional Radiography Simulation

For the conventional radiographic technique, X/gamma ray film interpretation is based on human eye perception. There is no criterion of "universal" visibility / detectability of flaws and IQIs for simulated radiography. However, at least one detectability criterion is required for an automatic analysis study of a given set-up. The Rose criterion, based on the contrast to noise ratio of the imaged flaw normalized to the spatial image resolution, is the current reference detectability measure. It is by definition well-adapted in the case of roughly circular flaws (e.g. flat bottom holes or step hole IQIs) but shows its limits for cracks with an elongated shape or close to the limit of spatial resolution as well as for wire IQIs. In this paper, we propose a modified detectability criterion to take into account the variability of flaw shape. This paper shows a performance comparison between human expertise and this new criterion, using a large flaw database and IQIs with associated operator evaluations developed in a prior work.

Introduction

In conventional radiographic inspection, a human observer interprets the radiographic image to conclude on the presence of a flaw or the detectability of an image quality indicator (IQI). The problem of characterizing the human ability to detect such a flaw or IQI has been studied since decades, especially through the work of Rose [START_REF] Rose | Vision: human and electronic[END_REF], who formulated the human operator ability as a problem of imaging system performance. According to Rose model, detectability of a flaw can be determined by a criterion based on the contrast to noise ratio (CNR) measured in the image, where the signal is the contrast between the flaw and its background and the noise is the uncertainty based on the photon statistics. Using an experimental approach, Rose defined a perception threshold value around 5 for its criterion, above which human operator is able to detect the signal with significant certainty. Ewert et al. extended the perception equation and introduced the normalisation to the basic spatial resolution to take into account the different resolutions and pixel sizes in the case of modern digital X-ray detectors [START_REF] Ewert | Image Quality in Digital Industrial Radiography[END_REF]. Despite the actual limits of Rose model, which have been pointed out by Burgess [START_REF] Burgess | The Rose model, revisited[END_REF], the notions of detectability criterion and perception threshold are essential in the field of radiographic imaging and more particularly in the context of automatic simulation studies. Indeed, when modelling a radiographic inspection with simulation software, it is particularly interesting to provide a feedback on the detectability of a given flaw that corresponds to the actual interpretation of human operator reading radiographic film. In this paper, we use Rose's model as starting point for defining a detectability criterion suitable for conventional radiographic images simulated with CIVA [3] and MODERATO [START_REF] Bonin | MODERATO: a Monte-Carlo Radiographic Simulation[END_REF] software, which are both based on the same simulation model. This criterion is defined so as to take into account the specificities of the radiographic modelling and the variability of the flaw shape. This paper shows a performance comparison between human expertise and this new criterion, using a large flaw database and IQIs with associated operator evaluations developed in a prior work.

Radiographic Modeling

Photon-matter interaction

CIVA RT module is used to simulate the results of an inspection carried out with an X-Ray tube or a radioactive gamma ray source. It simulates direct radiation [START_REF] Fernandez | Simulation studies of radiographic inspections[END_REF] generated by a source and propagating through a specimen, which is defined with potential flaws, and scattering from the specimen in order to create the final radiographic image. The direct radiation is obtained through the analytic Beer-Lambert (BL) law applied along each ray joining the source point to each detector pixel. The scattered radiation is modelled by Monte-Carlo simulation, which computes the path of an individual photon as a random walk, determining both the distance between two interactions (the so called free path length) as well as the type of interaction after having travelled the free path according to random numbers obeying the interaction probability laws. A fusion process is then applied to combine images obtained from these two simulations [START_REF] Tabary | Combination of high resolution analytically computed uncollided flux images with low resolution Monte-Carlo computed scattered flux images[END_REF].

Detector modelling

In the CIVA and MODERATO simulation platforms, radiographic film modelling is based on the European standard ISO 11699-1 [START_REF]Non-destructive testing -Industrial radiographic film -Part 1: Classification of film systems for industrial radiography[END_REF] as described in [START_REF] Schumm | The EN584 Standard for the Classification of Industrial Radiography Films and its Use in Radiographic Modelling[END_REF]. ISO 11699-1 substituted EN 584-1 with same procedure. For conventional radiography, ISO 11699-1 film modelling is carried out in two successive steps. The first one deals with the calculation of incident dose to the detector and the second one consists in converting the incident dose into signal produced by the complete detection system. This transformation is performed via a transfer function. For ISO 11699-1 film detector model, this function is pre-computed for each film via a second order equation and allows the generation of optical density (OD) images without noise.

Finally, the film granularity noise is approximated with Gaussian distribution, whose standard deviation is based on the film granularity value ( ) available in manufacturers certificates, modified to take into account the pixel size considered in the simulation process and the actual optical density . Indeed, the standard ISO 11699-1 defines film granularity in terms of diffuse optical density measurements on a zone with constant optical net density 2, using a microdensitometer with 100 µm circular aperture:

= √ • 4 √ , (1)
where is the simulation pixel area in µm² and is the mean optical density.

Simulated images

Multiple images can be created during the simulation process for estimating the detectability of a given flaw. They are computed for the object with flaw (complete image displayed to the user) but also for the object without flaw (reference image used for calculation only). These images are detailed here: -BL direct energy: it corresponds to the deposited energy after a straight line computation on each pixel of the detector. A binary image of the flaw, called flaw mask, is created by first subtracting the BL image of the object with flaw to the BL image of the object without flaw and then thresholding the difference image.

-OD without noise: it corresponds to the simulated radiographic image (including scatter contribution) before application of Gaussian granularity noise. The OD images without noise are computed with the flaw (resp. without it) and the mean value in the area of the flaw is taken as mean OD value of the flaw (resp. of the background).

-OD with noise: it corresponds to the final image (including scatter contribution) simulating the real radiographic image.

Detectability criterion

Based on the Rose model, we propose here a detectability criterion that depends on the signal value, on the noise level and on the flaw area. We detail the computation of these different parameters for ensuring a good performance of the criterion.

Contrast

In the context of flaw detection, the contrast is defined as intensity change between the flaw and its neighbourhood. To compute this value in the CIVA environment, we can use OD images without noise simulated with and without flaw, as detailed in the previous section. The knowledge of the flaw mask, computed from BL images allows the computation of contrast from mean OD values of the flaw and its background : = ‖ -‖

Noise level

According to detector modelling implemented in the CIVA software, the noise level measured in the artificial image is dependent on the pixel size used in the simulation process. It is to be noted that this simulation pixel size should be slightly better than the intrinsic resolution of the radiographic film at given radiation energy, and will subsequently be decreased by the application of MTF to correspond to this intrinsic film resolution. To free ourselves from simulation parameters and model the human operator ability, we express equation [START_REF] Rose | Vision: human and electronic[END_REF] in the case of a pixel size corresponding to eye resolution. The noise value is then:

= _ _
According to [START_REF] Schraufa | The visual resolution of Landolt-C optotypes in human subjects depends on their orientation: the gap-down effect[END_REF], we can consider that a human eye with an optimal acuity presents a resolution equal to 1 arc min. If we consider an eye to radiographic film distance equal to 40 cm, the eye resolution is around 120 µm.

Considered projected flaw area

One modification is brought to the Rose detectability criterion to expand the initial criterion, established for circular shapes (see Fig. 1), to the case of elongated shapes. This modification is based on the knowledge of equivalent visibility between step hole IQI and wire IQI given by standards. More particularly, by referring to French code "Design and Construction Rules for the Mechanical Components of PWR Nuclear Islands" (RCCM) [START_REF] Afcen | Design and Construction Rules for Mechanical Components of PWR Nuclear Islands RCC-M[END_REF], we can determine that step hole IQI of diameter ∅ has a visibility equivalent to wire IQI of diameter ∅ . ⁄ (see Fig. 2) for wire diameters < 1 mm and a visibility equivalent to wire IQI of diameter ∅ . for wire diameters > mm ⁄ . ISO 19232-3 and ISO 17636-2 use an equivalent value of /2.2 by different variation of thickness application ranges for wire IQIs and step hole IQIs. Similar work has been previously done for digital radiography and discusses a nonlinear relationship between wire and hole diameters based on ASTM E 747 [START_REF] Ewert | Image Quality in Digital Industrial Radiography[END_REF]. The discrepancy to ASTM E 747 was investigated. MC3162.1 in the typical range for X-ray inspections. [START_REF] Afcen | Design and Construction Rules for Mechanical Components of PWR Nuclear Islands RCC-M[END_REF] Due to these observations, we propose to estimate, in the case of elongated shapes, the area of a circular shape of equivalent visibility.

After extracting the mask of the flaw with BL images, we extracted flaw bounding box in order to obtain the length (L) and the width (W) (see Fig. 3). The flaw shape ratio r is then computed as:

= .
To ensure the continuity of the flaw area with respect to r value, we set a threshold value r th . Below this value, the flaw area is computed as = ². Above this value, the flaw is considered as a wire and the diameter of equivalent hole is ∅= . As previously detailed, the value of k is comprised between 2 and 2.5 depending on the considered standard. In practice this value has a limited impact on the obtained results and we will consider in the current paper k=2.2, which results in an equivalent area: Finally, a threshold is applied to this area value so as to model the fact that above a given value, a larger area of the IQI does not imply a better detectability of the IQI. According to a previous experimental study, we estimated a surface area threshold of 1.6 mm²:

= min ( , . ).

Implemented criterion

The proposed formula for flaw detectability in simulated conventional radiographic images is therefore:

= • √,
where C is defined in paragraph 2.1, is defined in paragraph 2.2 and A is defined paragraph 2.3.

Simulation of radiographic inspection

Case 1

First radiographic trials have been realized with an Ir192 source and C2 Kodak M100 film on mock-ups of artificial cylindrical flaws (see Fig. 4). Flaws have 10 mm diameter and various depths between 98 µm and 695 µm. Different control configurations have been considered with variation on pipe thickness (a), source distance (b) and number of crossed pipe walls. Radiographic images coming from real acquisition are interpreted by human operators who classify them into three categories:

-flaw not seen (0) -flaw seen with uncertainty (detectability limit = 1) -flaw seen (2)

Case 2

The second case study consists in artificial flaws created from parts of IQI of steel and copper and from wires of lead and tungsten. 192 flaws are put on the inner wall of a steel plate of 51 mm thickness and 30 cm x 30 cm size (see Fig. 6). The experimental set-up is constituted of a fixed frame on which the mock-up of 192 flaws and one Ir192 source are fixed. A C2 Kodak M100 film is placed upon contact with the mock up and is interpreted by three experts. Each flaw has been noted between from 0 (no seen) to 5 (clearly seen).

For each flaw, we take into account the mean evaluation from the three experts. This configuration is simulated with CIVA by using a pixel size of 20 µm. Two samples of OD images are displayed in Fig. 7. They correspond to one copper IQI of small diameter declared "not seen" by operators (on left) and one copper IQI of large diameter declared "seen" (on right).

Performance of the criterion

The following figure presents a synthetic view of the performance of the criterion versus expert notation. With this graph, we can separate the results in 4 domains:

-true positive -true negative -false positive -false negative With the new proposed criterion, a detectability threshold of 1.5 appears to be the most suited in determining the detectability of the defects, independently of their shape and of the pixel size of the simulation. With this threshold value, we found an agreement between the criterion and the expert's evaluation for 190 flaws for a total of 202 tested flaws (20 flaws for case 1 and 192 flaws for case 2).

Conclusion

The proposed detectability criterion shows good performances with respect to experts evaluations obtained through two case studies. By taking into account simulations performed with MODERATO and CIVA, a compromise between an "optimistic" criterion and a "pessimistic" one seems to show that it is necessary to use a detectability threshold of 1.5. With this value, we found an agreement between expert judgment and the criterion for 89.6 % of the flaws over 202 flaws tested. This new criterion will be available in CIVA and MODERATO in 2016. Further work will include case studies with background gradient and cracks type flaws, moreover a specific interest will be brought to the surface area threshold, whose value needs to be further consolidated. This work, which is specifically dedicated to conventional radiography, can be extended to computed radiography and digital radiography with some modification to take into account, in particular, the influence of the basic spatial resolution and the screen resolution.

Fig. 1 :

 1 Fig. 1: Test pattern (left) and resulting image (right) used by Rose in [1] to establish its theory.

Fig. 2 :

 2 Fig. 2: Wire/hole equivalence using French radiographic code RCCM tableMC3162.1 in the typical range for X-ray inspections.[START_REF] Afcen | Design and Construction Rules for Mechanical Components of PWR Nuclear Islands RCC-M[END_REF]

Fig. 3 :

 3 Fig. 3: Flaw eccentricity is estimated from PCA and for elongated shapes the width W is considered for surface computation.

Fig. 4 :

 4 Fig. 4: First case study involves two simple wall configurations (left), with a = 92 mm and b = 390 mm (respectively a = 56 mm and b = 421 mm) and one double wall configuration (right).

Fig. 5 :

 5 Fig. 5: Simulated images from double walls acquisition with different flaw depths.

Fig. 6 :

 6 Fig. 6: Mock-up of 192 flaws created from IQI parts and wires used in the second case study.

Fig. 7 :

 7 Fig. 7: Simulated images of copper cylindrical flaws with 0.8 mm (left) diameter and 3.2 mm diameter (right).

Fig. 8 :

 8 Fig. 8: Graph of the performance of the criterion results versus expert notation

More info about this article: http://ndt.net/?id=19537

Acknowledgement

The authors thank Dr. rer. nat. Uwe Ewert from BAM for valuable discussions and suggestions to improve the quality of the paper.


Navnina Bhatia
email: navnina.bhatia@cea.fr.

David Tisseur

Solène Valton

Jean Michel

Solene Valton

Jean Michel Létang

Separable scatter model of the detector and object contributions using continuously thickness-adapted kernels in CBCT

Keywords: CBCT, scatter artifact correction, CIVA, industrial NDT

may come

Separable scatter model of the detector and object contributions using continuously thickness-adapted kernels in CBCT

Introduction

One of the well-recognized challenge of cone-beam computed tomography (CBCT) is the presence of scatter contamination within the projection images. Existing reconstruction algorithms do not model the scatter radiation. Therefore scatter artifact appears on the reconstruction images as shading, cupping effect, reduced contrast etc. This leads to overall inaccuracies in the reconstruction values.

Majority of the scatter correction techniques focus on scatter contribution from the object only. But recent studies [START_REF] Bub | Image blur in a flat-panel detector due to compton scattering at its internal mountings[END_REF] [2] [START_REF] Poludniowski | Removal and effects of scatterglare in cone-beam CT with an amorphous-silicon flat-panel detector[END_REF] have proved that in the high energy range used in industrial Non-Destructive Testing (NDT), the contribution of detector scatter also becomes important. While evaluating the role of detector in the reconstruction artifacts, a number of scattering and blurring processes within the detector need to be taken into account.

Firstly, X-ray radiation can be Compton scattered by any part of the detector surroundings like mountings, back plate or even the detector layer itself [START_REF] Bub | Image blur in a flat-panel detector due to compton scattering at its internal mountings[END_REF]. Bub et al [START_REF] Bub | Image blur in a flat-panel detector due to compton scattering at its internal mountings[END_REF] show that this scattering can also lead to the edge blurring of the object in the obtained projections. The part of the detector directly exposed to full beam, produces more Compton scattering than the part of the detector under the shadow of the highly attenuating object. This is because of attenuation of the primary intensity under the object. As a result the sharpness of the edges of the object appear degraded. This can cause additional grey levels appearing in the reconstruction leading to deformations. Another important effect at high X ray energy source is the backscattering of photons from the material behind the detector [START_REF] Hoheisel | Influence of backscattering on the spatial resolution of semiconductor x-ray detectors[END_REF]. If the scintillator layer is made of low absorbing material, a large part of radiation can be transmitted to the back-plate. For the energies above K edge of the back plate, there is appreciable increase in backscattering by the production of low energy fluorescence X rays. These backscattered photons may be reabsorbed at a different site than the first interaction site. As a result the overall spatial resolution of the detector decreases.

Additionally, when X-rays interact with a phosphor (by most pronounced photo-electric effect), X-ray fluorescence photons are produced which may be reabsorbed by the detector areas adjacent to the primary x-ray interaction site. This may cause a loss of spatial resolution and an increase in image noise [5] [6]. Moreover, the fluorescence optical photon may also scatter within the scintillator layer which causes blurring, also known as veiling glare [7] [8]. Its magnitude mainly depends on the thickness and material characteristics of the detection layer.

In this article, we propose to evaluate the contribution of detector scattering at NDT energy range using continuously thickness adapted Scatter Kernel Superposition (SKS) method [START_REF] Bhatia | Scattering correction using continuously thickness-adapted kernels[END_REF]. The continuous method takes into account better sampling of the kernels with respect to the thickness of the object to get an accurate model of variability in shape and in amplitude of the scatter kernels over the whole thickness range. However, the continuous method and other classical SKS method [START_REF] Sun | Star-Lack, Improved scatter correction using adaptive scatter kernel superposition[END_REF] use a two-Gaussian model for the fitting of kernels. This two-Gaussian parametrization of kernels has several shortcomings. Firstly, the scatter contributions from the detector and the object are entangled, which makes the parameter fitting of the continuous model tricky. Moreover, the high frequency contribution of the detector scatter generates a strong peak in the center pixel of the detector where the pencil beam is impinged. This shape calls for the necessity to explore an increase in order of the Gaussian model. Therefore, we propose in this paper, by means of both experiments and simulations, to identify the respective scatter contributions of the object and detector using a four-Gaussian model to have a more stable modeling.

We begin by outlining the four-Gaussian analytic description of the kernels. Subsequently, the CBCT acquisition set up is described in detail. An in-depth analysis of the four-Gaussian contributions is carried out in Section 3. Experimental validation is finally performed with both fan beam and cone beam geometries.

Method and materials

Four-Gaussian model

In the SKS scatter correction approach with continuously thickness-adapted kernels [START_REF] Bhatia | Scattering correction using continuously thickness-adapted kernels[END_REF], the scatter signal can be modeled as the sum of the scatter contributions from a group of pencil beams passing through the object and the detector. For each pencil beam input, a resulting kernel which has the weight of the scatter to primary ratio is determined. The total scatter signal S(m, n) with m and n as the pixel position on the detector, can then be modeled as:

S(m, n) = k l P(k, l)h T (k,l) (m -k, n -l) (1)
where, h T is the thickness (T ) dependent kernel, with amplitude equal to the ratio of the scattered signal at the current pixel to the primary signal, at the pencil beam centered pixel.The sum in the convolution process runs over all pixels (k, l) of the detector. P is the primary signal contributed by the photons passing directly without any attenuation. Instead of using Beer-Lambert law based on an effective linear attenuation coefficient [START_REF] Sun | Star-Lack, Improved scatter correction using adaptive scatter kernel superposition[END_REF], the thickness T (k, l) in Equation 2is directly computed from a look-up table f BH -computed during the calibration stage of the kernels -that relates the true slab thickness with respect to the transmittance

T (k, l) = f BH P(k, l) O(k, l) (2)
where O is the unattenuated image. It is worthy to note that the beam-hardening is taken care of with this procedure. The acquisition parameters and the material of the calibration slabs must be the same as the object under study. Value of directly transmitted primary fluency P were calculated for each thickness of the simulated slab. The thickness in terms of the transmittance P(k, l)/O(k, l) is calculated as described in Section 3.1.

The pencil beam kernel h T can be fitted into the equation formed by four circularly symmetric Gaussian functions describing the shape of the kernel:

h T (m -k, n -l) = A exp - (m -k) 2 + (n -l) 2 2σ 2 1 + B exp - (m -k) 2 + (n -l) 2 2σ 2 2 + C exp - (m -k) 2 + (n -l) 2 2σ 2 3 + D exp - (m -k) 2 + (n -l) 2 2σ 2 4 (3)
The four-Gaussian model is necessary in order to clearly separate the contributions of the object and of the detector.

Kernel generation and fitting

Monte Carlo (MC) simulations were performed in the CT module of CIVA software [11] for the generation of kernels. Pencil beam source was impinged on slabs of same material as the object under study and discrete set of point spread 2D kernels were obtained on the flat panel detector.

The flat panel was modeled in a standard multi-layer representation consisting of 0.1 mm aluminium front layer followed by air-gap of 0.8 mm, a 0.06 mm CsI layer, 1 mm silicon substrate and finally a 1 mm lead back plate.

The eight parameters of Equation 3, A, B, C, D, σ 1 ,σ 2 ,σ 3 ,σ 4 are also interpolated in terms of thickness to obtain a continuous kernel map with respect to thickness [START_REF] Bhatia | Scattering correction using continuously thickness-adapted kernels[END_REF]. We have used a four-Gaussian model in order to separate the contribution of object and detector. To get realistic kernels and in particular to take into account optical processes in the detector, real acquisitions on slabs of various thickness could also be advantageously used in practice with an X-ray pencil beam geometry.

Acquisition set up with aluminum turbo

For the acquisition set up, the source to detector distance was 845 cm and the distance between source and axis of rotation was at 424 cm. The set up mainly consisted of a X-ray source, an object rotational table and a flat panel detector. The X-ray source unit of maximum 230 kV was used. A Acquisitions were performed on an aluminum turbo as given in Fig. 1 which had a maximum dimension of around 300 mm.

Acquisition set-up with collimator slit

In order to validate our results with experimental results, acquisitions were performed with a collimator slit inserted in between the object and the detector. The set up is described in Fig. 2. The collimator slit was made of steel with a thickness of 30 mm and width 15 mm. The introduction of the collimator removed approximately all the contribution of the object scatter.

Results

Analytical fitting of calculation of thickness

As discussed in Section 2.1, in order to calculate the thickness at each pixel, simulation were performed with slabs of different thickness. The acquisition parameters and the material of the slabs was kept the same as the object under study. Value of directly transmitted primary fluency P were calculated for each thickness of the simulated slab.

The thickness vs transmittance LUT f BH given in Equation 3 has been analytically calculated using least square fitting as shown in Fig. 4 to determine the coefficients a 1 , b 1 , a 2 , b 2 in Equation 4. The classical thickness determination based on the effective linear attenuation coefficient is also shown by the red curve in Fig. 4. The beam-hardening, although not really strong, is clearly visible. Equation 4gives the relationship of thickness T value in terms of transmittance P(k, l)/O(k, l).

T (k, l) = f BH P(k, l) O(k, l) =-a 1 ln P(k, l) O(k, l) b 1 -a 2 ln P(k, l) O(k, l) b 2 (4) using a 1 = 20.8, b 1 = 0.83, a 2 = 0.000572, b 2 = 1

Analytical fitting of kernels for continuous kernel map

The fitting of parameters A, B, C, D, σ 1 ,σ 2 ,σ 3 ,σ 4 of the four-Gaussian model with respect to thickness using least square fitting is shown in Fig. 3. From the fitting of the parameters, we observe that the standard deviation σ 1 and σ 2 vary over the thickness of the object whereas σ 3 and σ 4 remain constant. We can draw inference that σ 1 and σ 2 give the the scattering contribution of the object which increases over the thickness of the object. Moreover, we notice that σ 1 is very far from σ 2 . Henceforth, we analyze that σ 1 displays the low frequency contribution of multiple scattering inside the object, whereas σ 2 gives comparatively low order scattering contribution. We also mark not much difference in the parameters A & B which weight the amplitude of the shape of the Gaussians. This variation of parameters A, B, σ 1 ,σ 2 , demonstrate that a two-Gaussian model for the object is necessary.

Similarly, observing σ 3 and σ 4 remain constant over the thickness of the object, we infer that σ 3 and σ 4 define the high frequency contribution from the detector. Following the same line of reasoning, σ 3 and σ 4 are different from each other whereas and parameters C, D are not outlying each other. Therefore, a two-Gaussian model for the detector is also crucial.

Scatter correction on aluminium turbo

Figure 5 a) displays the reconstruction slice obtained with uncorrected projections using FDK algorithm. We first evaluated the scatter contribution of the object alone and we corrected the projections with only scatter kernels of the object. The result obtained is shown in Fig. 5 b). It clearly shows that the scatter correction due to only object is not sufficient as scatter artifacts are still visible in the reconstruction image. This is also demonstrated in Fig. 6 which displays the plot profile of the corrected and uncorrected reconstruction slices. The scatter kernels of detector and object were then used to perform the corrections of the projections. The reconstruction obtained with this correction is shown in Fig. 5 c). The obtained result with the scatter correction of object and detector is in agreement with the expected value of effective linear attenuation coefficient at mean energy 98 keV (0.48 per cm).

Table 1 displays the mean and standard deviation of the reconstructed values for corrected and uncorrected data in air and aluminum region calculated using binary masks. Uncorrected value of 0.258 cm -1 for the linear attenuation coefficient of aluminum is estimated. By using only object scatter kernels we obtain a value of 0.324 cm -1 for the linear attenuation coefficient of aluminum. In the considered energy range, the value of linear attenuation constant per cm for mean energy 100 keV is 0.48 cm -1 . The relative absolute error in percentage is 32.5% for the scatter correction with object kernels. Whereas, for detector and object kernels both we obtain a value of 0.510 cm -1 for the aluminum. The relative absolute error is reduced to 6.25%. The remaining artifact that we see in the scatter corrected reconstruction arise from the very high attenuation along the largest dimension of the object. The dynamic range of the detector was not high enough to take into account the attenuation along the highest dimension.

Validation by experimental result using a collimator

In order to validate the results obtained with the continuously thickness adapted SKS scatter correction algorithm, we performed acquisitions using a collimator made of steel with 30 mm thickness. The set up is described in the Section 2.4. Fan beam was produced and the contribution of the scatter from the object was eliminated by introducing a collimator slit between the object and the detector. All the other acquisition parameters were kept same as the previous set up without the collimator slit. The reconstruction was performed on the projections obtained with this set up and the result is shown in Fig. 7 a). It clearly shows the presence of scatter artifacts due to detector. We compare this experimental result with the result obtained by scatter correction performed by the algorithm using only object scatter kernels shown in Fig. 7 b). Figure 8 compares the plot profile of the experimental result with the collimator and scatter correction by the algorithm using object scatter kernels. The plot profiles demonstrate identical results validating the results obtained by the algorithm and proving considerable contribution of detector scatter.

Table 2 displays the mean and standard deviation of the reconstructed values for air & aluminum region for experimental result and correction with object scatter kernels. The linear attenuation coefficient obtained for aluminum and air is 0.312 cm -1 and 0.096 cm -1 respectively for the experimental result. This is in agreement with the scatter correction with object kernels result which is 0.324 cm -1 for aluminum and 0.106 cm -1 for air. In the considered energy range, the value of linear attenuation coefficient for mean value of spectrum (100 keV) is 0.48 cm -1 and 0.0001 cm -1 for aluminum and air respectively. This result demonstrates that in the considered energy range, object scatter correction is not sufficient and the detector scatter contribution also needs to be taken into account to obtain correct reconstruction values.

Discussion and conclusion

The analytical description of the scatter kernels using four-Gaussian model separates the low frequency contribution of scatter due to object and the high frequency contribution of the detector. This separation of the contributions is necessary to clearly follow the effect of detector scatter on the reconstruction in CBCT by developing a separate model for the detector.

The object scatter itself requires a two-Gaussian model to take into account higher order and lower order scattering from the object. The amplitude parameters of scatter kernels A&B increase with increase in thickness of the object because of the increase in SPR. σ 1 representing the very low frequency contributions from the object after multiple scattering of photons and σ 2 representing comparatively high frequency contribution from the object after fewer scattering of the photons, both increase with the thickness of the object. Similarly, the high frequency contribution of the detector model also requires a two-Gaussian model. The amplitude parameters for the detector Gaussian, C&D, decrease with thickness. Due to higher attenuation, lesser primary intensity reaches the detector leading to fewer Compton scattering events in the detector and its surrounding. Also, D, which weights the high frequency detector contribution, remains constant while C, which weights comparatively lower frequency detector contribution, decreases with respect to thickness. One explanation to this behavior could be that C is related to the back scattering from the back plate and since effective energy increases with respect to thickness, the scattering from the back plate becomes less and less back scattered. Whereas, D could be related to florescence in the scintillator, which remains constant over the thickness. The high frequency contribution of the detector given by σ 3 ,σ 4 remain constant over the thickness of the object. Using this analytical description of the scatter kernels, the projections were corrected to perform a comprehensive study of the contributions of object and detector scattering. The correction of projections using only object scatter kernels produced reconstruction image with scatter artifact. The relative absolute error with respect to the expected value is 32.5% for the scatter correction with object kernels. The correction of projections using object and detector scatter kernels reduced the relative error to 6.25%. The results obtained were validated with experimental results using a collimator. The relative absolute error between the experimental result using collimator and the scatter correction using object kernel was 3.7%.

The obtained result proves in this particular case study that the correction of the scatter due to the object only is not sufficient to completely remove scatter artifact in the reconstruction. The contribution of the detector scattering is very significant at the energy range used. We remark that the detector scatter depends on several parameters including the spectrum used and components (front filter, back plate etc.) configuration of the detector. The importance of the contribution of the detector scatter over the object scatter will therefore depend on each case study. Although the information about the component structure of the detector was only approximate in the simulation model of this study as it is generally kept anonymous by the manufacturer -the improvement in the scatter reduction using both object and detector scatter kernels is noteworthy. To further improve the realism of the detector kernels, either a more accurate 3D description of the detector could be used in the Monte Carlo simulation instead of a simple multi-layer model or direct measurements of the detector kernel could be carried out. Moreover, it could be additionally possible to implement a detector-specific tuning of the apodization function of the FDK reconstruction, for example, by measuring the noise power spectrum of the detector to take into account the detector variability of noise levels.

Fig. 1 .

 1 Fig. 1. Picture of sample of the aluminum turbo.

Fig. 2 .

 2 Fig. 2. Schematic of the acquisition set up with the collimator slit.

Fig. 3 .

 3 Fig. 3. Fitting of parameters A, B, C, D, σ 1 ,σ 2 ,σ 3 ,σ 4 with thickness.

Fig. 4 .

 4 Fig. 4. Fitting of thickness Vs transmittance curve to obtain correct value of thickness in terms of transmittance.

Fig. 5 .

 5 Fig. 5. Reconstruction slice with a) uncorrected projections b) corrected projections by only scatter kernels c) corrected projections by scatter and detector kernels.

Fig. 6 .

 6 Fig. 6. Plot profile of uncorrected and corrected reconstruction slice by only scatter kernels and scatter and detector kernels.

Fig. 7 .

 7 Fig. 7. Reconstruction slice by a) experimental results with collimator b) corrected projections by only object scatter kernels.

Fig. 8 .

 8 Fig. 8. Plot profile of experimental result with collimator and scatter correction with object scatter kernels.

Table 1

 1 Mean and standard deviation values for aluminum and air region for uncorrected and corrected reconstruction slices

	mean (cm -1 )	std. dev.

Table 2

 2 Mean and standard deviation values for aluminium and air region for experimental result with collimator and correction with object scatter kernels

	mean(cm -1 )	std.dev


Stéphane Zieba
email: stephane.zieba@cea.fr

Franc ¸ois-Xavier Russotto
email: francois-xavier.russotto@cea.fr

Max Da

Silva Simoes
email: max.simoes@cea.fr

Yvan Measson
email: yvan.measson@cea.fr

Assistance tools for generic definition of ITER maintenance tasks and scenarios in advanced supervisory control systems

This paper concerns the improvement of supervisory control systems in the context of remote handling for the maintenance tasks in ITER. This work aims at providing a single formalism and tools to define in a generic way the ITER maintenance tasks and scenarios for in-vessel and hot cell operations. A threelayered approach is proposed to model these tasks and scenarios. Physical actions are defined for the scene elements. From these physical actions, behaviours are defined to represent high-level functionalities. Finally, interaction modes define the way that behaviours are achieved in terms of human-machine interactions. Case study concerning the blanket maintenance procedure is discussed concerning the contributions of the descriptive model and the context-based assistances to the activities of supervisory control.

Introduction

The work presented in this paper takes place in the EFDA GOT-RH project. This program's aim is to train engineers for activities supporting the ITER project and the long-term fusion programme in European Associations, associates, Fusion for Energy (F4E) and the ITER organization, and Industry. The major objective is to implement a structured Remote Handling (RH) System design and a development-oriented training task that is carried out in a multidisciplinary Systems Engineering framework by using ITER/F4E task and quality assurance processes and available documents, document templates and ITER-relevant software products. The global topic of this project concerns RH maintenance for ITER and works detailed in this paper concern more specifically the advanced functionalities for Supervisory Control Systems.

ITER maintenance requires a combination of scheduled and unscheduled replacement tasks both on the machine and in the hot cell during periodic shutdown times and operational periods [START_REF]ITER Remote Handling High-Level Control System White Paper[END_REF]. Maintained components are to be moved between the Tokamak building and the Hot Cell building through the ports located in the upper, equatorial and divertor regions of the vacuum-vessel (VV). Due to restricted visibility conditions, all these RH tasks require the use of advanced Supervisory Control Systems able to provide operators with efficient virtual reality representation of the environment and context-based assistances, optimizing operations effectiveness, reliability and safety. Complexity and diversity of maintenance tasks require the use of a large set of RH equipment supervised from a control room by human operators organized in work cells. It would be highly inefficient to develop specific supervision systems for each task or equipment. This work thus aims at providing a single formalism and tools to define in a generic way ITER maintenance tasks and scenarios for in-vessel and hot cell operations.

The formalism proposed in this paper is based on three levels defining the actions opportunities available in the environment, the high-level functionalities built on these physical actions and the interactions modes required to achieve these functionalities. This The remainder of this paper is as follows. The Section 2 details the interactions in the ITER RH control room. The Section 3 presents the descriptive model of the environment based on three levels: actions, behaviours and interaction modes. The Section 4 presents applications of this model through the definition of context-based assistances and an illustrative example for the case of Blanket Remote Handling System.

Interactions in the ITER RH control room

The ITER RH control room is composed of at least six work cells working in parallel and one supervisor station [START_REF]ITER Remote Handling High-Level Control System White Paper[END_REF]. Each work cell is composed of four operators supervising the process. Different types of interactions are bound to occur in the RH control room between people in charge of the process.

Supervision of such complex systems requires different types of interactions depending on the role of the human operator. In the ITER context, the roles of supervisor and operator are identified in the RH control room. The supervisor is in charge of supervising the activity of the control room and coordinating the work cells. The operators are in charge of performing the maintenance tasks with master-slave teleoperation systems.

Cross-scale interactions must be taken into account, that is to say interactions are to be defined between the operators of the same work cell, between the operators and the supervisor and finally between the work cells (Fig. 1). Vertical interactions correspond to the interactions that exist between the supervisor and the operators in the control room. Horizontal interactions correspond to the interactions between operators in the same work cell or between different works cells. These interactions require different forms (written, verbal or computer-supported) and different types of information (joints positions, speed, task progress...) according to the current interaction mode.

The ITER RH operations involve multiple parallel, relatively independent activities carried out by the RH work cells [START_REF]Annex B -High-Level Control System Specification[END_REF]. Maintenance operations in the hot cell can involve different work cells in parallel, working on different equipment and components. A failure in one work cell may thus require shifting from a work cell to another one in order to ensure continuity of the maintenance task. Moreover, the activity of the supervisor station is achieved constantly and in parallel with the activity of the operators' stations.

Shared situation awareness is likely to emerge in the control room via all these interactions. Team processes and communication methods must be implemented to facilitate a shared understanding among the team. A well-known model of situation awareness (SA) is proposed by Endsley [START_REF] Endsley | Automation and situation awareness[END_REF] and introduces three levels: the perception of information in a finite volume in time and space (SA1), the understanding of their signification (SA2) and the projection of the system state in the future (SA3).

This paper will illustrate later to what extent the model detailed in the next section and the context-based assistances can improve the operator SA.

Three-layered model for the description of ITER maintenance tasks

Definition of the three-layered model

A three-layered approach is proposed to model the maintenance tasks. This model aims at describing all the potential actions required for the maintenance scenarios in the ITER context (transfer, in-vessel and hot cell operations). The objective is to provide a generic framework in order to avoid the development of specific supervisory control applications for each maintenance task.

The first level of this framework defines the available operations via physical interfaces which are attached to the scene elements. Description of the scene with these interfaces provides a functioncentred model of the environment. Interfaces shall provide physical data to enable actions between elements of the scene according to the operator's needs and to the task requirements (Fig. 2). Interfaces are defined with the following data: type of action, gender of interface and availability in order to check compatibility, position on the object and tolerances to locate the interaction area, approach position and inclusion constraints to enable correct positioning. All these data allow defining precisely the location and the modalities of every potential physical interaction with an object. Interfaces offer learning perspectives for the remote handling system, the operator being able to teach the automated system some new tasks. Such a unified representation for the elements of the scene also facilitates the planning activity for the human operator and its intervening activity by allowing simple modifications of the original action plan.

The second level of the framework is drawn from these physical actions and corresponds to behaviours which are defined to represent high-level functionalities. Behaviours correspond to the logical link between interfaces of two or more objects. They can be initiated provided that there is complementarity between the interfaces. Complementarity is assessed by logical rules on the interfaces data to determine if interaction is possible and to enable the activation of the required behaviour. Learning of the rules which lead to the activation of behaviours is a part of the supervisory control activities for both the human operator and the machine agent.

Initiation, execution and stopping of the behaviours are ruled by the third and last level of the framework in terms of interaction modes. Four interaction modes can be defined based on the modes of autonomy defined in [START_REF] Zieba | Using adjustable autonomy and human-machine cooperation for the resilience of a human-machine system -application to a ground robotic system[END_REF]:

• Mode 1: Manual mode.

• Mode 2: Supervised control mode under the authority of the human operator.

• Mode 3: Autonomous control mode under shared authority (the human operator has a limited amount of time to validate or cancel actions proposed by the system before automatic execution).

• Mode 4: Fully autonomous mode without operator intervention.

These modes shall be dynamically adjusted in case of unplanned situations (human errors, technical failures, environmental disturbances). Automatic adjustment of the interaction mode should only be possible in modes 3 and 4. According to the design of the Operations Management System (OMS), maintenance procedures are hierarchically decomposed into tasks, subtasks, methods and steps [START_REF]Annex B -High-Level Control System Specification[END_REF]. Interaction modes can be set at the level of methods and thus define the task allocation between the human operator and the system for each step of the method.

For instance, for the step of the blanket maintenance procedure concerning the flexible support bolts unbolting, the following task allocation can be proposed:

• Mode 1: no action is initiated by the system; the operator is in charge of everything.

• Mode 2: the operator validates every step of the unbolting (by selecting the starting and end poses for the motion and checking correct positions); the motion and the unbolting are achieved automatically by the system.

• Mode 3: the system selects starting and end poses based on the task procedure, then computes and displays possible alternatives for the proposed motion and finally selects one of them; the operator is given a limited amount of time before the automatic execution of these steps.

• Mode 4: the operator only validates the initiation of the procedure; information about progress is displayed.

Table 1 summarizes the contributions offered by the descriptive model and the context-based assistances to the supervisory control application. The objective is to improve the activities in supervisory control as defined by Sheridan: planning, teaching, monitoring, intervening and learning [START_REF] Sheridan | Human supervisory control[END_REF]. Some of these contributions concern the improvement of the operator's SA according to the three levels defined by Endsley [START_REF] Endsley | Automation and situation awareness[END_REF]. Indeed, SA must be guaranteed at all times for the operator, that is to say, the operator must know the actions he has to achieve and the actions that remain under the authority of the machine.

Integration of the three-layered model in the ITER RH control system architecture

The objective of the three-layered model is to propose advanced supervision functionalities that can be applied not only to ITER and the existing modules of the High-Level Control System (HLCS) but also to other domains of application. These functionalities include autonomy and procedure management, context-based assistances and management of human-machine interactions. In the ITER context, the proposed model should mainly interact with two elements of the HLCS: the Supervisor System and the OMS (Fig. 3).

The Supervisor System acts to provide a high level view of the status of work cells and the progression of the tasks [START_REF]System Requirement Document (SRD) for PBS 23-07 -Remote Handling Control System[END_REF]. It shall provide features such as the communication with Control, Data Access and Communication system (CODAC), a graphical chart of work cell tasks with clear indications of interactions between work cells and live tracking of the work cells task progress including the possibility to issue high-level commands. The OMS is a system for creating and re-playing procedures written in an unambiguous natural language [START_REF]System Requirement Document (SRD) for PBS 23-07 -Remote Handling Control System[END_REF]. It shall provide features such as the management of equipment, tools and components required for tasks and the flexibility to suspend tasks or switch to other tasks.

Cooperation can be initiated between operators in a same work cell or between different work cells (Fig. 1). HMI of the workstation must clearly identify the tasks of each work cell and the planned interactions in the procedure. Dynamic adjustment of the interaction mode and proposal of context-based assistances are ensured by the behaviour and the mode managers. These functionalities aim at being added in the OMS and the Supervisor System. Other blocks of the proposed model have to communicate with HLCS modules such as Virtual Reality Visualization and Computer Assisted Teleoperation so as to display and use context-based assistances and required behaviours.

The next section is devoted to illustrative examples of this model: the definition of context-based assistances and the description of the ITER Blanket module maintenance procedure.

Context-based assistances for RH maintenance tasks and application to the ITER Blanket module maintenance

Context-based assistances for maintenance tasks

Context-based assistances shall be provided to the operators for different maintenance tasks. Examples of such assistances are being implemented in SCORE, which is the current version of MAGRITTE, a supervisory control application developed at CEA-LIST for several years [START_REF] Leroux | MAGRITTE: a graphic supervisor for remote handling interventions[END_REF]. This application is based on the communication between Master and Slave controllers of a classical teleoperation system with force feedback and fusion of virtual and real data. SCORE updates MAGRITTE by integrating a real-time physics engine named XDE [START_REF] Merlhiot | The xde physics simulation kernel[END_REF] (developed at CEA) which allows performing accessibility simulation, simulation for operators training and assistances to the operators such as collisions avoidance or haptic virtual guides. SCORE design makes the algorithmic part independent from the visualization part. SCORE can thus be interfaced to different human-machine graphical interfaces such as the Solidworks CAD environment via specific APIs for virtual reality visualization of the scene. Visual assistances consist in displaying the available actions in the environment. When a procedure step is selected by the operator, the system can display the interfaces which are compatible in the environment. Augmented reality is useful in this case to display relevant information in the field of view of the operator by overlaying the virtual reality visualization for instance. Objective of such assistances is thus to improve the operator's SA by relieving the workload for perception of relevant information in the environment and understanding of this information.

Virtual guides are used to restrain degrees of freedom in order to facilitate the achievement of actions. The objective is to release the operator from the complete control of the motion. Virtual guides are implemented according to two phases: an approach phase and an interaction phase as an example can be seen in the Fig. 4 for an operation of tool clamping. Augmented reality is also relevant for such haptic assistances. Indeed, a transparent representation simulating the object motion that is to be achieved with the virtual guide can be displayed in the virtual reality visualization to help the operator understand the assistance.

Application to the ITER Blanket module maintenance procedure

ITER Blanket maintenance procedure (Fig. 5) is a relevant illustrative example for the application of the proposed formalism. This RH task is described in [START_REF]Design Description Document: Remote Handling Equipment, Chapter 3: Blanket Remote Handling Equipment[END_REF] and is composed of 13 subtasks. For the purpose of this paper, only parts of two subtasks -the installation of in-vessel transporter (IVT) inside the VV and the blanket module removal -are detailed (Table 2). They give an overview of different tasks that can be defined using the three-layered model and the context-based assistances.

Blanket remote handling requires a combination of sequential and parallel activities, the supervisor station being in charge of coordinating these different tasks. Coordinated motions of the rail deploying equipment and the vehicle manipulator are required during the rail deployment procedure. Monitoring of the rail deformation can be achieved in parallel with the maintenance operations such as bolting and cutting in order to prevent any deviation from correct position. This coordination shall be monitored by 2 different work cells or by 2 operators within the same work cell, which could avoid latencies in communication.

Communication and coordination between the work cells must be provided in order to ensure natural transitions between the tasks. The supervisory control system must be able to provide to the operators the most relevant actions which are available in the environment according to the required point of view; that is to say, operator on a specific task or supervisor of the global process. This part of coordination process is directly linked with the OMS functionalities, which can be augmented by taking into consideration dynamic adjustment of interaction modes according to the context.

Conclusion and perspectives

A three-layered model is proposed in this paper to describe tasks of remote handling maintenance in a generic way allowing the definition of context-based assistances. Future works on the proposed model will focus on a more complete definition of the interaction modes for the task allocation between the human operator and the system. Proposals made in this paper will have to be assessed via an experimental campaign which will compare remote handling tasks without and with assistances for performance criteria such as completion time, collisions, accuracy or number of errors in the procedure.

Perspectives concerning advanced assistances shall be related to the development of an intention recognition module. The objective of intention recognition is to relieve the operator mental workload, that is to say the factors that are to be expanded to perform the required task, by computing the next actions to be performed based on situation analysis. Relevance of this intention recognition module regarding the operator workload shall be assessed by subjective and performance-based techniques. Perspectives also concern collaborative work that is to be carried out in the context of the EFDA GOT RH programme. Theoretical and applied exchanges centred on the concept of haptic shared control [START_REF] Abbink | Haptic shared control: smoothly shifting control authority?[END_REF] shall take place in the continuity of the project. Merging intention recognition and haptic shared control is likely to offer perspectives in terms of assistances which shall contribute to the improvement of effectiveness and reliability of maintenance operations in ITER and other application domains.

Fig. 1 .

 1 Fig. 1. Interactions in the Remote Handling Control Room. adapted from [1]. three-layered model is used to propose context-based assistances to the operator for heterogeneous robotic tasks. The remainder of this paper is as follows. The Section 2 details the interactions in the ITER RH control room. The Section 3 presents the descriptive model of the environment based on three levels: actions, behaviours and interaction modes. The Section 4 presents applications of this model through the definition of context-based assistances and an illustrative example for the case of Blanket Remote Handling System.

Fig. 2 .

 2 Fig. 2. Definition of interfaces on the scene elements.

Fig. 3 .

 3 Fig. 3. Integration of the three-layered model in the HLCS architecture.

Fig. 4 .

 4 Fig. 4. Illustration of virtual guides for clamping operation.

Fig. 5 .

 5 Fig. 5. Blanket Remote Handling System. Credit: ITER Organization. http://www.iter.org.

Table 1

 1 Contributions and applications of descriptive model and context-based assistances to maintenance tasks.

	Activities of	Descriptive model	Context-based assistances	Application to maintenance tasks
	supervisory control
	Planning	Ability to plan heterogeneous robotic	Improvement of level SA3	Determine transitions between work
		tasks via the common description of	Display projected changes	cells and minimize inactivity time
		available actions
	Teaching	Improvement of the model	Improvement of level SA2	Definition of operations for equipment,
		Add new interfaces dynamically to	Instruct new actions opportunities in	tools and components
		increase functionalities	the environment
	Monitoring	Function-centred representation	Improvement of level SA1	Common view for the work cells of the
		allows an easy transfer from	Reduced workload and time for	task progress
		descriptive model to implementation	situation understanding
		in the environment
	Intervening	Easy and quick method to define online	Improvement of level SA2	Adjustment of interaction modes in
		modifications of the action plan	Reduced workload and time for	case of unexpected event
			decision-making
	Learning	Predict actions of the system with the	Improvement of level SA3	Training of operators with simulation
		function-centred representation model	Learn reasoning of the system	models

Table 2

 2 Application of the three-layered model to Blanket Remote Handling.

	N o .	Subtask description	Methods	Steps	Interfaces	Behaviours	Possible interaction	Context-based
							modes	assistances
	3	Installation of IVT	IVT system	Load RH cask	Interfaces defined	Load	Manual validation of	Procedure following
		inside the VV	transport by RH	Seal RH cask	on cask and port	Seal	steps completion and	Virtual guides for
			cask	Move IVT system	plugs for sealing	Move	automatic sealing	motion tasks
				from hot cell to VV	and transfer		and motion
					operations		Or
							Automatic validation
							of each step
	5	Blanket module	Flexible support	Grasp unbolting	Interfaces defined	Grasp	Automatic	Procedure following
		removal	bolts unbolting	tool	on tool for grasping	Move	achievement of steps	Virtual guides
				Move to flexible	Interfaces defined	Unbolt	Or	Highlight next action
				support bolts	on tool and bolts	Move	Manual achievement	Highlight relevant
				Unbolt flexible	for bolting	Release	of steps	object for bolt
				support bolts	Interface defined		Or	selection
				Move to RH cask	on RH cask and tool		Automatic motion
				Release unbolting	for tool releasing		and manual
				tool			achievement of other
							tasks
	excerpt adapted from [9].

Acknowledgments

This work was carried out under the EFDA Goal Oriented Training Programme (WP10-GOT-GOTRH) and financial support of CEA, which are greatly acknowledged. The views and opinions expressed herein do not necessarily reflect those of the European Commission.