Jitendra Singh Rathore

Chetra Mang

Caroline Vienne

Yann Quinsat

Christophe Tournier

A methodology for CT based non-destructive geometrical evaluations of lattice structures by holistic strut measurement approach

Keywords: Lattice structure, non-destructive evaluation, X-ray computed tomography, point cloud, strut

The presence of lattice structures is increasing in the manufacturing domain especially in the air/spacecraft and biomedical applications due to their advantages of high strength-to-weight ratios, energy absorption, acoustic and vibrational damping, etc. Dimensional accuracy of a lattice structure is one of the most important requirements to meet the desired functionality as there could be significant deviations in the asproduced part from the designed one. Evidently, an approach (non-destructive) to evaluate the dimensional accuracy of all the elements and eventually the lattice quality is of great significance. X-ray computed tomography (CT) has emerged as a promising solution in the field of industrial quality control over the last few years due to its non-destructive approach. In this work, we propose a methodology for geometrical evaluations of a lattice structure by measuring the deviation in the shape and size of its strut elements holistically. The acquired CT data of the complete lattice is extracted in the form of a point cloud and then segmented and stored as a single strut element with unique identification so that measurements can be performed on the strut individually. As demonstrated with a metallic BCCz type lattice structure, the methodology helps in critical evaluation of its quality and the correlation with spatial position of the individual struts; e.g. the lattice exhibits large variations of shape among the inclined struts while the vertical struts possess consistency in their shape.

Introduction

Lattice structures are defined as a periodical arrangement of unit cells interconnected in three dimensional (3D) space. Thanks to the advancements in manufacturing, mainly additive manufacturing (AM) these structures have become very prominent in recent times due to their number of advantages including optimum use of material, shorter manufacturing time, reduced energy utilization and enhanced mechanical properties [START_REF] Helou | Design, analysis and manufacturing of lattice structures: an overview[END_REF][START_REF] Thompson | Design for additive manufacturing: Trends, opportunities, considerations, and constraints[END_REF]. These advantages make the lattice structures very suitable for high-value aerospace (lightweight thermal controller), biomedical (implants), and engineering applications, more details about the application can be found in [START_REF] Maconachie | Slm lattice structures: Properties, performance, applications and challenges[END_REF][START_REF] Calignano | Design of additively manufactured structures for biomedical applications: a review of the additive manufacturing processes applied to the biomedical sector[END_REF]. Furthermore, they are also advantageous in context to the entire product life cycles, e.g., lattice structures are particularly beneficial in minimizing material waste [START_REF] Williams | Additive manufacturing of metallic cellular materials via three-dimensional printing[END_REF] and can be recycled easily, particularly when comprised of a single material. There are various types of lattice structures based on the composition of their unit cells. Helou et al. [START_REF] Helou | Design, analysis and manufacturing of lattice structures: an overview[END_REF] categorized most of the lattice structures as manually and mathematically generated structures. In many cases of additive manufacturing, the unit cell is composed of well-organized struts in various forms such as octet-truss, body-centered cubic (BCC), body-centered cubic with z struts (BCCz), face-centered cubic (FCC), face-centered cubic with z struts (FFCz), etc. [START_REF] Leary | Inconel 625 lattice structures manufactured by selective laser melting (slm): mechanical properties, deformation and failure modes[END_REF], which are represented in Fig. 1.

The lattice structure should possess good dimensional and geometrical quality to meet the desired mechanical performance of the part. The additive manufacturing processes (especially for metallic structures) induce a lot of geometrical irregularities such as surface deviations, roughness, and waviness, etc. especially with metallic materials [START_REF] Leach | Geometrical metrology for metal additive manufacturing[END_REF]. The surface can be controlled to a certain extent with post-processing methods [START_REF] Lhuissier | Geometrical control of lattice structures produced by ebm through chemical etching: Investigations at the scale of individual struts[END_REF] but the geometrical characterization of the struts is extremely important to predict their mechanical properties as demonstrated in [START_REF] Suard | Mechanical equivalent diameter of single struts for the stiffness prediction of lattice structures produced by electron beam melting[END_REF], where an equivalent diameter of a single strut was proposed for the stiffness prediction. Kadirgama et al. [START_REF] Kadirgama | Statistical and optimize of lattice structures with selective laser melting (slm) of ti6al4v material[END_REF] used X-ray computed tomography (X-ray CT or CT) based global comparison for evaluating the dimensional accuracy of the lattice. In most of the work, they use either a representative strut element or a global deviation but there is a lack of geometrical evaluation of the lattice considering all its strut elements, which can be crucial when correlating the geometrical accuracy with process parameters and mechanical responses. The behavior of strut elements within a lattice can be different due to the fact that their relative position and orientation with respect to the build direction are different, which makes it difficult to generalize their behavior based on a single strut or a global comparison.

As regards measuring technology, X-ray CT is the most suitable for analyzing lattice structures since classical optical and mechanical (probe-based) measurement systems suffer from very limited third-dimensional range and reach-ability to the complex feature respectively. X-ray CT is a computer-aided non-destructive technique (NDT) that uses irradiation to produce 3D internal and external representations of a scanned object [START_REF] Kruth | Computed tomography for dimensional metrology[END_REF][START_REF] Hermanek | Principles of x-ray computed tomography[END_REF]. X-ray CT scanning has been used in many areas of industry for various quality aspects such as flaw detection, failure analysis, metrology, assembly analysis, and reverse engineering applications [START_REF] Gorji | A new method for assessing the recyclability of powders within powder bed fusion process[END_REF][START_REF] Saxena | Soft tooling process chain for the manufacturing of micro-functional features on molds used for molding of paper bottles[END_REF][START_REF] Saxena | Process characterization for molding of paper bottles using computed tomography and structure tensor analysis[END_REF][START_REF] Rathore | Investigation on tomographic-based nondestructive characterization of short glass fiber-reinforced composites as obtained from micro injection molding[END_REF]. Thompson et al. [17] have highlighted the advancements of CT including novel porosity measurements, artifact development, and hybrid dimensional measurements, which make CT a preferred solution for quality assessment of AM parts. Van Bael et al. [START_REF] Van Bael | Microct-based improvement of geometrical and mechanical controllability of selective laser melted ti6al4v porous structures[END_REF] utilized X-ray CT for optimizing the robustness and controllability of the production of porous Ti6Al4V structures produced by Laser Powder Bed Fusion (LPBF) [START_REF]Additive manufacturing -general principles -terminology[END_REF] by reducing the mismatch between designed and as-produced morphological and mechanical properties. Yan et al. [START_REF] Yan | Evaluations of cellular lattice structures manufactured using selective laser melting[END_REF] revealed with the help of micro CT that the gyroid cellular lattice structures with various unit cell sizes ranging from 2 to 8 mm can be manufactured free of defects by LPBF without the need of additional support structures. It is demonstrated in [START_REF] Kim | Additive manufactured porous titanium structures: Through-process quantification of pore and strut networks[END_REF] that micro CT provides not only 3D quantification of structure quality but also a feedback mechanism, such that improvements to the initial design can be made to create more stable and reliable titanium structures for a wide variety of applications. Researchers [START_REF] Bauza | Study of accuracy of parts produced using additive manufacturing[END_REF][START_REF] Moylan | Progress toward standardized additive manufacturing test artifacts[END_REF] have also studied the accuracy of CT measurement of AM parts using a test artifact. As reported in [START_REF] Pyka | Surface modification of ti6al4v open porous structures produced by additive manufacturing[END_REF][START_REF] Kerckhofs | Highresolution microfocus x-ray computed tomography for 3d surface roughness measurements of additive manufactured porous materials[END_REF], they used X-ray CT for surface topography measurement, by extracting profiles from the slice data obtained from measurement of lattice struts. Furthermore, a more extensive examination of CT based surface topography measurement performance in comparison to conventional optical surface measurement was reported in [START_REF] Zanini | Characterisation of additively manufactured metal surfaces by means of x-ray computed tomography and generalised surface texture parameters[END_REF][START_REF] Thompson | Topography of selectively laser melted surfaces: a comparison of different measurement methods[END_REF][START_REF] Townsend | Investigating the capability of microfocus xray computed tomography for areal surface analysis of additively manufactured parts[END_REF]. It is evident that X-ray CT can be used for extracting surface topography, dimensional measurements, and geometrical deviation in context to AM parts.

In this work, we present a CT-based general methodology to assess both the global and local quality of a lattice structure by means of strut-by-strut evaluations, which leads to identifying the geometrically critical aspects of lattices and the influence of the relative position and orientation on the strut geometry. The raw data is acquired with an X-ray CT system with optimized scanning parameters, which undergoes several processing steps to ensure a robust measurement approach. The paper is organized as follows: first, the methodology is explained step-wise including the data acquisition, data processing, indexing, and measurement approach. Secondly, a case study is presented with an Inconel 718 based BCCz lattice structure produced by additive manufacturing with results obtained with the methodology followed by discussions. The paper is concluded with a summary of the major findings of the study and future work.

Methodology

This section describes the proposed methodology with a generalized approach applicable to different types of lattice structures, which consist of an arrangement of unit cells of several interconnected cylindrical strut elements. The commonly used unit cells are BCC, BCCz, FCC, and FCCz which are shown in Fig. 1. The methodological procedure from data acquisition to measurement will be explained in detail in the next sections. X-ray CT is a very extensive measurement technique that involves several steps for performing the requisite task [START_REF] Hermanek | Principles of x-ray computed tomography[END_REF] and whose result depends on factors related to the system, object, data processing, environment as well as the operator as explained in [START_REF] Villarraga-Gómez | Dimensional metrology with x-ray ct: a comparison with cmm measurements on internal features and compliant structures[END_REF].

During the scanning procedure, the part is placed between an X-ray source and a 2D detector and several hundreds of projections are recorded while the part is rotated. The cone shape of the X-ray beam allows different magnification and thus different spatial resolution with the same material. The closer the part is placed to the source, the higher the resolution (lower voxel size) is achieved, the best achievable resolution being relative to the size of the part. Indeed, for reconstructing the whole part with the best quality, all the object has to project inside the field of view of the detector. The quality of the CT result depends on the selection of the scanning parameters (current, voltage, exposure time, etc.), which need to be optimized considering the size, geometry, and the material of the part as explained in section 2.6.1. The voltage and the current of the X-ray tube influence the energy of X-rays and the flux (number of photons) respectively. All the projections are then acquired with those optimized parameters [START_REF] Kruth | Computed tomography for dimensional metrology[END_REF].

Point cloud extraction

The acquired projections are processed through a reconstruction algorithm to obtain 3D volumetric data. The most widely used filtered back-projection approach based FDK (Feldkamp, Devis, and Kress) algorithm is utilized [START_REF] Feldkamp | Practical cone beam algorithm[END_REF][START_REF] Lauritsch | Theoretical framework for filtered back projection in tomosynthesis[END_REF], which has the advantage of much lower computation time compared to other techniques. The next step is the surface determination of this volume, which consists of identifying the limit between the object and the background. This surface determination is performed using the ISO-50% method that defines the surface at the mean of the average material grey value and average background grey value, which is a global method and offers better reproducibility.

The volume is then registered in the 3D scene in such a way that the x-y plane represents the building plane (BP) the z-axis represents the building direction (BD).

Then, the volumetric dataset of the lattice is exported in the form of a point cloud. This raw point cloud is post-processed to segment all the strut elements and obtain a separate point cloud as explained in the next section.

Segmentation

The segmentation process is done by superimposing a regular pattern of the strut elements in the lattice structure. The pattern admits the classification of the strut elements by categorizing them into groups termed as families. The family is defined as a group of struts following a set pattern which generalizes their segmentation from the lattice structure. There are three types of families identified as a strut-type family (F B ) or cell-type family (F C ) and node family (F N ), where the first two contain different strut elements and the last one contains the nodes (the nodes are the positions where the strut elements intersect). In BCCz type lattice, there are two categories of struts where the vertical strut belongs to the strut-type family as they need to be extracted individually while the inclined strut belongs to the cell-type family as they are extracted cell-by-cell. Followed by the surface determination step (explained later in section 2.6.2), the raw point cloud of the lattice surface is obtained which is treated further with distinct approaches for achieving strut-type family or cell-type family. The process of point cloud extraction for the strut-type family is directly performed by storing each strut point cloud from the bounded box with the unique indexing of each strut as detailed in the following section. As depicted in Fig. 2, three operations are performed for the cell-type family as follows: firstly, the cell point cloud is extracted using the cell bounded box and is indexed for each individual cell. Secondly, each strut point cloud within the cell (obtained from the first step) is extracted using the strut bounded box and is indexed uniquely. As the last step, each strut point cloud is vertically rotated for the measurement process. The rotation angle is given by either a nominal direction of each strut where determined by the direction of cylindrical fitting of the strut point cloud.

Indexing Strategy

The indexing strategy is performed for a general lattice structure with N families of F B,i , i = 1, ..., N , M families of F C,i , i = 1, ..., M and a node family. In each of F B,i , the struts are designated with three indices ([ib 3 ][ib 2 ][ib 1 ]) which define their positions in the lattice structure coordinate frame. Equivalently, for the node family, the nodes are indexed by

[in 3 ][in 2 ][in 1 ]. On the other hand, for each F C,i , the designation of struts consists of six indices ([ic 3 ][ic 2 ][ic 1 ][ib 3 ][ib 2 ][ib 1 ]
), where the first three indices correspond to the cell position which is defined in the structure coordinate frame and the last three indices correspond to strut position corresponding to the cell coordinate frame.

Measurement approach

Based on the previous steps, all the strut elements are now extracted from the lattice, assigned a unique identification, and stored individually for further treatment. Strut-type and cell-type families can be handled with the same measurement approach, but the node family needs to be treated separately. Depending on the requirements, different measurement attributes can be assigned to the strut elements for their geometrical quality assessment. In this work, we present an example of a simple projection based fitting method where each individual strut point cloud is projected on a plane orthogonal to the vertical axis. The projection points are then fitted by an ellipse fitting method as illustrated in Fig. 3. The method is based on the work of Fitzgibbon et al. [START_REF] Fitzgibbon | Direct least squares fitting of ellipses[END_REF] which utilizes the direct least-square fitting to obtain fast-fitting for the projected point cloud of the strut to an ellipse point set. We obtain the measurement of each strut in the form of the (semi) major axis, (semi) minor axis, and the least square error E of the elliptical fitting.

The measurement data is stored systematically according to the two families of indexing (vertical and inclined struts). The data is used to perform further statistical analysis to be able to observe the quality of each strut and more importantly to understand the overall behavior of the lattice structure. For instance, the spatial classification of the groups of struts according to their section quality. The explained methodology is summarized schematically in Fig. 4. The application of the methodology and use of measurement data for statistical analysis are demonstrated in the next section.

Application on a metallic lattice structure

The methodology was applied on an Inconel based lattice structure produced from the LPBF additive manufacturing process on an EOS 290 machine. The lattice structure is in a form of an isometric cube with an equal number of unit cells in all three 1b). The vertical struts are shared among four neighboring unit cells whereas the inclined struts are entirely part of one unit cell. The struts of the lattice are designed as identical solid cylindrical elements with a nominal strut diameter of 1 mm. The material of the lattice is Inconel 718 with a density of 8.47 g/cm 3 . The two common configurations of the lattice structure are 5 × 5 × 5 and 3 × 3 × 3 with five and three unit cells in each direction respectively as shown in Fig. 5a; however, only the latter is discussed in this work. Fig. 5b presents the nominal dimensions of the lattice grid.

Data acquisition with X-ray CT

The tomographic acquisitions have been carried out using a Viscom XT 9225D

micro-focus open X-ray tube, with a maximum voltage of 225 kV and a maximum power of 320 W , as illustrated in Fig. 6. The detector is a matrix of photodiodes with CsI scintillator, brand Perkin Elmer, model XRD 0822, having 1024 × 1024 pixels of 200 µm. The lattice is placed between the source and the detector on the rotary stage and the projections are acquired for complete 360 • rotation.

In order to find out the right set of scanning parameters for the Inconel (3×3×3) lattice structure, the transmission-based approach was utilized which states that a minimal transmission between 10% and 20% is required to reach an optimal signal-to-noise ratio (SNR) [START_REF] Rathore | Influence of resolution on the xray ct-based measurements of metallic am lattice structures[END_REF][START_REF] Kraemer | Projection based evaluation of ct image quality in dimensional metrology[END_REF]. The transmission is the ratio between the minimal and the maximal X-ray intensity at the detector, which is expressed in the respective grey values of the X-ray projection. For performing the optimization of scanning parameters, the radiography module of NDT simulation software CIVA ® developed by CEA [START_REF] Civa | The simulation and analysis platform for nde[END_REF] was used. Simulated radiographs were acquired at different settings on voltage, current, and filter thickness following a design-of-experiment approach. The minimum, maximum grey levels of the radiograph and their ratio were examined and the parameters satisfying 200 the above-mentioned minimal transmission criteria were chosen. The final optimized parameters for the Inconel 718 metallic lattice structure of 3 × 3 × 3 configuration are provided in Table 1 as "LR-CT".

Data processing and preparation

The obtained projections are processed to reconstruct the lattice volumetric dataset,

205
which is in turn processed with surface determination to obtain the raw point cloud of

Measurement qualification

The measurement qualification approach allows having an insight into the accuracy of the CT measurements as compared to a reference measurement obtained from other measuring techniques. Optical profilometer based measurements have shown a good measurement uncertainty in [START_REF] Thompson | Topography of selectively laser melted surfaces: a comparison of different measurement methods[END_REF][START_REF] De Pastre | Polymer powder bed fusion surface texture measurement[END_REF][START_REF] Townsend | Surface texture metrology 515 for metal additive manufacturing: a review[END_REF][START_REF] Senin | Characterisation of the topography of metal additive surface features with different measurement technologies[END_REF]; hence, it is utilized for our reference measurement. Individual strut elements were measured with an Alicona optical profilometer with an objective of 10X. The struts from the center cell (cell designation: 111) were cut precisely from a 3 × 3 × 3 lattice structure using Electrical Discharge Machining (EDM) process. Then, the individual strut elements are extremely small in size, so they were embedded in resin for better handling during CT scanning. Compared to previous CT acquisition of the complete part, new parameters are defined (in Table 1 as "HR-CT") and a higher resolution can be achieved when measuring a single strut. While the voxel size was 38 µm for the lattice scanning, the voxel size is reduced to 10 µm. The corresponding point clouds were registered with the widely used Iterative Closest Point (ICP) algorithm in CloudCompare opensource software [START_REF]CloudCompare, 3d point cloud and mesh processing software open source project[END_REF] which minimizes the difference between there two clouds of points. After the registration, each point on the CT (measured) point cloud has a corresponding point on the Alicona (reference) point cloud which is defined by the shortest distance, and the remaining points are termed as non-corresponding points. The cloud-to-cloud (C2C) distance function is utilized to compute the distance from the measured point cloud relative to the reference point cloud with a height function (quadric) computed on all the neighbors falling in a sphere of specified radius around each point of comparing point cloud. The results are presented in Fig. 10 where part a and b show the C2C distances obtained on the CT point cloud when compared against the Alicona (as reference) for HR and LR respectively, which is indicated as the relative error in the CT measurements. The mean errors are 8 µm and 12 µm for a voxel size of 10 µm (HR-CT) and 38 µm (LR-CT) respectively; which is relatively smaller with an approximate increment of 1 µm per 10 µm voxel size increment. The higher standard deviation is resulted due to the higher skewness on the measured distances. Furthermore, the projection-based ellipse fitting results provide very good agreement with the Alicona measurement as visible in Fig. 11; the numerical information of all three point clouds is listed in Table 3. Nevertheless, it is understood that the projection-based measurement results in the loss of variability along the strut axis, which can be studied by assigning other measurement attribute to the strut elements.

Results and discussions

The measurement results of the 3×3×3 lattice structure obtained from the proposed methodology are presented and discussed in this section. The lattice structure consists of three identical layers printed in a continuous manner over to each other which are termed as the bottom layer, middle layer, and top layer; however, each layer has two levels (ibz = 0 and ibz = 1) of inclined struts.

Global measurement

The global deviations of the manufactured lattice structure compared to its nominal geometry give an overview of the quality of a part. The volumetric CT data can be compared with nominal geometry (CAD model) following a best-fit registration in VGStudio Max 3.0 and the results are included in Fig. 12. It can be seen in Fig. 12a, that inclined strut elements show a positive deviation (red) and negative deviation (blue) in the orthogonal direction, which indicate their tendency to an elliptical cylinder as

Measurement with the methodology

The ellipse fitting parameters (semi-major axis, semi-minor axis and least square error of fitting) have been obtained for all the strut elements in 3×3×3 lattice. Fig. 13a and Fig. 13b show the summary of these measurements for inclined and vertical struts respectively. In general, it can be concluded that the inclined struts exhibit a greater variability (longer range) and contrast (the difference between major and minor axes) in measured ellipse axes as compared to the vertical struts, which was also evident in the global comparison. Therefore, the vertical struts are closer to circular cylindrical shape as the difference between major and minor axes is very small with a mean of 0.03 mm as compared to 0.065 mm for inclined struts. These results are further elaborated to study the repeatability of the manufacturing process and statistical correlations.

Repeatability study

The periodicity of the lattice structures makes it possible to study the influences of the spatial position and orientation on the strut measurements thanks to the indexing strategy of the methodology. Fig. 14 and Fig. 15 present the measurement results of inclined struts, and Fig. 16 provides the results of vertical struts. Fig. 14 and Fig. 15 consist of two parts each where a is the minor axes and b is the major axes plots along x -z and y -z plane respectively. Each figure has three partitions corresponding to the bottom (blue), middle (red) and top (green) layers; each layer is further partitioned into two levels corresponding to the lower and upper cell levels. The circular marker represents the individual point and the mean value is represented by the colored solid Overall, the measurements of inclined struts show that the minor axis of ellipse fitting is very consistent throughout the lattice irrespective of the levels but the major axis exhibits variations within a level, which could be attributed to the negative surface with a higher roughness level. As depicted in Fig. 14b and Fig. 15b, the variations of major axis measurements within one level are comparatively higher along the y -z plane than that of x -z plane; however, the struts demonstrate good repeatability along the build direction (z) in the x -y plane. Generally, the mean value of the minor axis (0.49 mm) is closer to the nominal radius (0.50 mm) of the strut whereas the mean value of the major axis (0.55 mm) is considerably higher (the ratio of major and minor axes is 1.22), which results in a prominently elliptical shape of the inclined struts.

On the contrary to inclined struts, the vertical struts are more circular in shape as the semi-major and semi-minor axes are very close to each other as evident in Fig. 16. The mean value of the minor axis and major axis are (0.47 mm) and (0.50 mm) respectively which result in a more circular cylindrical shape (the ratio of major and minor axes is 1.06). The struts show a good consistency in their shape except slight deviations observed at the corner locations which was also evident in the global comparison in Fig. 16. On comparison of the three layers along the build direction, the overall repeatability seems to be very good in both the x and y directions.

Strut shape study

The ratio of the semi-major axis to the semi-minor axis can represent the deviation from a circular geometry (= 1), a higher ratio (> 1) means the ellipse gets flattened. The contour plots of the ratio have been obtained for inclined and vertical struts along the build direction of the lattice which are shown in Fig. 17 and Fig. 18. The indices have been combined for inclined struts in all three directions as icx -ibx, icy -iby, and icz -ibz which eventually have six levels (0 -0, 0 -1, 1 -0, 1 -1, 2 -0 and 2 -1) each considering the two levels within one cell and the original indices are used for vertical struts. As evident in Fig. 17, the central portion of each level experiences smaller deviations thus struts remain closer to a circular geometry and the deviations are increased in moving away from the center position towards the corners, where the highest deviations from circular geometry (bigger ratio) are observed.

Statistical study

A design-of-experiment scheme was generated based on spatial positions (indices) of the struts as factors and the measurements (ratio of major/minor axes) as a response variable. For inclined struts, the combination of two indices ic and ib was considered as one direction. Analysis of variance (ANOVA) was used to identify the significance of the spatial position on the morphology of the struts. The results are presented in the forms of Pareto charts for inclined and vertical struts in Fig. 19a and Fig. 19b respectively. The Pareto chart shows the absolute values of the standardized effects from the largest effect to the smallest effect. The standardized effects are the tstatistics which test the null hypothesis that the effect is 0. The chart also plots a reference line to indicate which effects are statistically significant. The reference line for statistical significance depends on the significance level (denoted by α) which equals to 0.05 with a confidence level of 95% for the analysis.

It can be seen from the charts, that the most significant direction affecting the ratio is along the Y -axis for both inclined and vertical struts. The interaction (Y • X) and X direction are also significant which indicates that the relative position in the x-y plane affects the strut geometry in addition to their respective x and y position. However, the effects are more prominent for inclined struts as the variation in the ratio for vertical struts has a very narrow range. As it has been demonstrated that the struts show good repeatability along the z direction, thus it resulted insignificant for both types of struts.

The model summary included in Table 4 interprets the goodness of the ANOVA fitting with high R 2 . The predictability is also very high for the model of inclined struts but limited for vertical struts.

Conclusions

A global approach for non-destructive evaluations of AM lattice structures is of great importance to predict their behavior under working conditions. Quantification of the deviations in desired geometry helps in tuning the manufacturing process parameters (direction of the laser, positioning of the lattice on the plate, the grain size of powder, and post heat treatment). Furthermore, the information achieved from such methodology can also be utilized for parametric modeling of the lattice and subsequently more realistic mechanical simulation. A generalized methodology for global non-destructive evaluations of lattice structures is presented in this work. Thanks to the strut-by-strut measurement approach, this methodology can be applied to various types of lattice structures. The robustness of this methodology can be attributed to the several steps especially the registration and the indexing of the lattice. The indexing strategy allows performing analytical observations of the struts with respect to their spatial position within the lattice structure. The same has been demonstrated with results obtained from a BCCz type metallic lattice structure of 3×3×3 configuration. All the struts have been divided into two categories as vertical and inclined. In an overview, the vertical struts exhibit minimal deviation from the nominal circular cylindrical geometry, while the inclined struts have a higher deviation from the nominal geometry resulting in an elliptical cylindrical shape. The measurements plots reveal that the struts show significantly high repeatability along the build direction despite local variation of the struts' shape within each z level. The contour plots of the ratio (semi-major/semi-minor) report the shape variation is extreme at the corners and reduces towards the center. The most significant direction affecting the shape of the strut is along the Y -axis for both inclined and vertical struts. The interaction (Y • X) and X direction are also significant which indicates that the relative position in the x -y plane affects the strut geometry in addition to their respective x and y position.

As demonstrated, the methodology provides both qualitative and quantitative information about the geometrical aspects of the lattice structure locally as well as globally. It helps in understanding the preferential occurrence of the geometrical deviations in the lattice building direction/plane. The measurement information can be very useful in optimizing the lattice manufacturing parameters which is envisaged in our future work. Further extension of the work is with numerically modeling the dispersion of the lattice structure which could lead to achieving more realistic mechanical responses.

List of Figures

The most common types of unit cell utilized in AM lattice structures . 2

Extraction of a strut in a lattice structure and the extracted strut has its 525 local coordinate system independent of the parent lattice structure . .

Figure 1 :

 1 Figure 1: The most common types of unit cell utilized in AM lattice structures

Figure 2 :

 2 Figure 2: Extraction of a strut in a lattice structure and the extracted strut has its local coordinate system independent of the parent lattice structure

Figure 3 :

 3 Figure 3: The strut measuring approach: individual strut point cloud (a), projection on orthogonal plane (b) and ellipse fitting (c)

Figure 4 :

 4 Figure 4: Schematic diagram of the methodology

Figure 5 :

 5 Figure 5: Inconel cubic lattice structures with two configurations (a) and the top view of 3 × 3 × 3 with the nominal dimensions (b)

Figure 6 :

 6 Figure 6: The set-up of X-ray CT acquisitions

38 10 Figure 7 :

 107 Figure 7: The data processing steps: projections (a), reconstruction and surface determination (b) and point cloud extraction (c)

Figure 8 :

 8 Figure 8: Indexing of inclined ([icz][icy][icx][ibz][iby][ibx]) and vertical struts ([ibz][iby][ibx])

Finally, there

  were three measurements (in the form of point clouds) of the same strut 111[111] which are: a. Optical reference measurement (Alicona); b. CT measurement of single strut scanned after cutting (HR-CT) and c. CT measurement of the strut extracted from the full lattice scan before cutting the lattice (LR-CT) as shown in the Fig. 9.

Figure 9 :

 9 Figure 9: Point clouds of a single strut obtained from optical measurement after cutting and from CT (scanned as a single strut after cutting and scanned as a full lattice structure)

  (a) HR-CT vs. Alicona mean = 7.946µm, std. dev. = 11.026µm (b) LR-CT vs. Alicona mean = 11.726µm, std. dev. = 12.079µm

Figure 10 :

 10 Figure 10: Histograms of C2C distances obtained by the comparison of CT and Alicona point clouds

Figure 11 :

 11 Figure 11: The projection of point clouds and the ellipse fit (the dimensions are in mm)

Figure 12 :

 12 Figure 12: Global deviation of lattice structure from the nominal geometry as obtained with best-fit registration and presented with 3D view (a), front view (b) and virtually sectioned central cell (c)

Figure 13 :

 13 Figure 13: The summary of the ellipse fitting measurements of all the struts consisting the mean and standard deviation

( a )Figure 14 :

 a14 Figure 14: The measurement results of inclined struts along x -z (individual standard deviations were used to calculate the intervals with 95 % confidence (CI))

Figure 15 :

 15 Figure 15: The measurement results of inclined struts along y -z (individual standard deviations were used to calculate the intervals with 95 % confidence (CI))

Figure 16 :

 16 Figure 16: The measurement results of vertical struts (individual standard deviations were used to calculate the intervals with 95 % confidence (CI))

Figure 17 :

 17 Figure 17: Contour plot of ratio (semi-major axis/semi-minor axis) for inclined struts (the X and Y axes correspond to the indices icx -ibx and icy -iby respectively)

Figure 18 :Figure 19 :

 1819 Figure 18: Contour plot of ratio (semi-major axis/semi-minor axis) for vertical struts

3

 3 The strut measuring approach: individual strut point cloud (a), projection on orthogonal plane (b) and ellipse fitting (c) . . . . . . . . . . . 4 Schematic diagram of the methodology . . . . . . . . . . . . . . . . 5 Inconel cubic lattice structures with two configurations (a) and the top 530 view of 3 × 3 × 3 with the nominal dimensions (b) . . . . . . . . . . 6 The set-up of X-ray CT acquisitions . . . . . . . . . . . . . . . . . . 7 The data processing steps: projections (a), reconstruction and surface determination (b) and point cloud extraction (c) . . . . . . . . . . . . 8 Indexing of inclined ([icz][icy][icx][ibz][iby][ibx]) and vertical struts 535 ([ibz][iby][ibx]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Point clouds of a single strut obtained from optical measurement after cutting and from CT (scanned as a single strut after cutting and scanned as a full lattice structure) . . . . . . . . . . . . . . . . . . . . . . . . 10 Histograms of C2C distances obtained by the comparison of CT and 540 Alicona point clouds . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The projection of point clouds and the ellipse fit (the dimensions are in mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Global deviation of lattice structure from the nominal geometry as obtained with best-fit registration and presented with 3D view (a), front 545 view (b) and virtually sectioned central cell (c) . . . . . . . . . . . . 13 The summary of the ellipse fitting measurements of all the struts consisting the mean and standard deviation . . . . . . . . . . . . . . . . 14 The measurement results of inclined struts along x-z (individual standard deviations were used to calculate the intervals with 95 % confi-550 dence (CI)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 The measurement results of inclined struts along y -z (individual standard deviations were used to calculate the intervals with 95 % confidence (CI)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 The measurement results of vertical struts (individual standard devia-555 tions were used to calculate the intervals with 95 % confidence (CI)) . 17 Contour plot of ratio (semi-major axis/semi-minor axis) for inclined struts (the X and Y axes correspond to the indices icx -ibx and icyiby respectively) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Contour plot of ratio (semi-major axis/semi-minor axis) for vertical struts 560 19 Pareto chart (α = 0.05) of ratio (semi-major axis/semi-minor axis) for inclined struts (a) and vertical struts (b) . . . . . . . . . . . . . . . .

Table 1 :

 1 CT data acquisition settings

	Factor	LR-CT HR-CT
	Voltage [kV ]	170	180
	Current [µA]	100	50
	Exposure time [s]	0.5	2
	No. of projections [-]	900	900
	Filter thickness (Cu) [mm]	0.6	0.6
	Voxel size [µm]

Table 3 :

 3 Measurement qualification

			X-ray CT
	Factor	Alicona	HR-CT LR-CT
	Resolution [µm]	2	10	38
	Number of points	131157	52773	4082
	Semi-major axis [mm]	0.623	0.611	0.611
	Semi-minor axis [mm]	0.485	0.482	0.478
	Least sq. error [mm]	0.0015	0.0016	0.0018

Table 4 :

 4 ANOVA model summary

	Strut type	S	R 2	R 2 (adjusted) R 2 (predicted)
	Inclined	0.0275291 91.32	85.07	74.08
	Vertical	0.0139572 89.42	72.37	24.76

Email address: jitendra-singh.rathore@hotmail.com (Jitendra Singh Rathore)

List of Tables


Khalil Aouadi
email: aouadikhalil@hotmail.com

Corinne Nouveau
email: corinne.nouveau@ensam.eu

Aurélien Besnard
email: aurelien.besnard@ensam.eu

Brahim Tlili
email: tlilii_brahim@yahoo.fr

Alex Montagne

Moez Chafra
email: chafra_moez@yahoo.fr

Characterization of CrAlN Films Synthesized by DC Reactive Magnetron Sputtering

Keywords: CrAlN coatings, Hardness, Friction coefficient, Wear

come   L'archive ouverte pluridisciplinaire

Introduction

For the past few years, chromium nitride coatings are widely used in various applications and especially for the protection of cutting tools. This is due to their good wear resistance, high hardness, and good oxidation and corrosion resistance [START_REF] Kong | Composition, microstructure, and properties of CrN x films deposited using medium frequency magnetron sputtering[END_REF][START_REF] Jianxin | Erosion wear of CrN, TiN, CrAlN, and TiAlN PVD nitride coatings[END_REF][START_REF] Shan | Effect of N 2 flow rate on microstructure and mechanical properties of PVD CrN x coatings for tribological application in seawater[END_REF]). However, the incorporation of Al in the cubic lattice of CrN system improves their properties and especially enhances its hardness. Indeed; Wang and Nie [START_REF] Wang | Effect of annealing temperature on tribological properties and material transfer phenomena of CrN and CrAlN coatings[END_REF] studied the effect of annealing temperature on CrAlN and CrN coatings properties. They confirm that CrAlN coating exhibits a better thermal stability than that of CrN. Indeed, at 900 °C, CrAlN film presents a strong XRD intensity and it exhibits a higher hardness than that of CrN. The increase of the Al content can lead to the change of the structure from cubic to hexagonal [START_REF] Reiter | Investigation of the properties of Al 1-x Cr x N coatings prepared by cathodic arc evaporation[END_REF]. Also, Nouveau et al. [START_REF] Nouveau | Comparison of CrAlN layers obtained with one (CrAl) or two targets (Cr and Al) by magnetron sputtering[END_REF] deposited CrN and CrAlN films by DC magnetron sputtering. They varied Al rate and revealed that CrAlN coating hardness reaches a value of 35 GPa however the CrN coating hardness is about 18 GPa. Likewise, CrAlN films are known by their good oxidation resistance above 1000 °C which is due to the formation of a dense oxide layer of (Al, Cr) 2 O 3 [START_REF] Lin | A study of the oxidation behavior of CrN and CrAlN thin films in air using DSC and TGA analyses A study of the oxidation behavior of CrN and CrAlN thin films in air using DSC and TGA analyses[END_REF]. Additionally, the incorporation of Al in CrN system improves it corrosion resistance. [START_REF] Ding | Corrosion resistance of CrAlN and TiAlN coatings deposited by lateral rotating cathode arc[END_REF]) compared the corrosion resistance of CrAlN and TiAlN films. They confirm that both coatings exhibit a good corrosion resistance while the CrAlN showed a better one. To study CrAlN coatings and to improve their properties many parameters were investigated. [START_REF] Lv | The structure and properties of CrAlN fi lms deposited by mid-frequency unbalanced magnetron sputtering at different substrate bias duty cycles[END_REF] deposited CrAlN coating by mid-frequency unbalanced magnetron sputtering system. They studied the effect of the duty cycle on the properties of CrAlN films. They confirm that coatings present cubic crystalline structure.

In the present work, a series of CrAlN coatings were deposited on stainless steel and silicon substrate using a DC reactive magnetron sputtering technique. The Al content is investigated. The microstructure, hardness and tribological properties of the CrAlN coatings were studied.

Experimental Procedures

CrAlN films were synthesized on silicon wafer and stainless steel (90CrMoV8) samples (20 Â 20 mm 2 and 5 mm thick) using a Dc reactive magnetron sputtering technique. The deposition time was fixed to 4 h. The pressure during deposition was 0.5 Pa and the substrate temperature was held at 300 °C. The substrate bias voltage was held at -500 V. The flow rates of Ar and N 2 were 68.8 and 33.3 sccm respectively. To deposit CrAlN coatings a chromium and aluminum targets with 99.95% was used. All this parameters are optimized in a previous work [START_REF] Aouadi | Influence of substrate bias voltage on corrosion and wear behavior of physical vapor deposition CrN coatings[END_REF]). To study the influence of Al content on the properties of CrAlN films, different power were applied to the Al target (from 500 to 2800 W). Table 1 summarizes the CrAlN deposition conditions.

The cross-section and film thicknes of obtained films was characterized by SEM field emission (JEOL JSM 7610F). The rotative ball-on-disk test is used to determine the friction coefficient: The sliding speed was 3 cm/s, the sliding distance is about 100 m and the applied load was 5 N. An alumina ball (Al 2 O 3 ) with a diameter of 6 mm is used as counterpart. After friction sliding, wear volume was calculated by profilometre profiles. The coating hardness and the Young's modulus were measured by nano-indentation test using MTS XP Nano indenter. To determine hardness and Young's modulus, Rahmoun's model is used [START_REF] Rahmoun | A multilayer model for describing hardness variations of aged porous silicon low-dielectric-constant thin films[END_REF]). The adhesion tests were realized by means of a micro-scratch tester (Scratch Tester Millennium 200). The indenter is a Rockwell spherical diamond and equipped with an acoustic emission detector. For each CrAlN film, three tests were carried out.

Results and Discussion

Microstructure and Morphology

Figure 1 shows the SEM cross section observation of CrAlN films deposited under different Al rates.

All CrAlN coatings exhibit a dense and a strong columnar structure. The columns are perpendicular to the substrate surface. The SEM images show that the size of the columns increases with the increase of the Al rate. This is ascribed to the increase of the grain size which increases with the increase of the Al rate. Likewise, it observed that the interface between the substrate and the coating doesn't represent any defects. This plays a crucial role to enhance the adhesion of films and consequently the improvement of their mechanical properties, resistance to wear and friction. Also, it's well seen that the film thickness increases by increasing Al content to 19 and 24% at. This is explained by the increase in the deposition rate for these two films.

Hardness

The hardness and Young's modulus of CrAlN films as a function of Al content are presented in Fig. 2.

From this figure, it can be seen that the addition of Al rate to the Cr-N binary system improves its hardness and Young modulus. Indeed, all CrAlN coatings exhibit a higher hardness and Young's modulus than that of CrN and it varies respectively between 22 and 30 GPa and 244 and 347 GPa. Similar values have been obtained in other works [START_REF] Barshilia | A comparative study of reactive direct current magnetron sputtered CrAlN and CrN coatings[END_REF]). The addition of 3.5% at. of Al permits to increase the hardness from 22 to 28 GPa. This improvement in hardness can be attributed to several factors such as the decrease of the grain size, the small inter-atomic distance of CrAlN films and the solution hardening [START_REF] Barshilia | A comparative study of reactive direct current magnetron sputtered CrAlN and CrN coatings[END_REF]. By increasing the Al rate up to 11 at.%, the hardness and the Young modulus slightly decrease and reach respectively 24 and 287 GPa. This can be explained by the relaxation of residual stresses. When the Al rates increase to 19 and 24 at.%, hardness and Young's modulus increase and are maximum, they reach respectively 30 and 347 GPa for 24% at. of Al. This is due to the formation of a solid solution that results from the substitution of Cr atoms by Al.

Friction Coefficient

The variation of the friction coefficient versus the sliding distance for the CrAlN films with different Al rates is shown in Fig. 3.

The addition of Al to the binary system (Cr-N) increases its friction coefficient. Indeed, the friction coefficient of CrN is about 0.68 and remains lower than that of CrAlN films. These results coincide with the work of Lin et al. [START_REF] Lin | Microstructure, mechanical and tribological properties of Cr 1-x Al x N films deposited by pulsed-closed field unbalanced magnetron sputtering (P-CFUBMS)[END_REF]). Ding and Zeng [START_REF] Ding | Structural, mechanical and tribological properties of CrAlN coatings deposited by reactive unbalanced magnetron sputtering[END_REF] explained this by the effect of the high roughness of CrAlN compared to that of CrN. Also, this increase in the friction coefficient is due to the AlN phase that exists in the CrAlN film. Indeed, the AlN phase has a coefficient of friction higher than that of CrN [START_REF] Bobzin | Wear behavior of Cr1 -x Al x N PVD-coatings in dry running conditions[END_REF]). According to Lin et al. [START_REF] Lin | Microstructure, mechanical and tribological properties of Cr 1-x Al x N films deposited by pulsed-closed field unbalanced magnetron sputtering (P-CFUBMS)[END_REF], the increase of the friction coefficient of CrAlN films compared to that of CrN is ascribed to the increase of the oxidation resistance. They consider that the oxide layer formed in the surface of CrN coating acts as a lubricant because of its low shear strength, resulting in a low coefficient of friction. The friction coefficient of CrAlN films varied between 0.7 and 0.8. Similar values were obtained in other works [START_REF] Wang | Fabrication of CrAlN nanocomposite films with high hardness and excellent anti-wear performance for gear application[END_REF]) [START_REF] Aihua | Friction and wear properties of TiN, TiAlN, AlTiN and CrAlN PVD nitride coatings[END_REF]). The addition of a small amount of Al of 3.5% at. to the binary system Cr-N causes a slight increase in the friction coefficient up to 0.7. This can be explained by the low presence of the AlN phase in this film. By adding a quantity of Al between 7 and 24% at., the friction coefficient is almost stable (about 0.8) and the increase in the Al content hasn't any effect. Similar results were found by Wang et al. [START_REF] Wang | Fabrication of CrAlN nanocomposite films with high hardness and excellent anti-wear performance for gear application[END_REF]. At the end of the test, all coatings exhibit an increase of friction coefficient and it reaches that of the substrate. Thus, the CrAlN layer is delaminated. It can be observed that CrAlN coating with 3.5% at. of Al has the best wear resistance and that with 24% at. possesses the worst one.

Wear Volume and Critical Load

The adhesion of thin films to cutting tools is an important parameter that affects their lifetime. Thus, it's imperative to perform a scratch-test to determine the adhesion of CrAlN films.

Figure 4 shows the evolution of Lc 2 as a function of Al rate in the layer. Here, the adhesion is represented by the resistance to spallation (Lc 2 ). The critical load (Lc 2 ) of CrAlN films varies between 49 and 64 N. Indeed, by adding 3.5% at. Al, Lc 2 increases up to 64 N. By increasing Al rate to 7% at., Lc 2 decreases to 54 N and then stabilizes for higher Al contents. The reduction in the resistance to spallation with the increase in Al content is attributed to its microstructure [START_REF] Hua | Tribological behaviours of patterned PVD TiN spot coatings on M2 steel coated with different bias voltages[END_REF]. Indeed, the CrAlN film with an 3.5% of Al exhibits the densest structure (Fig. 1). This dense structure has strong inter-columnar bonds, thus a strong resistance to the formation of inter-columnar cracks. Also, Li et al. [START_REF] Li | Phase segregation and its effect on the adhesion of Cr-Al-N coatings on K38G alloy prepared by magnetron sputtering method[END_REF]) explained this trend of adhesion by the evolution of the grain size. They observed that the increase of grain size leads to the decrease of Lc 2 .

After the ball-on-disk tests, the wear volume is calculated and it presents in Fig. 4. The increase of the Al %, is accompanied by a slight increase in the wear volume. Indeed, it varies from 1.2 10 -5 mm 3 for an A1 rate of 3.5% at. to 1.9 10 -5 mm 3 when the Al rate is about 24%. This increase in wear volume is related to the decrease in hardness, adhesion and microstructure density. Nevertheless, from Fig. 3 the hardness decreases by increasing the percentage of Al from 3.5 up to 11 at.%. Then, it increases for 19 and 24% at. However, the critical load Lc 2 decreases with increasing Al content in the layer (Fig. 4). So, the increase in wear volume is due to the decrease in adhesion. [START_REF] Shew | The effects of nitrogen flow on reactively sputtered Ti-A1-N films[END_REF] reported that mechanical properties and chemical stability have a great influence on the wear resistance of films. As the oxidation temperature of CrAlN films is high (% 1000 °C), it is always higher than the ball/deposit contact temperature. Thus, the wear behavior of CrAlN films is controlled by the mechanical properties and not by the chemical stability.

Conclusion

The aim of this work was to investigate the effect of Al content on the properties of CrAlN films obtained by DC reactive magnetron sputtering. The above results show that the addition of Al rate affects the CrN properties. CrAlN coating hardness was increased with the increase of Al rate. The maximum hardness is about 30 GPa obtained in the coating with 24% of Al content. The friction coefficient of CrAlN films was superior than that of CrN and is about 0.8. CrAlN coatings present a good behavior of adhesion which reaches 64 N. However the increase of Al rate in the layer of CrAlN films is accompanied by a decrease of Lc 2 . CrAlN film with 3.5% rate of Al exhibits the best wear resistance. The increase of Al% rate leads to the decrease of the wear resistance.

Fig. 1 .

 1 Fig. 1. SEM images of cross-section of coatings with different content of Al: (a) 3.5% (b) 7% (c) 11% (d) 19% (e) 24%

Fig. 2 .

 2 Fig. 2. Hardness and Young modulus of CrAlN films under different Al content

Fig. 3 .

 3 Fig. 3. Friction coefficient of CrAlN coatings

Fig. 4 .

 4 Fig. 4. Critical load and wear volume of CrAlN coatings under different Al content

Table 1 .

 1 CrAlN deposition conditions

	Deposition parameter	Nominal value
	Substrate bias voltage (-V)	500
	Temperature during deposition 300
	Argon flow rate (sccm)	68.8
	Nitrogen flow rate (sccm)	33.3
	Power of the Cr target (w)	1500
	Power of the Al target (W)	500, 1000, 1500, 2200, 2800
	Holder rotation speed (rpm)	3
	Time of deposition (H)

Acknowledgments. The authors are grateful to the Regional Council of Burgundy for its financial support, Mr. Denis LAGADRILLERE for the SEM observations. Also, authors would like to think Pr. Alain IOST and Dr. Alberto MEJIAS for their help in nano-indentation and scratch test measurements.


domain: info spi stat math

text:
Vinicius Alves De Oliveira

Thomas Oberlin

Marie Chabert

Charly Poulliat

Bruno Mickael

Christophe Latry

Mikael Carlavan

Simon Henrot

Frederic Falzon

Roberto Camarero

M Bruno

Simplified entropy model for reduced-complexity end-to-end variational autoencoder with application to on-board satellite image compression

Keywords: image compression, neural networks, transform coding

ABSTRACT

In recent years, neural networks have emerged as datadriven tools to solve problems which were previously addressed with model-based methods. In particular, image processing has been largely impacted by convolutional neural networks (CNNs) [B + 09]. Recently, CNN-based autoencoders have been successfully employed for lossy image compression [BLS17, TSCH17, RB17, BMS + 18]. These end-to-end optimized architectures are able to dramatically outperform traditional compression schemes in terms of rate-distortion trade-off. The autoencoder first applies an analyzing transform to the input data to produce a latent representation with minimum entropy after quantization. The latent representation, derived through several convolutional layers composed of filters and activation functions, is multi-channel (the output of a particular filter is called a channel or a feature) and nonlinear. The representation is then quantized to produce a discrete-valued vector. A standard entropy coding method losslessly compress this discrete-valued vector from a model of the representation probability distribution. The analyzing transform and the representation distribution model are both learned from the data by minimization of a rate-distortion trade-off. The assumed representation probability distribution, leading to a particular entropy model, is a key element of these frameworks. In earlier works [BLS17, TSCH17, RB17], the learned representation was assumed independent and identically distributed within each channel and the channels were assumed independent of each other, resulting in a fully-factorized entropy model. Moreover, a fixed entropy model was learned once, from the training set, prohibiting adaptation to the input image during the operational phase. The variational autoencoder proposed in [BMS + 18] used an auxiliary autoencoder. This autoencoder estimates the hyper-parameters of the representation distribution, for each input image even in operational phase. It does not require the assumption of a fully-factorized model which conflicts with the need for context modeling. This variational autoencoder achieves compression performance close to the one of BPG (Better Portable Graphics) [START_REF] Bellard | Bpg image format[END_REF] at the expense of a considerable increase in complexity. However, in the context of on-board compression, a trade-off between compression performance and complexity has to be considered to take into account the strong computational constraints. For this reason, the computational requirements of the CCSDS (Consultative Committee for Space Data Systems) [START_REF] Book | Consultative Committee for Space Data Systems (CCSDS)[END_REF] have been considerable reduced with respect to JPEG2000. This work follows the same logic, however in the context of learned image compression. The aim of this paper is to design a simplified version of the variational autoencoder proposed in [BMS + 18] in order to meet the on-board constraints in terms of complexity while preserving high performance in terms of rate-distortion. Apart from straightforward simplifications of the transform (e.g. reduction of the number of filters in the convolutional layers), we mainly propose a simplified entropy model that preserves the adaptability to the input image. A preliminary reduction of the number of filters reduces the complexity by 62 % the number of floating point operations per pixel (FLOPp) with respect to [BMS + 18]. It also reduces the number of learned parameters with a positive impact on the memory occupancy. The entropy model simplification exploits a statistical analysis of the learned representation for satellite images, also performed in [START_REF] Dumas | Autoencoder based image compression: can the learning be quantization independent?[END_REF] for natural images. This analysis reveals that most of the features are well fitted by centered Laplacian distributions and by Gaussian distributions to a lesser extent. The computationally expensive auxiliary autoencoder in [BMS + 18] is replaced by a classical and simple estimation of a single parameter referred to as the scale (resp. the standard deviation). Our simplified entropy model reduces the complexity of the variational autoencoder coding part by 18 % and outperforms the autoencoder proposed in [START_REF] Ballé | End-to-end optimized image compression[END_REF] for the relatively high target rates.

INTRODUCTION

The spatial resolution of Earth observation satellite images regularly increases thanks to the sensor technological evolution. In order to save transmission channel bandwidth, memory storage and data-transmission time, on-board compression needs to cope up with this increasing volume of digital data [START_REF] Huang | Satellite Data Compression[END_REF]. Compression techniques can be classified into two categories: lossless and lossy compression. Lossless compression is a reversible technique that compress data without loss of information. However, lossless compression rates are limited: for optical satellite images, the typical lossless compression rate that can be achieved is less than 3:1 [START_REF] Shen-En Qian | Optical satellite data compression and implementation[END_REF]. Lossy compression achieves high compression rates through transform coding [START_REF] Vivek | Theoretical foundations of transform coding[END_REF] and the optimization of a rate-distortion criterion. Traditional frameworks for lossy image compression operate by linearly transforming the data into an appropriate continuousvalued representation, quantizing its coefficients independently, and then encoding this discrete representation using a lossless entropy coder. To give an onground example, JPEG uses a discrete cosine transform (DCT) on blocks of pixels followed by a Huffman coder whereas JPEG2000 uses an orthogonal wavelet decomposition followed by an arithmetic coder. In the context of on-board compression, the consultative committee for space data systems (CCSDS), drawing on the on-ground JPEG2000 standard, recommends the use of the orthogonal wavelet transform. However, the computational requirements of the CCSDS have been considerably reduced with respect to JPEG2000, taking into account the huge hardware constraints on satellites. This work follows the same logic, however in the context of learned image compression. In recent years, neural networks have emerged as powerful data-driven tools to solve problems previously addressed with model-based methods. In particular, image processing has been largely impacted by convolutional neural networks (CNNs). CNNs have proven to be successful in many computer vision applications [B + 09] such as classification [START_REF] Hu | Squeezeand-excitation networks[END_REF], object detection [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF], segmentation [KWL + 17], denoising [ZZC + 17] and feature extraction [START_REF] Wiatowski | A mathematical theory of deep convolutional neural networks for feature extraction[END_REF]. Recently, CNNs have been successfully employed for lossy image compression [BLS17, TSCH17, RB17, BMS + 18]. CNN end-to-end optimized architectures are able to dramatically outperform traditional compression schemes in terms of rate-distortion trade-off, however at the cost of a high computational complexity. In this paper, we start from the state-of-the-art CNN image compression scheme proposed in [BMS + 18] to design a reducedcomplexity framework in order to adapt to satellite image compression. Apart from a straightforward network reduction, we mainly propose a simplified entropy model that preserves the adaptability to the input image. The entropy model simplification exploits a statistical analysis of the learned representation for satellite images, also performed in [START_REF] Dumas | Autoencoder based image compression: can the learning be quantization independent?[END_REF] for natural images. The paper is organized as follows. Section 2 presents some background on learned image compression. Section 3 presents the proposed reduced-complexity compression scheme. Section 4 quantitatively assesses its performance on a set of real satellite images and performs a comparative complexity study. Section 5 concludes the paper.

LEARNED COMPRESSION BACKGROUND

Autoencoder structure

Autoencoders have been initially designed for data dimension reduction similar to e.g. Principal Component Analysis (PCA) [B + 09]. In the case of image compression, the goal is not only to reproduce the image, but to produce a representation with low entropy after quantization. The autoencoder is composed of an analyzing transform denoted by G a and a synthesis transform denoted by G s both learned from the data. The interface between the analysis transform and the synthesis transform is called the bottleneck. In the case of compression, this bottleneck is composed of a quantizer, an entropy encoder and its associated decoder. The analysis transform is applied to the input data x to produce a representation y = G a (x). This representation, derived through several convolutional layers composed of filters and activation functions, is multi-channel (the output of a particular filter is called a channel or a feature) and non-linear. At the input of the bottleneck, the representation is quantized to produce a discrete-valued vector ŷ = Q(y) with minimum entropy. A standard entropy coding method, such as arithmetic, range or Huffman coding [START_REF] Rissanen | Universal modeling and coding[END_REF] uses the entropy model inferred from the representation, denoted by p ŷ(ŷ), to losslessly compress ŷ. The last step consists in decoding and transforming back the quantized representation into the original space: x = G s (ŷ) by means of the synthesis transform, composed of so-called transpose convolutional layers. In [BLS17, BMS + 18] the activation functions in G a (resp. G s ) are generalized divisive normalizations (GDN) (resp. Inverse Generative Divisive Normalizations (IGDN)). Contrarily to usual activation functions (e.g. ReLU, sigmoid,...), GDN and IGDN are parametric functions that implement an adaptive normalization. The learning of their parameters is thus required. They have been shown to reduce statistical dependencies [Bal18, ML10, Lyu10] and thus appear particularly appropriate for transform coding. According to [START_REF] Ballé | Efficient nonlinear transforms for lossy image compression[END_REF], the GDN better estimates the optimal transform than conventional non-linearities for a wide range of rate-distortion trade-offs. Although the GDN increases the number of parameters to be learned, this increase represents a percentage of less than 2% of the overall structure with respect to conventional non-linearities. For that purpose, our complexity reduction does not target the GDN/IGDN.

Autoencoder learning

The autoencoder parameters (filter weights, GDN/IGDN and representation distribution model parameters) are jointly learned by optimization of a loss function that establishes a trade-off between the rate R(ŷ) and the distortion D(x, x) between the original image x and the reconstructed image x. The rate-distortion criterion then writes as the weighted sum:

J = λD(x, x) + R(ŷ), (1)
where parameter λ tunes the rate-distortion trade-off. The rate achieved by an entropy coder is lower-bounded by the entropy derived from the actual discrete probability distribution of the quantized vector ŷ, denoted as m(ŷ). The rate increase comes from the mismatch between the probability distribution model p ŷ(ŷ) required for the coder design and m(ŷ): the smallest bit-rate is given by the Shannon cross entropy between the two distributions:

H(ŷ) = E ŷ∼m [-log 2 p ŷ(ŷ)] . (2)
The probability model p ŷ(ŷ) has thus a strong impact on the coder performance.

The distortion measure is chosen to account for image quality as perceived by a human observer. Due to its many desirable computational properties, the mean square error (MSE) is generally selected. However, a measure of perceptual distortion may also be employed such as the multi-scale structural similarity index (MS-SSIM) [START_REF] Wang | Multiscale structural similarity for image quality assessment[END_REF]. The autoencoder parameters are learned by minimizing the loss function defined in Equation 1 through gradient descent with backpropagation [B + 09] on a representative image training set. However, this requires the loss function to be differentiable. In the specific context of compression, a major hurdle is that the derivative of the quantization function is zero everywhere except at integers, where it is undefined. To overcome this difficulty, Ballé et al. ( 2016) [START_REF] Ballé | End-to-end optimized image compression[END_REF] proposed to replace the quantization by the addition of an independent and identically distributed (i.i.d.) uniform noise, while Theis et al. (2017) [START_REF] Theis | Lossy image compression with compressive autoencoders[END_REF] proposed to replace, in the backward pass (i.e. when back-propagating the error), the derivative of the quantization function with a smooth approximation. In both cases, the quantization is kept as it is in the forward pass (i.e. when processing an input data). Note that, in the following, we will consider the first approach [START_REF] Ballé | End-to-end optimized image compression[END_REF].

Entropy model

As stressed above, a key element in the end-to-end learned image compression frameworks is the entropy model defined through the probability distribution model p ŷ(ŷ) assigned to the quantized representation for coding. The bit-rate is minimized if the distribution model p ŷ(ŷ) is equal to the actual distribution m(ŷ). Unfortunately, this distribution may differ from the actual unknown distribution of the quantized representation m(ŷ),

arising from the actual distribution of the input image and from the analysis transform G a .

As mentionned previously, for back-propagation derivation during the training step, Ballé approximates the quantization process (ŷ = Q(y)) by the addition of an i.i.d uniform noise ∆y, whose range is defined by the quantization step. Due to the adaptive local normalization performed by GDN non-linearities, the quantization step can be set to one without loss of generality. Hence the quantized representation ŷ, which is a discrete random variable taking values in Z, is modelled by the continuous random vector

ỹ = y + ∆y (3)
taking values in R.

In [START_REF] Ballé | End-to-end optimized image compression[END_REF][START_REF] Theis | Lossy image compression with compressive autoencoders[END_REF], this approximated quantized representation was assumed independent and identically distributed within each channel and the channels were assumed independent of each other, resulting in a fullyfactorized distribution:

p ỹ|ψ (ỹ|ψ) = i p ỹi|ψ (i) (ỹ i ), (4)
where index i runs over all elements of the representation, through channels and spatial locations, ψ (i) is the distribution model parameter vector associated to each element. The addition of the uniform quantization noise leads to the following expression for p ỹi|ψ (i) (ỹ i ) defined through a convolution by a uniform distribution on the interval [-1/2, 1/2]:

p ỹi|ψ (i) (ỹ i ) = p yi|ψ (i) (y i ) * U (-1/2, 1/2) . (5)
In [START_REF] Ballé | End-to-end optimized image compression[END_REF][START_REF] Theis | Lossy image compression with compressive autoencoders[END_REF], the parameter vectors are learned from data during the learning phase. This learning, performed once and for all, prohibits adaptivity to the input images during operational phase. Moreover, the simplifying hypothesis of a fully factorized distribution is very strong. In particular, elements of ŷ show spatial dependency in practice, as observed in [BMS + 18].

To overcome these limitations and thus to obtain a more realistic and more adaptive entropy model, [BMS + 18] proposed a variational autoencoder which takes into account possible spatial dependency in each input image. Auxiliary random variables z, conditioned on which the quantized representation ỹ elements are independent, are derived from y by an additional autoencoder, connected in parallel with the bottleneck. The hierarchical model hyper-parameters are learned for each input image in operational phase. Firstly, the hyperprior transform analysis H a produces the set of auxiliary random variables z. Secondly, z is transformed by the hyperprior synthesis transform H s into a second set of random variables σ.

In [BMS + 18], z distribution is assumed fully-factorized and each representation element ỹi , knowing z, is modeled by a zero-mean Gaussian with its own standard deviation σ i . Finally, taking into account the quantization process, the conditional distribution of each quantized representation element is given by:

ỹi |z ∼ N 0, σ i 2 * U - 1 2 , 1 2 . ( 6
)
The rate computation involves this distribution model as well as the prior distribution of z, that will have to be transmitted to the decoder with the compressed data, as side information. This variational autoencoder allows to reach state-of-the-art compression performance, close to the one of BPG (Better Portable Graphics) [START_REF] Bellard | Bpg image format[END_REF] at the expense of a considerable increase in complexity with respect to [START_REF] Ballé | End-to-end optimized image compression[END_REF], reflected by a runtime increase between 20% and 50%. The two reference architectures [START_REF] Ballé | End-to-end optimized image compression[END_REF] and [BMS + 18] are compactly displayed on Figure 1. The left column represents the autoencoder [START_REF] Ballé | End-to-end optimized image compression[END_REF] whereas the combination of left and right columns represents the variational autoencoder [BMS + 18]. N represents the number of filters which is common to all layers except the ones directly connected to the bottleneck. These layers are generally composed of M filters with M > N to obtain a so-called wide bottleneck [START_REF] Cheng | Deep residual learning for image compression[END_REF], for increased performance.

REDUCED-COMPLEXITY VARIATIONAL AUTOENCODER

In the literature, the design of learned image compression frameworks hardly takes into account the computational complexity: the objective is merely to obtain the best performance in terms of rate/distortion. However, in the context of on-board compression, a trade-off between performance and complexity must be considered to take into account the strong computational constraints. Our focus here is to propose a complexity-reduced alternative to the state-of-the-art structure [BMS + 18] while minimizing the impact on the rate-distortion performance. Note that this complexity reduction is particularly relevant when it operates on the coding part of the framework, the one subject to the on-board constraints.

Reduction of the number of filters

A straightforward simplification to be first considered is the reduction of the number of filters composing the convolutional layers. The state-of-the-art frameworks generally involve a large number of filters with the objective of increasing the network approximation capacity, which is needed at high bit rates [BLS17, BMS + 18]. However, the learning of the associated parameters (e.g. the filter coefficients) is computationally demanding, in addition to the increased memory it requires. Moreover, a reduction in the number of filters indirectly implies a reduction in the number of parameters and operations in the GDN/IGDN, as it reduces the depth of the tensors (equal to the number of filters) at their input. However, the impact of reducing the number of filters depends on the convolutional layers it applies. Indeed, a high number of filters M has to be maintained in the last layer of the encoder and in the first layer of the decoder, following the so-called wide bottleneck strategy [START_REF] Cheng | Deep residual learning for image compression[END_REF]. For the other layers, the number N of filters can be subsequently reduced. The same strategy benefits to the auxiliary autoencoder implementing the hyperprior illustrated in Figure 1 (right column). We consider the number of parameters N p and the floating point operations per pixel (FLOPp) to compare the proposed and reference frameworks in terms of complexity. These quantities are provided in [START_REF] Cheng | Deep residual learning for image compression[END_REF] for the convolution layers including GDN/IGDN. Quantization is parameter free.

Simplified parametric entropy model

The entropy model simplification aims at achieving a compromise between simplicity and performance while preserving the adaptability to the input image. In [START_REF] Ballé | End-to-end optimized image compression[END_REF], the representation distribution is assumed fully-factorized and the statistical model for each feature is non-parametric to avoid the a priori choice of a given distribution shape. Note that "non-parametric" means that the shape of the distribution is not known in advance, however it is defined by some parameters. These parameters are learned once, during the learning step. In [BMS + 18], the strong independence assumption leading to a fully-factorized model is avoided by the introduction of the hyperprior distribution, whose parameters are learned for each input image even in the operational phase. Both models are general and thus suitable to a wide variety of images, however the first one implies a strong hypothesis of independence and prohibits adaptivity while the second one is computationally expensive. This paper exploits a statistical analysis of each feature of the learned representation in the particular case of real satellite images. A similar statistical analysis has been previously conducted in the case of natural images in [START_REF] Dumas | Autoencoder based image compression: can the learning be quantization independent?[END_REF] with the objective to properly design the quantization step in [START_REF] Ballé | End-to-end optimized image compression[END_REF]. The probability density function related to each feature was estimated through a normalized histogram from a representative set of natural images. The study showed that most features can be accurately modelled as Laplacian random variables. A similar result has also been obtained in [START_REF] Edmund | A mathematical analysis of the dct coefficient distributions for images[END_REF] for block-DCT coefficients of natural images under the assumption that the variance is constant on each image block and that its values on the different blocks are distributed according to an exponential or an halfnormal distribution. We conducted this statistical analysis on the representation obtained by the end-to-end framework [START_REF] Ballé | End-to-end optimized image compression[END_REF] when trained on a representative dataset of satellite images and for the highest rates obtained with this framework (between 2.5bpp and 3bpp as displayed on Figure 5). According to Kolmogorov-Smirnov goodness-of-fit test [START_REF] Pratt | Kolmogorov-smirnov two-sample tests[END_REF], most features follow a Laplacian distribution defined by:

f (ζ, µ, b) = 1 2λ - |ζ -µ| b for ζ ∈ R. ( 7
)
where value and scale varying according to the considered feature and to the kind of image. Note that the Gaussian fitting is also appropriate albeit to a lesser extent. We thus propose to consider the following parametric model for all the j th feature elements, denoted as y ij for i j ∈ I j , where I j denotes the set of indexes covering the j th feature:

y ij ∼ Laplace(0, b j ) (resp. y j i ∼ N (0, σ 2 j ))
with: b j = V ar(y j i )/2 (resp. σ 2 j = V ar(y j i )).

(

) 8
The problem then boils down to the estimation of a single parameter per feature referred to as the scale b j (respectively the standard deviation σ j ) in the case of the Laplacian (resp. Gaussian) distribution. Starting from [BMS + 18], this proposal reduces the complexity at two levels. First, the hyperprior autoencoder, including the analysis H a and synthesis H s transforms, is removed. Second, the side information initially composed of the compressed auxiliary random variable set (z) of size 8 × 8 × M now reduces to a M × 1 vector of variances. The auxiliary network simplification is displayed on the right part of Figure 4.

PERFORMANCE ANALYSIS

Implementation setup

To assess the relevance of the proposed complexity reductions, experiments were conducted using TensorFlow. the rate-distortion averaged over the validation dataset for the trained models for both MSE and MS-SSIM quality measures. Recall that the architecture was trained for MSE only. The proposed simplified entropy model achieves an intermediate performance between the variational model with a reduced number of filters (VAE-N64) and the non-variational model AE-N128 [START_REF] Ballé | End-to-end optimized image compression[END_REF]. Obviously, due to the entropy model simplification, Laplacian-N64 and Gaussian-N64 underperform the more general and thus more complex VAE-N64 model. However, the proposed entropy model, even if simpler, preserves the adaptability to the input image, unlike the model AE-N128 [START_REF] Ballé | End-to-end optimized image compression[END_REF]. Note that the simplified entropy models perform close to the hyperprior models at relatively high rates such as targeted for satellite image compression. One possible explanation for this behaviour can be the increased amount of side information required by the hyperprior model [BMS + 18] for increas-ing rates [START_REF] Hu | Learning end-to-end lossy image compression: A benchmark[END_REF]. Table 3 shows that the coding part complexity of Laplacian-N64 and Gaussian-N64 is 22% lower than the one of Hyperprior-N64.

CONCLUSION

By combining the reduction of the number of filters, and by proposing a simplified entropy model, we have developed a reduced-complexity compression architecture for satellite images that outperforms the CCSDS 122.0-B [START_REF] Book | Consultative Committee for Space Data Systems (CCSDS)[END_REF] while maintaining a competitive performance for medium to relatively high rates in comparison with the previous learned image compression models [BLS17, BMS + 18]. In future research, we plan to improve the performance of the learned satellite compression models at high bit-rates and high resolutions by fine-tuning the size of the network (e.g. number of filters) according to the target rates. Preliminary results are given in Figure 5, for MSE distortion measure only, the MS-SSIM shows the same behaviour. They have been obtained by an increase of the number of filters on both sides of the bottleneck only (from M = 192 to M = 256) keeping N = 64. Theses curves show that the simplified learned architecture outperforms the JPEG2000 and CCSDS standard even at higher rates subject to a finetuning of the network dimensioning, in each rate range, for a good trade-off between performance and complexity.

Figure 1 .

 1 Figure 1. Architecture of the autoencoder [BLS17] (left column) and variational autoencoder [BMS + 18] (left and right columns).

  µ is the mean value and b > 0 is a scale parameter related to the variance by V ar(ζ) = 2b 2 . As an illustration, let consider the satellite image displayed on Figure 2. This image of the city of Cannes (French Riviera) is a 12-bit simulated panchromatic Pléiade image with size 512 × 512 and resolution 70cm. According to the Kolmogorov-Smirnov goodness-of-fit test [PG81], 93% of the features follow a Laplacian distribution with a significance level α = 5%. Figure 3 shows a particular 32 × 32 feature derived from the Cannes image and its normalized histogram with Laplacian fitting.

Figure 2 .

 2 Figure 2. Simulated 12-bit Pléiade image of Cannes with size 512 × 512 and resolution 70cm

Figure 4 .

 4 Figure 4. Architecture of the proposed simplified entropy model: autoencoder handling the input image (left column) and proposed simplification of the autoencoder implementing the hyperprior (right column).

( b )

 b Distortion measure: MS-SSIM (dB).

Figure 5 .

 5 Figure 5. Rate-distortion curves for the considered learned frameworks and for the CCSDS and JPEG2000 standards for MSE and MS-SSIM (dB) (derived as -10 log 10 (1-MS-SSIM)).

Figure 6 .

 6 Figure6. Rate-distortion curves at higher rates for learned frameworks and for the CCSDS and JPEG2000 standards for MSE in log-log scale.

  Starting from [BMS + 18] denoted as VAE-N192, the number of filters is reduced from N = 192 to N = 64 for all layers, in the main autoencoder and in the hyperprior one, except from the two layers on both sides of the bottleneck composed of M = 192 filters. The resulting architecture is termed VAE-N64. The complexity of this model is detailed in Table1.

									4.2. Impact of the number of filter reduction
		10 3
	MSE	10 2
				Laplacian-N64
				Gaussian-N64
				AE-N128
				VAE-N64 VAE-N192					Table 1. Detailed complexity of VAE-N64
				CCSDS standard
				JPEG2000
		10 1	1	1.5		2	2.5	3	3.5
					bit rate [bit/px]
				(a) Log-log scale. Distortion measure: MSE.
			44
			42
			40
			38
	MS-SSIM (dB)	32 34 36
									Laplacian-N64
			30						Gaussian-N64
									AE-N128
			28						VAE-N64
									VAE-N192
			26						CCSDS standard
									JPEG2000
			24
			0.5	1	1.5	2	2.5	3	3.5	4
					bit rate [bit/px]
		The batch size (i.e. the number of training samples to
		work through before the parameters are updated) was set
		to 8 and up to 1M iterations were performed. Both train-
		ing and validation datasets are composed of simulated 12-
		bit Pléiades panchromatic images provided by the CNES,
		covering various landscapes (i.e. desert, water, forest, in-
		dustrial, cloud, port, rural, urban). The training dataset is
		composed of 8M of patches (of size 256 × 256) randomly
		cropped from 112 images (of size 585×585). The valida-
		tion dataset is composed of 16 images (of size 512×512).
		MSE was considered as the distortion metric for train-
		ing. The rate and distortion measurements were averaged
		across the validation dataset for a given value of λ. In ad-
		dition to the MSE, we also evaluate those results in terms
		of MS-SSIM. Note that they exhibit a similar behavior
		even if the models were trained for the MSE only. The
		proposed framework is compared with the CCSDS 122.0-
		B [Boo05], JPEG2000 and with the reference methods
		AE-N128 [BLS17] and VAE-N192 [BMS + 18].

Table 3 .

 3 Reduction of the encoder complexity induced by simplified entropy model on the coding part

	Method	Np	FLOPp	Relative
	VAE-N64	2386621	1.42 × 10 4	1
	Laplacian/Gaussian-N64	526461	1.11 × 10 4	0.78

ACKNOWLEDGMENTS

This work has been carried out under the financial support of the French space agency CNES and Thales Alenia Space.

Compared with VAE-N192, the VAE-N64 complexity is 62% lower in terms of FLOPp, as displayed in Table 2. Note that the subsequent reduction of the number of learned parameters has also a positive impact on the memory occupancy. Moreover, as displayed on Figure 5, VAE-N64 achieves a rate-distortion performance close to the one of VAE-N192 [BMS + 18], both in terms of MSE and MS-SSIM, even at relatively high rates, contrary to what was stated in [BLS17, BMS + 18, Bal18].

Impact of the entropy model simplification

The proposed simplified models Laplacian-N64 and Gaussian-N64 are compared with the original VAE-N192 of [BMS + 18], with VAE-N64, and with the nonvariational method AE-N128 [START_REF] Ballé | End-to-end optimized image compression[END_REF]. Figure 5 shows