Ikram El

Noureddine Kerzazi
email: n.kerzazi]@um5s.net.ma

Where Are Females in OSS Projects? Socio Technical Interactions

Keywords: Gender, Diversity, Open Source Software, Social Network Analysis, Socio-Technical interactions

Recent researches provide evidence that women are underrepresented in the field of computer science. It has been reported that less than 10% of Open Source Software (OSS) contributors in GitHub are women. Although related qualitative and quantitative studies point out the gender gap, the technical and social interaction of females within OSS still remain unexplored and largely misunderstood. As a first step towards proposing articulated actions towards diversity and inclusion, we need first to explore the gender gap in terms of activities and interactions. Thus, we propose to answer the questions: where are females in OSS projects? How they evolve? and How they contribute to the sustainability of the OSS social capital?. We particularly focus on building sociotechnical networks and analyze them to explain how females contribute and interact in practice. We reflect on interactions' graphs and examine through a preliminary study, using data from six OSS projects, possible links between existing findings and the directions we suggest for more gender diversity. We found that females are extremely underrepresented within OSS communities, but when they participate they are productive just as males, they evolve following relatively the same patterns than males and remain more involved in projects than males.

Introduction

Women are underrepresented in the software development industry and particularly within OSS communities [START_REF] Feller | A framework analysis of the open source software development paradigm[END_REF][START_REF] Nafus | Patches don't have gender': What is not open in open source software[END_REF][START_REF] Steinmacher | Preliminary empirical identification of barriers faced by newcomers to Open Source Software projects[END_REF][START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF][START_REF] Filippova | From diversity by numbers to diversity as process: supporting inclusiveness in software development teams with brainstorming[END_REF]. In the software industry, females only account for 21% of the whole software development workforce and earn on average $22,251 less than their male peers [START_REF] Datausa | Demographics of Software Developers[END_REF]. In GitHub 1 , a well-known open-source platform, the annual diversity report on OSS communities reported that the overall number of females decreased from 37% in 2017 to 33% in 2018. Repository data from GitHub projects provide an interesting source of information which, under appropriate analysis, may reveal facts related to females' activities and their dynamic interactions in a collaborative development environment. To this end, we undertake a socio-technical analysis to get more insights into females' involvement in OSS projects. More specifically, we seek to answer the questions: Where Are Females in OSS Projects? How They Evolve? And How they contribute to the sustainability of the OSS social capital? Why Diversity Matters? Diversity in the workplace including diversity of gender, ethnicity, and even religion has been shown to improve retention and reduce the costs associated with employee turnover [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF][START_REF] Hui | Designing for Inclusion: Supporting Gender Diversity in Independent Innovation Teams[END_REF][START_REF] Imtiaz | Investigating the Effects of Gender Bias on GitHub[END_REF][START_REF] Foucault | Impact of developer turnover on quality in open-source software[END_REF]. In a diverse workplace, employees are more likely to remain loyal when they feel respected and valued for their unique contribution [START_REF] O'reilly Iii | Barnett Work group demography, social integration, and turnover[END_REF]. That said, while GitHub is supposed to be a meritocracy based platform and free of gender barriers [START_REF] Wang | Competence-confidence gap Proceedings of the 40[END_REF], the situation of females involvement is below the expectations [START_REF] Datausa | Demographics of Software Developers[END_REF] which limits the workforce required for communities growth. To benefit from gender diversity, OSS communities should lower barriers for female developers' selfguided personal development, which is crucial for them to achieve their own technical distinctions.

In order to support gender diversity within GitHub communities, we should understand how members, especially women, interact in these community environments. Unerstanding social interaction of female's collaboration could reveal insights not only about the structure of collaboration but also how productive are cross-gender collaboration: we know who contributed on what and when by examining historical data from GitHub. From there, we can build a social network of contributors (for both males and females) who have collaborated on the same source code files. Social Network Analysis (SNA) provides a class of metrics known as "centrality"' metrics that provide a useful abstraction of the gender interaction information. Thus, we analyze and compare activity data (i.e., #commits, #comments, #fileModified, and code churn) between genders. Then we analyze SNA metrics of interactions (i.e., Female-Female, F-M, and M-M).

In particular, we answer the three following research questions:

RQ1: Where are females in OSS projects? RQ2: How the top females' performers evolved over time? RQ3: What is the role of females in building a sustainable collaborative social capital?

Paper Structure. We first discuss related work in section 2. Then we present our methodology in section 3 including data collection and gender detection approach. Section 4 introduces the basic terminology and concepts needed to comprehend how we built social networks, while section 5 offers an overview of our findings along with discussion. In section 6 we discuss possible threats to validity. Finally, section 7 concludes and outlooks future work.

Related Work

The study by Vasilescu et al. [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF] is the one that shares objectives closest to ours. The authors acknowledge the importance of gender diversity and explored how diverse are online teams with respect to gender and tenure based on the findings of a survey of GitHub contributors. Authors point out that when forming or recruiting a software team, increased gender and tenure diversity are associated with greater productivity.

Similarly, James et al. [START_REF] James | What is the perception of female and male software professionals on performance, team dynamics and job satisfaction?: insights from the trenches[END_REF] studied the perception, performance, team dynamics, and opportunities using a survey targeting software professionals and reported that there is no significant difference between genders. Medenz et al. [START_REF] Mendez | Gender in open source software: what the tools tell[END_REF] investigated a gender inclusive method and how it can help increase gender inclusiveness in the tools that are used by OSS communities.

Wang et al [START_REF] Wang | Competence-confidence gap Proceedings of the 40[END_REF] discussed the existence of the competence-confidence gap. Authors developed a theoretical explanation for female developers' low rate of initiating a pull request in OSS projects arguing that it is not easy for female developers to directly translate competence to confidence [START_REF] Wang | Competence-confidence gap Proceedings of the 40[END_REF]. Similarly, Terrell [START_REF] Terrell | Gender differences and bias in open source: Pull request acceptance of women versus men[END_REF] compared acceptance rates of contributions from men and women in an open-source software community and finds that, in overall, women's contributions tend to be accepted more often than men's -but when a woman's gender is identifiable, her Pull requests are rejected more often.

In this study, we investigate the socio-technical interactions of females in OSS communities using SNA. We leverage on the historical data of six projects from GitHub. The benefit of assessing females' position in the overall collaborative networks is that it does not require qualitative information that can only be provided by contributors, such as questions about what they have done before. Analyzing networks of collaboration such as file co-edition, comments, pull requests offer opportunities for understanding the value provided by women in software development and help other researchers recommending improvements.

Methodology

Data Collection

The primary goal of our study is to understand how females interact and evolve within OSS communities. To this end, we performed a preliminary analysis of socio-technical interactions on publicly available historical data from six open source projects, mined from GitHub: Angular.js, Moby, Rails, Tensorflow, Django, Elasticsearch. We selected these well-known OSS projects because they are long-lived with more than a thousand contributors, and under diverse programming languages. Error! Reference source not found. shows descriptive statistics regarding the studied projects.

In order to understand the female's distribution along with their activities within OSS projects, we first extracted information for each commit including the login of contributors, Timestamp of the commit, number of files modified, and code churn information (i.e., quantification of the commit size). Next, we used a Rest GitHub API 2 to extract detailed information of the contributor for each commit. For instance, the HTTP GET request "https://api.github.com/users/Narretz" sends back available details of the account including contributor's name "Martin Staffa". However, users registered in GitHub can choose to disclose their names in their profiles, so that out of the six projects studied, 1059 contributor names were missing. To discover as many of the missing names as possible, the GitHub API provides access to user's public events which list all public events performed by a user on the site. This list provides another way to view the personal information associated with GitHub data. For instance, calling "https://api.github.com/users/bumbu/events/public" returns a Json object that includes a full name associated with the user and commits 'Alex Bumbu'. Using this method, we were able to detect 155 names from the missing list since GitHub users can upgrade their privacy settings to hide personal information 3 . We verified that less than 10% of contributors' names are missing for each project. Unknown names in the profile cannot be used to identify genders, we ignored them in our analysis.

Gender Detection

GitHub does not store information about contributors' gender identification. There are few approaches to automatically infer a contributor's gender [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF][START_REF] Terrell | Gender differences and bias in open source: Pull request acceptance of women versus men[END_REF][START_REF] Vasilescu | Gender, representation and online participation: A quantitative study of stackoverflow[END_REF]. Vasilescu et al. [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF] used first name and country to infer a user's gender. Terrell et al. [START_REF] Terrell | Gender differences and bias in open source: Pull request acceptance of women versus men[END_REF] suggested a method using email to link a user to her Linkedin profiles which contains rich information. Although this method shows a high precision, the recall is not good, especially for female developers from East Asian countries where the usage of Linkedin is not that high. However, these heuristics have not been empirically validated with GitHub data. To alleviate issues related to previous approaches, we used the commercial tool called Namsor API 4 . Error! Reference source not found. shows a comparison of females and males percentage distributions.

Social Network Representation

Social Network Analysis (SNA) is the process of investigating social structures through the use of networks and graph theory [START_REF] Zhang | Developer social networks in software engineering: construction, analysis, and applications[END_REF]. In network analysis, we have nodes (i.e., contributors) which represent vertices of a graph and connections which represent edges (i.e., a type of interaction). An interaction occurs when two developers modify the same source code file or comment on the same topic.

SNA Metrics -Metrics that measure a node's direct connections to other nodes are connectivity metrics. The first metric is the density of a network which captures the number of actual connections between members divided by the number of possible connections, as depicted in Error! Reference source not found.. Density values range from [0 to 1], a higher density indicates that network nodes have tighter connections with each other. Second, connectivity metric is the degree centrality of a node which represents the number of connections incident on a node. Each time two contributors change the same file or comment on the same topic we have one non-weighted connection (i.e., a link). In contrast, a node is considered disconnected if it has no edges with other nodes meaning no interactions with other contributors. Centrality metrics quantify how closely contributors are indirectly connected to other contributors in the network. We consider two metrics: closeness and betweenness. Closeness stands for the average number of steps required to go from the current node to all other nodes. Closeness measures the distance between each participant and all other participants (i.e., is a participant connected directly to all other participants, or would information need to pass through several other participants to reach that individual?). Betweenness stands for the average number of shortest paths between pairs of other nodes that run through the node. Betweenness is used to measure the extent to which a node lies between other nodes. More shortest paths run through a node, more likely important this node is. Clustering Coefficient is calculated as the probability that any two neighbors of the current node are connected. In our study, the clustering coefficient measures the collective collaboration of contributors from different genders.

We used SNA metrics to explore diversity of interactions of Female-Female (F-F), Female-Male (F-M), and Male-Male (M-M) using files co-edition networks from six GitHub projects.

Results

RQ1. Where Are Females in OSS Projects?

Motivation. Social capital of open source software needs gender diversity among other diversities (i.e., cultural, ethnic, etc.), to be sustainable [START_REF] Dabbish | Social coding in GitHub: transparency and collaboration in an open software repository[END_REF]. Gender diversity demands coordinated and delicate interactions [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF]. Unfortunately, little is known about how females behave and interact within OSS communities, comprehensive view is rarely discussed at least to understand what would be specific for females to ease their integration within OSS communities.

Approach. We first extract historical data of Commits, Comments, and Pull Requests from GitHub with their respective authors similarly to the approach provided by Joblin et al. [START_REF] Joblin | Mauerer Evolutionary trends of developer coordination: a network approach[END_REF]. After identifying the gender of each contributor, we focused on three groups of interactions cross-gender F-F, M-M, and F-M. Thus, for each project, we built a social network, along with subnetworks regarding the three groups, related to contributors' interactions for the six studied projects. More precisely, by interactions we mean the relation by which two or more contributors collaborate with each other through an activity such as working on the same source code file (i.e., co-edition) or commenting on the same commit. We tracked back this information by looking at the version change history and other elements provided by the GitHub platform.

Results. Error! Reference source not found. shows social networks related to contributors' interactions for the six studied projects. Nodes represented in red color point out males and yellow ones highlight the position of females within the overall network. Visually, as shown in Error! Reference source not found., females are distributed throughout the overall network. They are positioned within the Core as well as Peripheral members and are interacting with both genders. Furthermore, to examine interactions regarding gender, we calculate the SNA metrics of three sub-networks Figure 2 : (i) interactions between females F-F, (ii) interactions between males M-M, and (iii) interactions with the opposite gender F-M. Error! Reference source not found. reports the averages distribution of the most important SNA metrics cross-networks. For all projects, F-F interactions are as dense as M-M and F-M interactions are less dense meaning that there are more interactions between contributors within the same gender group than the opposite gender. For example, within Angular.JS project, the two networks F-F and M-M have the same density equal to 0.05, however, the density of cross-gender interactions network M-F is very low (= 0.007).

The Avg. degree metric for the sub-networks F-F is extremely low compared to M-M meaning that females are less directly connected to other females (2.7 for Angular.js) and also less connected to males (7.05). We hypothesize that this result is skewed because of the unbalanced numbers of contributors for each gender.

The Avg.ClusCoef related to the sub-network M-M is much higher than F-F meaning that there are established groups of collaboration (for Angular.js, Avg.ClusCoef= 0.89 between males (M-M) against 0.46 for F-F) co-editing the same components for a long time. While Avg.ClusCoef value close to 0 for the sub-networks M-F suggesting that there are few cross-gender interactions.

Closeness metric is roughly similar cross-gender meaning that gender has no effect on the proximity of members with other members of the community and how fast the members interact with each other (i.e., fewer steps to reach other nodes).

Betweenness metric has a very small value suggesting that nodes are not that much connected (value=1 means a hub node and value=0 means a disconnected node). For instance, in Angular.js project, the average Betweenness for the network F-F equal to 0.02, while it is equal to 6e-4 for the sub-network M-M. Also, as one can see in the subnetwork M-F in Figure 2, females can play a broker role ensuring the communication between sub groups, which can decrease the centralization of the OSS community and increase communication between Core (i.e., experts) and Peripheral members (i.e., casual contributors) [START_REF] Toral | Analysis of virtual communities supporting OSS projects using social network analysis[END_REF].

RQ2. How the top females' performers evolved over time?

Motivation. A common problem that OSS communities face is the high instability of their contributors [START_REF] Robles | Evolution of the core team of developers in libre software projects[END_REF]. This problem is even amplified by the fact that females are underrepresented, their permanence is also an open issue. We sought to gain more understanding of the evolvement of female contributors over time and to learn from the experience of the top performers.

Approach. For each project, we have retrieved the third quartile (i.e., upper quartile that has the top 25 percent above it) of the female developers that contribute the most according to the: number of commits, comments, and Pull Requests. From it, we calculate the performance for each contributor according to the following formula.

𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 (𝐶

𝑖 ) = 1 𝑇𝑜𝑡𝑎𝑙_𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 [𝑑𝑎𝑡𝑒_𝑙𝑎𝑠𝑡𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝐶 𝑖 ) -𝑑𝑎𝑡𝑒_𝑓𝑖𝑟𝑠𝑡𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝐶 𝑖 )]
Results. Figure 3 shows the distribution of performance between males and females. We performed Mann-Whitney-Wilcoxon statistical tests, with a confidence level of alpha = 0.05. We found that for all projects except Moby the tests were not statistically significant (p > 0.05) suggesting that there is no statistical difference of the performance cross-gender except for the project Moby as reported in Table 3.

Although females are underrepresented within OSS communities, we found them in the Core teams as well as in Peripheral. Women are more likely than men to interact with other contributors. However, the density of cross-gender interactions network M-F is very low (=0.007) with less established groups of females (0.46) compared to males (0.89).

Where are females in OSS projects?

in such a constraint can yield evolving observations in a non-consecutive way. Furthermore, some important events (e.g., major releases, vision changes, etc.) that communities may undergo across time-stamps will not be detected and will be difficult to predict.

Threats to external validity relate to the generalization of our findings. We only considered six OSS projects from GitHub. Thus, we cannot assume a generalization to all projects hosted on GitHub or other platforms such as GitLab and Bitbucket, even though there is no inherent reason why they would be biased.

Conclusion

We have used SNA approach to study gender diversity within six GitHub communities. We first examined the position of both genders within social networks and their interactions and found that females are spread over the overall network including Core and Peripheral members. Next, we tracked back the evolvement of the upper quartile of the female developers that contribute the most according to the: number of commits, comments, and Pull Request. We found that there is no statistical difference regarding the performance cross-gender except for the project Moby. Finally, even if females are underrepresented in OSS communities, they contribute in building a sustainable collaborative social capital for open software.

The results of this study motivate further fine-grained analysis of female's implication in OSS that will (i) investigate the quality of work in terms of introduced bugs or complexity; (ii) explore further socio-technical interactions of women to understand the value of their contributions; (iii) characterize projects attractiveness for women.

Figure 1 :

 1 Figure 1 : Social Position of Females within the Socio-technical Network (Females are represented in Yellow).

Figure 2 :

 2 Figure 2 : Sub Networks Representing Cross-gender Interactions.

Table 1 :

 1 Quantification of Activities by Gender. (1) Unknown gender is filtered out; (2) numbers are normalized by the number of contributors for each gender.

							Commits Comments Edited Files	Code Churn	p_value
	Project	Lang	Contrib Commits %Females %Males	F(%) M(%) F(%) M(%) F(%) M(%) F(%)	M(%)	(F vs M commits)
	Angular.js JavaScript	1601	8897	3.4	76.1 2.79 5.86 0.18 0.94	7.62 20.37	291.5 1162.13	0.17
	Moby	Go	1824	36007	3.5	88.1 20.08* 18.73* 0.01 0.19 131.6 93.69 7051.97 5612.75	0.2
	Rails	Ruby	3723	70762	4.2	91 8.07 19.21 0.73 4.63 29.62 70.25	77.94 1912.8	0.79
	Django	Python	1672	26283	5.3	88 5.51 16.43 0.11 0.84 17.34 70.05 271.48 3467.39	0.09
	Elasticsearch Java	1127	42702	4.2	86.1 25.45 42.24 0.04 0.56 166.08 481.9 6839.1 27271.75	0.43
	TensorFlow C++	1735	44132	5.8	80.7 17.92 25.65 0.09 0.21 131.23 258.34 19601.38 43082.54	0.14

Table 2 :

 2 Summary of the Most Important SNA Metrics using Sub-Networks Related to Gender.

https://github.com/about/diversity

https://api.github.com/users/

https://medium.freecodecamp.org/github-privacy-101-how-to-remove-personal-emails-from-your-publicrepos-58347b06a508

[START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF] http:/blog.namsor.com/api

RQ3. What is the role of females in building a sustainable collaborative social capital?

Motivation. Sustained participation in crucial for successful OSS project [START_REF] Robles | Evolution of the core team of developers in libre software projects[END_REF]. We expect that the more often individuals participate in OSS, the higher their chance of prolonged engagement.

Results. Table 1 summarizes the involvement of females in OSS projects. The percentage of females range from 3.4% to 5.8% which is drastically less than the average numbers presented in the annual report of GitHub [START_REF] Datausa | Demographics of Software Developers[END_REF]. When normalizing these numbers by genders, we noticed that women contribute slightly less than men except for the Moby project where women outperform (20.08% vs. 18.73% for men). Apparently, in the Angular.js project, the productivity of men is two times higher than women in terms of commits (2.79% vs. 5.86%). Similarly, we report on the difference of productivity for other projects (Moby=0.9; Rails=2.3; Django=2.9; ElasticSearch=1.6; TenserFlow=1.4).

Females evolve just as males within OSS projects. There is no statistical difference of the performance cross-gender except for the project Moby.

How the top females' performers evolved over time?

Moreover, Table 4 shows the evolution of the activity related to both genders (due to lack of space, we report data only for Angular.js). Although OSS projects keep attracting both genders, the number of active contributors (i.e., committing and commenting) decreases proportionally for both genders.

Threats to Validity

This section discusses the threats that might have affected our findings, and how we have alleviated these threats.

Threats to Internal Validity concern alternative factors that could have influenced our results. This exploratory study might suffer from at least the similar threats that other studies using GitHub Data do [START_REF] Kalliamvakou | The promises and perils of mining GitHub[END_REF] related to possible issues with data gathering and the missing of validation. We believe that using a large amount of data mitigates this threat. Another threat relates to the accuracy of gender prediction. Various approaches and tools to infer gender based on names and countries have been proposed in the literature [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF][START_REF] Lin | Recognizing gender of stack overflow users[END_REF][START_REF] Karimi | Inferring gender from names on the web: A comparative evaluation of gender detection methods[END_REF]. Most of these tools rely on English names stored in databases. However, these heuristics have not been yet empirically validated with GitHub data. We tried three tools [START_REF] Vasilescu | Gender and Tenure Diversity in GitHub Teams[END_REF][START_REF] Terrell | Gender differences and bias in open source: Pull request acceptance of women versus men[END_REF][START_REF] Vasilescu | Gender, representation and online participation: A quantitative study of stackoverflow[END_REF], and found that each has strengths and drawbacks. We used Namsor, a commercial tool with the assumption that it provide the most accurate results. We also assume the gender is a binary attribute.

Threats to construct validity consider the agreement between a theoretical concept and a specific measuring procedure. One threat considers the intrinsic blind spots when investigating consecutive snapshots of a dynamic social network over time-stamps (years). Indeed, there is no way to ensure that years are the "optimal" time-stamps to represent the snapshots of our social networks in order to capture the evolvement and interaction between nodes (contributors). Therefore, tracking a community evolution Even if females are underrepresented in OSS communities, they contribute in building a sustainable social capital for open software.

What is the role of females in building a sustainable social capital?


Min Yao

Valerie Kaftandjian

Angéla Peterzol-Parmentier

Andreas Schumm

Philippe Duvauchelle

Valérie Kaftandjian

Valérie Kaftandjian

Hybrid Monte Carlo and deterministic simulation approach for modeling a computed radiography imaging chain from X-ray exposure to optical readout

Keywords: Computed Radiography, Imaging Plate, Monte Carlo simulation, deterministic simulation, optical readout modelling

come

Hybrid Monte Carlo and deterministic simulation approach for modeling a computed radiography imaging chain from X-ray exposure to optical readout

Introduction

For over a century, film-based radiography has been used for industrial inspection. Recently, the NDT community started considering alternative digital techniques [START_REF] Ewert | Strategies for Film Replacement in Radiography[END_REF]. Computed radiography (CR), as the first standardized digital radiographic imaging technique, is an interesting alternative [START_REF]Non-destructive testing -Industrial computed radiography with storage phosphor imaging plates -Part 2: General principles for testing of metallic materials using X-rays and gamma rays[END_REF], as it employs a flexible (i.e. which can be bent and cut) storage phosphor imaging plate (IP) as digital detector, which shares the same advantages in terms of handling as film. However, the performance of standard CR systems is not as good as film-based radiography at high energies (i.e. several hundred keV up to MeV). For the inspection of high attenuation specimens (e.g. pipeline welding), high energy gamma sources, such as isotopes Iridium-192 and Cobalt-60, are often required. Therefore, the unsatisfied CR performance at high energies is an issue to be overcome in industrial applications.

The performance improvement of CR can be achieved by means of introducing appropriate filters and thin metallic screens in the system. Current international standards, concerning NDT radiography with digital detectors, address general metallic screen employment guidelines to ensure a good imaging quality [START_REF]Non-destructive testing -Industrial computed radiography with storage phosphor imaging plates -Part 2: General principles for testing of metallic materials using X-rays and gamma rays[END_REF][START_REF]Non-destructive testing of welds --Radiographic testing --Part 2: X-and gamma-ray techniques with digital detectors[END_REF][START_REF]ASTM Work Item WK34936, Revision of E2033 Standard Practice for Radiographic Examination Using Computed Radiography[END_REF]. However, the type and thickness of such screens are not clearly defined and a large panel of possible configurations does exit. Experimental studies on the CR image quality [START_REF] Ewert | Strategies for Film Replacement in Radiography[END_REF][START_REF] Mohr | Factors affecting probability of detection with computed radiography[END_REF][START_REF] Mango | Practical considerations and effects of metallic screen fluorescence and backscatter control in gamma computed radiography[END_REF][START_REF] Oliveira | Lopes Validation of Procedures for Welding Inspection Using Computed Radiography[END_REF], indicate that CR cannot fulfill the requirements in all NDT cases, due to the IP response and optical readout process.

Apart from experimental studies, computational simulation is also an important tool for physical phenomena comprehension and system performance optimization [START_REF] Rogers | Fifty years of Monte Carlo simulations for medical physics[END_REF][START_REF] Liaparinos | Modeling granular phosphor screens by Monte Carlo methods[END_REF]. It makes it possible to study how the relevant operating parameters affect the X-ray image without actually testing it in real life. At present, Monte Carlo and deterministic techniques are widely used to simulate radiation transport. Monte Carlo simulation is well accepted as the most accurate method [START_REF] Wagner | Review of hybrid (deterministic/Monte Carlo) radiation transport methods, codes, and applications at Oak Ridge National Laboratory[END_REF]. It can give insight on physical phenomena, but due to its random nature, a large amount of computational time is required, especially for complex geometry simulation [START_REF] Liaparinos | Modeling granular phosphor screens by Monte Carlo methods[END_REF][START_REF] Wagner | Review of hybrid (deterministic/Monte Carlo) radiation transport methods, codes, and applications at Oak Ridge National Laboratory[END_REF]. Deterministic methods, on the other hand, can handle easily complex geometries, and are quite computationally efficient, but the estimation of scattering and fluorescence effects is quite difficult.

In prior works, many CR modeling and simulation studies were dedicated to medical applications [START_REF] Vedantham | Modeling the performance characteristics of computed radiography (CR) systems[END_REF][START_REF] Kausch | Monte Carlo simulations of the imaging performance of metal plate/phosphor screens used in radiotherapy[END_REF][START_REF] Brettle | Dual-energy digital mammography utilizing stimulated phosphor computed radiography[END_REF][START_REF] Barnea | Use of storage phosphor imaging plates in portal imaging and high-energy radiography: The intensifying effect of metallic screens on the sensitivity[END_REF][START_REF] Li | Dose response of BaFBrl: Eu2+ storage phosphor plates exposed to megavoltage photon beams[END_REF][START_REF] Jaffray | X-ray scatter in megavoltage transmission radiography: Physical characteristics and influence on image quality[END_REF][START_REF] Cunningham | A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems[END_REF][START_REF] Cunningham | Cascaded models and the DQE of flat-panel imagers: noise aliasing, secondary quantum noise, and reabsorption[END_REF][START_REF] Souza | Methodology for digital radiography simulation using the Monte Carlo code MCNPX for industrial applications[END_REF][START_REF] Correa | Computed radiography simulation using the Monte Carlo code MCNPX[END_REF]. Vedantham and Karellas have developed a complete (from X-ray exposure to digital readout) analytic CR model to analyze the system performance factor propagation during image formation process such as detective quantum efficiency (DQE) and modulation transfer function (MTF) [START_REF] Vedantham | Modeling the performance characteristics of computed radiography (CR) systems[END_REF]. This model is based on a cascaded linear system approach [START_REF] Cunningham | A spatial-frequency dependent quantum accounting diagram and detective quantum efficiency model of signal and noise propagation in cascaded imaging systems[END_REF][START_REF] Cunningham | Cascaded models and the DQE of flat-panel imagers: noise aliasing, secondary quantum noise, and reabsorption[END_REF], and based on the assumption that the X-ray scattering effect is negligible. However, for high energy CR, where the scattering effect becomes dominant, this assumption is not appropriate. A more precise model is needed for scattering effect estimation. In [START_REF] Souza | Methodology for digital radiography simulation using the Monte Carlo code MCNPX for industrial applications[END_REF] and [START_REF] Correa | Computed radiography simulation using the Monte Carlo code MCNPX[END_REF], E.M. Souza et al. proposed a methodology for computed radiography simulation for industrial applications using Monte Carlo code MCNPX taking into account the energy-dependent response of imaging plate (IP) and the digitization effect. But in their approach, the spatial degradation due to X-ray interaction in the detector has not been considered. Full Monte Carlo simulation could be the solution to overcome the mentioned issues. However, due to its random nature, the computation time might be extremely long.

In this paper, we propose a CR model which combines the use of both Monte Carlo and deterministic codes. Such a complete hybrid model is the first available one to our knowledge.

The CR imaging process is split into three successive stages: i) X-ray attenuation by the object;

ii) energy deposition resulting in X-ray latent image generation; iii) optical readout resulting in the final digital image generation. The first stage is based on a deterministic code which provides a realistic radiant image of a complex-shape object in a short time (typically 0.1 s) based on the object CAD model. The second stage is based on an offline CR detector response model which is obtained by means of off-line MC simulations accounting for all physical effects such as fluorescence, scattering and electrons interactions. The response function is then convolved with the object radiant image. A database of several detector systems has been built in order to cover all the industrial application range. As concerns the optical readout (third stage), the laser spreading distribution function is obtained off-line by a dedicated optical MC tool developed on purpose, while the laser scanning operation is modeled by an analytic function. Thus, we obtain a complete model which is able to simulate a realistic inspection case study in a reasonable time, while taking into account all physical effects both for X-ray and optical photons effects. It is worth noting that the presented model allows to determine mean values and obviously does not include noise. This approach allows to add noise afterwards while keeping a reasonable computation time, even for a complex shape object. Thus, all Monte Carlo simulations are carried out off-line, allowing to model all physical effects in the form of response functions.

In the following, the CR principle is briefly reminded in section 2, together with an overview of the model, then a detailed description of the different simulation stages is given in section 3.

Section 4 and 5 show some results, before concluding in section 6.

CR principle and general overview of the modelling approach

CR principle

As illustrated in Figure 1a, CR imaging consists first in the X-ray exposure itself (A), where the energy transmitted by an object is deposited in the detector. The particularity of CR yields in the type of detector, a photo-stimulable imaging plate (IP), in which the deposited energy allows to create electron/hole pairs in the material. Some of these charges are trapped in the material, forming a latent image which is stable during several hours. The second step (B) consists of reading this latent image. A laser beam allows to excite the storage centers and light is emitted (photo-stimulation mechanism). The third step is the erasure of the plate which makes the detector available for a new image (C).

Only some specific materials present this photo-luminescence effect with sufficient stability of the trapped electrons yielding a useful latent image. The most common material is BaFBr:Eu 2+ , available in the form of grains in a binder. Since the discovery of the photo-stimulability of BaFBr:Eu 2+ , several works have been done attempting to find out the physical mechanisms occurring during X-ray radiation. Present day's well accepted electron/hole production mechanism is proposed by Koschnick et al. [START_REF] Koschnick | Experimental evidence for the aggregation of photostimulable centers in BaFBr:Eu2+ single crystals by cross relaxation spectroscopy[END_REF][START_REF] Leblans | Storage phosphors for medical imaging[END_REF]. It is worth noting however that those mechanisms are extremely complex and not fully understood.

BaFBr:Eu 2+ imaging plates are successfully used in the medical field, because the X-ray energy range gives rise mainly to photoelectric effects in the material. For higher energies (such as Cobalt or Iridium sources), the efficiency of imaging plates is known to be poor. To improve performances, NDT standards [START_REF]Non-destructive testing -Industrial computed radiography with storage phosphor imaging plates -Part 2: General principles for testing of metallic materials using X-rays and gamma rays[END_REF] require the use of metallic screens to be used together with IP (front and back screens), such as what is done for radiographic films. However, unlike films where the use of screens yields sufficient imaging performance at high energy, in CR, the optimal nature and thickness of screens is still to be found, such as optimal properties of the IP itself. This is the reason why simulation can be interesting, to understand the physical mechanisms during image formation, and find optimal combinations of IP/screens.

Overview of the simulation approach

During X-or gamma-ray exposure, the radiation beam first interacts with the object, and owing to the object attenuation, only part of the beam can arrive at the CR detector 1 . This transmitted beam carries the object pattern, which is received by the CR detector; a portion of the transmitted beam penetrates through the detector and escape from the system, while the other portion interacts with the detector resulting in a latent image. The CR image formation is viewed as a three-stage process (Figure 1b): X-ray attenuation, latent image generation and digital image generation. Different simulation methods (Monte Carlo or deterministic) are applied to different stages. The CR simulation method is summarized as follows.

Stage 1: X-ray attenuation by an object (X-ray beam → attenuated X-ray beam). In this step, the source beam interacts with an object resulting in an object image. In this paper, the Virtual Xray Imaging (VXI) software, a deterministic code for fast complex imaging [START_REF] Duvauchelle | A computer code to simulate X-ray imaging techniques[END_REF], [START_REF] Freud | Deterministic simulation of first-order scattering in virtual X-ray imaging[END_REF], is used.

The output image should contain the energy information, namely a spectral image, here denoted Obj(E,x,y). The laser spreading is simulated with a Monte Carlo tool developed on purpose. This tool outputs a laser distribution function f(x,y,z). The scanning is then modelled analytically, based on the scanning parameters i.e. laser power P laser , scanning speed v scan and pixel size l pxl .

(b) Signal collection, amplification and digitization (PSL photons → gray levels).

In this sub-step, the emitted PSL is collected by a light guide, then detected and amplified by a photo-multiplier tube and finally digitized with an analog-to-digital converter. A PSL to gray level conversion factor g psl can be applied.

Stage 3 is modeled by an operator H2:

Dimg(x,y) = H2(Limg; f; scanning parameters) (2)
To summarize, as represented in Figure 2, the presented method allows to simulate the complete CR imaging chain, in which all the operating parameters such as source, detector configuration and optical readout parameters are taken into account through the operators H1 and H2.

Figure 2: Schematic representation of the simulation of the entire CR imaging chain

Before introducing the details of the model, let's introduce the assumptions adopted:

 As concerns the X-ray exposure, the CR detector is considered as a linear system, so that the convolution operator H1 can be applied to obtain the X-ray detector response to any object spectral image obj.

 The electrons emerging from the object are neglected. Our approach deals with high attenuation object (i.e. high thickness); therefore, the fraction of electrons in the radiation emerging from the object is very small. Moreover, before arriving at the detector, a great part of the electrons are absorbed by air and cassette (normally the CR detector is handled in a cassette). Be aware that the electrons produced by metallic screens and IP are not neglected, and are taken into account in the detector model obtained by MC simulations.

Spectral image of object

Obj(E,x,y)  Normal incidence of radiation on the detector. In reality, the transmitted X-ray photons arrive at the CR detector with a certain incident angle. In our model, we assume the X-ray photons travel forwardly, with a normal incidence on the detector.

X-ray attenuation in object

 Normal incidence of laser beam on the imaging plate during the readout process.

3 Detailed description of the model

Object image generation (spectral image)

In this step, to generate Obj(E,x,y), a deterministic code for simulating complex imaging set-up is preferred since it can offer a realistic object image in a short time.

To generate Obj(E,x,y), a virtual detector is used and placed at the actual detector plane. This virtual detector is divided into M×N pixels to record the spatial distribution of the incident photons. Each pixel pitch counts the incident photon number, and classifies the photons into different energy channels. The direct output of this virtual detector is the photon number per energy channel per pixel pitch, and the Obj(E,x,y) should be the output value divided by the pixel pitch surface. Figure 3 is an example of the object image generation: (a) is a geometry set-up generated using VXI software [START_REF] Duvauchelle | A computer code to simulate X-ray imaging techniques[END_REF][START_REF] Freud | Deterministic simulation of first-order scattering in virtual X-ray imaging[END_REF], where a virtual detector (in green) is placed at the actual detector plane; and (b) is the spectral image detected by the virtual detector Obj(E,x,y). The example here is obtained with VXI software [START_REF] Duvauchelle | A computer code to simulate X-ray imaging techniques[END_REF][START_REF] Freud | Deterministic simulation of first-order scattering in virtual X-ray imaging[END_REF] x y E

Detector dose response model generation

The detector dose response model, denoted PSF det (E,x,y,z), is the second input required by the operator H1.

The detector considered in this study is a multiple-layered structure, in which the imaging plate is sandwiched between metallic screens (Figure 4a). The imaging plate also consists of multiple layers such as overcoat and phosphor layer. The phosphor layer is the effective medium which stores the latent image, and will be later readout by CR scanner. Hence the PSF here is a 3D energy absorption efficiency map within the IP's phosphor layer. A Monte Carlo simulation tool [START_REF] Yao | X-ray imaging plate performance investigation based on a Monte Carlo simulation tool[END_REF], based on the use of PENELOPE [START_REF] Salvat | A code system for Monte Carlo simulation of electron and photon transport : workshop proceedings[END_REF], has been developed to characterize the CR detector response at different energies. In order to record the PSF, a uniform three-dimensional grid is applied to the phosphor layer. As shown in Figure 4a, we send a mono-energetic pencil beam (E i ) to strike the detector det. The raw output DEP(x,y,z) of the simulation is illustrated in Figure 4b, which is the deposited energy map (absorbed energy per unit volume keV•cm -3 ) within the phosphor layer. The PSF is obtained with:

(3)
where N i is the number of the incident photons. As a Monte Carlo calculation contains statistical noise, the incident photon number should be as large as possible to limit this noise. The impulse response is of cylinder symmetry around z-axis, hence we also apply a radial averaging to the PSF to reduce the noise, and the PSF is reduced to a 2D function.

In such a way, the storage space can be saved. The storage digits can be further reduced by applying an analytic fitting function to each 1D profile at different z. energies ranging from E min to E max are sampled to excite the detector det. After the radial averaging operation, we have a set of PSF, and all these PSFs make up the response model of the detector det. In order to cover the energy range of common NDT radiation sources (such as Ir192 and Co60), E min is assigned 0 keV, and E max 1400 keV.

In order to build a database of detector models, several detector configurations have been simulated. At present, we have covered all the metallic screens (front/back) combinations proposed in the standards EN ISO 16 371-2 [START_REF]Non-destructive testing -Industrial computed radiography with storage phosphor imaging plates -Part 2: General principles for testing of metallic materials using X-rays and gamma rays[END_REF] and ISO17636-2 [START_REF]Non-destructive testing of welds --Radiographic testing --Part 2: X-and gamma-ray techniques with digital detectors[END_REF] as well as other screens, for different thicknesses and properties of BaFBr imaging plates, to form a database of 128 configurations.

Latent image computation

The latent image generation involves the energy deposition and storage center formation. Only a portion of the deposited energy is stored in the form of storage centers. At present day, the storage center forming mechanism is still not clearly understood [START_REF] Seggern | Photostimulable x-ray storage phosphors: a review of present understanding[END_REF][START_REF] Rowlands | The physics of computed radiography[END_REF][START_REF] Thoms | The quantum efficiency of radiographic imaging with image plates[END_REF]; moreover, it is different from one to another material. Therefore, the latent image (storage center) formation process is simply modeled as a conversion factor g sc (unit: keV -1 ). In the review of Rowlands [START_REF] Rowlands | The physics of computed radiography[END_REF], the absorbed X-ray energy to storage center ratio in BaFBr is 2.4 keV -1 ; while in [START_REF] Thoms | The quantum efficiency of radiographic imaging with image plates[END_REF], a different ratio 7.98 keV -1 is reported. In the following, we assign the normalized value 1 keV -1 to g sc . Equation (4) gives the operation realized. where:

-H1 represents the latent image generation model which is a 2D spatial convolution (along x and y), at a given depth z, integrated over all energies, and finally multiplied by the conversion factor g sc ;

gsc represents the absorbed X-ray energy to storage center conversion efficiency (unit: keV -1 ); -Obj(E,x,y) is the spectral object image, namely the number of photons per unit surface per energy channel (unit: cm -2 . keV -1 ); E,x,y,z) is the detector model, which is in fact a set of point spread functions (unit: cm -3 ) for all energies;

-PSF det (
-E is the X-ray photon energy (unit: keV);

The term which is multiplied by g sc represents the deposited energy distribution (unit: keV. cm -3 ).

end end

Note that the numerical convolution requires the pixel size matching between Obj and PSF det . In this paper, the sampling match is achieved by means of interpolation.

The algorithm output is a 3D latent image. We keep the information along detector depth (z) direction, because the latent image is read by a scanning laser, the laser power modifies the penetration of the laser light, and thus the deep storage centers have less contribution to the readout image. With this in mind, we choose to keep the information along z.

Optical readout

Readout is a crucial process that affects the final image quality (e.g. efficiency, contrast and spatial resolution). As shown previously in Figure 1a, the basic principle of CR readout is the "flying spot": via a rotating mirror, the finely focused stimulating laser beam scans horizontally the imaging plate (IP). Together with a continuous translation of IP, the stored information can be released line by line through the whole imaging plate. This scanning process is usually called raster scan (or raster scanning).

The imaging plate has a multiple-layered structure which basically consists of a protective layer, a photo-stimulable phosphor (PSP) layer (the phosphor grains are embedded in polymer binder) and a support layer. Sometimes, a reflective or an absorbing layer is added between PSP layer and support layer. Concerning the optical readout simulation, we are only interested in the PSP layer and the two layers in contact with it. The reason is that the optical photons are much less energetic comparing with X-or -rays, thus the effects of the 'outer layers' can be neglected.

Therefore in this part, we simulate the light transport problem in a three-layered structure (see The optical readout process is viewed as a transfer function H2 (Figure 7a), which also requires two inputs: latent image and IP optical response model. Flying spot scanner is the most common CR reader: a finely focused laser is used to scan and release, line by line, the latent image; the latent image is modified while the laser spot traverses the IP [START_REF] Leblans | Storage phosphors for medical imaging[END_REF]. Thus, unlike the previous operator H1, H2 is a modified convolution operation. The final digital image is computed using the following equation, where x m , y n denotes the coordinates of pixel m,n in the image (x and m refering to the laser scan direction, while y and n to the IP translation direction):

              y x
where Limg (m,n) (x,y,z) is the scanning modified latent image at reading point (x m ,y n ), whose formula is given in relation [START_REF] Mango | Practical considerations and effects of metallic screen fluorescence and backscatter control in gamma computed radiography[END_REF]. f(x,y,z) is the IP optical impulse response to a laser beam, P(z) is the probability that a photon (emitted at z) could escape from the front side of IP, σ is the optical cross section of photo-stimulation, P laser is the laser power and t scan is the dwell time of laser spot at (x m ,y n ). This formula ( 5) is based on the laser latent image interaction model in the work of Thoms [START_REF] Thoms | Image properties of polycrystalline storage films[END_REF].

The IP optical response model f(x,y,z) is again obtained through the Monte Carlo method. A specific Monte Carlo code has been programmed on purpose in Matlab to simulate the light propagation problem in IP [START_REF] Yao | Computed Radiography System Modeling, Simulation and Optimization[END_REF]. Some physical models of light/IP interaction adopted in the code are based on [START_REF] Wang | MCML-Monte Carlo modeling of light transport in multilayered tissues[END_REF] and [START_REF] Fasbender | Monte Carlo modeling of storage phosphor plate readouts[END_REF]. Figure 7b) shows an example of IP response to a normal incident laser beam, for which 2×10 6 photons have been generated to strike the imaging plate. It is worth noting that the value of Limg (m,n) (x,y,z) is modified by the laser scanning process, i.e. it is changed while the laser spot moves from one position to another. For this reason, we emphasize that Limg (m,n) (x,y,z) here refers to the storage center distribution right before the laser beam arrives at pixel (m, n). In order to obtain Limg (m,n) (x,y,z), namely, the scanning modified latent image at reading point (x m ,y n ), the following formula is applied. More details can be found in [START_REF] Yao | Computed Radiography System Modeling, Simulation and Optimization[END_REF].

(

) 6
with l pxl being the optical readout output pixel size.

The corresponding computation algorithm is:

Initialize the digital image array Dimg(x,y) = 0. The MC simulation package PENELOPE [START_REF] Salvat | A code system for Monte Carlo simulation of electron and photon transport : workshop proceedings[END_REF] containing detailed physical models of both xray/matter and charged particle/matter interactions, is used here. Since it takes into account all kinds of interactions, the simulation running is slow. As a first step to validate our model, we have chosen a very simple imaging set-up to compare the simulation results obtained with a full Monte Carlo code and our model, comparing only the X-ray exposure part (i.e. without the optical readout), in order to validate the H1 operator. We have simulated the imaging set-up as presented in Figure 8 with a full PENELOPE simulation and our model H1. The source used was a fixed energy cone beam. The energy was 100 keV, and the beam aperture was set to 2/300 rad. The number of the incident photons was 10 9 . The PENELOPE simulation running took about 64 hours, we see that the object profile is still noisy, while our H1 model takes about 1 hour including VXI running time and H1 operation time. Note that the comparison was done on a fine scale in order to see the accuracy. Thus, a very fine sampling was used both in spectral and spatial domain:1 keV energy sampling step and a spatial IP sampling with a 100×100×100 grid for x, y, and z directions for a 2 mm × 2 mm × 0.150 mm imaging plate.

Figure 9 presents the object profiles across the iron steps. All profiles have been normalized by their mean signal value. The black one is the object ideal profile. The profile obtained with our H1 model (blue) agrees perfectly with that obtained with PENELOPE (magenta). The H1 operator being a convolution operator, the profile obtained with our model does not contain any noise, which is normal. This comparison allows to show that the contrast due to the 1 mm step is well modelled by the H1 operator, in comparison with a full MC simulation.

Result: complex imaging set-up simulation

The model has then been applied to simulate the responses of different detector configurations to the same geometric set-up as illustrated in Figure 3a. A complex shape object with an image quality indicator (IQI) was irradiated by a monochromatic (100 keV) point source. This constitutes a realistic inspection case study where the IQI allows to quantify the image quality in terms of contrast resolution for different hole sizes. The virtual detector was set to 70×70 mm 2 in size with a pixel size of 10×10 µm 2 . The photon energy was stored into different energy channels from 1 keV to 100 keV with a channel width of 1 keV.

The detector was modeled as an imaging plate sandwiched between metallic screens. The imaging plate was set as a multiple-layered structure which consists of, in sequence: a 6 µm protective layer, a 150 µm phosphor layer, a 254 µm support layer and a 25.4 µm backing layer.

The materials of these layers are respectively Mylar for the protective and support layers, BaFBr:Eu 2+ for the phosphor layer and polycarbonate for the backing layer.

The responses of the following detector configurations were compared: a) IP alone; b) IP with 0.2mm Pb screens on both sides (denoted as IP+0.2Pb) and c) IP with 0.2 mm Pb and 0.8 mm Sn screens on both sides, where Sn is in contact with IP (denoted as IP+0.2Pb0.8Sn).

Figure 10 presents the full object image accounted by the virtual detector, i.e. the image Obj(x,y).

We see the object shape, and the image quality indicator (IQI) in the image center. Then we apply our H1 model, to obtain the latent image detected with the three detector configurations, Limg(x,y,z). In order to have a better comparison, we only illustrate the region of interest containing the IQI. Figure 11 compares the IQI zone images obtained using different detectors, where Limg(x,y) is obtained by summing Limg(x,y,z) over z. Owing to the response of the detector, the signal level drops and the resolution decreases. With the three detectors, the smallest hole can still be identified; however, the sharpness of IP+0.2Pb is not as good as IP alone and IP+0.2Pb0.8Sn. In order to compare the images sharpness, we have normalized the four images to their maximum value. We plot the normalized profiles along AB (see Figure 10) in Figure 12.

The sharpness of IP alone is very close to the ideal detector, except a small contrast loss at high spatial frequency (difference at sharp edges). With IP+0.2Pb, the image sharpness is the worst. We then investigated the influence of the readout process on image quality, for one detector configuration. The readout signal depends on the product of the laser power P laser and dwell time t scan , therefore, in the following, we simply use their product as a readout factor p read =P laser .t scan .

Figure 13 shows the effect of the optical readout. The images in the upper half are the object image Obj(E,x,y) and the energy deposition image in IP alone Limg(x,y,z) shown in Figure 11a&b which are reminded here for a better visual comparison. Only a fraction (~ 5%) of the object image is detected by IP. In the lower half, we show the readout images using two different reading factors p read = 10 16 and p read = 10 10 . With large values of reading power, most of the storage centers can be released (not all the released storage center can contribute to the final image), however a visible shift is observed (comparing Figure 13c&d) due to the scanning process. We focused then on the dependency between the reading efficiency (output signal over input signal) and the laser power (Figure 14). It was observed that the efficiency increases slowly at low laser powers, while a significant rise was pointed out between 10 13 and 10 15 p read values; and at 10 16 the curve starts to reach its maximum. One may notice that the maximum efficiency does not equal to one. Indeed, a high power increases the photoluminescence, but the photons are emitted isotropically and only a small fraction can escape from the front surface of IP and contribute to the final image. In order to compare the image sharpness, the images have been normalized by their maximum values. In Figure 15, profiles along the IQI are presented, along the y direction corresponding to the IP translation direction (with the notations of equations ( 5)).

The red curve refers to the latent image profile. The curves of the first 2 powers overlap each other, then we lose contrast by increasing the power. Comparing the profiles, we also see an obvious shift between the black and the red curves in the IP translation direction due to the scanning process modeled by equation ( 6).

Discussion and conclusion

This paper presents a CR system model, where the CR detector and the optical readout are modeled as two different transfer functions. As concerns the X-ray exposure part, which is the most crucial step because it conditions the greater part of the final image, the comparison of H1 operator with the full MC simulation using PENELOPE shows a very good accordance. More details are given in [START_REF] Yao | Computed Radiography System Modeling, Simulation and Optimization[END_REF] about the optical part simulation which is in good correspondence with [START_REF] Fasbender | Monte Carlo modeling of storage phosphor plate readouts[END_REF].

A realistic inspection case study has been defined to illustrate the interest of this full model. As an example, the performances of three different detectors were compared in this particular inspection case. By comparing the obtained images, one can determine the most appropriate detector configuration. Then, different readout factors have been simulated (representing either a change in laser power or a different scanning time), showing the influence on the final image.

Increasing the laser power allows to obtain greater signal, although at the expense of spatial resolution. The effect of scanning has been modelled analytically for the first time to our knowledge, and appears as a translation of the image when the readout factor is important.

With this method, one can simulate the complete CR image formation, and take into account the operating factors such as source parameters (in the first step), detector configuration (in the second step) and scanning parameters (in the last step). This full model is "user-driven", which means that special emphasis has been taken to the selection of parameters which are accessible to the user (such as laser power). Also a database of 128 detectors has been built thanks to the MC off-line tool, with all physical effects up to energy of 1.4 MeV, which has never been done before. This represents a huge number of simulation hours.

It has to be noted that the application of H1 and H2 operators requires the sampling match of Obj with PSFdet and Limg with f. Interpolation can be used for this purpose. The computation efficiency strongly depends on the array size of Obj(E,x,y), Limg(x,y,z), PSF(x,y,z) and f(x,y,z).

Great accuracy requires a small sampling size, and thus a large array size, which makes the simulation slower. The total simulation time varies from minutes to several tens of minutes or even more. It is worth noting that this model does not include noise and allows reasonable simulation time. The user can thus optimize parameters for contrast optimization even for complex shape objects without using noise. However, noise can be added afterwards for a complete image quality assessment.

To summarize, the interests of this global model are:

 Reducing simulation time. The detection efficiency of CR detector at high energy (> hundreds keV) is very small (<1%), therefore, to obtain the same SNR level, a full MC simulation including detector effects would need to generate hundreds times more incident photons than our model H1. Thus, the running is accelerated by at least 100 times.

Using a deterministic code to simulate the object image also reduces the global simulation time.

 Avoiding repeating simulation running. With a full MC simulation, one needs to rerun the MC code for each detector configuration in order to determine the optimal conditions. Thanks to the detector transfer functions, no MC run is needed during the current simulation, as the MC codes are run off-line.

 3D deposited energy distribution within IP. The CR optical readout is a crucial process that limits the system sharpness and efficiency. The light diffuse along its penetrating depth, hence knowing the 3D deposited energy distribution is important.

The presented simulation code has been successfully applied in a realistic case study with Selenium gamma source in order to compare the image quality obtained using different screens [START_REF] Yao | Modeling computed radiography with imaging plates[END_REF].

Figure 1 :

 1 Figure 1: (a) CR principle with the acquisition procedure highlighted: A. X-ray exposure which yields a latent image, B. Optical readout of the latent image, and C. Erasure of the image; (b) only part A and B are simulated, sub-divided into three stages.

Stage 2 : 1 ) 3 :

 213 X-ray latent image generation (X-ray photons incoming the CR detector → storage centers in IP). This stage is split into two sub-steps. (a) X-ray/detector interaction (X-ray photons incoming the detector → deposited energy in IP), via the detector response model (denoted PSF det ) resulting in a 3D deposited energy image. The detector response model is obtained by means of an off-line Monte Carlo simulation. (b) Latent image formation (deposited energy in IP → storage centers in IP). The latent image is in fact the map of storage center distribution in IP. At present day, the latent image formation mechanism is not clearly understood. Hence this step is modeled as conversion factor, denoted g sc . The entire Stage 2 is modeled by a convolution-based operator H1: Limg(x,y,z) =H1(Obj; PSFdet) (Stage Digital image generation (storage centers → gray levels). This stage is also split into two sub-steps. (a) Optical readout (storage centers → photo-stimulated luminescence (PSL) photons). In CR, the latent image is readout by a scanning laser. Due to the IP's granular property, the laser light spreads out in IP; storage centers within the laser volume can be released resulting in PSL.

3 :

 3 digital image generation (Transfer function of optical readout) Stage 2: X-ray latent image generation (Transfer function of IP)

Figure 3 :

 3 Spectral object image: (a) geometry setup and (b) illustration of a spectral image.

Figure 4 :

 4 Impulse response of a detector: (a) Geometry configuration and, (b) 3D energy deposition map: the red arrow indicates the beam propagation direction which is also the IP depth direction. The second step of detector response model generation is to repeat the previous operations (i.e.raw PSF simulation and radial averaging) by scanning all energies (see Figure5). Different

Figure 5 :

 5 Figure 5: Generating the detector dose response function of a fixed detector det.

  Multiplying by g sc allows to convert this energy into a storage center distribution i.e. latent image.Numerically, this equation is realized energy by energy. For each energy channel, we compute the storage center distribution at different z; by summing the latent images obtained for all energy channels, we get the final output latent image.The corresponding computation algorithm is:Initialize the latent image array Limg(x,y,z) = 0. for each energy channel Ei =0 to Emax do for each IP depth: zj = 0 to d do Compute the latent image at depth zj given by photons of energy Ei Limg(x,y,zj) = g sc .[Obj Ei (x,y) * PSF Ei,zj (x,y)]; Accumulate Limg(x,y) to the corresponding depth slice zj in latent image array Limg(x,y,zj) = Limg(x,y,zj) + Limg(x,y,zj).

Figure 6 )

 6 Figure 6): top layer (e.g. protective layer), PSP layer and bottom layer (e.g., reflective layer or support layer). The top and bottom layers are considered to be clear media where the laser light travels in a straight line, while the PSP layer is modeled as granular layer where the scattering effect is pronounced.

Figure 6 :

 6 Figure 6: Optical effects within imaging plate. A three-layered structure is considered: a top layer, a PSP layer and a bottom layer, where the top and bottom layer are clear media, and the PSP layer is granular. The laser beam (red) strikes perpendicularly the front side of IP; it first passes through the top layer without expanding the beam size; in the PSP layer, the laser light diffuses along its traveling path; at the interfaces, top-PSP and PSP-bottom, the laser photons might be absorbed or reflected. Part of the storage centers within the red volume will be stimulated by laser photon resulting in PSL (blue arrows), which also suffers multiple scattering effect; only a fraction of the emitted PSL could reach the front surface and be detected contributing to the final image

Figure 7 :

 7 a) Generation of the digital image using the optical readout transfer function H2; b) an example of IP model (impulse response of IP to laser light).

for 4

 4 each line: n = 1 to N do for each pixel: m = 1 to M do Update the latent image Limg (m,n) (x,y,z) Compute the output signal of the current pixel Dimg(x m ,y n ) end end Comparison with full Monte Carlo simulationMonte Carlo method is commonly considered as the reference for radiation transport simulation.

Figure 8 :

 8 Figure 8: Geometric set-up of the comparison simulation. The object is a two-step iron stepwedge. The detector is a 2 mm × 2 mm × 0.150 mm imaging plate. The beam aperture was set 2/300 rad.

Figure 9 :

 9 Figure 9: Object grey-level profiles obtained with our H1 model compared with a full MC simulation (PENELOPE).

Figure 10 :Figure 11 :

 1011 Figure 10: X-ray image obtained with VXI. This 2D illustration is obtained by summing the X-ray image Obj(E,x,y) along its energy axis.

Figure 12 :

 12 Figure 12: Normalized profiles along the IQI holes (AB line in figure 10): the red curve corresponds to the X-ray image obj(y) at the fixed x(AB) position; the green, pink and blue curves correspond respectively to the latent image profiles Limg(y) obtained with the three detector configurations IP, IP+0.2Pb and IP+0.2Pb0.8Sn.

Figure 13 :Figure 14 :

 1314 Figure 13: Simulation result: a) object image obj(E,x,y), b) latent image Limg(x,y) obtained with IP (same as Figure 11b), c) final Dimg(x,y) image with a readout factor p read =10 16 , d) readout factor p read =10 10 .

Figure 15 :

 15 Figure 15: Normalized profiles along IQI (line AB shown on figure 10).

In the following, the term "detector" should be understood as the complete system including the IP itself and front and back screens, which are metallic screens as recommended in the international standards.

Highlights :

We have developed and implemented a novel simulation tool for computed radiography, including not only the X-ray exposure part, but also optical readout.

In order to keep reasonable computing time, all physical effects have been modeled using Monte Carlo code off-line. Two operators have been introduced to then simulate the complete process in an analytic way.

A database of 128 imaging systems (comprised of the phosphor imaging plate and front and back metallic screens) have been modeled.


Odile Blanchard

Pierre Le Queau

Philippe Menanteau

The socio-economic analysis of collective behavior and decision making of co-owners to invest in thermal retrofits in private multi-family buildings

Goal of the study : to better understand the factors leading to the collective decision of investing in thermal retrofit in multi-family buildings

The massive energy retrofit of the private building stock is crucial to reach the GHG emission reduction targets set in France's national low-carbon strategy. Knowing the motives underlying the decision to renovate is necessary to define efficient public policies in this field. This knowledge has considerably increased in individual housing over the last years but it is still very scarce in collective housing. More specifically, in private multi-family buildings, the collective decision turns out to be complex, due to the number of actors who participate in the decision-making process, and to the heterogeneity of individual situations and preferences.

The goal of the research undertaken by Gael Laboratory of Grenoble-Alpes University is to shed light on the collective behavior of the co-owners in the decision making-process for energy retrofitting their multi-family building.

Our research draws on the thermal retrofit incentive programme called MurMur2, which is currently underway and targets the private multi-family buildings of the Grenoble urban district "Grenoble Alpes Métropole", shortly named "Metro".

Research protocol : analysis of the dialogues of the collective moments in the building process of the retrofit decision

The research process analyses the dialogues between the various stakeholders involved in the decision to invest or not in thermal retrofitting. It is innovative as, to our knowledge, it has never been undertaken in the context of energy retrofitting of multi-family buildings thus far.

Research material

Within the MurMur2 programme, the decision to undertake the thermal retrofit comes after four formal steps with which each condominium has to comply. The steps of the "Parcours de service" (service process) include the following meetings of the co-owners:

a preliminary information meeting (called REP meeting) organized by ALEC (Agence Locale de l'Energie et du Climat), presenting the thermal characteristics of the coowners' building, the advantages and challenges of insulating, as well as the general collective financial support brought by MurMur2;

a general assembly of the co-owners (called MOE meeting) to select and vote for a prime contractor ; if the general assembly votes against the selection of a prime contractor, the condominium cannot benefit from the MurMur2 Program; the next two meetings described below do not occur; an information meeting (called SOL meeting) organized by SOLIHA, focusing on all the possible financial assistance mechanisms for co-owners (including MurMur subsidies, loans and individual financial support) a general assembly of the co-owners (called FIN meeting) to make the final decision whether to invest or not in the thermal retrofit of their building.

Among the 200 condominiums entered in the MurMur2 program, we selected twenty-three condominiums representative of the diverse situations found in the Metro area (condominium size, heating type, energy used for heating, location). For each selected condominium, we had planned to attend all the meetings of the service process, as observers. As of August 2019, we have attended 51 meetings overall, of which 20 REPs, 13 MOEs, 10 SOLs, 8 FINs, and 3 other optional meetings. We have not been able to attend all the meetings that we had initially intended, as we were not always informed of the meetings. Each meeting lasts between one and two hours; some of them may even reach almost 3 hours.

At the stage of the MOE meetings, a few condominiums of our sample decided to vote against a prime contractor, which brought the MurMur2 Programme to a halt for them. Another one decided not to join the Programme after their SOL meeting. All the condominiums of our sample that went through the four steps decided to invest in a thermal retrofit of their building. Some condominiums have not gone through the whole service process yet, due to slow procedures within the condominiums: their SOL and FIN meetings will be planned before the end of 2020.

Our research process starts with our presence in the REP, MOE, SOL and FIN meetings of each condominium. We act as observers in these meetings, on the basis of an observation protocol. While watching, taking notes, and qualifying the interactions between the actors, we record all the dialogues. After the meetings, we have all the dialogues transcribed and anonymized by two well-trained students. This written corpus is our main analysis material.

The considerable corpus stemming from the transcripts is then analyzed with two different softwares of textual data analyses, namely IRAMUTEQ and N'VIVO.

Research softwares

The first software, IRAMUTEQ, is a tool for the automatic analysis of textual data. It analyses the structure of text segments, the distribution and concomitance of the words used within the segments. Therefore it identifies the prevailing subjects addressed in the dialogues, without defining them ex ante. Its output is automatic classes of words sorted by similarities found by the software. Figure 1 is an illustration of IRAMUTEQ output.

Figure 1: main subjects addressed during the REP meetings (IRAMUTEQ)

The second software, N'VIVO, requires us to code the transcripts of the meetings ex ante, before any analysis. We code different types of information in N'VIVO. First, we code and qualify all the people taking part in the dialogues e.g., "co-owner", "property manager", "ALEC officer", so that we know which type of person says what. Then, we identify and code the dialogues according to the various subjects addressed, based on the subjects identified by IRAMUTEQ. Finally, we also code some rhetoric elements that may be important in the decision making process, e.g. "disagreement", "expertise", "question". Overall, we have defined 7 speaker codes, 20 subject codes, and 13 rhetoric codes. Once the coding has been carried out, we can start analyzing the content of the dialogues through N'VIVO. The outputs of N'VIVO are multiple graphs and numerical tables at the discretion of the researchers.

In conclusion, IRAMUTEQ and N'VIVO are complementary tools to carry out textual data analysis: while IRAMUTEQ automatically analyses the content of the dialogues, N'VIVO leads to a finer analysis of the dialogues because fine codes are defined and N'VIVO combines the content of the dialogues with the speakers.

Analysis process

Several processes were carried out, using IRAMUTEQ and N'VIVO outputs, as well as the notes that we have taken during the meetings. The first process is a cross-sectional analysis that compares the contents of the dialogues in all the condominiums at each step of the service process: REP, MOE, SOL, FIN.

A second process is to carry out comparisons of the condominiums that have voted in favor of the thermal retrofit with those that have voted against the retrofit The goal is to find out major differences that may explain their respective votes.

A third process is a longitudinal analysis of the dialogues in the condominiums that voted against the retrofit, over all the steps that they went through in the service process.

Results in a nutshell

Three main subjects addressed during the four types of meetings

Surprisingly enough, it comes out that three types of meetings out of four (REP, SOL, FIN) addressed three main subjects, although the goals of these 3 types of meetings were very different. The subjects addressed were the following:

-Technical questions -Questions relating to the MurMur process -Economic and financing questions

The distribution of the dialogues relating to each subject differs across the three types of meetings, as shown below on figure 2. But the three main subjects are at the core of the meetings, with the financing subject a bit less pregnant on a general basis. Similarly, the distribution of the three subjects varies across the condominiums and across the types of actors. But the three subjects always come out as the most pregnant ones.

Focus on the condominiums that voted against the MurMur programme

The three condominiums that voted against the MurMur programme stand out differently from those that voted in favor of the programme, or have not voted yet. Indeed the condominiums that voted against the programme address questions relating to the MurMur process relatively more than the other condominiums. The latter, conversely, focus more on technical questions.

Figure 3 shows the subjects addressed during all the meetings (of all types) across all the condominiums (toutes copros), and across those that voted in favor of the programme (OUI), against the programme (NON), or have not voted yet (ND)

Figure 3: subjects addressed by all the condominiums in all the meetings (using N'Vivo)

Focus on the condominiums that voted in favor of the Mur Mur programme

Even at the final general assembly, the co-owners continue to raise technical questions about how their windows and balconies will be renovated during the retrofit. But these technical issues are more or less pregnant depending on the condominiums. Condominiums B_003 and B_004 focus very little on these issues. Interestingly enough, debates in those two condominiums about whether to vote positively or negatively went on for a very long time at the general assembly compared with the other condominiums : the outcome of the vote was not straightforward at all. The profile of these two condominiums looks close to that of the condominiums that voted against MurMur earlier in the process: the co-owners put more emphasis on the MurMur process than on what their building might look like after the retrofit.

Discussion and public policy recommendations

Major lessons learned from our research :

-The speech registers are stable and variable at once: in all meetings, co-owners speak of three subjects, ie technical issues, the MurMur process and economic and financing questions, but they do so in variable proportions ; -When they address technical issues, co-owners project themselves into the future retrofit. This corresponds to the profile of the co-owners who, in the end, vote for the retrofit. In some way, they are already on the verge of retrofitting their building; -But co-owners who, in the end, vote against the MurMur programme, do not tackle technical questions during the meetings so much. They are much more focused on the MurMur process.

Public policy recommendations

Our recommendations mainly stem from the observation of the 51 meetings that we attended.

-It is very important to take the whole context of the condominium into account before accepting the condominium into the Mur Mur program. An additional set of criteria could be defined so as to target even more the condominiums. It could avoid spending time in organizing meetings with condominiums that may have a high probability to vote against the programme. This includes condominiums for which the façade retrofit is not an urgent matter and for which the added value brought by a thermal retrofit does not make much difference on the real estate market; -As technical questions relating to private parts of the building are prominent, raising those issues first could be an entry-point for ALEC, SOLIHA and property managers to lead co-owners to questions relating to the common parts of the building; -Working on the consistency of the speeches of ALEC and SOLIHA, and enhancing the strategic role of the SOLIHA meeting may help to make the co-owners vote in favor of the MurMur program -Reassuring co-owners with additional information tools may contribute to the same goal. Such tools may include a timeline of the various cash flows between the decision to do the retrofit and the time when the retrofit work starts -Training all the actors of the MurMur process (ALEC, SOLIHA, co-contractors, property managers) to facilitate meetings may also help

Figure 2 :

 2 Figure 2 : main subjects addressed by the condominiums during the 4 types of meetings (using Iramuteq)

Figure 4 :

 4 Figure 4 : subjects addressed at the final general assembly by the condominiums that voted in favor of the MurMur programme (using N'Vivo)

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  Technical questions relating to private parts of the building (windows and balconies of the apartments) are prominent relative to those linked to the common parts. -Still some wealthier co-owners point to the need to vote in favor of the MurMur programme as it brings substantial subsidies to the poorer households. Altruism is called for in some discussions. -The outcome of the collective decision often seems uncertain during the meetings as different elements come into play such as uproars, testimonies of previous (good or bad) experiences with Mur Mur in other condominiums, emerging leaders among the co-owners. -The consistence of the speeches of the various speakers of the MurMur process (ALEC, SOLIHA) is very important, as it reassures the co-owners

MurMur2 funded by Grenoble-Alpes Métropole