Eloïse Libourel

TEN-T PROJECTS IN THEIR GEO-ECONOMIC CONTEXT: A CASE STUDY OF THE TRADE SHAPE OF THE SPANISH MEDITERRANEAN RAILWAY CORRIDOR

INTRODUCTION

The Mediterranean Railway Corridor (MRC) is one of the priority projects of the Trans-European Networks of Transport (TEN-T) in their consecutive versions since 1996 (European Commission, 1996;European Commission, 2005;European Commission, 2013). At the same time this project has been included in the Spanish national planning documents (Ministerio de Fomento, 1994;Ministerio de Fomento, 2000;Ministerio de Fomento, 2005; Ministerio de Fomento, 2012) both as a high-speed line for passengers and an international gauge line connecting with the European market for freight. In Spain, it would be the first great railway axis circumnavigating Madrid, which is the centre of a very radial shape network. In this sense, the MRC is at the same time a transport issue and a political topic which implies all the institutional levels (European, national, regional and even local), which all try to take advantage of this macro-project to reach their own goals such as urban renewal at a local scale [START_REF] Bellet | Infraestructuras de transporte y territorio. Los efectos estructurantes de la llegada del tren de alta velocidad en España[END_REF], a higher degree of autonomy at a regional scale [START_REF] Bricall | Note sur la structure territoriale de l'Espagne[END_REF] or a change in territorial governance by getting closer to the European institutions [START_REF] Romero González | Las regiones y el principio de subsidiaridad[END_REF][START_REF] Farinós Dasí | La gobernanza como método para encarar los nuevos grandes retos territoriales y urbanos[END_REF].

As a trans-European project, the MRC is part of the "core network" as decided at the continental level by the European Commission in 2013 (European Commission, 2013). It is part of a trans-national or continental scale decisionmaking process involving different types of stakeholders -not only institutional but also economic and civil society actors-and mobilising a variety of discourses mainly based on economic arguments and especially on freight transport topics [START_REF] Libourel | Trans-European railway corridors creating new territories: the Spanish Mediterranean Corridor project[END_REF].

The MRC outline (in bold green on figure 1) as it was presented in the latest version of the TEN-T documents in 2013 (European Commission, 2013), now called Connecting Europe Facility (CEF) (European Commission, 2012), is one of the nine core network multimodal corridors. It is quite different from the proposal of Ferrmed Great Axis [START_REF] Ferrmed | Ferrmed global study. Ferrmed Great Axis Rail Freight Network and its area of influence[END_REF][START_REF] Cenit | Mediterranean Corridor's south layout proposed by Ferrmed[END_REF] for an interoperable efficient freight network (in purple on figure 1). This economic actors' lobby proposes a great axis form Casablanca to Saint-Petersburg considering it as the most important freight axis for Europe. If we consider the whole TEN-T network, there are connecting corridors which complete the same north-south shape as Ferrmed's proposal. Nonetheless, the CEF settles one particular authority per corridor composed of representatives of each involved country. In that sense the implementation of a north-south corridor may need concordant actions of the different authorities. In this context, it seems relevant to use precise freight data in a medium or long term horizon in order to put the discourses on the Mediterranean corridor into perspective and to provide some key elements helping the decision making process thanks to the implementation of a Geographic Information System. In order to describe the freight profile of the Spanish Mediterranean regions at the level of provinces, we will use Datacomex, a national institutional database provided and managed by the Spanish Ministry of Economy (Ministerio de Economia, n.d.). It provides valuable information at a low level of geographical aggregation (provincial level, corresponding to the NUTS 3 European statistical classification) and with a high degree of detail regarding type of merchandise and transport mode.

THE SPANISH MEDITERRANEAN PROVINCES' TRADE PROFILE: A COMPARISON WITH QUALITATIVE ASPECTS

The Datacomex data base allows analysing the commercial exchanges of the provinces with countries or macro-regional groups of countries which enables mapping the main flows of merchandise between the provinces of the Spanish Mediterranean regions and the rest of Europe.

Datacomex database is very complete and provides a vast amount of information, which can be extracted by mode of transport and by type of merchandise and expressed in different units. For this paper, it was decided to focus on a few indicators in order to highlight the commercial profile of the Mediterranean provinces and their relationship with the European countries accessible by terrestrial modes of transport. The aim is to represent the main economic partners of these regionswhich could potentially be well deserved by railin order to put the discourses of the different stakeholders into perspective.

The first step of this study was to identify the main actors of the MRC project and to analyse their discourses and their arguments to justify or criticise the project. This objective is achieved thanks to a set of 43 interviews conducted between 2011 and 2014 and to a media information analysis. The main results were presented in detail in previous communications [START_REF] Libourel | L'insertion de Valence dans le corridor ferroviaire méditerranéen[END_REF][START_REF] Libourel | Trans-European railway corridors creating new territories: the Spanish Mediterranean Corridor project[END_REF]. The necessity for the Mediterranean regions to improve their connection by rail to the rest of Europe in order to make their industry and economic sectors more competitive is the most important argument. This paper will concentrate on confronting this aspect of the discourse to the trade shape of the Mediterranean regions.

A panorama of the trade shape of the different Spanish Mediterranean provinces can be set by studying the data of Datacomex:  from 1996 to 2012, which are the years of the beginning of the TEN-T projects and of their latest revision by the European Commission;  comparing the terrestrial transport modes (rail and road), in order to evaluate the potential of a modal report on rail if the MRC is implemented;  comparing the different types of transported goods in order to estimate the chances of a modal transfer up to their particular characteristics and to the economic shape of the different regions. By using Datacomex, a statistical panorama can be proposed including the analysis of the modal share and of the load share. A Geographic Information System integrating localised data can be implemented. The maps will use aggregated data at the level of the regional institutional frames and show therefore the main foreign trade relationships with European countries. It would also be interesting to draw the maps with disaggregated data, but as this work would not be easily legible it should be implemented as an interactive atlas of rail transport in Europe.

Nonetheless, GIS are more and more used by public and private actors as a powerful tool for decision making, particularly in the field of planning and territorial topics [START_REF] Jankowski | Integrating geographical information systems and multiple criteria decision-making methods[END_REF]. The GIS should allow comparing the trade shape with the different proposals for the MRC freight axis and be considered as a good decision making instrument.

THE MEDITERRANEAN WAY TO EUROPE: MAPPING UNBALANCED SITUATIONS

In order to map the trade flows of the Spanish Mediterranean regions with European countries, it was chosen to group the provinces by Autonomous Communities in order to make it more legible. The maps are interesting to compare the geographical profile of trade to the different proposals of Mediterranean corridor. They show the main partners of the Spanish Mediterranean regions and also the intensity of the trade relations thanks to the choice of homogeneous thresholds in the legend both for export and import and for the different studied regions.

Catalonia and Valencian Community: improving a well-established link to Europe

Barcelona and Valencia are the main metropolises in Spain after Madrid and they both are touristic and industrial capitals as well as important harbours in the Mediterranean. Furthermore, they have good connections to Madrid and to France as far as time-space and infrastructure are concerned. Catalonia is the most important region in Spain after the region of Madrid as far as GDP (Gross Domestic Product) and trade are concerned. Barcelona is important as well as one of the main Spanish ports. Furthermore, the proximity of the French border and a long history of cultural and political alikeness between Spanish and French Catalonia reinforce the links of Catalonia to its European neighbourhood. It is significant that the main pro-MRC lobby, Ferrmed, was created by Catalonian entrepreneurs and that the new EU Core Net Cities platform was inaugurated in Barcelona.

As far as trade is concerned, the coastal provinceswhich are first concerned by the implementation of the Mediterranean corridorexport nearly 10 billion Euros to France and more than 6 billion Euros to Germany in 2012. The main import flows also come from these two partners. The third most important partner is Italy, another country concerned by the TEN-T Mediterranean corridor outline. Both import and export flows increased during the 1996-2012 period. Finally, it is interesting to note the huge increase of the exportation flows between 1996 and 2012. They progressively became more important than importation flows, except from Germany. Catalonia seems to be well integrated to the European core market and is therefore an actor which cannot be circumvented in the debate about the MRC project. Valencian Community has a quite similar profile marked by a strong trade partnership with France, Germany and Italy. The United Kingdom is also a key partner. Even if the general trend is the increase of the trade flows with all Europe (except with Greece), this increase is lower than in Catalonia. Furthermore the levels of trade in million Euros are much lower than those of Catalonia. The exchanged volumes are also lower but in a less important way, which means that the value of the exchanged products is lower in Valencia than in Catalonia.

Nevertheless, Valencia is nowadays the main Spanish harbour in terms of containers which means that it certainly has a great potential of modal shift from road to rail. The boxes are very easy to transfer from road to rail and to carry in case of offloading. The province of Valencia is already well connected to Barcelona by rail, even if some improvements are necessary to make rail competitive, the port of Valencia is connected to the railway network and could easily upgrade its connection to the European standards. At the same time, an important actor as Ford automotive industry built its own railway connection to the network and participates actively to the claim of a Mediterranean corridor.

Murcia and Andalusia: connecting peripheral regions to the core network

South, Murcia Region and Andalusia present quite different profiles in terms of trade to Europe. They are far less present in the exchange flows with the European economic core countries. Their railway and rod connections are mainly oriented to Madrid as centre of the national economy. Therefore, the construction of the MRC infrastructure would be more difficult and is for now delayed because of the economic crisis. Therefore the thresholds of the legend were adapted to this particular situation. It is also important to notice that the harbour of Cartagena is not the regional capital and that Murcian industries are mainly looking to Alicante and the southern part of the Valencian Community.

As for the other Spanish Mediterranean regions, the main export partners are the western European countries and especially France, Germany, Italy and the United Kingdom. Holland has a particularly elevated rank among the trade partners of Murcia, especially because of fruits and vegetables. The freight flows to these countries are quite stable even though they increased. A more interesting fact is the great increase of the flows to Northern Africa (mainly Morocco, Algeria and Tunisia) and to Turkey.

Murcia Region seems to have a privileged partnership with the Mediterranean countries. It is both due to a geographical and historical closeness, and to the nature of exchanges: the main port of Murcia, Cartagena, is specialised in oil products. This means that Murcia's main harbour is less likely to provide load for railway transportation, especially to other European countries. Andalusia is a very singular case study because it is a big region made of very different profile provinces. Some of them are Mediterranean (Almeria, Granada, Malaga and Cadiz) but the others are oriented towards the centre of Spain or even towards Portugal. This situation is reinforced by the lack of a coastal infrastructure because of the rugged terrain and the huge costs of construction and operation it implies. The port of Algesiras, one of the greatest in the Mediterranean, is well connected to Madrid and is no longer a member of Ferrmed.

The coastal Andalusian provinces have the lowest trade flows to Europe. Their main economic partners still are France and Germany for exportation but the levels are quite low around 1.5 billion Euros. The most noticeable fact is that Andalusia imports quite few from the rest of Europe but has particularly high importations from Algeria. This is mainly due to the commerce of oil and natural gas to be consumed in Spain.

Based on the analysis of a database on international trade, this study leads to two types of conclusions: the first family, related to the modal and load shares, confirms the arguments of the actors to a certain extent but could be controversial if we come into a detailed analysis. The second family, consisting on the findings from the GIS, shows that the new outline of the Mediterranean corridor drawn by the European Commission in 2013 (European Commission, 2013) doesn't fit with the trade shape of the Mediterranean regions.

MRC: FROM ECONOMIC FACTS TO TERRITORIAL POLICIES

The trade shape of the Spanish Mediterranean regions shows an important gap between Catalonia and Valencia on the one hand and Murcia and Andalusia in the other hand. Nevertheless the Mediterranean corridor as it is presented both by the European Commission (European Commission, 2013) and in the planning documents of the Spanish government (Ministerio de Fomento, 2012) is supposed to reach Algesiras via the coast. We can assume that this project fits to new political priorities to connect the European peripheral regions.

Comparing the trade data with the MRC outlines

The MRC outline as it was drawn in the latest TEN-T document (European Commission, 2013) doesn't fit to the trade shape of the Spanish Mediterranean region. Nevertheless the European Union core network as a whole draws a more complete outline (Figure 1). Furthermore, the European Commission is partly guided by territorial cohesion and balance considerations, which may lead to choose a high potential shape for the corridor rather than an already well-known trade axis, in order to empower the trade relationships and infrastructure integration with Eastern Europe.

In fact, Italy remains one of the greatest trade partners of the Spanish Mediterranean regions. If the Eastern countries, among which Slovenia and Croatia, still are secondary partners, they experience the highest increase of their commercial relationships with Spain. One of the goals of the TEN-T networks is to improve dramatically the accessibility of the new member states of the European Union to the European market.

The mapping of the trade shape of the Spanish Mediterranean regions shows that the Ferrmed proposal for the Mediterranean corridor perfectly fits to the reality of the commercial partnerships. This is partly due to the analysis by Ferrmed of the economic structure of Europe [START_REF] Ferrmed | Ferrmed global study. Ferrmed Great Axis Rail Freight Network and its area of influence[END_REF] and to a larger extent to the structure of the lobby which members are mainly important trade companies, port authorities and industries. The Eastern European countries are more represented in EU Core Net Cities, a new lobby created in June 2013 in Barcelona and focused on the European core network facilities as a mean to develop new economic perspectives.

It is also demonstrated that the highest increase potential is located in the eastern part of the European Union and this is where the MRC as it is drawn by the TEN-T documents finds its relevance. It is nonetheless suggested that the implementation of the European Union core network should be done in a synchronised way in order to avoid a lack of interconnection between the different corridors. The same logic leads to implement the MRC project to Murcia and Andalusia as an instrument to connect peripheral regions to the centre of Europe.

The conditions for a rail/road competition according to the types of load

By now, road transport along the Mediterranean axis represents nearly 96% of the total freight transport in this corridor [START_REF] Serrano Martinez | Del arco al eje mediterraneo en España. Hacia la consolidacion de un corredor de transportes[END_REF][START_REF] Monzón | Evaluación de los impactos territoriales y económicos de planes de infraestructuras de transporte PEIT[END_REF]. The aim of the MRC is to transfer a significant part of the flows to the railroad thanks to a well-connected interoperable high-level of service line.

In this dataset, the modal choice is defined by the mode used to cross the Spanish border. Towards the continental European countries, we can assume that the same transport mode is used by the load during the major part of its transfer. The most noticeable fact is that the road transit dominates the cross border transport flows in a huge proportion. Rail has a little part of the modal repartition in Valencian and Catalonian provinces but it is insignificant in the other regions. Furthermore the modal part of rail tends to decrease between 1996 and 2012. This is partly due to the insufficient condition of the current railway network along the Mediterranean axis and also to the difficulties of interoperability.

It is also interesting to compare the flows according to the different types of load in order to be able to compare them to the ones highlighted by the dominant discourses. For example, the MRC very first project was proposed by the Federation of Orange Exporters (Federación de Exportadores de Naranjas, FEN) in the 1920's as a powerful axis for the exportation of their products. But nowadays the most interested sector is the industry (mainly the automotive industry) and many actors underline that railway is not suitable for agro-food products. It is said that it cannot be competitive with road which can deliver the products straight to their final destination and guarantee the arrival time as well as the continuity of the conservation system. railway network offers shorter trips and more attractive prices for freight, it could become highly competitive for the fruit exporters. But at the same time, many entrepreneur associations and economists have the opposite opinion: they support the idea that point-to-point delivery is an essential factor that railway cannot offer and they underline the fact that the main agribusiness firms have their own transport service that they may not want to leave. Meanwhile, automotive sector is growing and progressively becoming one of the most interested in the railway opening. For example, Ford connected its plant of Almussafes near Valencia to the conventional network through its own 40km railway line and argues that the quick rail connection to Europe is a heavy argument for the firm to stay in Spain in the future.

CONCLUSIONS

Freight data assessment is crucial in order to understand the territorial structures of production and trade flows between the Spanish Mediterranean regions and Europe. It allows us to assess, criticise and put into perspective the arguments used by the MRC project actors. We would like to underline three main findings.

First, the importance of the agrobusiness sector will be decisive for the use of the future MRC. The controversy on the possible interest of a railway axis to Europe for agro-food products is therefore interesting. If it is highly probable that a part of this load will remain on the road, but a significant improvement of the rail freight services could easily drain an important part of the productions to the main European cities.

Second, the very significant axis from Spain to France and Germany from a quantitative point of view underlines the Ferrmed proposal relevance. This axis could probably be immediately competitive when implemented. Nonetheless, the very few flows along the "Mediterranean corridor" TEN-T project as it is now shaped have to be nuanced by the huge increase of the trade flows between 1996 and 2012 which make this axis potentially highly competitive in the future. This idea joins the political assessment of the need to connect the new member states to the European market centres.

Finally, considering the trade shape region by region in Spain, it is shown that there is a gap in the trade flows to Europe between Valencia and the southern regions. This gap can be explained by a less industrial and competitive profile, but also by a higher distance to the centre of Europe.

In this context, it appears that the southern part of the TEN-T "Mediterranean corridor" should not be implemented in a separate way from the "North Sea-Mediterranean" and the "Scandinavian-Mediterranean" corridors up to Holland, Germany and the United Kingdom. Nevertheless, the huge increase of commercial flows with the eastern European countries between 1996 and 2012 is a determinant factor for the design of the MRC outline in the Trans-European Networks of Transport planning documents.

GIS appears as a useful and powerful decision making tool. It allows producing competitive visions of the Mediterranean corridor as an axis for current freight flows. Without making a prospective study, it shows that there is a gap between the TEN-T planning document and the current main partners but it also highlights the coherence of a Mediterranean axis to Italy, Croatia, Slovenia and Hungary from a territorial development point of view.

As a final remark, we would like to notice that the trade flows with the North African countries also increased a lot in the period, to the extent that Algeria and Morocco can be considered as important partners as the main European countries. This observation highlights the need to include the European neighbourhood in the transport policies, particularly in an intermodal perspective.

Figure 1 :

 1 Figure 1: Different shapes of the Mediterranean Railway Corridor in the European Core Network

Figure 2 :

 2 Figure 2: Mediterranean provinces' trade with Europe (million Euros)

Figure 3 :

 3 Figure 3: Catalonian coastal provinces' export (a) and import (b) flows in 1996 and 2012

Figure 4 :

 4 Figure 4: Valencian provinces' export (a) and import (b) flows in 1996 and 2012

Figure 5 :

 5 Figure 5: Murcia Region export (a) and import (b) flows in 1996 and 2012

Figure 6 :

 6 Figure 6: Andalusian provinces' export (a) and import (b) flows in 1996 and 2012

Figure 7 :

 7 Figure 7: Freight trade on the Mediterranean axis according to the type of load

ACKNOWLEDGEMENTS

The authors would like to sincerely thank Professor Raymond Ghirardi for his kind help and support to this paper.


Keywords: Analogue-digital conversion, Microwave Photonics, Optical Signal Processing, Semiconductor optical amplifiers

This paper describes an optical Thresholder (o-Thresholder) intended to be part of a transmitter module for future all-optical Digitising Radio-over-Fibre (o-DRoF) transceivers. The proposed device is based on an Attenuation-Imbalanced Semiconductor Laser Amplifier Loop Mirror (AI-SLALOM) in self-switching regime, using the nonlinearities of a semiconductor optical amplifier. Simulations of the proposed AI-SLALOM based o-Thresholder have shown promising results in comparison with the use of standard optical fibre and highly nonlinear fibre only. The newly proposed device is rather compact, optically integrable and requires much less input optical power than conventional devices (by several orders of magnitude). It provides enhanced optical RZ bits at 1550 nm wavelength window, 1.25 GHz repetition rate and 80 ps timewidth.

I. INTRODUCTION

NALOGUE Radio-over-Fibre (ARoF) is a keytechnology for the convergence of fibre-based wireline and wireless networks [START_REF] Williamson | RF Photonics[END_REF] and by means of which a large variety of mobile and wireless services including UMTS, LTE, Wi-Fi and WiMAX may be seamlessly delivered to customers. Merging RoF and FTTx (Fibre-To-The-x) technologies, namely FTTA (A = Antenna), is a promising approach to provide reliable mobile and wireless broadband access with a higher level of densification and enhanced network capacity. ARoF allows a relatively simple distribution of RF signals over an optical carrier along optical fibres connecting a Central Station (CS) to Base Stations (BSs) or Remote Antenna Units (RAUs). Therefore, all signal processing may be centrally carried out at the CS [START_REF] Williamson | RF Photonics[END_REF][START_REF] Nirmalathas | Digitized Radio-Over-Fiber Technologies for Converged Optical Wireless Access Network[END_REF], leading to simple RAUs design that only needs to implement optoelectronic conversion and power amplification.

Ricardo M. Ribeiro is permanently with the Laboratório de Comunicações Ópticas, Departamento de Engenharia de Telecomunicações, Universidade Federal Fluminense, 24.210-240, Niterói, RJ, Brasil (phone: +55-21-2629-5602; fax: +55-21-2629-5521) and thanks Foundation Capes/MEC-Brasil for the financial support through a Post-Doctoral fellowship under the grant BEX 9096/11-6.

Ricardo M. Ribeiro, Frédéric Lucarz and Bruno Fracasso are with the Département d'Optique, Telecom Bretagne, Technopôle Brest-Iroise, CS 83818, 29238, Brest, Cedex 3, France (e-mails: rmr@pq.cnpq.br, frederic.lucarz@telecom-bretagne.eu, bruno.fracasso@telecom-bretagne.eu).

However, ARoF systems are constrained by two basic requirements, which are inherent to analogue transmissions [START_REF] Williamson | RF Photonics[END_REF]: all used devices should be highly linear and the received signal should have higher SNR (Signal to Noise Ratio) when compared with digital systems. Since ARoF networks require high SNRs, their analogue nature limits the accepted fibre attenuation and the splitting ratio of optical signals, both critical in FTTH (H = Home) networks. Furthermore, the accelerated deployment of wireless networks operating at increased carrier frequencies up to ~ 100 GHz, leads to networks with naturally reduced coverage area per antenna.

In order to circumvent the limitations of ARoF networks, the use of digitised radio-over-fibre (DRoF) technologies [START_REF] Nirmalathas | Digitized Radio-Over-Fiber Technologies for Converged Optical Wireless Access Network[END_REF][START_REF] Abdollahi | Fully-Photonic Analogue-to-Digital Conversion Technique for Super-Broadband Digitized-Radio over Fibre Link[END_REF] is an interesting alternative. In electronic DRoF links, the analogue RF input signal is first digitised by an analogue-todigital converter (ADC). The generated electrical bits drive a light source thus generating optical bits then transported over optical fibre and finally reconstructed by a digital-to-analogue converter (DAC) at the output of a photo-detector. Each BS (or RAU) comprises one ADC and one DAC, while more complex digital signal processing is carried out in the CS [START_REF] Nirmalathas | Digitized Radio-Over-Fiber Technologies for Converged Optical Wireless Access Network[END_REF]. Due to the digital nature of the optical link, the dynamic range is independent of the fibre length as long as the power of the received signal is lower than the link sensitivity. Electronic DRoF technologies still exhibit some advantages of ARoF [START_REF] Nirmalathas | Digitized Radio-Over-Fiber Technologies for Converged Optical Wireless Access Network[END_REF][START_REF] Abdollahi | Fully-Photonic Analogue-to-Digital Conversion Technique for Super-Broadband Digitized-Radio over Fibre Link[END_REF] except for its relative higher complexity, but include further characteristics as follows: centralized digital signal processing such as digitisation itself, enhanced sharing capacity and better compatibility of digital equipments and communication channels, significant increase in transmission distance using optical fibre (larger dynamic range), larger coverage capacity or larger number of RAUs, possible cost reduction and energy saving.

The all-photonic signal conversion and processing are required due to the accelerated growth of demanded traffic reaching Exabyte per month. Therefore, high-speed processing and transmission are essential. Next-generation networks will face congestion in the backbone, metropolitan and access networks. Congestion in the backbone is due to the bottleneck of 3R processing (re-timing, re-shaping and re-amplifying) in the electronic domain. All these processes require optical/electrical (O/E) conversion that introduces complexities and delays. The switching and routing electronic process of the traffic in the backbone and metropolitan networks may also cause congestion. The use of all-optical switching and routing devices together with proper protocols A Thresholder for All-Optical Digitising Radio-over-Fibre Transceivers Ricardo M. Ribeiro, Frédéric Lucarz and Bruno Fracasso A ONDM 2013 1569706771 2 can significantly mitigate this problem. Therefore, by using all-photonic DRoF more operations and signal processing centralisation at the CS could be achieved. The main challenges in the electronic DRoF link implementation are: high-speed ADC and DAC, dispersions, nonlinearities (in the electrical and optical domains), additive noise, integration of system and devices, size and system cost.

An o-DRoF transmitter comprises an RF interface, an alloptical ADC and an enhancer/amplifier to significantly increase the optical-bit contrast. To the best of our knowledge, no complete experimental all-optical DRoF communication system has been reported in the literature. However, some recently published papers [START_REF] Abdollahi | Fully-Photonic Analogue-to-Digital Conversion Technique for Super-Broadband Digitized-Radio over Fibre Link[END_REF][START_REF] Abdollahi | Digital Radio over Fibre for Future Broadband Wireless Access Network Solution[END_REF][START_REF] Abdollahi | Non-Uniform Wavelength Allocation in All-Photonic Digitized-Radio over Fibre Access Network[END_REF][START_REF] Viglienzoni | Net! Works -Next Generation Network: Wireless-Optics Technology[END_REF] from Brunel University (UK) report valuable theoretical simulations of an o-DRoF system but without any detailed description of the operational principles of both all-optical ADC and DAC.

In the present paper, the use of an AI-SLALOM configuration is proposed as a self-switched o-Thresholder circuit to be part of a future o-DRoF transceiver. Simulation results on VPI Transmission Maker TM and comparisons of the proposed AI-SLALOM and Attenuation Imbalanced Nonlinear Optical Loop Mirrors (AI-NOLMs) using standard (SF) and highly nonlinear optical fibres (HNLFs) o-Thresholder configurations are presented for 1550 nm wavelength window, 1.25 GHz repetition rate with 80-ps RZ pulses. Because the proposed o-Thresholder uses a laser amplifier as the nonlinear optical element, their optical circuit may potentially perform additional signal processing, such as wavelength conversion and modulation format conversion [START_REF] Phillips | Simultaneous demultiplexing, data regeneration, and clock recovery with a single semiconductor optical amplifier-based nonlinear-optical loop mirror[END_REF][START_REF] Yang | Application of Semiconductor Optical Amplifiers in High-Speed All-Optical NRZ to RZ Format Conversion, ICTON 2007[END_REF]. The o-DRoF systems may well integrate the next generation of all-photonic telecommunication networks [START_REF] Abdollahi | Fully-Photonic Analogue-to-Digital Conversion Technique for Super-Broadband Digitized-Radio over Fibre Link[END_REF][START_REF] Abdollahi | Digital Radio over Fibre for Future Broadband Wireless Access Network Solution[END_REF][START_REF] Abdollahi | Non-Uniform Wavelength Allocation in All-Photonic Digitized-Radio over Fibre Access Network[END_REF][START_REF] Viglienzoni | Net! Works -Next Generation Network: Wireless-Optics Technology[END_REF] and provide the connection between the access and metropolitan or even transport networks.

II. ALL-OPTICAL DIGITISING RADIO-OVER-FIBRE (O-DROF) TRANSMITTER

This section proposes an o-DRoF transmitter able to receive and process ARoF signals that essentially comprises a photonic-ADC and a photonic-thresholder.

Electronic ADC and DAC boards seem to exhibit an intrinsic limitation in their stability, "bit resolution x input frequency" product and data conversion rates of up to a few tenths of GSa/s [START_REF] Abdollahi | Fully-Photonic Analogue-to-Digital Conversion Technique for Super-Broadband Digitized-Radio over Fibre Link[END_REF][START_REF] Abdollahi | Digital Radio over Fibre for Future Broadband Wireless Access Network Solution[END_REF][START_REF] Abdollahi | Non-Uniform Wavelength Allocation in All-Photonic Digitized-Radio over Fibre Access Network[END_REF][START_REF] Viglienzoni | Net! Works -Next Generation Network: Wireless-Optics Technology[END_REF][START_REF] Miyoshi | All-Optical Analog-to-Digital Conversion Using Splitand-Delay Technique[END_REF]. Besides, the vast majority of alloptical ADC and DAC systems have always been separately reported and for various types of applications, but excluding any communication link application.

Figure 1 depicts a typical and simplified transmitter module flowchart of an o-DRoF link [START_REF] Miyoshi | All-Optical Analog-to-Digital Conversion Using Splitand-Delay Technique[END_REF][START_REF] Currie | High-Performance Photonic Analog-to-Digital Converter and Low-Noise Mode-Locked Fiber Laser[END_REF]. The o-Thresholder is provided mainly to enhance the contrast between the "0" and "1" optical bits at the output of the o-Encoder.

The o-Generator is preferably implemented by a modelocked laser, a key component used to generate a series of picosecond pulses at GHz rates with high temporal stability, i.e. with very low jitter in the femtosecond time-scale [START_REF] Miyoshi | All-Optical Analog-to-Digital Conversion Using Splitand-Delay Technique[END_REF][START_REF] Currie | High-Performance Photonic Analog-to-Digital Converter and Low-Noise Mode-Locked Fiber Laser[END_REF] so that these pulses can be used as the clock signal for the optical sampling and coding. The o-Interleavers essentially multiply the repetition rate of the clock signal generated by the o-Generator.

III. MODELLING AND SIMULATIONS OF THE O-THRESHOLDER

Sagnac interferometric fibre rings have been used as a nonlinear device based on self-phase modulation (SPM) or cross-phase modulation (XPM) -NOLMs -that are very useful for many ultrafast signal-processing applications [START_REF] Huang | All-Optical OOK to 16-QAM Modulation Format Conversion Employing Nonlinear Optical Loop Mirror[END_REF]. The use of a laser amplifier as a nonlinear medium instead of the optical fibre leads to an interesting class of devices usually named as SLALOM [START_REF] Eiselt | Optical Loop Mirror with Semiconductor Laser Amplifier[END_REF] or Terahertz Optical Asymmetric Demultiplexer (TOAD) [START_REF] Sokoloff | A Terahertz Optical Asymmetric Demultiplexer (TOAD)[END_REF].

Three different optical circuits of the o-Thresholder were designed and simulated using VPI Transmission Maker TM . All circuits were probed at 1550 nm wavelength window with 1.25 GHz repetition rate, 80 ps time-width RZ pulse stream. The peak power of the input pulses (P input ) could be varied from 10 µW to 10 W in order to obtain the transfer functionsthe P output /P input curves -for the three optical circuits.

The input pulses at 1553.6 nm wavelength were generated from a continuous-wave laser diode with null linewidth after traversing a Mach-Zehnder modulator (MZM). The MZM is biased at the quadrature point and is driven by 2.5 Gb/s RZ electrical pulses in an alternate pattern with 0.1 duty-cycle.

The optical circuits are attenuation-imbalanced Sagnac interferometers instead of using fibre-couplers with coupledratio ≠ 50:50 thus allowing a maximum interference visibility contrast. The insertion of an attenuator (passive component) in the Sagnac fibre ring provides the necessary differential phase-shift between the clockwise (CW) and counterclockwise pulses (CCW). The polarisations of the CW and CCW pulses are assumed to be always aligned. Such a condition can be achieved in practice by using polarisation controllers in the optical circuits or by using polarisationmaintaining fibres.

Figure 2a depicts a first design of the o-Thresholder with an optical circuit using a NOLM with standard fibre. Table I shows the optical fibre parameters as used in the simulations. The A eff is the effective area of the fibre. The physical model solves the nonlinear Schrödinger equation (NLSE) taking into account the SPM and XPM in the single-mode fibre [START_REF]Self-Phase Modulation in Optical Fiber Communications: Good or Bad?[END_REF].

The 10 dB attenuator breaks the reciprocity of the Sagnac ring thus CW and CCW pulses accumulate a Δφ differential phase-shift. Therefore, the Δφ parameter determines the relative amount of reflected (Pr) and transmitted (Pt) power. Figure 2b shows the result of the transfer function simulations according to the first design (see Figure 2a). All pulses up to ~1 W peak power are reflected, i.e. the "0" bits with almost zero power are transmitted. A least from 1 W to 6 W input, the power of the transmitted "1" bits are not really limited. As expected, despite the P IN input power, the Pr + Pt power sum is 10 dB attenuated. For this first design the threshold power Pth of the AI-NOLM-SF may be set at 1 W.

According to a second design, the topology of the NOLM-HNLF optical circuit was exactly the same as shown in Figure 2a, with the exception that now the fibre is Dispersion-Shifted Fibre (DSF) [START_REF] Miyoshi | All-Optical Analog-to-Digital Conversion Using Splitand-Delay Technique[END_REF]. Table I shows the optical fibre parameters as used in the simulations where the optical nonlinearity of the HNLF is 50/3.25 ~15 times higher than that of the SF. Figure 2c shows the result of the simulations obtained with the second design. All pulses up to 75 mW peak power are reflected, i.e. the "0" bits with almost zero power are transmitted. A least from 75 to 500 mW input peak power, the output power of the transmitted "1" bits are not really limited. As again expected, despite the P IN input power, the Pr + Pt power sum is 10 dB attenuated. For this second design the threshold power of the AI-NOLM-HNLF may be set at Pth = 75 mW. In these first two designs, the switching mechanism is driven by the SPM effect occurring into the optical fibre [START_REF] Huang | All-Optical OOK to 16-QAM Modulation Format Conversion Employing Nonlinear Optical Loop Mirror[END_REF][START_REF]Self-Phase Modulation in Optical Fiber Communications: Good or Bad?[END_REF].

Figure 3a depicts a third design of the o-Thresholder based now on an AI-SLALOM optical circuit using a SOA as the nonlinear optical element instead of an optical fibre. The physical model takes into account a bulk SOA with low feedback neglecting the polarisation effects (isotropic model) and uses the Transmission Line Model (TLM) to compute the differential nonlinear phase-shift induced by a change in carrier density in the semiconductor. In this way, the switching is again driven by the SPM effect now occurring into the SOA. Table I shows the SOA parameters as used in the computer simulations. The asymmetric placement of the SOA at 150 ps from the mid-point of the fibre ring ensures that the gain is completely recovered for either the CW or CCW pulses. This limits the speed of the device as explained in the "Conclusions". The optical circulator allows the separation between the input and reflected pulses. The band-pass filters reduce the Amplified Spontaneous Emission (ASE) generated by the SOA and detected by the analysers. The centre frequency and spectral width of the filters are set to be 1553.6 nm and 100 GHz (0.8 nm), respectively.

Figure 3b shows the simulation results obtained for the third design (see Figure 3a) with a bias current set to I DC = 150 mA. All pulses with a peak power of up to 2 µW are reflected, i.e. the "0" bits with almost zero power are transmitted. In the 2-10 µW range is observed a fast transition from ~ 0 to 8 mW output power. For input optical pulses with a peak power greater than 10 µW, the output power of the transmitted "1" bits are now limited at 8 mW. Therefore, the transmitted (and also the reflected) pulses are now optically amplified/limited. For this third design with I DC = 150 mA, the threshold power may be set at Pth = 2 µW.

Figure 3c shows the simulation results obtained for the third design (see Figure 3a) with a bias current set to I DC = 75 mA. Figure 3d is the zoom of Figure 3c at low input powers. All pulses with peak power of up to Pth = 30 µW are essentially reflected because only noisy signals are calculated, even for Pin = 0 µW. This may be due to ASE noise combined with numerical artefacts. Therefore, the "0" bits with almost zero power are transmitted. In the 30 µW -6 mW input power range is observed a non-abrupt transition presenting output gain. For input optical pulses with a peak power greater than 8 mW, the output power of the transmitted "1" bits are now limited at 6 mW (negative gain). Therefore, the transmitted (and also the reflected) pulses are optically amplified and/or limited. For this third design with I DC = 75 mA, the threshold power may be set at Pth = 30 µW. As expected, the amplifier gain is reduced because the bias current is also reduced. However, the ASE power level is also significantly reduced. It is also shown that it is possible to easily tune the threshold power of the o-Thresholder from 2 µW to 30 µW.

Comparing the three designs of o-Thresholders, the use of HNLF instead of SF requires over 11 dB less input power. The use of SOA instead of HNLF requires less than 30 dB input power to obtain the switching. Furthermore, the SOA is only 1-mm long while the HNLF is 830 m in length. The results with SOA are in agreement with a similar work [START_REF] O'neill | All-Optical Loop Mirror Switch Employing an Asymmetric Amplifier/Attenuator Combination[END_REF]. For fibre lengths greater than a few hundred meters, the stability of the NOLM is significantly degraded. Furthermore, the long fibre introduces excessive latency for some optical processing applications [START_REF] Cotter | Nonlinear Optics for High-Speed Digital Information Processing[END_REF]. By comparing the active length and threshold power between the AI-SLALOM and the AI-HNLF configurations, i.e. by setting (Δφ) AI-SLALOM = (Δφ) AI-HNLF , it is easy to estimate an optical nonlinearity (n 2 ) of ~ 5 x 10 10 times greater when a semiconductor laser amplifier is used as a nonlinear optical element instead of a DSF-fibre. D. Cotter et al have described the implementation of a SLALOM circuit on a single 1x2 mm InP semiconductor chip [START_REF] Cotter | Nonlinear Optics for High-Speed Digital Information Processing[END_REF] that demonstrates the possibility of optical integration of the proposed o-DRoF transmitter. After the simulation of Figure 3c and 3d using an AI-SLALOM biased at I DC = 75 mA, the threshold power of 30 µW at 50 % (or the corresponding threshold voltage level) may be a conservative choice for the decision circuit of a digital receiver. The example of Figure 4 shows a "00010101010" poor quality input bits sequence assumed to be generated by the o-Encoder. After traversing 1-stage o-Thresholder, the output optical bits are fairly enhanced, i.e. the "0" bits present 50 µW maximum output power whereas the "1" bits are all amplified to reach (175 ± 25) µW peak power. Using 4-stage o-Thresholders with alternated 3-dB attenuators, it is now possible to achieve "0" bits presenting 50 µW maximum output power whereas the "1" bits are all amplified to reach (3.1 ± 0.1) mW peak power, i.e. a highly improved limitation. Of course, a better design of the o-Thresholder shall enable the use of 1 or 2 circuit stages only.

Alternatively, the transmission port of a first AI-SLALOM biased at I DC = 75 mA may be followed by an ~17 dB optical attenuator in turn connected to the input port of a second AI-SLALOM biased at I DC = 150 mA (or 75 mA < I DC < 150 mA) presenting a threshold power of 2 µW or (2 µW P th < 30 µW) (or the corresponding threshold voltage level). The previous optical circuit comprising 2-stage AI-SLALOMs allows that the transmission output could be almost perfect "0" bits (null optical power) and "1" bits with 1.0 -2.5 mW optical power.

IV. CONCLUSIONS

To the best of our knowledge, neither experimental nor commercially available o-DRoF links or networks have been reported as they are still under R&D stage. This paper proposes a system comprising five optical sub-modules for use in an o-DRoF transmitter link. The present paper only described the back-end sub-module of the o-DRoF transmitter, i.e. the AI-SLALOM based o-Thresholder in a self-controlled (or self-switched) regime operating at 1550 nm wavelength window. The proposed AI-SLALOM configuration when compared with the AI-HNLF [START_REF] Miyoshi | All-Optical Analog-to-Digital Conversion Using Splitand-Delay Technique[END_REF] may provide some advantages: compactness, prone to optical integration, requirement of ~10 3 less optical power and automatically amplified output optical bits. Mainly to demonstrate the proofof-principle, in this paper the simulations were constrained to only 1.25 GHz & 80-ps RZ input pulses. However, SOAs operating at 80 Gb/s are already commercially available. Furthermore, SOAs in R&D stage able to operate up to 160 Gb/s [START_REF] Szuki | Error-free demultiplexing of 160 Gbit/s pulse signal using optical loop mirror including semiconductor laser amplifier[END_REF] and beyond were already reported. The newly proposed o-Thresholder is intended to significantly enhance the contrast of digitised signals (optical bits) exiting an o-Encoder thus improving the Bit-Error Rate (BER) and also providing optical amplification eventually dispensing the use of Erbium-Doped Fibre Amplifier (EDFAs) in a fibre link transmission.

Further simulations (and laboratory experiments) of the o-Thresholder and the other sub-modules of the o-DRoF transmitter are currently planned or in progress and will be presented in a near future. Examples of scheduled device simulation improvements to be carried out include: operation at higher pulse rate (> 1.25 GHz) with shorter timewidth (< 80-ps), smaller asymmetry (< 150 ps) of the SOA placement in the Sagnac fibre ring in order to speed the operation [START_REF] Eiselt | Optical Loop Mirror with Semiconductor Laser Amplifier[END_REF], to tune the threshold power and to obtain a steeper transition region, etc. ACKNOWLEDGMENT

Fig. 1 .

 1 Fig. 1. The simplified flowchart of a complete o-DRoF transmitter. The o-Thresholder sub-module treated in this paper is numbered as (5). The o-DRoF transmitter comprises at least five main optical sub-modules: (1) optical pulse generator (o-Generator), (2) optical sampler (o-Sampler), (3'and 3'') temporal interleavers (o-Interleaver), (4) encoder (o-Encoder) and (5) thresholder (o-Thresholder). The o-Sampler carries out the optical sampling of an input ARoF signal. It is driven by an optical pulse comb that is generated by the o-Generator. This pulse comb is also used as a reference clock signal by the o-Encoder that optically encodes the sampled signal, thereby accomplishing the photonic AD-conversion itself.The o-Thresholder is provided mainly to enhance the contrast between the "0" and "1" optical bits at the output of the o-Encoder.The o-Generator is preferably implemented by a modelocked laser, a key component used to generate a series of

Fig. 2 .

 2 Fig. 2. (a) The optical circuit of the o-Thresholder based on NOLM-SF (according to the first design) or NOLM-HNLF (according to the second design), (b) the transfer function of the NOLM-SF and the (c) NOLM-HNLF configuration as a result from simulations.

Fig. 3 .

 3 Fig. 3. (a) The optical circuit of the AI-SLALOM based o-Thresholder (according to the third design), the transfer function as a result from simulations (b) with IDC = 150 mA and (c) IDC = 75 mA bias current, and the zoom of the transfer function at low input power (from Fig. (c)).

Figure 4

 4 shows an example of application of the AI-SLALOM based o-Thresholder with the SOA set at I DC = 75 mA bias current, useful for an o-DRoF transmitter.

Fig. 4 .

 4 Fig. 4. An example of application of the 1-stage AI-SLALOM based o-Thresholder that is useful for an o-DRoF transmitter.

Ricardo M. Ribeiro would like to thank the team at Département d'Optique of Telecom Bretagne and the CapilR TM platform for hosting his Post-Doctoral study during which the present work was carried out.


Géry Casiez
email: gery.casiez@univ-lille1.fr

Stéphane Conversy
email: stephane.conversy@enac.frmatthieu.falce

Matthieu Falce

Stéphane Huot

Nicolas Roussel
email: nicolas.roussel@inria.fr

Looking through the Eye of the Mouse: A Simple Method for Measuring End-to-end Latency using an Optical Mouse

Keywords: Latency, lag, latency measure, latency jitter, computer mouse. ACM Classification H.5.2 User Interfaces: Input devices and strategies

We present a simple method for measuring end-to-end latency in graphical user interfaces. The method works with most optical mice and allows accurate and real time latency measures up to 5 times per second. In addition, the technique allows easy insertion of probes at different places in the system -i.e. mouse events listeners -to investigate the sources of latency. After presenting the measurement method and our methodology , we detail the measures we performed on different systems, toolkits and applications. Results show that latency is affected by the operating system and system load. Substantial differences are found between C++/GLUT and C++/Qt or Java/Swing implementations, as well as between web browsers.

INTRODUCTION

The end-to-end latency (or lag) of a graphical user interface is commonly defined as the duration between a user action (e.g. movement of an input device or human limb) and the corresponding on-screen visual feedback (e.g. cursor movement, object displacement). All interactive systems have some latency introduced by input and output devices, network, events handling and processing. Probably due to the difficulty to measure it and to the multiple factors that can influence its variability, latency is only occasionally reported on input or output devices datasheets, interactive systems specifications or HCI experiments reports. Latency and its variation over time, called latency jitter, are known for a long time to affect human performance and qualitative perception [START_REF] Mackenzie | Lag as a determinant of human performance in interactive systems[END_REF][START_REF] Ware | Reaching for objects in VR displays: Lag and frame rate[END_REF][START_REF] Pavlovych | Target following performance in the presence of latency, jitter, and signal dropouts[END_REF][START_REF] Ellis | Discrimination of changes of latency during voluntary hand movement of virtual objects[END_REF]. Latency with computer mice has been studied in Fitts' law experiments where it has been shown to have an interaction with the task index of difficulty [START_REF] Mackenzie | Lag as a determinant of human performance in interactive systems[END_REF][START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF][START_REF] Teather | Effects of tracking technology, latency, and spatial jitter on object movement[END_REF]. A latency of around 50 ms is known to affect performance in mouse-based pointing tasks and latency jitter above 20-40 ms is likely to be noticed [START_REF] Ellis | Discrimination of changes of latency during voluntary hand movement of virtual objects[END_REF]. The effect is even more pronounced in direct touch interaction, where it has been shown that latency as low as 2 ms can be perceived and that performance is affected from 20 ms [START_REF] Ng | Designing for low-latency direct-touch input[END_REF][START_REF] Jota | How fast is fast enough? a study of the effects of latency in direct-touch pointing tasks[END_REF].

Considering its importance in touch/direct-interaction systems, researchers have developed methods to ease its measurement [START_REF] Bérard | Two touch system latency estimators: High accuracy and low overhead[END_REF]. However, there is no such easy and affordable measurement method for traditional mouse-based interaction. The most common procedure to measure end-to-end latency is to use an external camera to record both the input device (or finger) and the associated response on screen, then to analyze the video to match the two related events in order to count the number of elapsed frames between them [START_REF] Liang | On temporal-spatial realism in the virtual reality environment[END_REF][START_REF] Ware | Reaching for objects in VR displays: Lag and frame rate[END_REF][START_REF] Ng | Designing for low-latency direct-touch input[END_REF][START_REF] Swindells | System lag tests for augmented and virtual environments[END_REF][START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF][START_REF] Teather | Effects of tracking technology, latency, and spatial jitter on object movement[END_REF]. Since this process is generally done by hand, getting one measure of latency is already a tedious and error prone process, whatever the interactive system. Getting repeated measures is thus cumbersome and time consuming, which can be one of the reasons why latency is rarely measured and mentioned in HCI experiment reports.

We believe that as HCI researchers, it is essential to measure and report the average latency and the latency jitter observed during our experiments, to enable more accurate replication, but also in case latency reveals to be a confounding factor (especially in Fitts' law and reaction time experiments). For practitioners and users, it is also important to provide methods to determine and troubleshoot how hardware, toolkits, softwares and parameters tuning can affect the latency of in- teractive systems. As suggested in [START_REF] Deber | How much faster is fast enough? user perception of latency & latency improvements in direct and indirect touch[END_REF], manufacturers and application programmers would be able to make sure that a relative gain in latency might be perceived by users to enhance the overall user experience. For that, we need a simple and affordable measurement method but that accounts for all the "real-world" parameters that are prone to influence latency.

The measurement method we introduce, consists in positioning an unmodified optical computer mouse on a monitor, displaying and moving a particular texture to fake a mouse displacement, and sampling the corresponding mouse events. Latency is then measured as the time elapsed between the texture update and the movement of the on-screen pointer. This method contributes to:

1 -a lightweight method to measure end-to-end latency in real time; 2 -the possibility to perform multiple measures up to 5 times per second in real time; 3 -the ability to insert probes at different levels of the system e.g. drivers, system pointer, toolkits or APIs -thanks to the use of a common clock (which is hardly possible with an external measurement system such as a video camera). This allows determining where the latency comes from; 4 -the measurement of latency and jitter on different operating systems, toolkits and in different conditions.

RELATED WORK

We first detail previous work showing the impact of latency and latency jitter on performance before presenting existing latency measurement techniques.

Impact of latency on performance

MacKenzie and Ware evaluated how latencies of 8.33, 25, 75 and 225 ms affect performance using a mouse in a pointing task of index of difficulties (IDs) up to 6.02 bits [START_REF] Mackenzie | Lag as a determinant of human performance in interactive systems[END_REF]. They showed a significant interaction between lag and the ID with an increasing degradation of the performance as the tasks get more difficult, the degradation being particularly important for latencies of 75 and 225 ms. In their experiment, they introduced additional latency to the system but they did not measure and report the actual one. In a Fitts' law experiment using a computer mouse, Pavlovych and Stuerzlinger also observed a more pronounced impact of latency with smaller targets, but did not notice any drop of performance up to 58 ms of latency when acquiring targets as small as 14 pixels wide [START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF]. In a similar experiment with targets of 12 pixels, Teather et al. measured a significant 15% decrease of performance between 35 and 75 ms end-to-end latency [START_REF] Teather | Effects of tracking technology, latency, and spatial jitter on object movement[END_REF].

Concerning latency jitter, Ellis et al. have shown that users are able to detect a change in latency of less than 33 ms and probably less than 16.7 ms, independently of the base latency [START_REF] Ellis | Discrimination of changes of latency during voluntary hand movement of virtual objects[END_REF]. Pavlovych et al. measured the effect of both latency and latency jitter in a target following task [START_REF] Pavlovych | Target following performance in the presence of latency, jitter, and signal dropouts[END_REF]. Using a 35 pixels target, they showed that errors increase very quickly for latencies above 110 ms and latency jitter above 40 ms.

On touch systems, it has been shown that users are able to perceive a latency of 2 ms (6 ms in average) during a dragging task [START_REF] Ng | Designing for low-latency direct-touch input[END_REF]. For tapping tasks, performance starts to decrease from 20 ms latency [START_REF] Jota | How fast is fast enough? a study of the effects of latency in direct-touch pointing tasks[END_REF].

In summary, latency around 50 ms impacts performance in mouse-based pointing tasks, with a more pronounced effect as target size decreases (minimum target size evaluated: 12 pixels). Variations of latency (latency jitter) above 20-40 ms are also likely to be noticed and detrimental to performance.

Latency measurement techniques

The classical approach to measure latency is to record a video of both the input device and graphical output and then to analyze the images in order to measure the end-to-end latency [START_REF] Liang | On temporal-spatial realism in the virtual reality environment[END_REF][START_REF] Ware | Reaching for objects in VR displays: Lag and frame rate[END_REF][START_REF] Ng | Designing for low-latency direct-touch input[END_REF][START_REF] Swindells | System lag tests for augmented and virtual environments[END_REF][START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF][START_REF] Teather | Effects of tracking technology, latency, and spatial jitter on object movement[END_REF].

Liang et al. measured the latency of a Polhemus Isotrak sensor by mounting it on a pendulum [START_REF] Liang | On temporal-spatial realism in the virtual reality environment[END_REF]. They used a video camera to record the periodic motion of the pendulum together with the timestamps of the device events displayed on the screen. They measured latency by playing back the video frame by frame, allowing them to determine the on-screen timestamp corresponding to the pendulum neutral position. They then processed their events log file to determine the timestamp of the associated neutral position. The difference between the two timestamps provided the overall latency.

Ware and Balakrishnan used a similar setup to measure the latency of a Polhemus Isotrak and a Logitech ultrasonic sensor [START_REF] Ware | Reaching for objects in VR displays: Lag and frame rate[END_REF]. Their replaced the pendulum by a stepper motor driven pulley assembly mounted on top of the computer monitor. They moved the attached sensor back and forth, at a constant speed. The latency was measured by playing back the video frame by frame, measuring the distance between the sensor and its corresponding on-screen position divided by the controlled moving speed.

Swindells et al. measured latency in a VR setup using a phonograph turntable equipped with a tracked marker [START_REF] Swindells | System lag tests for augmented and virtual environments[END_REF].

The virtual position of the marker was video-projected on the turntable and the whole setup was video recorded. Latency was determined by the ratio of the angular distance between the two markers and the turntable angular speed. The authors also proposed a second method consisting in connecting the RGB wires of the VGA monitor to A/D converters. Latency was measured as the time from when the software renders a color scene until the software detects a voltage change. In a similar way, Mine used an oscilloscope to detect the breaking of a beam of light between a photo diode/LED by the input device (a tracker) mounted on a pendulum [START_REF] Mine | Characterization of end-to-end delays in head-mounted display systems[END_REF]. A photo diode connected to the oscilloscope was mounted on the display to measure the time when the display turned from black to white upon detecting the input device crossed the photo diode/LED.

Pavlovych and Stuerzlinger measured mouse to display latency by moving a mouse back and forth along the top bezel of a monitor at a rate of about 1 Hz [START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF]. Movements of both the mouse and the cursor were recorded with a digital camera and analyzed by measuring the time-frame differences of their corresponding phases of motions. They reported latencies between 33.2 ± 2.8 ms and 102.9 ± 3.3 ms, depending on the type of mouse (wired or wireless) and screen (CRT, LCD or DLP projection screen). They found a latency equal to 43.2 ± 2.7 ms using a wired mouse and an LCD monitor.

In a similar work, Teather et al. positioned a mouse in front of the display behind a Styrofoam pendulum [START_REF] Teather | Effects of tracking technology, latency, and spatial jitter on object movement[END_REF]. The mouse measured the displacement of the pendulum oscillating at approximately 0.8 Hz and updated a line displayed on the screen, following the pendulum's arm. The manual analysis of the video provided the latency. Using a wired mouse and a 120 Hz CRT monitor, they found an average 35 ± 2 ms latency. Steed also proposed a method to automatically extract the position of the pendulums, fit sine curves and determine their phase shift to measure the latency [START_REF] Steed | A simple method for estimating the latency of interactive, real-time graphics simulations[END_REF].

In the context of touch screens, Ng et al. measured the latency by video-recording a finger and the associated moving object at 240 Hz. The finger was moved along a ruler at a speed as constant as possible. By analyzing the video, the latency was computed by measuring the distance between the finger and the displayed object, and by estimating the finger speed using the distance traveled between successive frames. They found the latency to be typically between 50 and 200 ms. Using a high speed video camera, microphone and accelerometer Kaaresoja and Brewster measured the visual, audio and tactile latencies of different smart phones [START_REF] Kaaresoja | late: measuring multimodal delays in mobile device touchscreen interaction[END_REF]. They found latencies from 60 and up to 200 ms, depending on the smartphone and the application. Bérard and Blanch proposed to measure latency on touch surfaces by following a wheel spinning at a constant speed with a finger [START_REF] Bérard | Two touch system latency estimators: High accuracy and low overhead[END_REF]. Using a Wacom Cintiq display with a 3.4 GHz processor, they found an average latency of 43 ms. Despite its simplicity this method is obviously not applicable to mouse based interaction.

To sum up, methods based on video recording are the most commonly used to measure latency. But they introduce problems and biases related to the frame rate (each measure cannot be lower than the capture period), spatial resolution (measured distances cannot be below the camera pixel accuracy, and high frame rate camera typically have low resolutions) and blur (fast moving objects get blurred, and since high frame rate cameras require good light exposure for the image to be sharp, this can also wash out the image from the monitor). Good measures require perfect alignment between the camera, physical device and screen and good lighting conditions. In addition videos generally require to be processed by hand, which is a time consuming and error prone process. Finally, these methods help at measuring end-to-end latency but do not allow to insert probes at different levels of the system in order to finely determine where the latency comes from.

MEASURING LATENCY USING AN OPTICAL MOUSE

A modern computer mouse consists of a small camera comprising a pixel array between typically 18x18 1 and 30x30 2 pixels, a lens and an LED or laser to illuminate the surface. The microcontroller processes the images at a high framerate, typically between 1,500 Hz and 12,000 Hz, to detect visible features in the image and measure their translation between consecutive images. The measured displacements are reported to the computer as counts. The sensor has a relative responsivity above 80% typically for wavelengths between 500 nm (green) and 950 nm (infra-red) 1,2 . The camera adjusts its shutter to keep the brightest pixel at a given value. The lens determines the dimensions of the area under the mouse recorded by the camera. Laser mice typically record a smaller area to see finer details.

Our method for measuring end-to-end latency consists in positioning a standard computer mouse at a fixed location on an horizontally oriented monitor. Alternatively, one can use adhesive (e.g. Blu-Tack) to stick the mouse on a vertical monitor but should take care not to increase the distance between the sensor and the screen too much in order to avoid blurring the captured image. Depending on the shininess of the screen surface, the LED of the mouse has to be obscured with e.g. black tape, if the mouse cursor hardly or does not move when moving the mouse on the monitor displaying a white background.

Once the mouse is correctly set up on the display, a given texture is displayed on the screen and moved of a controlled distance (e.g. 1px), while a timestamp is recorded. The texture displacement is intended to create a well-controlled closedloop by producing a fake mouse displacement at a given and measurable time, which will thus be detected and reported by the mouse sensor to the system as a normal event. Upon reception of this event and subsequent ones (drivers, system pointer, toolkit, etc.), successive timestamps are recorded and latency can be measured at several levels.

Finding the right texture to display

The main assumption of our method is that the texture we display and its translation will produce a displacement that (i) can be detected by the mouse sensor; and (ii) can subsequently produce a system cursor displacement.

Mice resolution is reported in CPI (counts per inch) which corresponds to the smallest displacement they can report. It starts at 400 CPI and can go up to 12,000 CPI 3 . Screens resolution, in PPI (pixels per inch), is far lower, around 100 PPI for current average-end LCD monitors, while high-resolution monitors can go up to 300-400 PPI. This means that a translation of a single pixel on the highest-end monitor is larger than what can measure the lowest-end mouse. As a result, moving a texture of one pixel ensures the displacement can be detected by the mouse. It is also the best case scenario to make sure that a part of the texture remains visible by the mouse sensor after it is translated: the mouse needs to see common features between two images to compute a displacement.

Moving the texture of one pixel is likely to produce mouse reports as low as 1 count. Thus, we have to make sure that 1 count produces a displacement of the system pointer of at least 1 pixel after the operating system transfer function is applied. Casiez and Roussel have shown that each operating ; black dots on a white background with no LED occlusion (same display); same pattern with LED occluded using black tape (same display); white background on a 148 PPI Apple Retina display; black letter 'd' on a white background captured on the same display. Note that pixels from the sensor range between 0 and 63. The above images are displayed using re-scaled values between 0 and 255 for better visibility.

system uses custom transfer functions, but their reverse engineering helps determining the appropriate mouse configuration panel settings [START_REF] Casiez | No more bricolage! methods and tools to characterize, replicate and compare pointing transfer functions[END_REF]. On Windows XP, 7, 8 and 10, setting the slider to one of the 2 last positions when the "enhanced pointer precision" box is checked results in at least a 1 cursor pixel displacement for every 1 count. When "enhanced pointer precision" is unchecked, any position higher than the middle one works. On Linux, any configuration of the settings in the mouse configuration panel works. On OS X, "acceleration" needs to be disabled4 because all settings for nonlinear transfer functions prevent to systematically get at least one pixel displacement for one count.

We first tried to display and move different textures designed on the rule of the thumb (grids, images, Perlin noise, random noise . . . ) but only some of those sometimes produced a mouse event. Obviously we needed a less arbitrary and more systematic approach.

What the mouse sees

To help finding the right texture to display, we first needed to get the raw image from a mouse sensor in order to better understand "what the mouse is seeing". We opened a 400 CPI Logitech M-BT58 mouse and wired its Avago ADNS-2610 1 sensor to an Arduino board. We chose this mouse as we could easily find its datasheet, it is widely available and it corresponds to the lowest mouse resolution available (our worse case scenario). We set the sensor in pixel grab mode, put the mouse on a LCD screen displaying white background and black text (without anti-aliasing), and sent the 18×18 captured pixels to a custom made application. This first helped us to figure out the physical dimensions of the area recorded by the sensor, which is around 1×1mm. On a 100 PPI screen, this corresponds to about 3×3 visible pixels, giving us the size of our unit pattern for the texture. Figure 2 shows images captured using the sensor.

We noticed on the captured images that the screen's pixel grid and the corresponding small physical separation between its pixels are visible (Fig. 2), which is known as the "screen door effect"5 . This explains why moving a mouse with the LED obscured on a white on-screen image is still producing pointer movements: the sensor detects the fixed pixel grid which is helpful to compute the mouse displacements (this is how the very first optical mice were working, with a grid printed on a dedicated pad). As we will see below, the screen door effect proved to be an important factor for reliable texture displacement detection.

What we decided to show

To systematically investigate the textures that could fake a mouse displacement, we built 512×512 pixels textures based on the repetition of all the possible 3×3 patterns composed of black and white pixels (we discarded gray levels as they reduce the contrast of the images and reduce the chance of finding relevant patterns). The mouse was roughly aligned with the screen edges, so the pixels of the sensor are approximately aligned with the screen ones. We tested the resulting 2 9 patterns using 9 offset positions and 15 repetitions. The offset position corresponds to a translation of the starting position of a texture, between 0 and 2 pixels in x and y. This ensured invariance with respect to the position of the mouse sensor on the screen, avoiding to get a texture working just by chance because the sensor would be well aligned with it.

We developed a testbed application in C++ using the Qt 5 framework. Textures were pre-computed and stored as PNG images. A trial consisted in displaying a texture with no antialiasing -making sure that one pixel of the texture was corresponding to one pixel on screen -and moving it one pixel along the x screen axis. Trials with no mouse event received within 200 ms were marked as failed.

We ran this experiment with several mice and monitors. After that we visually compared the patterns with the higher success rate for each pair of mouse and monitor to select the most robust ones over all the conditions. The patterns that work best are those that cancel the screen door effect: if the physical gaps between pixels are visible, the mouse sensor is likely to detect them as visual features that do not move or disappear between two captured frames, while other features in the texture move. In such situations, the mouse is not able to compute a displacement. As a result, two adjacent pixels in a texture cannot be white, and working textures are those made of oblique and non adjacent lines of pixels (e.g. a repetition of the pattern displayed in Figure 3).

Evaluating the texture in different conditions

We evaluated the texture presented in Figure 3 pixels resolution (148 PPI6 ), using OS X 10.10. The monitors were the laptop screen and an external Dell 1905fp connected through DVI. There were few applications running but we could not control the background processes from running. Each pair of mouse/display was evaluated 1000 times. A trial consisted in translating the texture one pixel along the x abscissa. Trials alternated translation from left to right and right to left. We measured the success rate (SR) to produce mouse events, the mean and standard deviation (std) for latency, measured from the texture translation to the first mouse move event in Qt. We noticed that the mouse does not always send a single report for one pixel texture translation.

We hypothesis this can be due to the high frame rate of the mouse sensor measuring some transition when pixels change color. Trials with no mouse event produced within 200 ms were marked as errors. Mice were always positioned at the center of the screen.

Results are presented in table 1. On average the texture works better on the higher resolution monitor, probably because the mouse sensor can see finer details. Except two mice that do not work at all on each monitor, the other mice show a success rate above 16%, which means it is at least possible to perform one measure of latency per second using these mice, using a 200 ms timeout. Two mice for the lower end monitor and four mice for the higher resolution monitor have a success rate above 95%, which means it is possible to have up to 5 measures of latency per second with them. On average the latency is close to 70 ms with a higher standard deviation for the external monitor.

Measuring latency at different positions on a display

We measured end-to-end latency at different positions on an Apple Retina display using a Logitech MX310. We found a mean of 58.9 ms (std=8.4 ms) for top right position, 65.6 ms (std=9.1 ms) for top left, 68.2 ms (std=7.8 ms) for center, 77.7 ms (std=8.0 ms) for bottom right and 78.8 ms (std=7.6 ms). Note that all positions were not measured simultaneously. Considering that LCD monitors usually update the screen from top to bottom, it makes sense to get lower values for the top of the screen. If we subtract the mean latency at the bottom of the screen and at the top of the screen, we get 16 ms which is close to the time screen time period (1000/60 = 16.67 ms). For all the following measures, the computer mouse was positioned at the center of the screen.

INSERTING PROBES IN THE SYSTEM

Conversely to other lag measurement methods that rely on external devices, our probe is a mouse connected to the computer on which we want to measure lag. Our method thus "closes the loop" and enables to establish time measurements based on a single (internal) clock. We use this property to insert probes at different places in the system to investigate the sources of latency: since all time measurements are based on the same clock, comparing these times is reliable, while it would require substantial supplemental work with external systems such as a video camera.

Our probes consist of callback functions registered at different places. Each callback logs a timestamp and information about the event. We start measuring time before the texture is moved (Window repaint in Fig. 4). The texture is then updated on-screen after a given amount of time (on-screen texture moved). Upon detecting a displacement, the mouse sends an HID report (HID report sent) that is handled by the lowlevel layers of the operating system before getting out of the HID stack (HID report received). The operating system then processes the event and applies the transfer function to move the system pointer (System pointer moved). Upon notification of this pointer movement, the toolkit creates an event (Mouse-Move event created) and dispatches it to the appropriate widget (MouseMove event dispatched). The end-to-end latency we measure is the time elapsed between Window repaint and MouseMove event dispatched. Three probes inserted at steps 1, 2 & 3 (Fig. 4) allow us to further characterize this latency.

Comparison of different toolkits

We used libpointing7 [START_REF] Casiez | No more bricolage! methods and tools to characterize, replicate and compare pointing transfer functions[END_REF] to get notifications of HID reports reception and platform-specific code (Quartz event taps) for notifications of system pointer updates on OS X. We implemented these probes along with toolkit-specific code for Mouse Move event creation and dispatching using C++ / GLUT, C++ / Qt and Java / Swing on the Apple Mac-Book Pro laptop previously described. All probes were implemented as asynchronous and non-blocking callbacks. All toolkits used double buffering for the display. Timestamps were measured with sub-millisecond precision 8 .

We compared the measurements obtained on 1000 trials with our three implementations using a Logitech MX310 mouse. Table 2 shows the success rate (percentage of texture displacements that resulted in a valid MouseMove event, i.e. one that matches the sequence of observations illustrated by Figure 4), mean end-to-end latency (time between repaint and the first dispatched MouseMove event) and the corresponding standard deviation. Results show substantial differences between GLUT and Swing or Qt in terms of mean latency but comparable standard deviations. Note that in the three cases, the latency introduced by the movement of the system pointer and the toolkit is below 2 ms. Figure 5 shows the distribution of lag measurements between repaint and the first MouseMove. This plot shows a clear difference between Java / Swing and C++ / Qt despite comparable mean values, for which we are unable to provide a definite explanation. The differences illustrated by Table 2 and Figure 5 clearly require further investigation.

Comparison with other systems

We measured end-to-end latency on Linux Ubuntu 14.04, Windows 7 Pro and web browsers, all on the same machine, an Asus N53JQ (i7Q740@1.73GHz, 4Gio DDR3@1333MHz, Nvidia Geforce GT425M 1Gio, 250 Gio SSD). We used the previously described Dell 1905fp monitor and the Logitech MX310 mouse. End-to-end latency was measured using our Qt 5 application. For web browsers we used an HTML5 / Javascript version performing the same measures. Latency was measured from texture translation to the mouse move event received by the toolkit. On Linux Ubuntu 14.04, latency is comparable with OS X 10.10, although measured on a different machine. The web browsers add between 15-20 ms latency compared to Qt 5 while jitter remains similar (Table 3). Results on Windows 7 are more surprising: latency on Chrome 41 is lower than the one found on Qt 5. We repeated the measures several times and we kept finding the same results.

C++ / GLUT

Java / Swing C++ / Qt SR mean std SR mean std SR mean std HID 100.0 % 46.2 ms 5.3 ms 97.9 % 62.0 ms 5.5 ms 99.9 % 65.4 ms 5.1 ms sysPointer 100.0 % 46.5 ms 5.3 ms 97.9 % --99.9 % 65.7 ms 5.1 ms tkEvent 100.0 % --97.9 % 63.2 ms 5.5 ms 99.9 % 65.9 ms 5.1 ms tkMouseMove 100.0 % 46.7 ms 5.3 ms 97.9 % 63.3 ms 5.5 ms 99.9 % 66.0 ms 5.1 ms

Influence of system load

We investigated how the system load can affect the latency. We simulated different loads on Ubuntu 14.04 using the stress utility 9 to control the load, with the command stress --cpu CPU --io IO --vm VM --timeout 300s --verbose.

The load was simulated with an increasing number of CPU, IO and memory allocation processes. For 25% load, we used CPU=2, IO=5, VM=1; CPU=4, IO=10, VM=2 for 50% load; CPU=6, IO=15, VM=4 for 75% load and CPU=8, IO=20, VM=8 for 100% load. We used the Asus N53JQ computer, Logitech MX310 mouse and Dell 1905fp monitor. We performed 1000 measured using the C++/Qt and Java/Swing toolkits. Results are summarized in Table 4. We can observe that both latency and latency jitter increase with system load. With both toolkits, latency increased by 25-30 ms and jitter by 20 ms between a low system load and a 100% system load.

DISCUSSION

The methodology we followed helped us determine a pattern and a texture that work with most optical mice (8 of 10 mice we tested). Understanding exactly why it works with some mice and not others is difficult: mouse sensors datasheets are often unavailable and the algorithms for computing mice displacements are never disclosed. Given that optical mice are widely available, it is however easy to use another mouse if one is not working. We could not make any laser mouse work with our method. A first reason can be that laser mice see primarily in the infra-red but they could also see in the visible spectrum according to some datasheets we found 2 . A second reason can be that the surface seen by the sensor is smaller for laser mice than optical ones: laser mice are intended to see finer details on surfaces not visible by optical ones. However, we hypothesize that optical and laser mice would have 9 http://people.seas.harvard.edu/ ∼ apw/stress/ the same latency as their sensors are similar. The main difference is that the red LED is replaced by an infra-red laser.

The results we found are consistent: measures obtained in similar conditions give similar results. For example we obtain a 50.9 ms mean latency for Linux Ubuntu 14.04 / Qt 5 using the Logitech MX310 and Dell 1905fp monitor on an Asus computer (Table 3) and 54.2 ms for the same system with less than 5% system load (Table 4). With the same mouse and monitor we obtain 55.2 on a Macbook Pro running OS X (Table 1). These results are similar to the only comparable result available in the literature that reported a 43.2 ms endto-end latency for a wired mouse with an LCD monitor [START_REF] Pavlovych | The tradeoff between spatial jitter and latency in pointing tasks[END_REF]. In addition, when measuring latency at different positions on a screen, we found lower latencies for the top of the display and a difference between its bottom and top of around 16 ms, which is consistent with the way LCD monitors are refreshed.

The different measures we performed indicate that latency and latency jitter are similar on C++/Qt and Java/Swing, even with different system loads. We expected that the Java virtual machine would add some latency, but it is not the case. Our GLUT implementation not only shows a lower latency but also a different distribution of latency values from our Qt implementation, which will require further investigation. Linux and OS X show similar latencies around 50-55 ms with the external Dell monitor and MX310 mouse. Windows 7 in contrast appears to show higher latency (75 ms). Web browsers increase latency by 15-20 ms on average. System load increases latency as well of about 25-30 ms with 100% load. In addition we have shown that latency jitter increases with system load while it remains otherwise below 10 ms. Note that we performed these measures using the mouse having one of the lowest latencies (Table 1). We measured latency from the texture displacement to the mouse move event received by the toolkit. Real usages would have to include the latency introduced by the application-specific code running upon reception of mouse events.

As discussed above, our method allows the insertion of probes at different places in the system to provide reliable time comparison. We observed that the time from when the event exits the HID stack until it enters the mouse move callback is very low, below 2 ms. We expected it would be higher considering the different application layers, computations to determine the widget beneath the mouse pointer and the queues to go through. It means that most of the latency we measured is caused by the display, mouse and low level layers of the operating system. A 60 Hz display introduces a latency of at most 16.67 ms (excluding the display's response time, which probably adds about 10 ms). A computer mouse reports up to 125 Hz which adds another 8 ms on average. This accounts for about 30 ms. Further investigations are required to clarify where the other 15-30 ms come from. The literature has shown that performance degrades above 50 ms latency and we have shown we are most of the time above this value. This means it is important to report latency in HCI experiments and that further work is needed to reduce latency or to compensate it using appropriate techniques.

Our measures can be affected by both the function used to query time and the resolution of the timers used by the application, the toolkit or the system. Windows, OS X and Linux functions 8 to query time have sub-millisecond precision. On Windows the default timer resolution is of 15.6 ms while it is 1 ms on Linux 10 and OS X. In addition modern versions of Windows, Linux and OS X all use timer coalescing techniques to reduce CPU power consumption. This certainly contributes to some variability in the measured end-to-end latency, but it can not be easily avoided. Overall, this is just another source of (small) variability found in "real life" conditions. An advantage of our method over camera-based ones is that it makes it possible to easily and quickly perform many measures to estimate this variability.

CONCLUSION

We introduced a method that makes latency measure of desktop interfaces simpler. This method relies on cheap hardware already in the hands of every users and a particular texture to display, which can thus be easily replicated. We have shown that our method works with most optical mice and provides real time measures of latency. The measures we performed can guide interface designers and HCI researcher to choose appropriate toolkits, operating systems and hardware. More generally we believe that our simple method for measuring latency has the potential to change the way HCI researchers run experiments and the way practitioners tune their interactive systems. An on-line interactive demo and additional material are available at http://ns.inria.fr/mjolnir/lagmeter/

Figure 1 :

 1 Figure 1: Sample setup used, with a Logitech MX310 mouse positioned on a horizontally-oriented laptop display. A particular texture is displayed and moved under the mouse sensor to fake displacements. Other mice discussed in the paper are positioned around the display.

Figure 2 :

 2 Figure2: Raw images captured using an Avago ADNS-2610 sensor. From left to right: white background on a 86 PPI Dell 1905FP; black dots on a white background with no LED occlusion (same display); same pattern with LED occluded using black tape (same display); white background on a 148 PPI Apple Retina display; black letter 'd' on a white background captured on the same display. Note that pixels from the sensor range between 0 and 63. The above images are displayed using re-scaled values between 0 and 255 for better visibility.

Figure 3 :

 3 Figure 3: The displayed texture (middle) is composed of a repetition of the 3×3 pixels pattern composed of black and white pixels (left). Image of the texture captured by the ADNS-2610 mouse sensor (right) showing the screen door effect is canceled.

Figure 4 :

 4 Figure4: Conceptual pipeline between a (simulated) physical movement of the mouse and the notification of this movement to the appropriate on-screen widget. Our system is able to measure end-to-end latency by inserting probes at different software locations, numbered from 1 to 4.

Figure 5 :

 5 Figure 5: Distributions of the time (in ms) elapsed between Window repaint and the first MouseMove event dispatched using the Logitech MX310 and different toolkits on a MacBook Pro.

Table 1 :

 1 Success rate (SR), mean latency and standard deviation for 10 mice with 2 monitors on a MacBook Pro using OS X 10.10. When known the sensor reference is provided in brackets. Latency is measured as the time elapsed between the one pixel horizontal texture translation to the reception of the first mouse move event in the Qt application.

	Dell 1905fp (86 PPI)	Apple Retina (148 PPI)
	SR	mean	std	SR	mean	std

with 10 different mice and with 2 monitors using the previously described application on a laptop MacBook Pro Retina 15-inch (Mid 2014) 2.5 GHz, 16GB Ram, SSD hard drive, 1920×1200

Table 3

 3

	: End-to-end latency on different operating systems and web
	browsers measured on the same computer (Asus N53JQ with a Logitech
	MX310 mouse and a Dell 1905fp monitor).

Table 2 :

 2 Comparison between GLUT, Swing and Qt implementations with four different probes on an Apple Macbook Pro with a Logitech MX310 mouse.

		C++ / Qt		Java / Swing
		mean	std	mean	std
	< 5 % 54.2 ms 6.7 ms	51.3 ms 6.7 ms
	25 %	71.9 ms 14.6 ms 59.7 ms 10.1 ms
	50 %	70.1 ms 15.1 ms 71.6 ms 23.5 ms
	75 %	77.3 ms 21.5 ms 71.0 ms 19.1 ms
	100 % 83.6 ms 25.8 ms 75.6 ms 25.6 ms

Table 4 :

 4 Influence of system load on end-to-end latency on Linux Ubuntu, measured on the same computer (Asus N53JQ with a Logitech MX310 mouse and a Dell 1905fp monitor). Comparison between C++/Qt and Java/Swing.

http://gaming.logitech.com/en-us/product/ g502-proteus-core-tunable-gaming-mouse

Using the command defaults write .GlobalPreferences com.apple.mouse.scaling -1 and logging out and back in to apply the setting.

http://en.wikipedia.org/wiki/Screen-door effect

We set the monitor to the maximum available resolution in the configuration panel (1920×1200 pixels) and the physical dimensions of the display are 330.63 × 207.347 mm.

http://libpointing.org

We used GetSystemTimeAsFileTime to query time on Windows 7 and gettimeofday on Linux and OS X.

ACKNOWLEDGMENTS

This work was supported by ANR (TurboTouch, ANR-14-CE24-0009).