Impacts of environmental access restrictions on freight delivery activities, the example of Low Emission Zones in Europe

Laetitia Dablanc, Antoine Montenon

Impacts of environmental access restrictions on freight delivery activities -The example of Low Emission Zones in Europe

INTRODUCTION, GOALS AND METHOD

European environmental programs encourage or impose measures that reduce air pollution. Air quality standards have been established which compel national governments and urban areas to implement measures to reduce pollutants emitted by traffic. An increasing number of European cities are introducing regulations that encourage clean vehicles. This involves the introduction of new criteria, which are more focused on protecting the environment than improving safety or mitigating congestion. A number of European cities have thus created Low Emission Zones (LEZ), from which the vehicles that pollute the most are banned. They frequently consist of goods vehicles as a result of the high levels of pollution emitted by today's urban delivery vehicles fleets.

The aim of this paper is to identify the position of goods vehicles in European Low Emission Zones and to analyze the impact of access restrictions on transport and logistics firms and on their logistical activities. Our starting hypothesis was that creating an LEZ will disrupt the market on which urban delivery carriers operate. We specified three potential levels of impacts, as described in Section 3. To test our hypotheses, we began by studying European LEZs through the scientific and technical literature. We then performed a series of interviews and field visits (see description in Section 3) in two European cities which introduced an LEZ several years ago, in order to conduct an ex post appraisal of freight transport companies' reactions. The two cities are London and Berlin. We have also elicited the aid of carriers' organizations in order to distribute a questionnaire among their member transport firms. These surveys and interviews (described in Section 3) were conducted jointly with local universities and professional bodies from the transport and logistics sectors: the University of Westminster, Transport for London, Central London Freight Quality Partnership, FTA, RHA, DLR, BdKEP, BGL, Senat Berlin. This research is the culmination of the first phase of the RETMIF (Reduction of Emissions from Freight Transport in the Greater Paris Region) project, which is funded by the French Environment Agency (ADEME, AACT-AIR program). A second phase of RETMIF, which started at the end of 2014, is testing the impact of several LEZ scenarios and appraising their potential effectiveness with regard to the socio-economic response of transport operators. We do this for Paris, which is one of the few urban areas in Europe which has not yet restricted access to polluting vehicles, in spite of the city's mediocre ambient air quality. This paper is structured as follows: Section 1 identifies the air quality problems that exist in European cities and how road freight transport contributes to them. In Section 2, we present the European Low Emission Zones and the position freight vehicles have in them. In Section 3, we present the results of our analyses with regard to socio-economic impacts of LEZs.

SECTION 1. AIR QUALITY IN EUROPE AND THE CONTRIBUTION OF ROAD FREIGHT TRANSPORT

Current European goals (Directive 2008/50/EC) with regard to concentration thresholds for atmospheric pollutants are not being reached. For example, in 2012, the mean concentration limits laid down for NO 2 were exceeded in 95% of the surface area of Paris [START_REF]Evolution de la qualité de l'air à Paris entre 2002 et[END_REF]. In 2014, the European Commission launched legal proceedings against the United Kingdom because of its excessive NO 2 emissions. The fine could amount to €365 million.

Road transport (freight and passenger) is one of the main sources of pollutant emissions. Freight transport in particular is recognized as a major contributor to emissions of ozone, fine particulates and nitrogen oxides (NO x ), which cause health problems [START_REF]Air Quality Guidelines Global Update 2005[END_REF]. In 2011, road transport produced 47% of all NO x emissions in Europe (3; 4). As far as particulates are concerned, road transport is responsible for 14% of all such emissions Europe-wide. Pollution from road transport has risen also as a result of the continual increase in the proportion of diesel vehicles in the fleet. Diesel engines generate between 4 and 10 times more NO x emissions than gasoline vehicles of equivalent power and weight [START_REF] Colvile | The transport sector as a source of air pollution[END_REF]. Even recent diesel vehicles emit NOx (mostly NO 2 ), also because of the use of filters to combat other types of pollution.

Increase in pollution has been particularly acute in urban areas, particularly because of the growth of delivery activities in cities [START_REF] Dablanc | Goods Transport in Large European Cities: Difficult to Organize, Difficult to Modernize[END_REF]. Urban freight transport is one of the principal sources of urban pollution. It has been calculated that in French cities it accounts for 35% of the NO x and 40 to 50% of the PM 10 emitted by urban transport as a whole [START_REF] Albergel | Méthodologie pour un bilan environnemental physique du transport de marchandises en ville[END_REF], while goods vehicles are responsible for only 15 to 20% of all vehicle-kilometers. In London, in 2010, goods transport was responsible for 38% of NOx emissions from road transport (27% from HGVs, 11% from LGVs) and 37% of PM 10 (14% HGVs, 23% LGVs) [START_REF] Allen | London Freight Data report 2013 update[END_REF]. One intrinsic reason for this poor environmental performance is the stop-and-start way vehicles are driven. Five stops over a distance of 10 km increase fuel consumption by 140% [START_REF] Martensson | Volvo's environmental strategy for next generation trucks[END_REF]. The pollution caused by urban freight transport is made even worse by the fact that, on average, urban goods vehicles are older than private cars. An HGV sold in 2014 (Euro VI standard1 ) satisfies maximum NO x pollution criteria that are 20 times lower than one sold in 1994 (Euro I standard), and the criterion for PM 10 emissions is 40 times lower. Furthermore, it has been observed that in the case of France the larger the city, the older the delivery fleet, as a result of the structure (see below) of the urban delivery market in major cities [START_REF] Dablanc | Urban Goods Movement and Air Quality, Policy and Regulation Issues in European Cities[END_REF]. In 2011, the Paris city authorities carried out a survey by examining the number plates of 3,200 HGVs and 13,000 vans: 11% of the vans and 20% of the HGVs in the dense urban zone did not meet the Euro 3 standard.

Old vehicles are used by the very large number of small independent carriers which operate in major cities, frequently as subcontractors and with very small financial margins. In the dense part of the Paris metropolitan area, there are estimated to be 12,000 light haulage companies (using vehicles with a gross weight of 3.5 tons or less), a significant proportion of which are operating illegally (doing undeclared work or not registered in the transport registry). The supply of subcontractors is regularly replenished due to the low entry barriers that apply to the road transport market for operators using light vehicles. In addition, more than 15% of urban deliveries are made by the consignee on its own account (this applies particularly to small shopkeepers), who often use very old vans for this purpose [START_REF] Routhier | Paris urban freight survey -First results[END_REF]. Small transport and logistics operators and shopkeepers cannot easily afford to update their vehicle fleet.

In recent years, one policy solution to urban freight impacts has been the implementation of Low Emission Zones.

SECTION 2. A TOOL TO REDUCE URBAN POLLUTION: LOW EMISSION ZONES (LEZ)

Only vehicles that meet specified pollution standards are allowed to enter Low Emission Zones. These are "geographically limited zones that cover more than a very local area where there are problems from the point of view of atmospheric pollution, noise, the quality of urban life, traffic congestion and/or safety and in which specific restrictions are applied with regard to the volume and/or the nature of traffic in the zone" [START_REF]Report from the Working Group on Environmental Zones -Exploring the issue of environmentally-related road traffic restrictions[END_REF].

The types of vehicles and the associated emissions criteria are laid down by the local, regional and/or national authorities. As of March 2014, on the basis of different websites (see in References), documents and further research, we identified 197 LEZs in the European Union, in 10 different countries. Simple LEZs (LEZs without a tollsee below) account for 106 of these, and 91 are tolled LEZs (only three of which are outside Italy).

The main European LEZs

Figure 1 shows the locations of Europe's LEZs (as in March 2014) distinguishing between cities where restrictions based on vehicle pollution are applied ("simple" LEZs), cities where traffic is regulated by an urban toll which increases according to the level of pollution (LEZ with toll), and cities with LEZs that are not enforced or not strictly enforced.

On this basis we can divide European countries into three main groups: Germany, Italy, the Netherlands and Sweden, where many cities have set up LEZs, and where such zones have strong national backing; a group of countries where only the main cities have an LEZ, generally as the result of a local initiative. This is the case in Europe's best-known LEZ, the London Low Emission Zone. Finally, there is a group of countries that have no LEZs or whose LEZs have a limited impact because of low compliance with regulations: this group essentially consists of France, most Eastern European countries and, to a lesser extent, Spain. In Madrid, the municipality has created a zona de bajas emisiones (literally a low emission zone) in the central area. This zone does not restrict vehicular traffic, but varies the price of parking according to the age of the vehicle and its fuel. Electric and hybrid vehicles have a 20% reduction, and Euro 6 diesel vehicles and Euro 4 gasoline vehicles have a reduction of 10%.

The size of Europe's LEZs varies from 0.6 km² (Lisbon) to 5,700 km² (the region of Styria in Austria). Very often this size is closely linked to the type of local or regional authority responsible for the zone and corresponds to an administrative division or a functional area (for example, that enclosed by a ring of railway lines in Berlin). The surface area has a direct impact on the cost of the measure and its environmental, social and economic impacts. For example, it is more cost-effective to equip a large zone with enforcement cameras than a smaller one. With regard to environmental and traffic issues, residents and transport operators will have a greater tendency to avoid a small zone than a very large one. London's Low Emission Zone is the second largest in Europe, covering almost 1,580 km².

Italy and Germany have the highest number of LEZs (see Germany below). In Italy, the primary aim of a zona a traffico limitato (ZTL) is to reduce traffic and congestion rather than improve air quality or reduce noise. Most cities with a zone of this type started by setting up what amounted to an urban toll in their central district. Increasing air quality problems, particularly in winter, let them to introduce Low Emission Zones. A consequence of this specific situation is that Italy's LEZs are very diverse, even within a given city. For example, of the 10 or so ZTLs in central Rome, some require payments and others impose night-time restrictions on certain types of vehicle, and zonal boundaries may vary according to the time of day and day of the week. This diversity also leads to overlaps and a number of derogations which is unsurpassed in Europe. In the former A1 zone in Lombardy, 22 types of derogation are possible, not counting the different exemptions applied by different cities. In contrast, no exemption is possible in the Netherlands.

At the present time, two main modes of enforcement are used for LEZs in Europe: video cameras which read number plates, and visual surveillance with the use of stickers. The means of enforcement has an impact on the rate of compliance. When the city of Amsterdam put in place a system of surveillance cameras for its Milieuzone in 2009, the compliance rate rose from 66% in 2008 to 97% in 2010 [START_REF] Boogaard | Impact of low emission zones and local traffic policies on ambient air pollution concentrations[END_REF]. In Germany, the principle of privacy restricts the use of cameras. In contrast, in the U.K., Transport for London was given access to the national vehicle registration database.

London and Berlin LEZs

When it was created, the main idea behind the London LEZ was to achieve a marked decrease in pollution from road traffic in the region without imposing a high economic cost [START_REF] Watkiss | London Low Emission Zone Feasibility Study[END_REF]. Implementation took place in four phases: in 2008 it applied to diesel vehicles weighing over 12 tons. Six months later, all vehicles with a GTW of over 3.5 tons had to comply with the Euro III PM standard. In 2012, vans with an unladen weight of over 1,205 kg had to comply with the Euro 3 PM standard while the standard for HGVs was raised to Euro IV PM. What marks out the London LEZ, apart from its size and its inclusion of light goods vehicles, is its massive use of automated plate-reading. Owners of non-permitted vehicles are asked to pay a charge of £100 or £200 per day to enter the zone. If they do not comply, fines range from £250 to £1000 per day.

Compliance rates with the standard by the targeted vehicles when phases three and four were implemented were 97% and 85% respectively, as shown in Figure 2. Phase 4 compliance rose quickly between the end of 2010 and the beginning of phase 4.

Germany has the second largest number of zones in Europe, with 76 Umweltzonen. To enter the zones every vehicle, irrespective of its weight and even if it is foreign, must have a sticker ("Plakette"), which is issued on the basis of its registration certificate and which represents a pollution standard by a color. Three colors are available: red, orange and green, according to the corresponding Euro PM standard. Vehicles can be retrofitted with devices to reduce particulate emissions. Thus, the green sticker corresponds, as a minimum, to a Euro 1 PM gasoline vehicle, a Euro 4 PM diesel vehicle or a retrofitted Euro 3 PM diesel vehicle. Each city or state selects which pollution limit standard will apply. By the end of 2013, most local and regional governments had chosen the green sticker (source: Federal Environment Ministry website). In the Berlin Umweltzone, there were quite a large number of exemptions, granted on a case-bycase basis. One is interesting, and to our knowledge unique in Europe, namely vehicles belonging to a firm "whose survival is threatened by the scale of the investment required" (source: City of Berlin derogation request form). There is a charge for exemptions (for example, a total of €431.20 will be due for a 7.5 ton vehicle seeking a nine-month derogation). As of January 2015, no more exemptions are provided.

Euro standards and the position of goods vehicles in LEZs

All of Europe's LEZs target heavy vehicles and only two (Norwich and Oxford in the U.K.) do not target freight vehicles but just buses. Of the 197 LEZs we have identified, 26 (12%) are only concerned with goods vehicles. Of these 26, only the London LEZ takes account of light goods vehicles. The importance of freight vehicles in LEZs regulations can be explained by their significant share in urban pollution (see Section 1).

In the 197 LEZs we have identified, the Euro 4 PM standard is used in most cases to impose access restrictions on goods vehicles. This is the case, for example in most German cities, several Italian cities (where some limits are even based on Euro 5), Copenhagen and London. In London, HGVs must follow the Euro IV PM standard and large vans the Euro 3 PM standard. Others, such as Amsterdam or Prague, require compliance with all parts of Euro IV, not only for PM. Another group of cities makes do with Euro 3, for example many Italian LEZs and those in Norwich and Stockholm (but in the latter case, the age limit for vehicles is six years). Finally, one group of "laxer" cities merely prohibits very old HGVs: in the case of Athens (in the entire metropolitan area) vehicles must be less than 13 years old, though a much stricter regulation applies in the city center for vehicles wishing to escape the alternate driving day system. Most small Italian cities have chosen the Euro 2 standard, and Lisbon applies Euro 1.

SECTION 3. SOCIO-ECONOMIC IMPACTS OF LOW EMISSION ZONES ON FREIGHT TRANSPORT

In the specific socio-economic context in which urban freight transport operates, which we have described in Section 1, the introduction of access restrictions based on the age of delivery vehicles may have major impacts. We identified three theoretical levels of impacts. At the macroeconomic level, the total number of delivery firms, the average number of employees and vehicles per delivery firm may change following the introduction of an LEZ. At the microeconomic level, firms may leave the market or relocate due to additional costs, or change their fleet and operate their activities more efficiently to offset new costs. Finally, on a more transversal level, more radical changes may be introduced towards innovative city logistics. Despite these potential impacts, and with the exception of two studies on the case of Milan [START_REF] Danielis | An economic, environmental and transport evaluation of the Ecopass scheme in Milan: three years later[END_REF] and a brief study on Dutch environmental zones [START_REF] Proag | Cost-Benefit Analysis of the Dutch Urban Environmental Zones[END_REF], no ex post analysis has been conducted of the socio-economic impacts on small road transport operators making urban deliveries in the European cities that have introduced such measures. The literature is more concerned with the environmental impacts of LEZs (13; 17; 18). Börjesson et al. (19) were mostly interested in the effects of the Stockholm urban toll on passenger traffic. They nevertheless mentioned a 15% reduction in all commercial traffic (freight and business trips). Browne et al. [START_REF] Browne | Low emission zones: the likely effects on the freight transport sector[END_REF] evaluated, but only on an ex ante basis, the foreseeable effect on the transport industry of the London LEZ. The operators they questioned were moderately in favor of the introduction of the environmental zone, or at least resigned to the idea. Although an evaluation and feedback mechanism was provided together with the LEZ implementation process, little in the way of findings concerning the economic benefits have been made public by Transport for London. With regard to environmental aspects, analysis was only performed just after the implementation of phase 1. The authorities are fairly silent on this topic at present, except for the health benefits of the measure [START_REF]London Freight Plan -Sustainable freight distribution: a plan for London[END_REF].

Our own surveys in London and Berlin took us to conduct 30 interviews (15 in London, 15 in Berlin) including freight organizations (one third of interviews), freight companies (one third) and local decision-makers (one third). We have also elicited the aid of carriers' organizations in order to distribute a questionnaire among their member transport firms, and we were able to process only five completed questionnaires, as the surveys did not generate much interest from local freight operators.

The results of our and other studies presented below will relate to the three levels of impacts of a LEZ identified in our hypotheses: the overall impact (at the city level) on the freight market; changes in microeconomic behaviors; more general progress towards clean urban logistics.

Overall economic impact

One of the few ex post economic impact evaluations has been conducted for Milan [START_REF] Danielis | An economic, environmental and transport evaluation of the Ecopass scheme in Milan: three years later[END_REF]. Milan introduced an urban toll in 2008, in which the charges varied according to Euro standards. The system went under the name of Ecopass until it was replaced in 2012 by a simpler one. Ecopass had a complex system of charges. For HGVs, all Euro IV and Euro V vehicles were exempt from payment, and older vehicles paid between 2 and 10 Euros per day. According to the authors, Ecopass achieved substantial results in the studied period (2008 to 2010). There were 13,040 freight vehicles per day in the zone prior to the introduction of the system, and 9,521 after. This means that firms and residents in central Milan continued to receive supplies with 27% fewer vehicles. The number of freight vehicles using alternative fuels, or zero emission vehicles, that drive through the zone has increased from 92 to 1089 during the same period. The authors assigned financial values to the costs and benefits of Ecopass. They found that the freight sector had saved €1.3 million as a result of reduced journey times and improvements in reliability, but lost €10.8 million in tolls and investment in new vehicles, i.e. a net loss of €9.5 million, which was the highest of all the stakeholder categories considered. Freight operators were the greatest losers as a result of the system and the city authorities the principal winners, in particular due to new sources of revenue (from fines rather than from tolls).

In London there was a very marked reduction in the number of commercial vehicle-kilometers between 2007 and 2011.

LGV traffic decreased by 12% between these two dates [START_REF] Allen | London Freight Data report 2013 update[END_REF]. There has been a decrease by 8% in the number of small workplaces (0-9 employees) in the field "Transportation and Storage" in Greater London between 2008 and 2011 (Office for National Statistics). It is difficult to establish a clear link between this reduction and the creation of the Low Emission Zone, all the more so that the economic downturn hit the United Kingdom at the end of 2008. Between 2007 and 2011, there was a 15% drop in the number of freight licenses in the United Kingdom as a whole (23). Based on the interviews we conducted, we can nevertheless say that the LEZ helped the logistics sector to speed up investment in more recent vehicles and more efficient fleets in the years prior to 2008 (first phase of the LEZ) and prior to 2012 (second phase). Firms like UPS explained to us that they increased their turnover as a result of the creation of the Low Emission Zone because it prompted them to reorganize their activities which allowed them to reduce their management costs and improve the efficiency of their freight flows. The impact was greater in the case of small transport operators and companies using own account transport. The Freight Transport Association and TfL think that some of these companies must have been forced to go out of business or relocate, but fewer than was forecast. This remark nevertheless needs to be specified. Few figures are available for the smallest firms allowing us to quantify and specify the changes they have experienced. Our interviews with freight organizations and companies confirmed difficulties for small operators.

The debate in London today is centered around the Ultra Low Emission Zone which is planned for 2020, and intended to ban all diesel vehicles (including private vehicles) which do not meet the Euro 6 standard in the zone currently covered by the city's Congestion Charging Zone (24).

Berlin's transport and warehousing sector consisted of approximately 4,800 firms in 2008, and this number fell to 4,500 in 2011 (25). These firms provided approximately 80,000 jobs in 2008 and 65,000 in 2011 (26; 27). In the case of the State of Brandenburg (which surrounds the citystate of Berlin), the number of firms was respectively 4,200 (in 2008) and 3,900 (in 2011). Therefore, as in London, the period (which starts with the implementation of the LEZ in 2008) saw a significant reduction in the number of firms and jobs in the sector. Figure 3 (28) shows how vehicle fleets have changed. It shows that, as in London, implementation of the zone speeded up replacement of vehicles, in particular in the case of goods vehicles. The impact on firms has been lower than in London, because of the more limited size of the zone and of the high number of exemptions (as an example, a company with multiple vehicles is allowed to have only one complying with the LEZ, the other ones being given an exemption for a year). As the zone in question is small and the economic crisis struck Berlin shortly after the zone was put in place, it is difficult to quantify company closures and/or relocations. This specific research will be carried out in phase 2 of the RETMIF project.

Changes in the behavior of firms

The first thing to note is that in countries where the LEZ was implemented solely for goods vehicles or heavy vehicles and not private cars, transport companies could have felt they had been treated unfairly, as private vehicles are responsible for as much or more of the total amount of pollution. However, our interviews showed that this was only a minor problem. Broadly, transport operators and companies that use heavy vehicles accept the LEZs. This acceptance was easy to obtain in London because the Low Emission Zone was the subject of a particularly sophisticated awareness and public relations campaign. Firms were warned about the system a long time in advance (about seven years) which meant it was better received because they were able to prepare for it in advance.

As a general rule, freight transport companies have adapted to the new regulations, at least those with an effective enforcement system. This may seem quite natural, but it is in fact quite remarkable in view of the severe fragility of the urban goods transport sector, as described in Section 1. We have already noted the high level of compliance with the standard in London and Berlin, and very old goods vehicles have virtually disappeared from these cities, and with them a certain way of doing business for urban delivery activities (Figures 2 and3). However, it is important to note that it is difficult to assess the levels of company closures that have ensued following the introduction of an LEZ. In the cities that we have studied in detail (London and Berlin) this level seems to be low, but city officials and the professional bodies representing transport companies admit that the disappearance of many small firms may have gone unnoticed as few of them belong to business groups, and some of them have no legal existence and were therefore not known to the authorities. In addition, the specific difficulties that affect specialized firms should be noted. The vehicles used for the construction industry require a greater investment and are replaced less frequently than other vehicles. To overcome this problem, some zones such as London or Berlin have made special limited-time exemptions, sometimes on an ad hoc basis. However, derogations of this type do not exist in all zones, vary a great deal from place to place, and do not always relate to the same vehicles.

As well as adapting to the new regulations, firms have implemented a number of accompanying or avoidance strategies. It emerged from our interviews and surveys that the first direct impact on firms was the transfer of vehicles out of the zone where restrictions operate. In the period immediately preceding the introduction of the LEZ, firms that thought the investment was too great relocated some or all of their most recent vehicles, using their oldest vehicles outside the zone. This practice was very common in London. Large firms such as TNT Express or DHL have a large fleet of vehicles spread over a large number of sites in the United Kingdom. The policy of these firms is to replace their vehicles every six to eight years, so replacement focused on the vehicles that operated in Greater London. At the same time, these firms are much more worried about the Ultra Low Emission Zone planned for 2020, as they will only be given five years' notice, which means they will have to review their investment policy.

With regard to small and medium-sized firms, our interviews revealed a change of a different typethe reorganization of routes. The firms in question lack both the financial reserves and the capacity to modify their activity sufficiently to completely replace their fleet, unless the use of recent vehicles gives them a competitive advantage. This has been observed in both the London and Berlin cases. Some firms admit that the creation of an LEZ benefited them as it forced them to improve their efficiency and optimize their vehicle routing, in particular by using specialized softwares. In Berlin, firms were only given 2½ years' warning of the change and some had to use vehicle rental companies to be able to use recent vehicles rapidly.

Two changes which are less widespread than those mentioned above have also taken place. The first is the sharing of resources between firms. In cases where the investment proved to be too great for the firm to survive, which occurred most frequently for small and medium-sized firms and very small firms, the possibility of sharing vehicles and resources between several partners was seen to present a number of benefits. In some cases this might lead to a merger between companies. For example, after the introduction of the London Congestion Charging Zone and the announcement of the LEZ, Wiles (an office supplies delivery company) decided to merge with another company focusing on environmental consulting, Greenworld, in 2006. The idea was to obtain a competitive advantage (see below) and a greener image. Wiles Greenworld now has 50 employees and is a gold member of the Fleet Operator Recognition Scheme (FORS) which was introduced by TfL to reward environmentally-friendly delivery companies.

Second, the development of new logistics hubs around a LEZ zone was mentioned in the interviews. In Berlin actually, the location of the major logistics hubs has directly influenced the boundary limits of the LEZ, in order to avoid a necessary relocation of these centers. Urban freight terminals around the zone can be used as transfer points from polluting vehicles to clean ones in order to make final deliveries. Such changes can encourage innovative city logistics activities that use electric delivery vehicles. In this context, some large firms (whose names we are not at liberty to disclose) are currently involved in projects to massively increase the size of their electric vehicle fleet in the London Ultra Low Emission Zone and set up dedicated freight hubs in view of the standard that will apply in the zone and thereby gain a competitive advantage for last mile logistics. In Berlin, operators are more inclined towards natural gas and biogas because of the larger size, in average, of freight vehicles (7.5 to 12 ton trucks where vans are used in London).

Modernization of the sector

We would like to draw attention to one other impact that emerged from our investigations. It is less clearly apparent than the others, but it may ultimately prove to be important. This is the impetus provided by the creation of an LEZ, and possibly by accompanying measures when there are any, to the modernization of the freight transport sector and urban logistics. The fact that the creation of an LEZ may provide a means of boosting investment in the transport and logistics sector thereby stimulating its development and above all its modernization was mentioned several times to us, in particular by the public authorities. An LEZ creates a competitive advantage for firms that are already committed to "good practices." The creation of an LEZ or other similar environmental measures provides companies whose policies include pollution reduction with an immediate competitive advantage over "conventional" firms that need to improve their vehicle fleet.

An LEZ may stimulate the market for clean delivery vehicles. To meet new regulations, some transport operators may decide to purchase very clean vehicles (and not just ones that pollute less), for example electric vehicles or vehicles that use natural gas. The use of biogas has already developed in Berlin, especially for public services (waste pick-up). The introduction of the new Euro 6 standard in some LEZs (i.e. London) may increase the market for more recent, more expensive, technologies, as the price difference between internal combustion engines and vehicles such as electric vehicles will be reduced. As the Euro VI standard, which came into force for the manufacturing of heavy vehicles on January 2014, is not yet enforced in existing LEZs, and as the availability of electric delivery vehicles is still unreliable (and for heavy goods vehicles still at the development phase), our experience is currently inadequate to allow us to reach a conclusion on this point.

CONCLUSION

In this paper we have shown that the Low Emission Zones that have been created in recent years in a considerable number of European cities are particularly associated with freight transport: all of them restrict HGV access, and many LEZs target HGVs exclusively. The most emblematic of Europe's LEZs, that in London, not only targets HGVs, but LGVs too.

It is easy to justify targeting goods vehicles because they cause a large proportion of the traffic based pollutant emissions which are partly to blame for the poor air quality of many European cities. It is, however, surprising that when they introduced their access restriction policies few cities wondered what impact they would have on the urban freight transport system. Few studies have been carried out by the scientific community, business organizations, or public authorities, even though the reaction of transport and logistics operators to a ban on old vehicles could potentially have a major impact on the organization of urban freight transport.

We have attempted to identify such behaviors by taking the example of cities that have put in place strict LEZs. Some of our conclusions are provisional, as our research is still ongoing, but they strike us as sufficiently firm to be presented here. The statistical data that we have examined show first of all that there has been a reduction in the number of transport and logistics firms operating in the cities with an LEZ. This reduction ranges from 15 to 30% depending on the city. It is difficult to establish a direct causal link between the creation of an LEZ and the reduction in the number of delivery firms and this part of the study requires further work, e.g. an analysis of data on companies in other cities in the same country which did not implement an LEZ or a more detailed analysis of the long-term trends in the number of companies which will show whether or not they were changed by the introduction of an LEZ.

Our studies show that those firms that are still operating on markets affected by an LEZ have adapted to the new rules. Many have implemented a process of adjustment and reorganization that has optimized their urban activities.

The conclusion we have reached is as follows. In the two cities we have looked at, London and Berlin, it is apparent that the creation of a Low Emission Zone reduces the number of transport firms making urban deliveries. Our investigation leads us to believe that this reduction has benefited the urban freight transport market by compelling stakeholders to find ways to promote more efficient activities. Such modernization is necessary as the market is dysfunctional in many respects: environmentally because of the old vehicles used until now, and socially because of the large number of small firms which find it difficult to maintain a sufficient level of business activity without breaking the sector's labor laws and safety standards. Structural measures such as Low Emission Zones provide a sound basis for the long-awaited reorganization of the sector which has rarely been undertaken hitherto.

LIST OF FIGURES FIGURE 1 The main LEZs in Europe

  Dablanc, corresponding author IFSTTAR/AME, University of Paris-Est 14-20 bvd. Newton -Cite Descartes -Champs-sur-Marne, 77447 Marne la Vallee cedex 2, France Tel: +33 1 81 66 87 78; Email: laetitia.dablanc@ifsttar.fr Antoine Montenon IFSTTAR/AME, University of Paris-Est 14-20 bvd. Newton -Cite Descartes -Champs-sur-Marne, 77447 Marne la Vallee cedex 2, France Tel: +33 1 81 66 89 20; Email: antoine.montenon@ifsttar.fr Word count: 6678 words text + 3 figures x 250 each = 7428 words TRR Paper number: 15-…. Submission date: March 15, 2015

FIGURE 1 FIGURE 2

 12 FIGURE 1 The main LEZs in Europe (Source: the authors, based on a map provided by Atelier Parisien d'Urbanisme)

FIGURE 3 :

 3 FIGURE 3: Percentage of vehicles qualifying for a green sticker in Berlin between 2006 and 2011 (28)

The Euro standards correspond to a limit of pollution emitted by category of vehicle, calculated through a driving cycle defined by the EU. Euro 0 was introduced in 1990, Euro I in 1993, Euro II in 1996, Euro III in

2001, Euro IV in 2006, Euro V in 2009 and Euro VI in 2014. The following convention generally applies: standards for light vehicles use Arabic numerals (1, 2, 3…) while standards for heavy vehicles use Roman numerals (I, II, III…). When a standard applies to both types of vehicles, we use Arabic numerals in this article.

ACKNOWLEDGEMENT

This article presents the results of phase 1 of RETMIF, a research project carried out for the French Agency for the Environment (ADEME). RETMIF benefitted from a grant from ADEME's AACT/AIR program. We also acknolewdge the Metrofreight Center of Excellence on urban freight, financed by the Volvo Research and Educational Foundations (VREF).


J Chandezon

J.-M Rampnoux

S Dilhaire

B Audoin

Y Guillet

In-line femtosecond common-path interferometer in reflection mode

Keywords:

An innovative method to perform femtosecond time-resolved interferometry in reflection mode is proposed. The experiment consists in the combined use of a pump-probe setup and of a fully passive in-line femtosecond common-path interferometer. The originality of this interferometer relies on the use of a single birefringent crystal first to generate a pair of phase-locked pulses and second to recombine them to interfere. As predicted by analytical modeling, this interferometer measures the temporal derivative of the ultrafast changes of the complex optical reflection coefficient of the sample. Working conditions are illustrated through picosecond opto-acoustic experiments on a thin film.

Introduction

Femtosecond time-resolved interferometry has been proposed in 1982 by Halbout and Tang [START_REF] Halbout | Femtosecond interferometry for nonlinear optics[END_REF]. This technique has proved to be a powerful tool in the broad field of laser-matter interaction since it is able to resolve the laser-induced transient modification of the complex refractive index of a sample. For instance, applications have been developed in nonlinear optics [START_REF] Halbout | Femtosecond interferometry for nonlinear optics[END_REF][START_REF] Cotter | Picosecond pump-probe interferometric measurement of optical nonlinearity in semiconductor-doped fibers[END_REF][START_REF] Finlayson | Optical nonlinearities in CdS x Se 1-x -doped glass waveguides[END_REF][START_REF] Tokunaga | Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy[END_REF], laser-dielectric interaction [START_REF] Audebert | Space-time observation of an electron gas in SiO 2[END_REF][START_REF] Temnov | Multiphoton ionization in dielectrics: Comparison of circular and linear polarization[END_REF][START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF], THz optical switching [START_REF] Lagasse | Ultrafast switching with a single-fiber interferometer[END_REF] and THz acoustics [START_REF] Perrin | Interferometric detection of hypersound waves in modulated structures[END_REF][START_REF] Hurley | Detection of ultrafast phenomena by use of a modified sagnac interferometer[END_REF].

Double-path interferometers have been the first setups used in femtosecond time-resolved interferometry, notably the Mach-Zehnder [1-3, 6, 9] and Michelson [START_REF] Decremps | Sound Velocity and Absorption Measurements under High Pressure Using Picosecond Ultrasonics in a Diamond Anvil Cell: Application to the Stability Study of AlPdMn[END_REF] interferometers, where the position of the reference mirror is controlled with an active feedback loop. On the other hand, common-path interferometers have emerged in the 90's [START_REF] Lagasse | Ultrafast switching with a single-fiber interferometer[END_REF]. Two widespread ways to generate the reference and probe pulses consist either in inserting a beamsplitter before the sample [START_REF] Tokunaga | Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy[END_REF][START_REF] Audebert | Space-time observation of an electron gas in SiO 2[END_REF][START_REF] Evans | Time-and space-resolved optical probing of femtosecond-laser-driven shock waves in aluminum[END_REF] or in using a Sagnac interferometer [START_REF] Hurley | Detection of ultrafast phenomena by use of a modified sagnac interferometer[END_REF][START_REF] Duquesne | Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency[END_REF][START_REF] Misawa | Femtosecond sagnac interferometer for phase spectroscopy[END_REF][START_REF] Nikoonahad | Picosecond photoacoustics using common-path interferometry[END_REF]. Depending on the temporal delay between the reference and probe pulses in the common-path interferometer, either the perturbation of the complex refractive index [START_REF] Tokunaga | Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy[END_REF][START_REF] Audebert | Space-time observation of an electron gas in SiO 2[END_REF][START_REF] Temnov | Multiphoton ionization in dielectrics: Comparison of circular and linear polarization[END_REF][START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF][START_REF] Lagasse | Ultrafast switching with a single-fiber interferometer[END_REF] or its temporal derivative [START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF] is measured. Ten years ago, van Dijk et al. [START_REF] Van Dijk | Detection of acoustic oscillations of single gold nanospheres by time-resolved interferometry[END_REF][START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF] have proposed an alternative approach. The beamsplitter used in a Sagnac interferometer to create the reference and probe beams has been replaced by a birefringent crystal which generates a pair of phase-locked pulses with orthogonal polarization. The temporal delay between the reference and probe pulses is then imposed by the birefringence of the crystal and by its thickness. This in-line interferometer is extremely stable and easy to align, leading to a high fringe contrast. Following this pioneering work, other groups have developed similar interferometers [START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF][START_REF] Dobner | In-line interferometric femtosecond stimulated raman scattering spectroscopy[END_REF]. Sarpe et al. have proposed to use additional birefringent crystals after the sample to reduce the delay between reference and probe pulses down to 200 fs before recording interferences in the spectral domain [START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF]. However, all the aforementioned common-path interferometers employing birefringent crystals have only been used in a transmission mode. Furthermore, two birefringent crystals are used: One temporally separates the reference and probe pulses whereas the second recombines them. An active control of the temperature of both crystals is thus required to ensure stability of the interferometer [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF].

In this article, we present a fully passive in-line femtosecond time-resolved common-path interferometer in reflection mode where a single birefringent crystal is used. This crystal first temporally separates the reference and probe pulses and then recombines them to get interferences. The reflection mode is ideally suited to study opaque samples [START_REF] Perrin | Interferometric detection of hypersound waves in modulated structures[END_REF][START_REF] Hurley | Detection of ultrafast phenomena by use of a modified sagnac interferometer[END_REF][START_REF] Antonelli | Characterization of Mechanical and Thermal Properties Using Ultrafast Optical Metrology[END_REF][START_REF] Geindre | Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma[END_REF] or to perform time-resolved Brillouin spectroscopy [START_REF] Thomsen | Surface generation and detection of phonons by picosecond light pulses[END_REF][START_REF] Lin | Phonon attenuation and velocity measurements in transparent materials by picosecond acoustic interferometry[END_REF]. The article is organized as follows. In Section 2, we describe the interferometric pump-probe setup and we present the principle of operation of the interferometer. In Section 3 the Jones formalism is used to show how the pump-induced modification of the real and imaginary parts of the complex reflection coefficient of the sample can be inferred independently. In Section 4, we illustrate the performance of the interferometer through picosecond opto-acoustic measurements on a thin film. The volume strain and the surface displacement induced by the longitudinal acoustic waves propagating back and forth in a thin film are detected with the common-path interferometer.

Interferometric femtosecond pump-probe setup

Figure 1 shows the interferometric femtosecond pump-probe setup. The laser source is a compact dual-oscillator (t-Pulse Duo, Amplitudes Systèmes, France) [START_REF] Deguil | Novel diode-pumped infrared tunable laser system for multi-photon microscopy[END_REF]. The pump-probe setup relies on the asynchronous optical sampling technique (ASOPS) where the pump-probe delay is generated by using two pulsed lasers at slightly different repetition rates [START_REF] Bartels | Femtosecond time-resolved optical pump-probe spectroscopy at kilohertz-scan-rates over nanosecond-time-delays without mechanical delay line[END_REF][START_REF] Abbas | Picosecond time resolved opto-acoustic imaging with 48 mhz frequency resolution[END_REF]. The probe and pump lasers deliver 330 fs pulses at 1027 nm and 430 fs pulses at 1040 nm, respectively. The beating frequency Δ f = 500 Hz between the probe laser repetition frequency f = 48 MHz and the pump laser repetition frequency f + Δ f is generated by a frequency synthesizer and is stabilized using an active feedback loop [START_REF] Dilhaire | Optical heterodyne sampling device[END_REF]. The resulting temporal resolution in pump-probe measurements is close to 1 ps over a 20 ns temporal window [START_REF] Abbas | Picosecond time resolved opto-acoustic imaging with 48 mhz frequency resolution[END_REF]. Fig. 1. Scheme of the in-line femtosecond common-path interferometer coupled to an ASOPS pump-probe experiment. HWP1 to HWP3: half-wave plates, NPBS1 and NPBS2: non-polarizing beam-splitters, QWP: quarter-wave plate, Pol: polarizer, P P : pump pulse, P I : pulse at the input of the interferometer, P O : pulse at the output of the interferometer, P S : probe pulse, P R : reference pulse. The time zero is defined as the overlap between the pump and the probe pulses. Angles are given relatively to the fast optical axis of the birefringent calcite crystal. See text for a detailed description.

The in-line femtosecond common-path interferometer in reflection mode is inserted in the pump-probe setup. The optical element playing a central role in this interferometer is the birefringent crystal [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF]. All angle values used hereinafter are given relatively to the fast optical axis of the birefringent crystal. The linear polarization of the pulse P I incident on the crystal is oriented at -45 degrees by a half-wave plate (HWP2). Due to different ordinary and extraordinary refractive indices of the crystal, two time-delayed pulses -the reference pulse P R and the probe pulse P S -emerge at the crystal output and are linearly polarized along its fast and slow optical axes, respectively. A 5 mm-thick calcite crystal have been used, leading to a 3 ps-temporal delay between the two generated pulses [START_REF] Ghosh | Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals[END_REF]. A ×20 microscope objective focuses the pulses P R and P S on the sample and collects them after reflection. The strength of this interferometer is to use a single birefringent crystal first to temporally separate the pulses P R and P S before they probe the sample and second to recombine them after their reflection on the sample to interfere. Before passing through the same calcite crystal, the backward optical path is separated from the forward optical path by the non-polarizing beamsplitter NPBS2. After the half-wave plate HWP3 oriented at 45 degrees, the pulse P R and P S have their linear polarization swapped. Thus, after the backward passage inside the calcite crystal, the pulses P R and P S are temporally overlapped. These pulses are sent into an analyzer composed of a quarter-wave plate (QWP, angle φ ) and a polarizer (Pol, angle θ ). The pulse at the output of the polarizer results from the interference between the electric fields of pulses P R and P S . An amplified silicon differential photodiode PD (Thorlabs, model PDB450C) directly measures the intensity of the interference state at the output of the polarizer.

Let us remind that before the first passage through the calcite crystal, the incident pulse is polarized at -45 degrees. The generated reference and probe electric fields after the second passage in the crystal thus have same amplitude, and interferences with a maximum contrast are ensured. In the absence of excitation, the temporal recombination of the pulses P R and P S leads to a unique pulse P O linearly polarized at 45 degrees. Now a detailed description is given on how the pump-induced perturbation to the interference state is detected. In the following, the time zero is defined as the overlap between the pump and the probe pulses. The half-wave plate HWP1 aligns the linear polarization of the pump along the fast or the slow optical axis of the crystal to get a single pump pulse at the crystal output. In the following, the polarization of the pump pulse has been arbitrarily chosen along the slow axis of the crystal. The pump pulse passes through the same microscope objective as the pulses P R and P S and is focused on the sample. The perturbation of the optical properties of the sample induced by the absorption of the pump pulse modifies both amplitude and phase of the electric fields of both reflected reference and probe pulses. Since pulses P R and P S are 3 ps time-delayed at the sample position, the perturbation of the electric field of the two pulses P R and P S are slightly different. Therefore, after the second passage inside the calcite crystal, the polarization of the recombined pulse P O becomes elliptical or is still linear but with a rotated angle [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF]. For pump-probe delays higher than 3 ps, the interference state at the output of the analyzer thus carries information on the temporal derivative of the perturbed optical reflection coefficient. As it will be detailed in Section 3, depending on the angle of the quarter-wave plate and of the polarizer, the derivative of either the real or the imaginary parts of the perturbed optical reflection coefficient can be measured independently. In the spectral domain, this time-resolved interferometer behaves as a band-pass filter. The lower cutoff frequency comes from the sensitivity to the derivative of the perturbation and the 3-ps temporal delay between the reference and probe pulses imposes a 150 GHz-higher cutoff frequency. However, this upper limit could be pushed towards the THz by using a thinner crystal, an acousto-optical delay line [START_REF] Schubert | Rapid-scan acousto-optical delay line with 34 khz scan rate and 15 as precision[END_REF] or a combination of several birefringent crystals [START_REF] Sarpe | Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses[END_REF][START_REF] Brida | Phase-locked pulses for two-dimensional spectroscopy by a birefringent delay line[END_REF][START_REF] Réhault | 2D IR spectroscopy with phase-locked pulse pairs from a birefringent delay line[END_REF].

Compared with the Sagnac interferometer [START_REF] Hurley | Detection of ultrafast phenomena by use of a modified sagnac interferometer[END_REF][START_REF] Duquesne | Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency[END_REF], the spatial splitting of a single probe pulse into two pulses has been replaced by the in-line generation of a pair of phase-locked pulses from a birefringent delay line. This original configuration allows a straightforward optical alignment since reference and probe arms are spatially overlapped all along the optical path. Furthermore, compared with the interferometer developed by van Dijk et al. [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF], the configuration we propose here is strongly simplified since we use one birefringent crystal only. In the van Dijk's configuration, an active control of the temperature of the birefringent crystals is required to ensure an optimal stability of the interferometer. In the reflection mode presented here, this active control is no longer needed, the interferometer then being entirely passive.

Modeling of the interferometer sensitivity

Let θ and φ denote the angles of the polarizer (Pol) and the quarter-wave plate (QWP), respectively. The Jones formalism [START_REF] Jones | A new calculus for the treatment of optical systems[END_REF] is well suited to predict in the (θ , φ ) space the optimum working point of this polarization based interferometer. This matrix approach has been used by van Dijk et al. for the transmission mode of their interferometer [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF]. Extension of the modeling to the reflection mode is given hereinafter.

The electric field E in (amplitude E 0 ) of the pulse P I incident on the calcite crystal is linearly polarized at -45 degrees, E in = E 0 / √ 2(1, -1). All optical elements are modeled by their representative Jones matrices. The electric field of the pulse at the output of the polarizer results from the multiplication of the equivalent Jones matrix representative of the whole optical elements by the incident electric field E in . Compared with the van Dijk's configuration, two Jones matrices have to be added in the calculation. The first one accounts for the reflection on the sample and the second is associated to the half-wave plate HWP3 oriented at 45 degrees. As mentioned in the previous section, since pulses P R and P S are 3 ps-time delayed, the perturbations of the optical reflection coefficient of the sample detected by these two pulses for a given pump-probe delay τ are slightly different. The relative perturbation of the magnitude of an electric field reflected at a pump-probe delay τ is denoted ξ (τ). The perturbed reflected reference and probe electric fields are thus equal to E R (τ) = -r 0 E 0 [1 + ξ (τ)] and E S (τ) = r 0 E 0 [1 + ξ (τ + t 0 )], respectively. r 0 denotes the equilibrium reflection coefficient and t 0 = 3 ps is the temporal delay between pulses P R and P S . For a given pump-probe delay τ, two unknown complex valued parameters have to be determined, namely ξ (τ) and ξ (τ + t 0 ). However, by choosing a working point of the interferometer close to a dark fringe, it is possible to assess directly Δξ (τ) = ξ (τ + t 0 ) -ξ (τ) [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF]. The intensity I at the output of the analyzer thus depends on θ , φ and Δξ (τ) only.

When the pump is switched off, i.e. for Δξ (τ) = 0, the pulse P O is linearly polarized at 45 degrees. In this specific case, a straightforward calculation shows that the intensity at the output of the polarizer is equal to I [θ , φ , Δξ (τ) = 0] = I 0 [1 + cos(2θ -2φ ) sin 2φ ]/2, where I 0 stands for the intensity at the bright fringe. When the pump is switched on, the transient perturbation ΔI of the intensity I measured by the detector is defined as:

ΔI [θ , φ , Δξ (τ)] = I [θ , φ , Δξ (τ)] -I [θ , φ , Δξ (τ) = 0] . ( 1
)
Inferring independently the real part Re(Δξ (τ)) and the imaginary part Im(Δξ (τ)) of the perturbation is a priori not straightforward. For an arbitrary choice of θ and φ , the relative variation ΔI/I 0 carries information on Re[Δξ (τ)] and Im[Δξ (τ)] at the same time. As mentioned above, transient reflectivity measurements are performed close to a dark fringe to directly assess Δξ (τ) [START_REF] Van Dijk | A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles[END_REF]. We discuss in the following the sensitivity to either the real part or the imaginary part of Δξ close to the dark fringe located at (θ , φ ) = (3π/4, 3π/4) (green square in Fig. 2 (a)). Note that owing to a π/2-periodicity of I[θ , φ , Δξ (τ) = 0] with respect to φ , the analysis would be similar close to (θ , φ ) = (3π/4, π/4). ΔI/I 0 has been calculated at the first order in δ θ and δ φ, where θ = 3π/4 + δ θ and φ = 3π/4 + δ φ : To analyze in more details the temporal shape of the echoes measured in interferometry, a magnification on the first acoustic echo is shown in Fig. 4. The real part of the interferometric signal corresponds to the continuous curve in Fig. 4(a) while the dashed curve results from the numerical derivation of the first acoustic echo detected in reflectometry. The two curves have been normalized for the purpose of comparison. The very good agreement between the two curves confirms that the interferometer is sensitive to the derivative of the reflectometric signal along the working line δ θ = δ φ (cf Fig. 2). On the other hand, the continuous curve in Fig. 4(b) represents the imaginary part of the interferometric signal, while the dashed curve corresponds to its numerical integration over time. The bipolar signature of the detected out-ofplane surface velocity (continuous curve) is perfectly consistent with the monopolar signature of the displacement field, as expected at the free surface of the film (dashed curve) [START_REF] Gusev | Laser Optoacoustics[END_REF].

Conclusion

We have presented an in-line femtosecond common-path interferometer suited for experiments in reflection mode. A single birefringent crystal is used first to generate a pair of phase-locked pulses and second to recombine them and build interferences. The alignment of the interferometer is straightforward since probe and reference arms are spatially overlapped all along the optical path. Furthermore, this very compact interferometer is fully passive: No mechanical or thermal active stabilization is necessary. The analytical modeling developed in the framework of the Jones formalism has shown that the temporal derivative of the real or imaginary parts of the complex perturbed optical reflection coefficient can be measured independently. We have demonstrated the ability of the interferometer to be sensitive either to the acousto-optic interaction or to the ultrafast surface displacements have been demonstrated. These results are illustrative of the performances of the interferometer. Furthermore, the sensitivity to the ultrafast changes of the complex optical index will also allow to investigate semi-conductors or dielectric. The range of application of this interferometer will thus span the broader domain of laser-matter interaction.

Figure 2 (

 2 a) shows the evolution of I [θ , φ , Δξ (τ) = 0] in the (θ , φ ) space. For θ and φ ranging in the interval [0, π], dark fringes are located at (3π/4,π/4) and (3π/4,3π/4) and bright fringes are located at (π/4,π/4) and (π/4,3π/4).

Fig. 2 .

 2 Fig. 2. (a) Evolution in the (θ , φ ) space of the intensity at the output of the polarizer when the pump is switched off. (b) and (c) When the pump is switched on, evolution close to the dark fringe (green square in (a)) of functions A(θ , φ ) and B(θ , φ ) with respect to the polarizer angle θ and the quarter-wave plate angle φ . The values in the color bars are in degrees. The continuous blue lines show the domains where A and B are equal to zero.

Fig. 3 .

 3 Fig. 3. (a) Experimental configurations for measurements in reflectometry or interferometry. (b) Experimental measurement in reflectometry (dashed curve) and in interferometry (continuous curves) of the transient optical response of the thin film. For measurements in interferometry, both the real part (gray continuous curve) and the imaginary part (black continuous curve) of the temporal derivative of the complex perturbed optical reflection coefficient are displayed. For the three signals, an almost instantaneous electronic response is followed by periodic acoustic echoes over a thermal diffusion background. The inset shows the acoustic part of the signals after subtraction of the thermal diffusion background.

Fig. 4 .

 4 Fig. 4. Magnification on the first acoustic echoe shown in the inset of Fig. 3(b). (a) Real part of the interferometric signal (continuous curve) and numerical derivation of the first acoustic echo detected in reflectometry (dashed curve). (b) Imaginary part of the interferometric signal (continuous curve) revealing the out-of-plane surface velocity. Integration over time of the imaginary part (dashed curve) shows monopolar surface displacement (in agreement with predictions).

Acknowledgments

This work has been financially supported by the Agence Nationale de la Recherche (project NanoVibe ANR-11JS09-013-01, project picoBond ANR-13-BS09-0021-01, project PHEMTO), the competitiveness cluster Route des Lasers, the Région Aquitaine (project 2012-16-03-011), the University of Bordeaux and Bordeaux INP.

ΔI

where A(θ , φ ) = δ φ and B(θ , φ ) = δ θδ φ. Figure 2(b) shows the evolution of A(θ , φ ) (top) and B(θ , φ ) (bottom) with respect to θ and φ . Two specific domains in the (θ , φ ) space can be identified from Eq. 2 and are shown in Fig. 2(b) by the continuous blue lines. These lines correspond to the contour where functions A (top panel) or B (bottom panel) are equal to zero. For δ φ = 0 and δ θ = 0, ΔI is proportional to Im[Δξ (τ)] only, while for δ θ = δ φ and δ θ = 0, ΔI/I 0 is proportional to Re[Δξ (τ)] only. Therefore, for a convenient choice of the couple (θ , φ ), it is possible to measure independently the pump-induced modification to either the real or imaginary parts of the complex reflection coefficient of the sample.

Application to the interferometric detection of ultrafast acoustic waves

We illustrate the performances of the interferometer by investigating the opto-acoustic response up to 100 GHz of a submicronic tungsten layer deposited on top of a (100)-silicon substrate.

Following the absorption of the pump pulse, the sudden thermal stress created in the sample generates high frequency acoustic waves in the GHz to THz range. These waves are detected through the transient perturbation of the optical reflection coefficient r 0 of the sample [START_REF] Thomsen | Surface generation and detection of phonons by picosecond light pulses[END_REF]. Except in specific cases [START_REF] Rothenberg | Observation of the transient expansion of heated surfaces by picosecond photothermal deflection spectroscopy[END_REF][START_REF] Wright | Coherent phonon detection from ultrafast surface vibrations[END_REF][START_REF] Yamazaki | Surface phonon imaging through the photoelastic effect[END_REF][START_REF] Chigarev | Surface displacement measured by beam distortion detection technique: Application to picosecond ultrasonics[END_REF][START_REF] Salenbien | Laser-based surface acoustic wave dispersion spectroscopy for extraction of thicknesses, depth, and elastic parameters of a subsurface layer: Feasibility study on intermetallic layer structure in integrated circuit solder joint[END_REF][START_REF] Higuet | Beam distortion detection and deflectometry measurements of gigahertz surface acoustic waves[END_REF], measurements sensitive to the intensity of the probe pulse bring information on the real part of the transient reflectivity [START_REF] Thomsen | Surface generation and detection of phonons by picosecond light pulses[END_REF] through photo-elastic coupling.

On the other hand, interferometric measurements allow resolving both the real and imaginary parts of the transient reflectivity [START_REF] Hurley | Detection of ultrafast phenomena by use of a modified sagnac interferometer[END_REF][START_REF] Duquesne | Ultrasonic attenuation in a quasicrystal studied by picosecond acoustics as a function of temperature and frequency[END_REF][START_REF] Perrin | Interferometric detection in picosecond ultrasonics[END_REF]. The imaginary part is mainly sensitive to the displacement of interfaces in the sample. As explained in the previous sections, the interferometer presented here gives access to the temporal derivative of the perturbation, i.e. to the measurement either of the temporal derivative of the photo-elastic contribution (real part), or of the out-of-plane surface velocity of interfaces in the sample (imaginary part) [START_REF] Sugawara | Spatiotemporal mapping of surface acoustic waves in isotropic and anisotropic materials[END_REF][START_REF] Matsuda | Ultrafast ellipsometric interferometry for direct detection of coherent phonon strain pulse profiles[END_REF]. We first present the transient dynamics of the thin tungsten film detected by a direct measurement of the intensity of the probe pulse. This experimental configuration is called reflectometry in the following and is presented in Fig. 3(a). For this purpose, the polarization of the incident pulse P I on the calcite crystal is set at 0 • . Thus, a single probe pulse is focused on the tungsten film. The resulting dynamics with respect to the pump-probe delay τ is plotted in Fig. 3(b) (dashed curve). The energy of the pump and probe pulses at the sample position are 1 nJ and 0.5 nJ, respectively. The sharp peak at τ = 0 is the signature of the almost instantaneous electronic response of tungsten [START_REF] Schoenlein | Femtosecond studies of nonequilibrium electronic processes in metals[END_REF]. Over the slow decaying thermal background after τ = 0, the acoustic echoes are detected periodically at the free surface of the film every ≈ 100 ps. They are the hallmark of the longitudinal acoustic wave bouncing back and forth in the thin film. The dashed curve in the inset of Fig. 3(b) shows the acoustic part of the reflectometric signal after subtraction of the thermal background. These echoes are detected by the single probe pulse through the photoelastic interaction over the optical penetration depth in tungsten. The temporal shape of the echoes is closely related to the strain profile inside the film [START_REF] Thomsen | Surface generation and detection of phonons by picosecond light pulses[END_REF].

The opto-acoustic response of the thin film is now investigated with the common-path interferometer described in the previous sections [Fig. 3(a)]. For this purpose, the polarization of the incident pulse P I on the calcite crystal is turned to -45 degrees. Measurements presented in Fig. 3(b) have been performed close to the dark fringe located at (θ , φ ) = (3π/4, 3π/4). Accordingly with the analysis built in section 3 (cf Fig. 2) , we choose δ θ = 4 • and δ φ = 4 • to measure the temporal derivative of the real part of the transient reflectivity (grey continuous curve) and δ φ = 0 • and δ θ = 2 • to measure the temporal derivative of the imaginary part of the transient reflectivity (black continuous curve). As for measurements in reflectometry, an almost instantaneous electronic response followed by acoustic echoes over a thermal diffusion


Ugo Marchand
email: ugo.marchand@ircam.fr

Geoffroy Peeters
email: geoffroy.peeters@ircam.fr

SWING RATIO ESTIMATION

Swing is a typical long-short rhythmical pattern that is mostly present in jazz music. In this article, we propose an algorithm to automatically estimate how much a track, a frame of a track, is swinging. We denote this by swing ratio. The algorithm we propose is based on the analysis of the auto-correlation of the onset energy function of the audio signal and a simple set of rules. For the purpose of the evaluation of this algorithm, we propose and share the "GTZAN-rhythm" test-set, which is an extension of a well-known test-set by adding annotations of the whole rhythmical structure (downbeat, beat and eight-note positions). We test our algorithm for two tasks: detecting tracks with or without swing, and estimating the amount of swing. Our algorithm achieves 91% mean recall. Finally we use our annotations to study the relationship between the swing ratio and the tempo (study the common belief that swing ratio decreases linearly with the tempo) and the musicians. How much and how to swing is never written on scores, and is therefore something to be learned by the jazzstudents mostly by listening. Our algorithm could be useful for jazz student who wants to learn what is swing.

INTRODUCTION 1.Swing

Music is not always played exactly as written on the score. These deviations from the score constitute the musician personal interpretation and are precisely chosen by the musician to make music more lively or to convey an emotion.

In this paper we focus on timing deviations. We distinguish different types of systematic timing deviation. The rubato refers to a rhythmic freedom, in which tempo is sped up then slowed down to make music more expressive. It was usual in Romantic period. The notes inégales is a performance practice of the Baroque and Classical period in which some notes with equal durations are performed with unequal durations. Finally the swing is often found in jazz music but also other music styles as we will see in part 3. Our work focuses on the swing estimation.

Swing is present at a specific time level. It describes the specific interaction between note durations at the eight-note level. When swing is present, two consecutive eight-notes are played following a long-short pattern: the first eight-note is lengthened, while the second is shortened proportionally.

The swing ratio is defined by the ratio between the duration of the long eight note and the short one. Common swing ratios found in jazz music are 1:1 (no swing at all), 2:1 (triple feel), 3:1 (hard swing). These three example are presented in Figure 1. It should be noted that the swing ratio value is not limited to the values 2 or 3, but it can take all floating values between 1 and 3.5. Swing ratios are not written on the score, they are implicit. Thus, swing ratio can vary considerably between two musicians or even inside a single music piece.

Related works

On swing. In [START_REF] Friberg | Swing ratios and ensemble timing in jazz performance: Evidence for a common rhythmic pattern[END_REF], Friberg et al. study the exact duration ratio between the long eight-note and the short one in recordings. The author shows that the swing ratio varies linearly with the tempo. At slow tempi, the swing ratio can reach 3.5:1. At fast tempi, it goes down to 1:1. The authors also show that the minimum absolute duration of the short eight-note in the long-short pattern is around 100ms. This suggests a physical limit to swing ratio, maybe due to perceptual factors.

In [START_REF] Honing | Swing once more: Relating timing and tempo in expert jazz drumming[END_REF], Honing et al. show that professional jazz drummers have an extremely precise control over the swing ratio they want to achieve. The authors also found no evidence that the swing ratio scale linearly with tempo, as was suggested previously.

On swing ratio estimation. In [START_REF] Gouyon | Rhythmic expressiveness transformations of audio recordings: swing modifications[END_REF], Gouyon et al. introduced a swing modification tool. The swing ratio is estimated by two methods. The first one is based on the estimation of the position of the second peak ds in the inter-onset-histogram which is supposed to corresponds to the duration of the short eight-note. The swing ratio is then de+ds de-ds where de is the theoretical duration of a non-swinging eight-note and ds is the estimated duration of the second peak of the histogram. The second method compares the inter-onset-histogram to several predefined histogram models (representing different swing ratio), and choose the model that best represent the inter-onset-histogram.

In [START_REF] Laroche | Efficient tempo and beat tracking in audio recordings[END_REF], Laroche presents a joint estimation of the tempo, the downbeat and the swing ratio. For this, he first estimates the timepositions where the energy in a given frequency band grows quickly. Then he exhaustively tests all the triplet (tempo, downbeat time, swing ratio) and keeps the one that have the best likelihood.

Paper overview and organization

In this paper, we propose a novel algorithm for estimating the swing ratio of a track (part 2). We then evaluate its performance for a task of finding music tracks with/without swing. For this, we present the test-set we created for the purpose of swing detection (part 3). We present our experiments and discuss their results in part 4.

SWING RATIO COMPUTATION

To estimate the swing ratio, we first compute an onset-energyfunction1 OEF (part 2.1). The auto-correlation function of the OEF allows highlighting the various metrical level of a rhythm pattern therefore the specific irregularities of the eight-note due to the swing (part 2.2). From the positions of the peaks in the autocorrelation function we then estimate the swing ratio (part 2.3).

Signal pre-processing

We calculate the onset-energy function o(t) using the method proposed by Ellis [START_REF] Daniel | Beat tracking by dynamic programming[END_REF] 2 . o(t) is then analyzed using a frame-analysis with a window length of 16s 3 , and a hop-size of 1s 4 . For each frame, we then compute the normalized (at lag zero) auto-correlation of o(t):

r(τ ) = 1 r(0) o(t)o(t -τ ) (1)

Auto-correlation

The auto-correlation function of o(t) allows highlighting the various metrical level of a rhythm pattern. Therefore it highlights the specific irregularities of the eight-note due to the swing. We illustrate this in Figure 2. The two panels illustrate the auto-correlation function for a signal without and with swing.

In a signal without swing (Figure 2 [Left]), there is one peak representing the tactus (the duration of a quarter-note) at 0.40s and one representing the duration of the eight-note at 0.20s. For a signal with swing (Figure 2 [Right]), the peak representing the quarter-note is still present at 0.45s, but the peak representing the duration of the eight-note is split into two peaks : one for the duration of the short eight-note at 0.15s and one for the duration of the long eight-note at 0.30s.

The goal of swing detection is to distinghish both cases.

Peak finding

Eight-note duration estimation

In order to distinguish the two cases we need to know the theoretical position of the eight-note without swing. This position is derived from an estimation of the tempo (the tactus-level). For this we use the joint estimation of beat, downbeat and tempo algorithm of Peeters et al. [START_REF] Peeters | Simultaneous beat and downbeat-tracking using a probabilistic framework: theory and large-scale evaluation[END_REF]. The tempo value is hypothesised to be constant over the whole track duration. If we denote by T the estimated tempo in bpm (beat per minute), the theoretical duration (in second) of the eight-note de is then computed as de = 1 2 60 T (half of the duration in second of a quarter-note : 60 T ). The values of the eight-note duration can be derived from the peak positions in the auto-correlation function of OEF. We also use the height of the peaks and the width of the corresponding lobes to have information on the reliability of these peaks. Because peak finding algorithms (such as finding local maxima) do not lead to good results (since the auto-correlation is often noisy), we propose to use a peak fitting algorithm [START_REF] Levenberg | A method for the solution of certain non-linear problems in least squares[END_REF][START_REF] Marquardt | An algorithm for least-squares estimation of nonlinear parameters[END_REF]. In this a predefined shape is fitted locally to a signal. This shape is defined by a Gaussian function (this leads to better results than the use of a 2nd order polynomial function).

In the absence of swing a peak must be present at de, in the presence of swing this peak is split in two peaks in the two intervals de 2 , de and de, 3de 2 respectively. We therefore looks for peaks in these three intervals.

• The first interval de 2 , de5 corresponds to the short eightnote.

• The second interval de, 3de 2 corresponds to the long eightnote.

• The third interval de ± de 2 correspond to a non-swinging eight-note (this interval is here only for illustration purpose, it is not used by our algorithm).

In order to estimate the peak within each interval, we use a nonlinear least squares algorithm to fit a Gaussian function. Thus we get 3 parameters for each peak: the amplitude A, the standard deviation σ and the mean µ (µ defines the estimated peak position). The parameters of the short and the long eight-notes are denoted As, σs, µs and A l , σ l , µ l respectively.

Swing detection

Given the 6 parameters described above, we propose the following set of rules to decide if there is swing or not. The Gaussian functions representing the short and the long eight-notes must comply with the following rules:

• positive amplitudes As > 0, A l > 0 • small widths σs < de 4 , σ l < de 4
• positions in the right interval de 2 < µs < de and de < µ l < 3de 2 If all the conditions are met, the frame is classified as swing.

Illustrations: Swing detection is illustrated in Figure 2. On both figures, we show the auto-correlation of the OEF of the signal (green thin line). The theoretical duration of the eight-note de is given by the vertical dotted line. We also show the 3 peaks that were fitted as previously described: the thick blue line is the Gaussian fit for the non-swinging eight-note, and the two red dashed lines correspond to the fit of the short and the long eight-note of the swing pattern. Given the parameters of these fitted Gaussian functions and using the proposed rules described above, our algorithm decide that there is no swing on the Left panel of Figure 2 while there is swing on the Right panel.

Swing ratio estimation

For each frame classified as swing, its swing ratio sr is finally computed as sr = µ l µs . Illustrations: For the previous example (Figure 2 [Right]), the swing ratio would be sr = 0.28 0.16 = 1.75.

THE GTZAN-RHYTHM TEST-SET

There is currently no test-set on which the swing ratio is annotated. It is therefore difficult to compare numerically our results to previous works. We therefore created our own test-set by extending the widely used GTZAN test-set for music genre 6 . While there exist controversies related to the use of the GTZAN test-set for music genre classification [START_REF] Bob | The gtzan dataset: Its contents, faults, and their effects on music genre recognition evaluation[END_REF], its audio content is however represensative of real commercial music of various music genre. Also, this test-set has a good balancing between tracks with swing (blues and jazz music) and without swing.

Annotations: Each track of the test-set has been annotated into downbeat, beat/tactus (quarter-note) and eight-note positions 7 . In order to take into account tempo or rhythm pattern variations (the swing ratio is never constant over time) the annotation is performed over the whole duration of each track. A time region is said to contain swing if the eight-note positions are not exactly at the middle between the two adjacent quarter-notes.

The distribution into swing, non-swing and ternary is shown in Table 1. As can been seen, most of the swinging tracks are jazz (45 tracks) or blues (44 tracks). Swing is also present in country (15 tracks), reggae (25 tracks) and rock (6 tracks). The classical track classified as swing has a "march" rhythm. In total the testset contains 136 swinging tracks, 835 non-swinging tracks and 29 ternary tracks.

EVALUATION

We evaluate our proposed algorithm for two tasks.

Table 2: Results of swing detection. Each column represents the results on a subset of the GTZAN-rhythm test-set. For this, each genre is subdivided into frames with swing and without. For each subset, we indicate its number of frames (# frame), the percentage of correct recognition of the automatic tempo estimation (Tempo-Estimation) and the two recalls for the classes swing and noSwing obtained using our algorithm (Exp-estimatedTempo and Exp-annotatedTempo). In part 4.2, we use our swing ratio annotation (part 2.3.4) for two experiments. First we test the commonly accepted belief that the swing factor decrease linearly with the tempo. Then, we test if the swing factor can be used to recognize the musicians.

blues

Swing detection

Exp-estimatedTempo

The algorithm we proposed in part 2.3.3 allows deciding if a frame of a given track has swing or not. We test our algorithm on each frame of each track of the GTZAN-rhythm test-set. Because, the method proposed in 2.3.3 uses a 16 s. window (for the computation of the auto-correlation), we compare our estimation to the corresponding local annotation. The corresponding local annotation is computed as follow: a 16-sec frame is said to be swing if it contains at least a single swing annotation.

In our experiment we assimilated ternary frames to swinging frames. This is because our method can not distinguish a ternary frame from a swinging jazz frame with the 'triple feel' (swing ratio of 2:1).

Results: The results are presented in Table 2. The first, second and third rows indicate the frame repartition in genre and in swing/noSwing classes. For example, we see that there are much more swinging frames in jazz (630) and blues (686) than in hiphop (0) or pop (12). The results of Exp-estimatedTempo are presented in terms of Recall 8 for each class (in %).

As one can see, the Recall for the noSwing classes are all very good (from 91.4% to 100%). In the opposite, the Recall for swing is not that good and strongly depends on the genre: in jazz, it is only 23.8%, in rock is is 48.2%, country 52.7% and reggae 54.4%. It is slightly better for blues (63.8%), classical (57.6%) and metal (61.9%). The Recall is perfect for disco and pop. However the number of swing frames to be detected is very small for these two classes.

The summary of the results over the genres is indicated in Table 3. The noSwing Recall is very high (98%) which means that almost all noSwing frames have been correctly detected. While the swing Recall is low (49.5%) the swing Precision is rather high (84%) which means that in most cases when a frame have been detected as swing it is indeed annotated as swing. Since our swing detection algorithm relies on a previous tempo estimation (the one provided by the algorithm of [START_REF] Peeters | Simultaneous beat and downbeat-tracking using a probabilistic framework: theory and large-scale evaluation[END_REF]), we test if the bad results obtained for the swing detection (low Recall) are due to wrong tempo estimations. For this, we compare the tempo estimation Te to our manually annotated tempo Ta. An estimation is said to be correct if |Ta-Te| |Te| < 4%. Results: The detailed results are presented in Table 2. The lowest results are obtained for genre for which tempo variation or timing can be large (rubato in classical music, expressive music timings in jazz). Highest results are obtained for genre with a steady tempo (hip-hop, pop and disco). Our tempo estimation is based on the assumption that the tempo is constant over a track, so tracks with a lot of tempo changes are poorly classified.

Overall, 75.1% of the tracks have their tempo correctly estimated. This value falls down to 56.4% if we consider only the tracks that have swing. This can explain the bad results obtained for the swing detection (Recall=49.5%) but the good results for the noSwing detection (98%).

Exp-annotatedTempo

Because of this, we redid the swing detection evaluation using manually annotated tempo instead of the automatically estimated one. The manually annotated tempo is derived from the beat annotations of our GTZAN-rhythm.

Results The detailed results are presented in Table 2. Using annotated tempo always improves the results for the swing class. The Recalls of blues, classical, country jazz, reggae and rock are 32 to 40% higher. The Recall for the class metal/swing is 15% higher, and the other Recalls were already perfect in the previous experiment (disco, pop).

Concerning the noSwing classes, the mean-Recall are now all comprised between 94.1 and 100%, which is better than in Exp1.

The summary of the results over the genres is indicated in Table 4. Using the annotated tempo improved a lot the results: the global mean-Recall increases from 73.9% to 90.6%.

These experiments show that we can estimate the swing knowing the 8th-note tactus. However deciding which level is the 8thnote remains a far more complicated problem.

Swing ratio as a function of tempo and artist

In this part, we use the annotation of the GTZAN-rhythm into swing ratio (part 2.3.4) for two experiments. First we test the commonly accepted belief that the swing factor decrease linearly with the tempo. Then, we test if the swing factor can be used to recognize the musicians.

Swing ratio as a function of tempo

In Figure 3, we illustrate the annotated swing ratio as a function of the tempo for the subset of our test-set corresponding to blues and jazz music (where swing is often present).

We test the commonly accepted belief that swing is a linearly decreasing function of tempo. This was proposed by the experiment of Friberg [START_REF] Friberg | Swing ratios and ensemble timing in jazz performance: Evidence for a common rhythmic pattern[END_REF]. We superimposed to Figure 3, the linear regression (dotted line) used in Figure 1 of Friberg [START_REF] Friberg | Swing ratios and ensemble timing in jazz performance: Evidence for a common rhythmic pattern[END_REF]. We can see that in our experiment the swing ratio does not scale linearly with the tempo. Our observed swing ratios are all far from the linear assumption proposed by Friberg (dotted line) at tempi < 130, and they does not show the same trend. Our results are therefore in agreement with the results of Honing et al. [START_REF] Honing | Swing once more: Relating timing and tempo in expert jazz drumming[END_REF] saying that there may be no correlation at all between tempo and swing ratio. We also see that there may be a preference for the triple feel swing ratio (2:1) in our test-set, as about a third of our examples have a swing ratio around 2 (comprised between 1.9 and 2.1).

Swing ratio as a function of an artist

In Figure 3, we also indicates the artist9 10 corersponding to each swing ratio.

We test if there is a relationship between the artist and the swing ratio. We see that some artists may tend to play with low swing ratio (Robert Johnson) or high swing ratio (Magic Slim). Tracks from Stevie Ray Vaughan share the same swing factor but also the same tempo. (it is therefore difficult to say if the swing is characteristic of the artist or of the tempo). Except these examples predicting the musicians from its swing ratio and tempo seems difficult.

Applications

Our swing ratio estimation could be useful to jazz students who want to learn swing and to musicologists who would benefit from a swing estimation tool to study jazz music/ musicians.

How much to swing is often learned by students by listening to a lot of jazz recordings. It is not something that can be learned from books, and it requires a lot of practice to master. One application of this swing estimation could be a system helping jazz students to learn how much to swing :

• A jazz teacher plays a jazz piece and its swing ratio is estimated.

• The student plays the same piece and the computer says if the student swings enough or too much (compared to the teacher's reference), allowing the student to learn the right swing ratio.

It should be noted that we do not indicate what is the ideal swing ratio for a music piece.

CONCLUSION AND FUTURE WORKS

In this article, we presented an algorithm to automatically detect the swing presence in an audio music track and estimate its swing ratio. For the purpose of the evaluation of this algorithm, we proposed and shared the "GTZAN-rhythm" test-set, which is an extension of a well-known test-set by adding annotations of the whole rhythmical structure (downbeat, beat and eight-note positions). We showed that the algorithm allows a mean-Recall of 74% for the recognition of swing/ noSwing. By analysing the errors, we discovered that most of the errors are due to wrong tempo estimation which is used as input parameter of our algorithm. Using annotated tempo as input of our algorithm, allowed to reach 91% mean-Recall. We finally used our annotations to study the relationship between the swing ratio and the tempo and the musicians. Future works will concentrate on the development of a swing ratio estimation algorithm which does not necessitate this tempo estimation. Finally, given that swing ratio is a rhythmic descriptor, it could be used as input, among other audio descriptors, to machine learning algorithms to perform other Music Information Retrieval tasks. Downloading the GTZAN-rhythm test-set.

We deeply thank Quentin Fresnel for helping us with the annotations of the "GTZAN-rhythm" test-set. The "GTZAN-rhythm" test set can be downloaded at http://anasynth.ircam. fr/home/media/GTZAN-rhythm/.

Figure 1 :

 1 Figure 1: Different swing ratio. From left to right : 1:1 (no swing), 2:1 (triple feel), 3:1 (hard swing)

Figure 2 :

 2 Figure 2: Auto-correlation function for [Left] a signal without swing ('disco.00020.wav', first frame), [Right] a signal with swing ('jazz.00099.wav', first frame). The auto-correlation of the onset-energy-function (OEF) of the signal is the green thin line. The dotted vertical line (around 0.2 s.) corresponds to the theoretical duration of an eight-note. The thick blue line corresponds to the fitting of the peak of a non-swinging eight-note. The two red dotted lines correspond to the fitting of the peaks of the swing pattern (short and long eight-note).

Figure 3 :

 3 Figure 3: Swing ratio as a function of tempo. Each type of point marker correspond to a different artist. The dotted line correspond to the swing as a function of tempo from the experiment of Friberg [1].

Table 1 :

 1 Distribution into swing, noSwing and ternary of the proposed GTZAN-rhythm test-set.

		blues classical country disco hip-hop jazz metal pop reggae rock Total
	# Track with swing	44	1	15	0	0	45	0	0	25	6	136
	# Track with noSwing	52	92	80	98	100	54	94	99	74	92	835
	# Track with ternary	4	7	5	2	0	1	6	1	1	2	29
	2.3.2. Eight-note detection in the auto-correlation

  In part 4.1, we test the ability of our algorithm (part 2.3.3) to correctly detect the tracks with swing and the ones without. Considering that the swing presence can vary over time, this is performed on a frame basis.

				classical	country		disco		hiphop
		swing noSwing swing noSwing swing noSwing swing noSwing swing noSwing
	# Frame	686	714	92	1308	294	1106	28	1372	0	1400
	Tempo-Estimation (%)	63	74	41	63	61	72	100	96	0	97
	Exp-estimatedTempo (recall %)	63.8	93.6	57.6	99.6	52.7	98.7	100	99.3	0	100
	Exp-annotatedTempo (recall %)	95.3	94.1	92.4	99.6	84.4	97.6	100	99.3	0	100
		jazz			metal	pop			reggae		rock
		swing noSwing swing noSwing swing noSwing swing noSwing swing noSwing
	# Frame	630	770	84	1316	14	1386	364	1036	112	1288
	Tempo-Estimation (%)	37	56	83	64	100	87	57	75	62	84
	Exp-estimatedTempo (recall %)	23.8	96.4	61.9	99.8	100.0	100	54.4	91.4	48.2	98.2
	Exp-annotatedTempo (recall %)	60.2	97.4	76.2	99.1	100.0	99.6	93.4	95.3	83.0	99.1

Table 3 :

 3 Confusion matrix for the estimation of the classes noSwing and swing for Exp-estimatedTempo.

	Annotated / Detected	noSwing	Swing	Recall
	noSwing	11479	217	98.14%
	Swing	1162	1142	49.57%
	Precision	90.91%	84.03%
	4.1.2. Tempo-Estimation

Table 4 :

 4 Confusion matrix for the estimation of the classes noSwing and swing for Exp-annotatedTempo.

	Annotated / Detected	noSwing	Swing	Recall
	noSwing	11514	182	98.44%
	Swing	399	1905	82.68%
	Precision	96.65%	91.27%

A onset-energy-function is a function taking high values when an onset is present and low values otherwise.

[START_REF] Honing | Swing once more: Relating timing and tempo in expert jazz drumming[END_REF] The OEF is computed as follow: first, the audio is resampled to 8kHz, then the short-term Fourier transform (STFT) magnitude (spectrogram) us

ing 32 ms windows and 4 ms step between frames is computed. Then it is converted to 40 Mel bands. The Mel spectrogram is converted to dB, and the first-order difference along time is calculated in each band. Negative values are set to zero (half-wave rec-tification), then the remaining, positive differences are summed across all frequency bands. This signal is passed through a high-pass filter with a cutoff around 0.4 Hz to make it locally zero-mean, and smoothed by convolving with a Gaussian enveloppe about 20 ms wide.[START_REF] Gouyon | Rhythmic expressiveness transformations of audio recordings: swing modifications[END_REF] A long window is required because there is not always a swinging eight-note around each beat. For some tracks, the swing information can be very sparse. Thus it is necessary to have a long window.[START_REF] Laroche | Efficient tempo and beat tracking in audio recordings[END_REF] A 1s hop-size was arbitrarily chosen. Taking a smaller hop-size wouldn't make sense considering that there are, at most, 4 beats per 1 second in our database.

The search ranges imply that the swing ratio is comprised between 1 and 3.

The GTZAN test-set is made of 1000 audio excerpts of 30 s. duration evenly distributed in 10 music genres (blues, classical, country, disco, jazz, hip-hop, metal, pop, reggae, rock).

We only annotated the eight-note position when swing exist or in case of ternary rhythm

The recall is the number of items detected for a class divided by the total number of annotated item for that class.

We are grateful to Bob Sturm for sharing the artist information of the GTZAN tracks.

Given that the various tracks of an artist are coming from the same album we suppose that the musicians are the same for a given artist.

Acknowledgements

This work was founded by the French government Programme Investissements d'Avenir (PIA) through the Bee Music Project.