Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model. Quantum game theory  unites gThe aim of this paper is to bring together the notions of game with unawareness and the notion of quantum duopoly. We shall introduce an element of unawareness to quantum versions of Cournot and Bertrand duopoly already studied by us in papers ,19. In pTo make the paper self-contained, we give the important preliminaries from theory of games with unawareness based on . Then, wThis section is based on the work in . The worG. Therefore, v is called a view. The empty sequence Let Definition 1.A collection 1.For every 2.For every 3.If The first property indicates what views are relevant. If the set of players The second property states that if player 1 thinks that player 2 is considering a player or a strategy as a part of the game, he/she takes those elements into account in the game considered by himself.The third property say that if player 1 finds a game Games of the form A Nash equilibrium  is a basDefinition 2.A strategy profile where The first step in defining the notion of Nash-type equilibrium for a normal-form game with unawareness is to redefine the notion of strategy profile.Definition 3.Let As an illustration of Equation , let us The next step is an extension of rationalizability from normal-form games to the games with unawareness.Definition 4.An extended strategy profile v are defined to be v is defined by Let us consider a normal-form game with unawareness Definition 5.An extended strategy profile the following is satisfied; Definition 5 requires that each strategy of the profile is a best reply to the other strategies of that profile. According to Definition 4, the strategy The following proposition  proves tProposition 1.Let G be a normal-form game and let 1.σ is rationalizable for G if and only if 2.σ is a Nash equilibrium for G if and only if Remark 1.We see from Equations  and 5)  5) that,Then, we get The Li–Du–Massar (LDM) protocol  is a quaCournot’s duopoly is one of the earliest economic models of competition between two players [the set of players is i is the strategy set of player i’s payoff function c satisfies player  players . Each plThe game so defined has exactly one Nash equilibrium i. The player i’s strategies are unitary operators of the formThe Li–Du–Massar quantum approach to the Cournot duopoly  . As a rn. We will prove that it holds for Assume by induction that Equation  holds foThe best reply correspondence associated with Note that Equation . As a reRemark 2.Note that for Equation  is the cAs an application of Proposition 3, we reconsider the example given by Equation .Example 1.Let us consider Equation . Then, iEquation , v¯=121,As shown in c such that The Bertrand model  was propSimilarly, the payoff function of player 2 isThe game defined by Equations  and 47)47) has tThe equilibrium implies the payoff of 0 for both players.According to the quantum model introduced in , the norTo determine extended Nash equilibria in a Bertrand duopoly example with unawareness, presented below, we need to find a player’s best reply to Lemma 1.Denote by quations  and 47)ΓCB and Γquations  and (51)Proof. If Therefore, according to Equation , it is oExample 2.Consider The collection To find an extended Nash equilibrium, we first note thatBy Proposition 1, an extended Nash equilibrium satisfiesAccording to Proposition 3, Equation  is(56)(The payoffs for players 1 and 2 corresponding to Equation  are illuTherefore, if, in the equilibrium , player Equation , player i finds that the other player finds that player i is considering the quantum game and so on. In case players’ perceptions are limited characteristics of the equilibrium payoff outcome varies depending on the level of awareness of the players. We have shown that an asymmetric distribution of players’ unawareness may be beneficial to the players in the quantum Cournot duopoly game, whereas rational strategies of equally unaware players imply the inefficient equilibrium outcome Our research has shown that a rational result in the quantum duopolies depends on whether the players play the quantum game is common knowledge or not. The Pareto optimal outcome The notion of game with unawareness finds also application in the quantum Bertrand duopoly. The example used in the paper indicates that the equilibrium result is more unified in the game with unawareness than in the case in which playing the quantum Bertrand duopoly is common knowledge.


The current paper presents a position statement of the Dutch Working Group of Transcatheter Heart Valve Interventions that describes which patients with aortic stenosis should be considered for transcatheter aortic valve implantation and how this treatment proposal/decision should be made. Given the complexity of the disease and the assessment of its severity, in particular in combination with the continuous emergence of new clinical insights and evidence from physiological and randomised clinical studies plus the introduction of novel innovative treatment modalities, the gatekeeper of the treatment proposal/decision and, thus, of qualification for cost reimbursement is the heart team, which consists of dedicated professionals working in specialised centres. Aortic valve stenosis is a common valvular heart disease, the prevalence of which increases with age, and is associated with a dismal prognosis and quality of life in the presence of symptoms and/or left ventricular (LV) impairment . SurvivaTAVI was conceptualised by Henning R. Andersen (Denmark), whose proposal was not accepted for publication several times, as the topic was considered to have too low a priority. Hence TAVI was first executed in clinical practice by Alain Cribier and co-workers in 2002 (France) . The NetIn contrast to percutaneous coronary intervention (PCI), which was first performed in a young male patient with a so-called low-risk coronary artery lesion, TAVI was first applied in a patient who was rejected for SAVR . ClinicaIn the Netherlands there is currently a debate among stakeholders in care—from healthcare providers and their clinical and scientific societies, policy makers and insurance companies to patients and their associated societies—concerning in which patients TAVI should be considered the preferred treatment and, more specifically, whether TAVI in patients with aortic stenosis for whom SAVR involves an intermediate or (more recently) also low risk should constitute medical care that qualifies them for cost reimbursement.This question is not only of clinical or clinical-scientific interest, it is also highly relevant and even critical for the organisation of care and resource planning both from the perspective of the professionals and their institutions who deliver care  and policy makers and affiliated institutions or organisations. For instance, a recent study reported that approximately 42% of patients with symptomatic aortic stenosis do not undergo SAVR and notwithstanding being deemed candidates for TAVI, 38% did not receive TAVI but medical therapy . In addiGiven the above, the concern of the Dutch Healthcare Authorities and the question as to whether the cost of TAVI should be reimbursed in patients with aortic stenosis for whom SAVR involves an intermediate risk is understandable.The best evidence available to answer the question are the results and conclusions of four landmark randomised controlled trials (RCTs) that directly compared TAVI with SAVR in patients at intermediate and low surgical risk –18. The p < 0.0001) and for the individual outcomes of death  and stroke . SAVR was superior to TAVI for ≥moderate aortic regurgitation . Based on their findings the authors conclude that ‘TAVR should be considered as the preferred alternative to SAVR in intermediate-risk patients and an expected extension of indication to the surgical candidate in the near future’.Thourani et al. used the PARTNER 2 observational and PARTNER 2A randomised trial to compare outcome (follow-up duration 12 months) between TAVI and SAVR in intermediate-risk patients . To corrThis committee believes, however, that the question of the Dutch Healthcare Authorities should be rephrased more generically, namely as ‘Which patients with aortic stenosis should be considered for TAVI and how should treatment decisions be made?’ The reasons for reformulating the question are elaborated in the following paragraphs, which address a number of issues related to the complexity of medical decision-making in the individual patient and the fast and incessant technological evolution and innovations in aortic valve replacement therapy affecting clinical medicine, followed by the conclusions and recommendations of the Dutch Working Group of Transcatheter Heart Interventions.The medical, medical-scientific and non-medical communities use a risk score or a risk score model to categorise patients into various risk categories on the basis of an arbitrary cut-off value. Various cut-off values are used. In the landmark RCTs, the Society of Thoracic Surgery (STS) risk score (risk of death at 30 days after surgery) was used –17. For Interestingly, neither the STS nor the Euro- or logistic EuroSCORE has been designed for patients undergoing TAVI but for patients undergoing open-heart surgery in general, while a model performs best when developed from a population that undergoes the specific procedure. The use of both the STS and the EuroSCORE in patients referred for TAVI has, therefore, been questioned openly. There are currently two TAVI-specific risk scores, the FRANCE‑2 model and the Risk Prediction model proposed by the STS/American College of Cardiology (ACC) Transcatheter Valve Therapy (TVT) Registry , 20. TheNevertheless, it is acknowledged by the experts and medical professionals that any risk model will remain a distant abstract of the complex reality of clinical decision-making, as no model will be able to include all covariates affecting mortality and non-fatal complications during and shortly after cardiac interventions and will always fall short as regards accurately predicting the risk in the individual patient. For that reason, the medical community and their scientific societies both in the EU and USA emphasise that a model should not indicate which patient is a candidate for TAVI but to be considered and used as a single element in the selection process in concert with all the other information collected by the physician when he/she sees and examines the patient  in addition to technical assessments such as laboratory  and cardiovascular imaging , 12. TheTo address the deficiencies of risk models, the medical-scientific organisations in both the EU and USA strongly endorse the role of the heart team in making the treatment decision . The updThe concept of the heart team and, thus, a collaborative approach between interventional cardiologists and cardiothoracic surgeons to jointly deliver appropriate care in a timely manner while minimising unnecessary investigations and procedures was recognised in the early 2000s for patients with (complex) cardiac disease. In the resulting joint publications of the scientific societies  in both the EU and USA, recommendations were provided for the delivery and organisation of care in 2006 and 2010 .The dominant role of the heart team is confirmed by the ESC Working Group on Valvular Heart Disease, which goes one step further by recommending the creation of Heart Valve Clinics (HVC), in which a group of healthcare professionals with expertise in heart valve disease (HVD) work in a dedicated environment to provide specialised and centralised evaluation, care and education to patients with HVD . The reaVerification of the correctness of the diagnosis and the indication for the intervention,written documentation of the motivation for the treatment proposal in the case of medical therapy andin the case of valve replacement therapy, written documentation of the motivation for the proposed mode of valve replacement therapy  and the preferred valve type .Treatment proposal; valve replacement or medical therapy withIn accordance with the updated 2017 European and American guidelines, this committee sees the role of the heart team as follows:For this purpose, the presence of an imaging specialist during the heart team meeting is essential , 12, 21.In clinical practice, cut-off values help to discern non-severe and severe aortic stenosis and, thus, the treatment indication. While on a population level these cut-off values  may be useful to differentiate patient categories at increased risk of death, they are less useful in the individual patient due to overlap of these cut-off values in the various risk groups and—similar to the assessment of the severity of mitral regurgitation—the dynamic interaction between the valve, left ventricular and arterial system when measuring these values. It reinforces the role of the heart team and HVC in the treatment decision (and selection) by providing an expert collaborative  and integrative approach .The presence of a geriatrician is recommended particularly when a patient ≥75 years or younger but with co-morbid conditions that raise the suspicion of neurocognitive dysfunction and/or frailty is discussed. It is recommended that such patients are first seen by the geriatrician before the heart team meeting and certainly before the final treatment decision so as to avoid the treatment being futile.The ESC guidelines are to be used as a framework for decision-making but, as pointed out by the ESC Guideline Committee, the decision should be individualised to each patient’s situation , 12. ThiValve type selection should be based upon balancing the risk of bleeding associated with oral anticoagulant therapy when choosing a mechanical valve and the risk of structural valve deterioration and the need for a redo operation or intervention when choosing a bioprosthetic valve. Both the ESC and American Heart Association (AHA) guidelines stress this should be a shared decision-making process in which the patient’s age, expected longevity and preferences need to be included (class 1 recommendation). In general, they recommend a mechanical valve in patients aged under 50 or 60 and a bioprosthetic valve in patients aged over 65 or 70 years . It has The above highlights the complexity of current medical decision-making. The role of the heart team is to make a balanced decision after careful weighing-up of the risks and benefits of catheter-based and surgical aortic valve replacement as suggested by the ESC guidelines and the ESC Working Group on Valvular Heart Disease and following the recommendation of healthcare policies regarding patient involvement. This committee, therefore, strongly recommends that the motivation for the treatment proposal made by the heart team is collected in the electronic patient dossier for reasons of auditing and verification both for clinical and clinical-scientific reasons, and should be accompanied by a shared-decision agreement with the patient, after a careful discussion on the topic.Since the heart team needs to weigh up the risk and benefits of the proposed treatment modality, the local heart team must be informed about the outcome of the proposed treatment in the local institution. This implies a local infrastructure and organisation of data collection that is capable of providing valid monitoring and evaluation of care as proposed by the ESC Working Group on Valvular Heart Disease . In concdefinition of a minimal data set that captures the indispensable data of the patient, procedure and initial follow-up  to monitor and evaluate the outcome and evolution of care,definition of the responsibilities of the persons involved in the organisation and management of the nationwide data base.The objective of the nationwide registry is to monitor and evaluate the care of patients with VHD referred to hospitals certified for valvular heart replacement therapy in the Netherlands in addition to the evolution of care. This implies essentially:evaluation of the results of the landmark RCTs ,post-market surveillance (an FDA prerequisite),covering of care ).While Europe was the cradle of TAVI, the USA took the lead in organising and conducting the landmark trials that have affected and still greatly affect the management of patients with VHD (aortic stenosis in particular) and the creation of a nationwide data registration system for:TVT Registry hospital participants capture data but these are collected and stored by the ACC. On a quarterly basis the ACC transmits the data to an independent research institute .Outcomes are adjudicated by a board-certified cardiologist at the DCRI using Valve Academic Research Consortium‑2 (VARC-2) definitions.The DCRI performs analyses for research and publications.A Research and Publication Committee has been established to evaluate and approve research proposals and to monitor their progress.A Registry Steering Committee overseeing the strategic direction of the registry is composed of physicians appointed from the STS and ACC, FDA and CMS representatives, and staff members of STS and ACC.A Stakeholder Advisory Committee includes members from device manufacturers, patients, consumers, FDA and CMS, physicians and health systems, and provides meaningful input regarding the needs and goals of each of the stakeholders.The EU, and the Netherlands in particular, must follow the mature and professional way in which the nationwide registry has been organised in the USA. The US professional medical societies (the Society of Thoracic Surgeons (STS) and the American College of Cardiology (ACC)) developed the Transcatheter Valve Therapy (TVT) Registry in collaboration with the FDA, CMS and valve manufacturers . The defSuch a professional and complete structure and infrastructure that guarantees the quality of the data set in addition to relevant outcome reports is essential. The Dutch Society of Cardiology and the Society of Cardiothoracic Surgery endorse this initiative, which is currently taking place in the Netherlands.There is currently debate in the Netherlands as to whether TAVI for patients with aortic stenosis for whom SAVR would involve an intermediate or currently also low risk should be considered for reimbursement. This committee believes that instead of using arbitrarily defined quantitative cut-off values to categorise patients into various risk groups, reimbursement of the cost of care should be based upon the appropriateness of care. Given the complexity of the disease in terms of diagnosis, treatment decision, treatment execution and evaluation, this is best done by a team of experts in VHD (heart team) working in dedicated centres that qualify for the treatment of VHD. As elaborated in this article, categorisation of patients into risk groups falls short when it comes to the evaluation of the individual patient. Also, the rapid technological evolution of minimally invasive treatment of VHD will change the management of patients with VHD, such as asymptomatic patients or patients with moderate aortic stenosis and impaired LV functions. Further developments in indications may be expected as treatment becomes less and less invasive while maintaining and even improving the current outcome measures of safety and efficacy . Given this outlook, the role of the expert heart team and heart valve centres is and will be even more crucial to guarantee the appropriateness of care, treatment decision and modality in particular. It obviates the need for repetitive reevaluation of whether a novel treatment modality or patient category meets the requirements of reimbursement of the costs of treatment.The dossier of the patient has been discussed in the multidisciplinary heart team meeting of an institution that qualifies to perform transcatheter heart interventions in accordance with the Competence Document of the Dutch Society of Cardiology (NVVC) and the Dutch Society of Thoracic Surgery (NvT).The treatment decision and modality are based upon the Indication Document of the NVVC and NvT  which are captured in the electronic patient file, including the motivation for these, in such a way that treatment decision, modality and motivation are suitable for retrospective verification for internal and external auditing.The institution that performs transcatheter heart interventions participates in a nationwide prospective registry that—for reasons of independence and quality—complies with the organisational infrastructure and set-up of the ACC/AHA TVT Registry.In accordance with the medical-clinical and clinical-scientific societies of cardiology and cardiothoracic surgery in both the EU and USA, the Dutch Working Group of Transcatheter Heart Interventions recommends that the Dutch Healthcare Authorities provide coverage of every patient with aortic stenosis who will be or has been treated with TAVI, provided:


Even though a specific electro-optic crystal is used to obtain the results, they are generally applicable to dielectric targets under exposure of a plasma jet when they are of 0.5 mm thickness, have a dielectric constant greater than 4 and are at floating potential. Other techniques to examine the induced electric field in a target do not exist to the best of our knowledge, making this technique unique and necessary. The influence of the AC kHz operating frequency is important because many plasma jet designs used throughout the world operate at different frequency which changes the time between the ionization waves and hence the leftover species densities and stability of the plasma. Results for our jet show a linear operating regime between 20 and 50 kHz where the ionization waves are stable and the temperature increases linearly by 25 K. The charge deposition and induced electric fields do not increase significantly but the surface area does increase due to an extended surface propagation. Additionally, temperature mapping using a 100 μm GaAs probe of the plasma plume area has revealed a mild heat exchange causing a heating of several degrees of the helium core while the surrounding air slightly cools. This peculiarity is also observed without plasma in the gas plume.The plasma-surface interaction is studied for a low temperature helium plasma jet generated at atmospheric pressure using Mueller polarimetry on an electro-optic target. The influence of the AC kHz operating frequency is examined by simultaneously obtaining images of the induced electric field and temperature of the target. The technique offers high sensitivity in the determination of the temperature variation on the level of single degrees. Simultaneously, the evolution of the electric field in the target caused by plasma-driven charge accumulation can be measured with the threshold of the order of 10 In addition it initiated a regained interest in plasma liquid interactions6 and brought forth the field of plasma agriculture7. Furthermore, these types of discharges have also been used for surface functionalization of temperature sensitive materials9, flow actuators11 and plasma catalysis12. Cold atmospheric pressure plasmas are considered advantageous for these applications due to a combined presence of electric fields, (UV) radiation, moderate heat transfer and reactive oxygen and nitrogen species (RONS)14. The plasma target interaction mechanism is evidently important for the resulting effects that have been observed for those various applications.Ever since cold atmospheric pressure plasmas were first applied for biomedical purposes15. The electric field in the gas phase cannot simply be extrapolated due to surface charges and the material’s dielectric constant. The use of electro-optic materials as a target is, as far as we know, the only direct way to obtain the induced electric field. This has been applied already in the past for our plasma jet to investigate the influence of applied voltage and gas flow16 but the influence of operating AC frequency wasn’t looked at. In our previous works, a constant background birefringent pattern was subtracted to obtain the electric field results. We have later shown that this background pattern relates to the inhomogeneous temperature elevation of the sample17, which we use in this work to our advantage to simultaneous detect electric field and temperature dependence on the AC operating frequency.The electric field caused by charge deposition on the targeted surface is an important parameter to monitor, since it influences the dynamics of the discharge propagation at the surfaceThe measurements of electric field and temperature inside targets directly exposed to a plasma are necessary with a high spatial and time resolution for electric field and very high accuracy about 1 degree for surface temperature. These challenging requirements can be achieved inside a dielectric by Mueller polarimetry.21. Recently it was found that simultanously with the electric field also information is obtained involving the temperature induced by the plasma by following the photo-elastic effect17. BSO (Bi12SiO20) is the electro-optic crystal used in this work with a dielectric constant of 56. This means that the studied plasma target interaction is characterized by this relatively high dielectric constant. Recent numerical work22 has shown that the experienced electric field inside targets of 0.5 mm thickness at floating potential are similar when the dielectric constant is higher than 4. This means that the reported electric field values and patterns in this work could be comparable to the electric field which is experienced inside e.g. a thin liquid layer, biological tissues, and polymers that are 0.5 mm when they are treated by a helium plasma jet and they are not grounded. Although, it is noted that cell models and biological tissues are more complex and hetrogeneous with a relative permittivity varying over a large range24. During the course of the measurements done in this work the BSO material has not shown signs of damage under the plasma exposure.Mueller polarimetry is used in this work to study to which level of intensity and spatial distribution of electric fields the studied samples are exposed to by a non-thermal plasma jet, by measuring the Mueller matrix of an electro-optic target. Electric fields measured with electro-optic crystals are due to surface charges deposited during the interaction, following the Pockels effect26. This validates our technique and electric field results and shows that indeed the electric field in the gas phase and inside a dielectric target are different and should be measured separately. The measured temperature profile is calibrated and validated by comparing the temperature increase measured with a 100 μm optical GaAs probe, as shown in the method section. The optical temperature probe is also used in this work to make a two dimensional map of the temperature profile in the plume area of the jet, showing how the mixing of the gas in to the surroundings causes a mild heat exchange, which is often overlooked.In the method section the calibration procedure is explained to show how the temperature spatial profile is obtained together with the induced electric field profile. This offers a unique diagnostic to investigate the plasma surface interaction. It has a significant advantage over conventional diagnostics where normally quantities are obtained inside the plasma in the gas phase and as such have to be extrapolated to estimate what the targeted materials experience at that instance. In our previous works, a comparison is made with a two dimensional fluid modelThis work will investigate the surface interaction induced by a non-thermal kHz-driven plasma jet. The influence of the operating AC frequency of the jet is examined in the kHz range. This parameter is important because it determines the time between consecutive ionization events. An introductory explanation of our plasma jet is given in the method section. When the operating AC frequency changes, the stability of the ionization waves can alter due to a change in left-over species densities. The effect this has on the targeted surface in terms of plasma surface propagation, charge deposition (an thus induce electric field) and temperature of the sample are reported in this work. Multiple jet designs are used throughout the world, all operating usually on different frequencies. The effect this has on the surface interaction is unknown and makes this work important.Mueller polarimetry is applied to examine the plasma surface interactions in terms of the electric field which is induced inside a target and the temperature pattern that is formed. It is used to study the effect of operating frequency of the AC plasma jet. The driving frequency is an important operating parameter since it determines the time in between the ionization events and as such influences the plasma dynamics.27. When the driving frequency of the AC applied voltage is increased, the maximum temperature increases (relative to the room temperature) and the shape of the electric field pattern changes as well as its maximum amplitude.The obtained electric field and temperature inside the targeted material as a function of operating frequency of the plasma jet are shown in Fig. With an operating frequency of 20 kHz the amount of total heat generated by the plasma jet causes the target to have an increased maximum temperature of 11. 7 °C. With a higher operating frequency the amount of ionization events per time interval increases and as such, the generated heat causes the temperature in the target to increase to 24 °C at 50 kHz. The shape of the temperature profile reveals a non-symmetrical structure. This is because the heat produced by the plasma jet is carried by the helium flow, which spreads in a non-uniform way, since the plasma jet is impacting the surface at a 45 degree angle in addition to buoyancy forces acting on the lighter helium. The maximum temperature increase is observed in the impact point at the targeted surface of the ionization waves generated by the jet.16. The material experiences electric fields due to surface charges of maximally 5.1 ± 0.2 kV/cm. This is an average throughout the 0.5 mm thick sample.In this region the charges are deposited during the plasma-surface interaction and the electric fields are generated as a consequence. The electric field patterns that are formed are much smaller compared to the temperature profiles, and a zoom image is also shown on Fig. 28). This illustrates the need for direct measurement of field induced inside a target that cannot easily be extrapolated from the field values measured in the plasma. If desired, also the radial field components can be measured, either by examining the BSO crystal with the polarized light beam at an oblique angle or by using a different electro-optic crystal like Fe:LiNbO329.The electric field values shown here corresponds to the axial component of the field, perpendicular to the targeted surface. This perpendicular field is induced by charges deposited on the electro-optic BSO target and is much lower than the field measured in the plume of the same jet  while the helium flow is maintained at 1 slm. This is also shown in the method section when the voltage amplitude is varied at 30 kHz. Understandably, since no plasma is present, the measured electric field is zero. The examined electric fields are caused by surface charges deposited during the plasma surface interaction and the temperature increase is a result from transferred heat by the plasma jet. To investigate the heat delivered by the plasma further, the optical GaAs probe is used to map the temperature profile in the plasma plume, i.e. the region in between the capillary of the jet and the targeted surface. Results obtained using polarimetry and the GaAs probe agree well to each other.The heating caused by the plasma jet is examined further by investigating the temperature profile in the plasma plume by using the temperature probe sensor without the presence of a target. The profile of the temperature variation inside the target with respect to unperturbed air, mapped in a vertical plane through the axis of the plasma jet at the exit of the capillary, is shown in Fig. The maximum temperature increase in the plume is 18 °C, while the surroundings have a lower temperature than ambient air, i.e. there is a 4 °C cooling effect. At approximately 7 mm from the exit of the capillary, the temperature in the freely expanding plume is similar to the temperature measured in the target at that distance. The visible length of the plasma plume at these conditions is maximally 1.0 cm. A temperature increase of 10 degrees Celsius is observed right at the exit of the capillary.30. The formation of a clear boundary layer is observed at the edges of the capillary tube (indicated in red).The cooling effect of the surrounding is more evident when the plasma is turned off and the temperature profile is measured with a 1000 sccm helium gas flowing out of the jet in to open air, see Fig. To investigate the origins of this heat exchange between the helium carrier gas and the surrounding air, different carrier gasses are examined. Fig. When 700 sccm helium gas flow is used the surroundings cool while the core where helium flows heats up. This effect is reversed when the heavier argon is used, though the effect is less significant. For air, nitrogen and oxygen as carrier gas changes in the temperature profile are insignificant, while still a flow of 700 sccm is applied.In this work Mueller polarimetry is applied to investigate a plasma-surface interaction by measuring simultaneously the electric field and temperature in a target under exposure of the plasma jet when operating at different driving frequencies. Spatial imaging reveals that the plasma interaction with the surface covers a greater area in terms of temperature increase than induced electric field. The latter is local and depends on the location of deposited surface charge, while the observed in-homogeneous temperature distribution is due to heat generated by the plasma jet transported by the helium-in-air mixing.22. The temperature of the target will vary with the volume of the dielectric, especially its thickness, because this determines how good the dielectric acts as a heat sink. As such for dielectric of comparable thickness the temperature results should be comparable as well. This means that even though living tissue and other biological samples are clearly too complex to be reduced to a plain dielectric for all the aspects of the interaction, for the induced electric field and the temperature elevation, the presented results are still applicable when the samples are 0.5 mm thick and far way from grounded planes.This was done using a BSO crystal with a dielectric constant of 56 and a thickness 0.5 mm. We expect our electric field and temperature results to be valid for the interaction of non-thermal helium plasma jets with dielectric surfaces greater than 4 without a grounded plane in the vicinity. This has been shown numerically for the experienced electric field in a recent investigationIn this work the effect of AC kHz operating frequency has been examined. Both the maximum value of electric field and temperature increase as a function of operating frequency of the plasma jet. For the induced electric field the increase in value is relatively minor ranging from 3.8 ± 0.2 to 5.1 ± 0.2 kV/cm, while the shape changes more significantly due to the appearance of the secondary surface discharge behind the impact point. The maximum temperature increase is found to scale linearly as a function of operating frequency.This can be explained by the linear increase of the number of ionization events occurring per time interval, while heat produced per ionization event remains approximately the same. For this specific plasma jet, the linear behavior corresponding to the regime with one single reproducible ionization front during each period of the voltage is observed from 20 to 50 kHz. With higher frequencies the ionization waves are produced too quickly after each other, making them unstable. For lower frequencies there is too much time in between the ionization waves, which also induces an a-periodical behavior. Within this AC kHz regime, our results have been reproducible over many separate experiments since the ionization waves are reproducible in time and space.Although the maximum electric field value does not change linearly within this identified regime, the surface pattern does seem to evolve in a linear way. The surface dynamics change with higher frequencies creating a spatially elongated surface interaction. The operating frequency changes the time in between the ionization events. Since spatial changes of the surface dynamics are observed, this stresses the importance and influence of leftover charges and species created in the previous power cycle. Less time in between the ionization events means that the left-over charge densities are higher, which assists the ionization wave in its propagation. This could explain the elongation of the surface patterns that are observed for higher operating frequencies.31.The identification of the linear operating regime of a plasma device is important for several reasons. First of all, it allows comparison between several measurements that are not done at exactly the same conditions. Also, it is important for possible model-based feedback control of a plasma jet32 or four-wave-mixing34, but this will only give you the electric field generated inside the plasma. Locally, this electric field will be relatively high (15-20 kV/cm) due to charge separation allowing for the propagation of the ionization wave, but this does not mean that a targeted material experiences the same quantitative fields, as is shown here with experienced electric fields of 5 kV/cm. The separated fields caused by either volume or surface charges have been examined in26. Due to charge deposition and alteration of the propagation dynamics in the vicinity of the dielectric target, the electric field values in the plasma plume cannot easily be extrapolated to determine what targets are experiencing. This makes our experiments as done as in this work crucial.To the best of our knowledge the only way to examine which electric fields are experienced by a targeted material under plasma exposure is by using electro-optic crystals and exploiting the Pockels effect. The electric field can also be examined in the gas phase, e.g. by using Stark spectroscopyAs of now the electric field inside "real” samples cannot be determined yet since the electro-optic properties of certain crystals like BSO have to be exploited, making this the only way to be able to study the induced electric field. As stated, the results are generally valid for dielectric targets with a relative permittivity greater than 4 of 0.5 mm thickness that are at floating potential.35, Raman or Rayleigh scattering36, Doppler broadening of metastables and optical  probes. A comparison of several techniques done by Hofmann et al. shows the complications and inconsistencies that can arise37 in addition to the significant error bars that are unavoidable with some of the above-mentioned diagnostics.Spatial profiles of the temperature obtained with Mueller polarimetry and the optical probe agree in both shape of the induced heating pattern and the induced temperature variation. Other approaches of examining the temperature induced by plasma focus again on the gas phase and will not give these accurate results. In general, gas or heavy particle temperatures can be estimated following different approaches, e.g. optical emission spectroscopy using rotational linesWeltmann et al. measured the temperature in the plasma plume of their RF-driven plasma jet 38 and found a temperature upto 63 °C. In a differently designed RF-driven plasma jet gas temperatures are observed of several hundreds of degrees39, while temperature measurements in the plasma plume of an AC kHz-driven plasma jet show only a gas temperature of 35 °C28. Numerical and experimental work done by Kelly et al. on the micro scaled reference jet show a great variance of gas temperature depending on the working mode of that jet40. The temperature increase due to the heat exchange between the heated helium core and the cooled surrounding air has not been observed and reported in literature before to the best of our knowledge.The maximum induced temperature difference relative to ambient conditions obtained from the spatially obtained profiles reported in this work are comparable with other non-thermal jets where only the maximum temperature is reported. 41 used solely to heat a volume of helium defined by the 1000 sccm gas flow. The mapping of the plasma plume using the temperature probe reveals that only an increase of 10 °C is reached inside the capillary tube of the plasma jet. This is most likely related to Ohmic heating due to elastic collisions in the region in between the electrodes. The temperature profile increases further downstream outside the jet due to the plasma plume and the newly found heat exchange caused by the helium-in-air mixing. The resulting temperature profile where the maximum is located downstream instead of at the exit of the capillary is often not incorporated in numerical models. This is important to take properly into account the effect of local heating in the modification of gas flow dynamic induced by plasma jet as discussed in43. The observed heat exchange was also present without any plasma (0 kV or 0 kHz) while still operating a constant 1 slm helium flow.The temperature induced by the plasma relates to the theoretical value of 23 °C, calculated using the dissipated power of the plasma jet (operated at 30 kHz and 2.0 kV) of 0.2 WThe examined gas plumes do not have an increased temperature at the exit of the capillaries. However, an increase is observed downstream along the core of the helium gas flow. This is accompanied with a cooling of the surrounding air. This heat exchange outside the capillary is not well understood since gas velocities are low and ambient pressure conditions are maintained, but it is related to a difference in either or both density and specific heat of the core carrier gas compared to the environment. With lighter helium, the core heats up while the environment cools. On the contrary, with heavier argon as carrier gas this effect is opposite. When nitrogen, oxygen or air is used as carrier gas of the jet (without an applied voltage) there is no heat exchange.48. No consensus has been reached yet whether heating or ion-wind is dominant. The contribution of the increase in temperature to the gas flow modification is usually estimated from the change in helium density with temperature and the continuity of mass flow rate just at the nozzle44. However Fig. The additional heat exchange between the helium core and the surrounding air complicates the discussion of flow alterations due to the plasma jet. From Fig. inside a targeted electro-optic material under exposure of a plasma jet. This examination allowed for the simultaneous imaging of the electric field and temperature generated inside a material, instead of measuring it in gas phase and extrapolating it towards the target. This has never been done before in this way and opens new possibilities to investigate spatially and time-resolved the plasma surface interactions that occur.The newly applied optical diagnostic technique has been applied to reveal plasma target interactions occurring in terms of the electric fields and temperature profiles induced 41. The amount of power dissipated by the jet is approximately 0.2 W. The jet impacts the surface at a 45° angle at 7 mm distance41.The plasma target interaction investigated in this work is done for discharges generated with a plasma jet operated in a coaxial configuration examined with a Mueller polarimeter, see Fig. 41. In proximity of a target, charge will be deposited on impact of the ionization wave. This is removed approximately 10 μs later when the polarity of applied voltage changes, observed through electric field imaging15. This is accompanied by a weak afterglow, indicating the occurrence of a (back) discharge at the target going back towards the capillary tube.When the plasma jet is operated using a 30 kHz driven AC signal, there is one ionization wave generated during every positive half period travelling away from the powered electrode17. Due to the examination of the material the plasma jet is positioned at a 45 degree impact angle, in order not to block the polarized light that is send through the target, see Fig. 27.The temperature and electric field induced in a target by the plasma jet is investigated using Mueller polarimetry. In this novel optical technique polarized light is sent through an electro-optic BSO crystal for which the refractive index depends on both the electric field and the temperature gradientsPSG) and the Polarizer State Analyzer (PSA). Both the PSG and PSA consist of a polarizer and two ferro-electric liquid crystals, for which the orientation can be switched between two states. Hence, 16 different states can be sequentially examined which allows for the acquisition of the 4 × 4 Mueller matrix of the examined sample, i.e. the electro-optic BSO under exposure of the plasma jet.The Mueller matrix of the targeted electro-optic BSO crystal is measured by generating and analyzing different states of polarized light, using the Polarizer State Generator , while the second Γ2 relates to the polarization components in the diagonal axes (i.e. the x − y and x + y-axis). They depend on the difference of experienced refractive indices in those respective coordinate systems, namely Δn0∕90 and Δn45∕135.This linear retardance Γ scales with the electric field and temperature gradient according to equation 2 scales with the electric field E parallel to the optical axis z according to the electro-optic coefficient r41 = 4.8 pm/V. The dependencies of Γ with the second derivatives of the temperature have to be determined through calibration, i.e. γ1,2,3. This is because they depend on the photo-elastic tensor elements of BSO, which are not so-well determined unlike the electro-optic coefficient. Γ is space dependent on x and y since both the electric field and temperature are non-homogeneous patterns.ΓTwice the Mueller matrix is obtained time-resolved while the plasma jet is continuously operated, one timed right before the ionization wave impacts the target and once right after. By subtracting the birefringences obtained before and after impact the electric field effect is separated from the temperature effect. This is because the electric field is only present after impact due to charge deposition, while a steady state temperature profile is present at both times. The electric field is then easily obtained by applying the inverted equation 27.For the retrieval/analysis of the temperature pattern it is less trivial since the birefringence depends on the second spatial derivative of the temperature profile, as shown in equation μm GaAs temperature probe which is attached to an optical fiber . Since no metallic parts are present and the size of the probe is significantly smaller than the plasma jet, perturbations are expected to be low. This is monitored through voltage–current waveforms. The temperature profile can be mapped pointwise by changing the position of the probe along a predefined grid, by capturing the local temperature at each point. It has been shown in17 that the obtained inhomogeneous pattern using the birefringent patterns acquired with Mueller polarimetry strongly relates with the mapped temperature profile on the backside of a targeted material. The maximum induced temperature difference relative to the surroundings can be used to calibrate the values of γ1,2,3.A second method for the examination of the temperature is used to verify the procedure to retrieve the temperature profile from the measured birefringent patterns. This is done using a 100 γ1,2,3. This procedure is calibrated by fixing γ1,2,3 by comparing temperature measurements obtained with Mueller polarimetry with measurements done with the temperature probe. By comparing the maximum temperature increase for different applied voltages of the plasma jet, the values of γ1,2,3 are optimized and calibrated, as shown in Fig. From the numerical fitting procedure, two dimensional images of the temperature are obtained. The shape of the temperature profile is dependent upon the matching of the second gradients with the measured profiles. The maximum value of temperature increase can be controlled using the values of γ1 = −4 ⋅ 10−12, γ2 = 5.4 ⋅ 10−12 and γ3 = 10.8 ⋅ 10−12 m2∕K. A positive or negative sign is needed to match the polarity of the birefringent patterns to the second gradients of a temperature profile. The variation of the values of γ1,2,3 can be found in27.The best match for the maximum temperature increase when applying different voltage amplitudes between the numerical temperature profile obtained from Mueller polarimetry and the mapping using the probe is obtained for The mapping with the temperature probe is done on the backside of a 0.5 mm thick glass under exposure of a plasma jet operated in similar conditions as when examining BSO with the Mueller polarimeter. It has been confirmed with the temperature probe on the backside in the impact region that similar values are obtained with a glass target as with BSO. This is understandable since the temperature increase is caused by heat delivered from the plasma jet.γ1,2,3) Fig. Besides a good agreement between the two methods (with the calibrated values of


One enduring challenge for controlling high frequency sound in local active noise control (ANC) systems is to obtain the acoustic signal at the specific location to be controlled. In some applications such as in ANC headrest systems, it is not practical to install error microphones in a person’s ears to provide the user a quiet or optimally acoustically controlled environment. Many virtual error sensing approaches have been proposed to estimate the acoustic signal remotely with the current state-of-the-art method using an array of four microphones and a head tracking system to yield sound reduction up to 1 kHz for a single sound source. In the work reported in this paper, a novel approach of incorporating remote acoustic sensing using a laser Doppler vibrometer into an ANC headrest system is investigated. In this “virtual ANC headphone” system, a lightweight retro-reflective membrane pick-up is mounted in each synthetic ear of a head and torso simulator to determine the sound in the ear in real-time with minimal invasiveness. The membrane design and the effects of its location on the system performance are explored, the noise spectra in the ears without and with ANC for a variety of relevant primary sound fields are reported, and the performance of the system during head movements is demonstrated. The test results show that at least 10 dB sound attenuation can be realised in the ears over an extended frequency range (from 500 Hz to 6 kHz) under a complex sound field and for several common types of synthesised environmental noise, even in the presence of head motion. Global active noise control (ANC) systems aim to reduce the undesired sound in a large environment, but require a large number of control loudspeakers, making them impractical in many applications5. By contrast, local ANC systems aim to reduce the sound only at specific  positions, often around a listener’s ears, with the most common example being increasingly ubiquitous personal ANC headphones. In such solutions, the cushion and shell structure of the earcups provide passive sound attenuation in the mid to high frequency range  for auditory comfort6. In parallel, the active control component uses integrated speakers and microphones to produce anti-noise signals to attenuate sound in the lower frequency range 7. ANC headphones are commonly used by passengers and aircrew in aircrafts, where the cabin noise during long haul flights is known to be detrimental to health and wellbeing8. However, longer-term use of such solutions can cause discomfort and/or fatigue because of the requirement to create a sealed volume around the ear which requires extra earcup clamping pressure. Solutions that can deliver sound reduction performance on par with that of earmuffs-based ANC headphones, but without the need to wear anything, would have value in many scenarios such as for machinery or equipment operators, for drivers of vehicles and for people working in open plan offices.Long-term exposure to either occupational or environmental noise can lead to a series of diseases, both auditory14. Indeed in an ANC headrest system , both the secondary loudspeakers and the error microphones can be installed within the seat to reduce the undesirable sound (commonly denoted as primary sound) at both of user’s ears9. Due to the difference between the sound pressure measured at these remote microphone locations and that at the user’s ears, such a solution cannot guarantee sufficient sound reduction, particularly in the higher frequency range. Since the first proposal of ANC headrest technology in 19539, many virtual error sensing algorithms have been proposed which estimate the sound pressure at the ears based on the signals obtained from physical microphones positioned at alternative remote locations20. The upper-frequency limit for effective sound control remains relatively low with a recently proposed system consisting of an array of four microphones and a head tracking system still only achieving sound reduction up to 1 kHz for a single sound source21. While this may be sufficient for certain low frequency ambient or machine induced noise, it is less effective for speech or other higher pitch sounds. In addition, the number of microphones required can be significant when using such a technique for real-world applications; this is not desirable in many applications.A substantial amount of effort has been made to move the required anti-noise loudspeakers (commonly denoted as secondary loudspeakers) and error sensors of ANC systems away from the user’s ears and head while still realising effective noise reductionwithout the use of passive sound attenuating materials (i.e. the earcup or earbud). However, due to the physical limitation of moving the required components and absorbing materials away from the user, the development of ANC headrests has seen little progress despite ongoing research and development over several decades. It should be emphasised that such ANC headrests are not necessarily comparable to other sound control/attenuation devices, such as earplugs22, ANC earphones with inserts23 or modified hearing aids with a potential ANC functionality24. The fundamental principle of and motivation for an ANC headrest system is not to impose any disturbance on the user, whereas all of these alternative devices do.Compared with ANC headphones, which are now well-developed and are increasingly popular and accessible products in the consumer electronics marketplace, the ANC headrest is an alternative solution which aims to provide a quiet environment for a user 25. Despite some effort on miniaturisation of the fibre-optic microphone, such a solution can still not be considered non-invasive, however, due to the physical presence of the optical fibres. In addition, while alternative MEMS microphones can be made extremely small, these devices require various accessories, such as batteries for power and wireless modules for data transmission, ultimately resulting in a solution with a considerable installation footprint. The challenge is clearly consistent with that for traditional condenser microphone-based solutions; the use of a direct fully remote acoustic sensing method in an ANC system would clearly offer advantages over these various other possibilities.There are other alternative ANC systems have been previously proposed. For example, the use of optical microphones based on optical fibres have been explored to replace traditional microphones in an ANC system deployed in an unfavourable environment, such as near a magnetic resonance imaging scanner26 (LDV) and a small membrane “pick-up” is examined in a real-time ANC headrest system. This arrangement includes a retro-reflective film as the membrane pick-up located at the cavum concha of a user’s ear with an error-sensing LDV being positioned at a location remote from the user. LDVs typically have very high sensitivity with commercially available instruments able to resolve vibration displacements down to pm and velocities down to nm/s resolution. The membrane pick-up can be designed to be small and lightweight and have a wide dynamic range. Furthermore, being retro-reflective, the membrane can tolerate a wide range of inbound laser beam incidence angles, making this combination suitable even when the user’s head moves . Importantly, however, such a remote acoustic sensing approach can be highly attractive in an ANC application because the bulk of the signal processing components are located away from the user. The only minor encumberment on the user, to yield a practically realisable solution, is that they must wear a small optical pick-up, of no more mass nor volume than a typical piece of ear jewellery, on or ideally close to each ear canal.In this paper, a remote acoustic sensing approach using a laser Doppler vibrometerSince the system does not include any largely intrusive actuators, sensors or bulky materials around the user’s ears, it is described as a “virtual ANC headphone” in this paper. It neither installs any bulky error microphones with accessories on or near to the user’s head, nor uses a large number of microphone arrays with certain virtual sensing algorithm methodologies to estimate the sound pressure at the ears based on measurements from elsewhere. As will be shown in the following section, this virtual ANC headphone system has significantly better performance than any other virtual error sensing solutions in the published literature thus far. While there remains further work to yield a commercially viable practical version of the solution, it is proposed that the technical benefits justify its proposal and continued investigation.The system design and results of the subsequent experimental investigation are organised into five subsections. Initially, the system design of the virtual ANC headphone is described. Subsequently, the location of the membrane for the best control performance is examined. Thirdly, ANC performance in the presence of broadband grey noise is determined with the system implemented on a head and torso simulator (HATS). Penultimately, system performance is then evaluated for different kinds of synthesised real-world environmental noise signals. Ultimately, the use of a simple measurement location tracking system is incorporated to enable inevitable user head motion to be tolerated.A schematic showing the proposed system components and their arrangement is shown in Fig. 4. When the membrane is placed close to the ear canal, such a quiet zone can be created around it, thereby reducing the sound propagating to the tympanic membrane (eardrum). The two secondary loudspeakers presented here were placed 0.44 m apart with an azimuth angle of 45 degrees pointing to the user as shown in Fig. Methods—Noise control algorithm subsection.For ANC systems, a quiet zone is defined as a region in which more than 10 dB sound attenuation is achieved, with the zone size being about a tenth of the wavelength of the sound in a diffuse sound fieldNormal head movements can be accommodated by a relatively straightforward camera-based tracking system, outlined in Fig. 27), 0.1 mm in thickness, stretched over and adhered to a short, enclosed polymeric cylindrical tube with a diameter of 9.2 mm, a depth of 4.6 mm and a mass of approximately 0.2 g. The resulting combination is therefore as minimally invasive as practically possible in terms of size and mass. The film was used as the membrane so as to maximise the backscattered optical signal in relation to the inbound laser beam, irrespective of a non-normal beam incidence, this being advantageous in the presence of inevitable head movements. The membrane works similarly to a microphone diaphragm, converting the acoustical pressure induced mechanical vibration ultimately to an electrical signal. However, in this case, there are neither any electronic components inside , nor the need for wiring for signal transmission. Instead, signal conditioning and conversion are completed remotely in the LDV opto-electronics. Detailed parameters for the retro-reflective material and the frequency response of the membrane pick-up have been determined and can be found in Supplementary Fig. The experimental setup is presented in Fig. The data acquisition system is at a remote location along with the LDV in the proposed arrangement. The LDV (Polytec PDV-100) has a measurable frequency range from 20 Hz to 22 kHz. The LDV was mounted on a tripod, vibration isolated from the HATS and the loudspeakers (Genelec 8010A). The sampling rate of the ANC controller (Antysound TigerANC WIFI-Q) was set to 32 kHz, and the filter lengths for both primary and secondary paths were set to 1024 taps. It should be noted that the adaptive control algorithm simply took the measured membrane velocity signal directly and attempted to minimise it. While the velocity signal could potentially be converted into sound pressure by some means, this was not necessary—the outcome would be the same whether it be the raw signal or some derivative of it.28 from 500 Hz to 6 kHz  was identified as the optimal location for the membrane; in the remaining experimental investigations described herein, this is therefore the membrane position employed.With ANC on, the performances at locations #1 and #2 were similar with the resulting overall SPL being 69.2 dB and 70.9 dB, respectively. However, the sound reduction was only significant at frequencies below 4 kHz. The reason may be that the sound pressures measured at these two points are only similar to that at the ear canal below 4 kHz. Thus, the control performances at the two points are also limited up to 4 kHz. The sound reduction at location #3 was the best with an overall SPL of 63.5 dB when ANC was on. The overall SPL was reduced by 14.2 dB over the entire frequency range from 500 Hz to 6 kHz. Location #4, the lobule, was further away from the ear canal than any of the other selected locations. The effective frequency range of the sound reduction was only up to approximately 3 kHz with an approximately 6 dB 20, where the sound up to 1 kHz was controlled, albeit here the improvement achieved is over a much wider frequency range, up to 6 kHz. It is worth noting that the tests were still performed at each side separately instead of being taken simultaneously in this case.Figure Figure 20, the primary source was located about 1.2 m directly behind the HATS, with only one channel (right ear) being controlled. The three experiments were performed in a hemi-anechoic chamber. Firstly, a recording of aircraft interior noise29 was used as the primary source signal. The 15-s signals observed by the HATS before and after ANC are shown in Fig. 30 was examined. Figure 31. Figure To further demonstrate the capability of the proposed solution, performance in the presence of three different kinds of pre-recorded common environmental noise scenarios was assessed. Similar to the configuration implemented recently26; the scenario herein represents a further interesting application. A simple tracking system was therefore implemented to demonstrate the proof of concept. This bespoke camera-based tracking system is shown in Fig. Methods—Head tracking system subsection. The scenario used here is the same as the one described in Fig. A person is prone to exhibit continuous head motion, therefore, the probe laser beam from the LDV should be able to track the corresponding arbitrary motion of the membrane in the ears. Such tracking LDV solutions have been widely researched, developed and applied for numerous complex measurement tasksThe movement of a marker on the ear lobule of the HATS, as illustrated in Fig. stationary HATS and when ANC is on with the head tracking system disabled (3) and enabled (4) for a moving HATS. The movement of the HATS was implemented manually with a forward–backward movement used to simulate a person moving back and forth while seated. The maximum distance the HATS travelled in the Supplementary Movie Figure  enabled  for a mo enabled  for a moincreased significantly from 81.1 to 99.5 dB. When the tracking system was enabled, the mirrors maintained the laser beam incidence on the membrane as the HATS moved. Thus, the LDV measurement remained valid for the adaptive control. As shown in Fig. When the HATS moved with ANC on but with tracking disabled, the head (therefore the membrane) moved away from the probe laser beam; the LDV signal thereby “dropped out” or made a vibration measurement not representative of the sound pressure at the ear. This can easily make the control system diverge and, as shown in Fig. 32 with the entire proposed system thereby being designed to be sufficiently compact and low cost to be used in headrests for example in airplanes or in (driverless) automotive applications in the future.Like many other systems, the demonstrated solution also faces certain limitations. Particularly, while the demonstrated system using the remote acoustic sensing approach can achieve an ultra-broadband control, the cost of the required LDVs can be high. However, it is possible that these can ultimately be made smaller and at a lower cost34. However, such comparison is unfair since the aim of an ANC headrest system is to eliminate the use of the passive attenuation materials which deliver such reduction.Some further limitations of the solution are also acknowledged. Firstly, the performance of such a virtual ANC headphone  is still inferior when compared to that of ANC headphones. In particular, sound attenuation achieved in the higher frequency range by active control is below that which can be simply achieved through passive control, i.e. earmuffs, with these often delivering over 30 dB reductionSecondly, while multiple primary sources were used to simulate unwanted sound from multiple, arbitrary directions, the reference signals for the ANC controller were taken directly from these loudspeaker signals; in a real-world situation, this would clearly not be possible. The reason for taking the reference signal directly from the primary source was to focus on the proposed remote acoustic sensing approach. Future developments include incorporating one or multiple actual reference sensors into the system. The locations of these reference signal sensors are less constrained than those of the error signal sensors. However, they should still be close to the entire system, including to the secondary sources. The constraint of the possible locations would affect the control performance and this remains a topic to be further studied in the ANC community.Thirdly, the head tracking system shown for illustration purposes was only capable of tracking two-dimensional motions. A more robust head tracking system with a higher frame rate camera and auto-focus could be implemented to accommodate faster, three-dimensional head movements in the future. Lastly, it should be noted that the laser type used in the experiment was the Class 2 Helium–Neon 633 nm. While eye-safe, it may cause an undesirable effect and distract/dazzle the user if visualised, even briefly. Alternatively, invisible infrared based LDVs could be used in future developments.35. The block diagram of the algorithm is shown in Fig. L and R are used in place of “Left” and “Right”. For each side of the ear, the reference signal x(n) was taken from the primary source for the adaptive ANC controller to calculate the control signal y(n) for the secondary loudspeaker. An LDV measures the error signal e(n), which can be represented asw is the vector of controller coefficients and r̂(n) is the estimated filtered reference signal vector, with ŝ(n) is the impulse response of the estimated secondary path filter and x(n) is the reference signal vector. The controller coefficients are updated withµ is the convergence coefficient. The error signal e(n) in this case is the membrane surface vibration velocity measurement from the LDV. The frequency plots of the error signals with ANC off and on are presented in the Supplementary Fig. The ANC controller uses the feedforward structure with the filtered-x least mean square (FxLMS) algorithm36. The controller used in the demonstration for the object tracking was a Raspberry Pi 3B + , accompanied with a 30 fps, 5MP Omnivision 5647 camera module. A circular piece of yellow tape was adhered on to the ear lobule as a marker for object tracking purposes  in the plane of the motion, were derived. An MCP4725 digital-to-analogue converter was used to convert the digital signals from the Raspberry Pi to analogue voltage signals for the galvanometer mirror controller. The galvanometer mirrors were from GSI Lumonics with a matching, tuned for position, precision driver, MiniSAX. As a result, the steering mirrors adjusted the laser beam path such that it remained on the membrane enabling the LDV to measure the membrane surface velocity as the error signal for the ANC system.The LDV used with the tracking system was a Polytec NLV-2500-5 laser vibrometer, which was placed about 0.3 m away from the left ear of the HATS. The measurement sensitivity was set to 5 mm/s/V leading to a typical velocity resolution of 20 nm/s/√HzI and B are the pixel value of the original image and the binarised image, respectively. λ is the threshold for the chosen marker.The recognition of the object was implemented through colour extraction in OpenCV. The marker was extracted using an adequate threshold of a series of colour images. The image becomes binary asvp. This in turn can translate to the velocity of the target object in reality vr, which is expressed asβ is a scaling factor for a given distance D between the camera and the target object. The value of β was determined during the setup and calibration stage, where the parameters of the tracking system, such as the distance D and the offset between the marker and the membrane, were specified.Due to the circular shape of the marker, the mass centre of the target object can be readily determined, this being the centre of the marker. Between adjacent frames, the pixel shift of this centre was used to obtain the moving velocity of the object The performance of an ANC headrest using a remote acousto-optic sensing approach, proposed to provide a significantly quieter environment for a user, is investigated. The remote sensing approach uses an LDV and a small, lightweight and retro-reflective membrane pick-up placed in the cavum concha of a user’s ear, thereby producing as little disturbance as possible. The membrane design using a retro-reflective film was presented and analysed, and the effects of its location on the system performance were explored. The noise spectra in the ears without and with ANC for different primary sound fields and diverse kinds of environmental noise were reported. A simple head tracking system was also developed to maintain the control performance during any possible head movements from the user. The results show that more than 10 dB sound attenuation can be obtained for an ultra-broadband frequency range up to 6 kHz in the ears for multiple sound sources and various types of common environmental noise. Future work will include enhanced membrane material design, a more robust head tracking system and the incorporation of reference signal sensors in place of signals taken directly from the primary sources.Supplementary Information.Supplementary Information.Supplementary Information.


The elongation and branching of long positive spark discharges in the laboratory and in lightning have been attributed to the formation of thermalized channels inside a diffuse, glow-like streamer section at the leader head. It is experimentally shown here that the structured morphology of streamers produce low-density stem channels that elongate and branch well before a new leader channel section is formed. These non-thermalized stems are also shown to develop ahead of a developing leader channel. These findings are based on high-speed photography and Schlieren imaging used to visualize both the morphology of streamer filaments and stem channels. Numerical analysis is also performed to estimate the axial temperature and density of the stem channels. A stem-driven mechanism for the propagation and branching of positive long air gap discharges is proposed and discussed based on the presence of not-yet thermalized, low density channels formed by streamer ensembles at the leader head. Streamers and leaders are the two main mechanisms involved in the development of electrical discharges in long air gaps. Streamers are non-thermal plasmas composed by a large number of filaments, developing from a sharp electrode or at the tip of a thermalized leader channel. Mobile electrons in streamers converge in the positive leader and diverge in the negative leader3. These streamer filaments and the current associated to them converge into one or several roots known as stems5. As the current flows through to the narrow stem, the gas is heated locally above atmospheric temperature causing a decrease in gas density. Following the path of the lower-density stem channel, a leader discharge can later develop when the gas reaches a temperature threshold between 1500 and 2000 K6. At such a temperature, there is a sharp increase in the stem conductivity such that the transition from streamers into a thermalized leader channel occurs. Recent calculations have shown that a leader discharge can propagate into the gap only when the gas is heated well above 2000 K during the transition7.The knowledge of the physical mechanisms of long positive sparks is necessary to solve a variety of engineering problems and to understand natural lightning flashes13 and theoretically16. However, the knowledge of their stems is still rather poor. Experimental data of the stem produced by positive streamers has been generally based on images obtained using standard photography, in which the bright region at the streamer root is regarded as the stem18. From these photographs, it is unfortunately difficult to observe the actual stem as it is outshined by the light emission from the streamer19. Only until recently, studies have started using Schlieren imaging21 to directly observe the low-density channels of stems and using computer simulation to understand in more detail their radial formation22. Unfortunately, no measurement or analysis is yet available about the elongation and branching of stems along the discharge axis.Research on the development of streamer discharges in the laboratory and in natural lightning is rather abundant, both experimentally28 has also been carried out to characterize the axial propagation of positive leader discharges both in long air gaps and in natural lightning. Abundant streak and frame photographs available in the literature have indicated that leaders developed from a bright diffuse streamer region at the thermalized channel tip, known as the leader head. Based on these observations, it has been hypothesized that a leader channel propagates due to the energy provided by the streamer current converging into the head, when the temperature threshold is reached. Thus, positive leader discharges have been assumed to propagate continuously through short steps equal to the length of the bright diffuse zone observed at their heads17.Much experimental and theoretical research18. They have clearly shown that the streamer filaments at the leader head do not converge into the bright diffuse zone observed in earlier studies using traditional photographs with long exposure times. Instead, streamers at the leader head have fine filamentary structures which can only be observed when short (lower than 2 μs) exposure times are used18. These finely structured streamer filaments converge into multiple bright roots branching from the leader channel tip. As the discharge proceeds, few of these branches can cause the spontanous bifurcation of the channel, which has been always observed with high speed photography in recent laboratory experiments30. Although branching is a very common feature observed in laboratory long air gaps and in lightning, the mechanism of positive leader bifurcation remains mysterious till now32.However, only recent high speed images of positive long air gap discharges have allowed the observation of the fine details of the propagation of the leader headIn this paper, high speed Schlieren images of the low-density channels created by stems are complemented with traditional photographs detecting the streamer morphology. In the experiments, multiple separated streamer bursts are produced at the electrode tip. The Schlieren images show for the first time that stems created by streamer bursts elongate and branch, a process that is invisible in standard brightness photographs. The transient variation of the temperature and the density of the stems is estimated with a thermohydrodynamic model using the measured injected current as input. One event developing into a leader discharge is also analysed. Together with the observations and simulations, the stem at the leader head is compared with that at the electrode tip. At last, a mechanism of stem-driven propagation is proposed for positive leader discharges in long air gaps.5. After a dark period of 21 µs in this case, the second streamer current pulse has however a larger rise and fall time (of 89 and 243 ns respectively), as it is the result of the superposition of at least two asynchronous current pulses.Figure The streamer morphology of the first and the second bursts, obtained by integration of the emitted light (i.e. brightness) of streamer filaments during their development, is shown in Fig. However, the observation of changes in temperature (or in gas density) rather than in brightness is the better way to truly visualize stem channels and to conclusively distinguish them from streamer filaments. This is here accomplished in the Schlieren images in Fig. 22 using as input the measured current pulses of the first and second streamers in Fig. 7. Thus, the stem temperature slightly increases to 400 K during the first streamer burst, while the ratio between the stem density N and the atmospheric density Namb is about 0.7. This minor relative density decrease is visible by the faint changes in the refractive index at the stems S1 and S2 as observed in the Schlieren image of the first burst in Fig. N/Namb slowly recovers to about 0.8 before suddenly dropping again at the inception of the second streamer burst to about 0.25. Furthermore, the stem reaches a temperature close to 1300 K at the current pulse maximum, which rapidly decreases due to strong convection losses produced by the gas expansion in the channel7. As a result, the streamer development is quenched followed by a second dark period.In order to estimate the density and temperature of the stem S1 in the Schlieren images in Fig. 22. The estimation of streamer charge is shown in the Supplementary Note The length of the produced low-density channel is a key parameter to characterize the stem elongation. The method to measure this length is detailed in the Supplementary Note Figure L2s depends on the injected second streamer charge Q2, following a relationship that can be best-fitted to a power law function as:L2s and Q2 are mm and μC, respectively. From Fig. Compared with the first streamer, the stem associated to the second burst develops much longer under the same injected charge as shown in Fig. Figure In order to assess whether the stem branches are formed simultaneously, the streamer current waveforms are analyzed for two additional second streamer events in Fig. N/Namb , defining a narrow path with intensified density-normalized electric field E/N (compared with the surroundings) at the initiation of the third burst. Then, the root of this third discharge develops along that preferred path, defining a narrower streamer morphology along the extension of the stem produced by the second burst as observed in Fig. As the applied voltage continues increasing after the second streamer, the discharge can further develop. Figure E/N along which the fourth discharge develops in a similar manner. Thus, the incepted fourth streamer is narrow at its root and branches into the gap ahead of the path of the remaining stem. The injected current pulse at the inception of this fourth streamer is concentrated in the stem cross section, further heating the channel base to about 2000 K with the resulting drop in gas density  with density slightly lower than atmospheric, requiring a significant amount of charge (up to 220 μC/m) to elongate the stem channel per unit length. In turn, the current injected by second streamers causes a significant decrease of the density of stem channels (below 30% of atmospheric conditions), making them elongate further  with a significantly lower charge per unit length (up to 15 μC/m) compared with the first streamer. Since more stems than those observed in the Schlieren images could have been produced in the experiment34, the values of charge required for the elongation of a single stem per unit length here reported should be however treated as upper-bound estimates. Despite of this uncertainty, the reported upper-bound charge per unit length required for a unit length elongation of the stem after the second streamer is comparable with the corresponding value reported for the propagation of leader channels in the laboratory, ranging between 18 and 50 μC/m5.The elongation of stems during streamer bursts have been here correlated to the injected charge, as it is generally assumed for leader discharges35. After the streamer firstly bifurcates, positive charges at each newly formed filament tip enhance the field ahead and facilitate the emergence of more streamer branches. As a result, the initial streamer branch becomes the root of the subsequent streamer branches. The electric current produced by the subsequent branches contributes to the heating process of its root, and a stem channel can form.The formation of stem branches along a main stem channel observed in the Schlieren images is correlated to the formation of streamer ensembles having an off-electrode root as observed by standard photography. This may be related to the streamer discharge structure named the collective streamer front18. Interestingly, these filament ensembles look similar to those for streamer bursts from sharp electrodes as shown here. Thus, the presence of stems at the tip of a leader channel is a likely process which challenges the traditional view of the thermalized channel head as a bright and diffuse, glow-like region36.The formation, elongation and branching of new stem channels away from the electrode have been here reported for the first time. This process has been observed at the tip of a newly formed thermalized channel, as observed in the temperature map estimated during a streamer to leader transition event. These elongating and branching stems can transform into thermalized channels if sufficient electrostatic energy is available for further development of streamer ensembles from them. Thus, it is here clearly shown that streamer stems are not only important for the inception of the leader channel. Elongating and ramifying stems will also affect the propagation and the branching of leader discharges, as stems are also produced by streamer ensembles at the head of a thermalized channel. Although this process is here observed during the early stages of an aborted leader, recent photographs captured with short exposure times have shown that streamer ensembles with different roots also converge into the tip of a continuously propagating leader36. While this mechanism has been completely ignored in early studies5, it has been later attributed to the current constriction caused by an ionization-thermal instability in the leader head, in a similar way as observed in glow discharges17. Despite of several subsequent studies adressing such a mechanism37, the problem of the evolution of a positive leader channel has not yet been completely solved.The traditional view of diffuse streamer ensembles starting from the leader tip however requires a mechanism for the current of multiple filaments to concentrate locally in order to enable thermalization within a region of small radius at the head5 and Bazelyan and Raizer36 is also proposed. Instead of assuming that the streamer-to-leader transition in front of an electrode is entirely different to that at the head of a thermalized channel, it is here suggested that stems are also produced during the positive leader development. These non-thermalized stem channels are formed by localized concentration of the current at the root of one or several streamer ensembles formed from the leader tip. This stem formation occurs in the same way as for pulsed subsequent streamers initiated from the tip of the electrode . Under normal conditions, one single stem concentrating the current of the dominant streamer ensemble will eventually be thermalized and a new leader segment will be formed from it. Depending on the spatial electrostatic energy distribution in the gap, two streamer ensembles connected to a branched stem at the leader tip could also dominate, such that two new low-density sections are thermalized instead and a leader branch is observed. This branching process will continue with the further development of two different leader heads with their corresponding streamer ensembles if enough electrostatic energy is available, causing a sudden increase in the injected current as observed in experiments29. The formation of a leader branch will therefore be influenced by the stochastic nature of the streamer stem formation and by the available three-dimensional spatial distribution of the electrostatic energy in the gap.Since low-density stems are also present at the leader head as reported here, an alternative mechanism to those suggested by Gallimberti37. Observe that the leader channel is always regarded as the elongation of the high-voltage electrode into the gap and the electric field around the leader tip is similar to that around the electrode tip. Furthermore, there is solid experimental evidence that the propagation of positive leaders taking place is small steps17, causing sudden transient changes in the tip electric field. Furthermore, the short dark period here observed (of less than 30 µs) also guarantees that the positive ion migration between streamer bursts is almost negligible as for streamers at the leader tip. The ions move a distance of less than 2 mm with an average speed of 100 m/s38, which is much shorter than the streamer length . A shunt resistor of 25 Ω is used to measure the streamer current at the sharp electrode. The measured analog signal is locally recorded by a data acquisition card with a sampling rate of 500 M samples per second. In order to reduce the electromagnetic interference and to ensure the electrical safety, the current measurements are locally converted into optical signals and then transmitted. All experimental data are synchronized with the same method described elsewhere2.A high-speed camera (C1: Phantom V1212) equipped with a Nikon 50 mm F1.4 fixed lens is employed to observe the streamer morphology. This camera C1 is placed 2 m away from the electrode and is directed perpendicular to the air gap axis. The camera C1 is operated at a maximum frequency of 190,000 frames per second (fps) with an exposure time of 3.72 μs, using a spatial resolution of 128 × 256 pixels. The corresponding observation area is 180 × 360 mmf) of 1500 mm and an aperture of 150 mm. A pinhole with a diameter of 6 mm and a knife-edge are located at the focal points of the convex lenses. The direction of the knife-edge is vertical, i.e., parallel to the air gap axis. The system is illuminated by a 50 W light-emitting diode (LED) with a central wavelength of 512 nm. In order to obtain high spatial and temporal resolutions, the camera C2 is equipped with a Sigma 300–800 mm F/5.6 zoom lens and is operated at 200,000 fps with an exposure time of 3.98 μs. A frame size of 152 × 256 pixels is used with a corresponding spatial resolution of 70 μm.The low-density channels in the discharge are visualized with a Toepler’s lens-type Schlieren imaging system. It consists of two convex lenses, a light source, a pinhole, a knife-edge and a high-speed camera (C2: Photron FASTCAM SA-X2), as illustrated in Fig. 22. It includes an extensive chemical scheme with 45 species and 192 chemical reactions for humid air at the conditions of the experiment. The model contains a set of continuity equations for the number density ith specie considered (The transient variation of the axial temperature and density of the stems is obtained with the one-dimensional thermal-hydrodynamic model developed and described in detail elsewhereument}ρv  as well 50. Eighteen points along the main low-density channel are selected to calculate the average relative temperature. The corresponding values all along the channel are linearly interpolated. Since most parts of the main channel (in Fig. 7, the density map is calculated from the temperature map by using the gas law at atmospheric pressure.The maximum temperature and minimum density maps for the event in Fig.  in Fig. f are notSupplementary Information.