Showing papers on "Calorimeter published in 2017"
TL;DR: In this article, the authors reported the first spin-independent dark matter particle-nucleon cross section for masses between 140 and 500 MeV/c ≥ 1.5 eV.
Abstract: Models for light dark matter particles with masses below 1 GeV/c
$$^2$$
are a natural and well-motivated alternative to so-far unobserved weakly interacting massive particles. Gram-scale cryogenic calorimeters provide the required detector performance to detect these particles and extend the direct dark matter search program of CRESST. A prototype 0.5 g sapphire detector developed for the $$
u $$
-cleus experiment has achieved an energy threshold of $$E_{th}=(19.7\pm 0.9)$$
eV. This is one order of magnitude lower than for previous devices and independent of the type of particle interaction. The result presented here is obtained in a setup above ground without significant shielding against ambient and cosmogenic radiation. Although operated in a high-background environment, the detector probes a new range of light-mass dark matter particles previously not accessible by direct searches. We report the first limit on the spin-independent dark matter particle-nucleon cross section for masses between 140 and 500 MeV/c
$$^2$$
.
146 citations
TL;DR: In this paper, commercial 18650 lithium-ion cells with LiMn2O4, LiFePO4, and Li(Ni 0.33Mn0.33Co0.34)O2 cathodes were exposed to external heating in an accelerating rate calorimeter (es-ARC, Thermal Hazard Technology (THT), Bletchley, UK), to investigate the thermal behavior under abuse conditions.
Abstract: In this work, commercial 18650 lithium-ion cells with LiMn2O4, LiFePO4, and Li(Ni0.33Mn0.33Co0.33)O2 cathodes were exposed to external heating in an accelerating rate calorimeter (es-ARC, Thermal Hazard Technology (THT), Bletchley, UK), to investigate the thermal behavior under abuse conditions. New procedures for measuring the external and internal pressure change of cells were developed. The external pressure was measured utilizing a gas-tight cylinder inside the calorimeter chamber, in order to detect the venting of the cells. For internal pressure measurements, a pressure line connected to a pressure transducer was directly inserted into the cell. During the thermal runaway experiments, three stages (low rate, medium rate, and high rate reactions) were observed. Both the pressure and temperature change indicated different stages of exothermic reactions, which produced gases or/and heat. The onset temperature of the thermal runaway was estimated according to the temperature and pressure changes. Moreover, the different activation energies for the exothermic reactions could be derived from Arrhenius plots.
92 citations
TL;DR: In this article, the spin-independent dark matter particle-nucleon cross section for masses between 140 MeV/c$^2$ and 500 MeV /c$2$ was obtained in a setup above ground without significant shielding against ambient and cosmogenic radiation.
Abstract: Models for light dark matter particles with masses below 1 GeV/c$^2$ are a natural and well-motivated alternative to so-far unobserved weakly interacting massive particles. Gram-scale cryogenic calorimeters provide the required detector performance to detect these particles and extend the direct dark matter search program of CRESST. A prototype 0.5 g sapphire detector developed for the $
u$-cleus experiment has achieved an energy threshold of $E_{th}=(19.7\pm 0.9)$ eV, which is one order of magnitude lower than previous results and independent of the type of particle interaction. The result presented here is obtained in a setup above ground without significant shielding against ambient and cosmogenic radiation. Although operated in a high-background environment, the detector probes a new range of light-mass dark matter particles previously not accessible by direct searches. We report the first limit on the spin-independent dark matter particle-nucleon cross section for masses between 140 MeV/c$^2$ and 500 MeV/c$^2$.
80 citations
TL;DR: In this paper, the difference in thermal stability of Li/LiFePO4| half cells with liquid and solid polymer electrolytes was presented, and the dependence of those parameters with respect to the SOC was also presented.
64 citations
TL;DR: In this article, a scaling law for energy threshold vs detector size is given, and the possibility of lowering the threshold of a gram-scale cryogenic calorimeter to the few eV regime is analyzed.
Abstract: The energy threshold of a cryogenic calorimeter can be lowered by reducing its size. This is of importance since the resulting increase in signal rate enables new approaches in rare-event searches, including the detection of MeV mass dark matter and coherent scattering of reactor or solar neutrinos. A scaling law for energy threshold vs detector size is given. We analyze the possibility of lowering the threshold of a gram-scale cryogenic calorimeter to the few eV regime. A prototype 0.5 g Al2O3 device achieved an energy threshold of Eth=(19.7±0.9) eV, the lowest value reported for a macroscopic calorimeter.
63 citations
TL;DR: In this paper, a generalized layer-by-layer model has been proposed to predict the thermal performance of the "Foam - Variable Density Multilayer Insulation combination" (FMLI) at different vacuum levels.
39 citations
TL;DR: The description of the response to anti-protons at low momenta is found to be improved with respect to previous analyses and the jet energy scale uncertainty and correlations in scale between jets of different momenta and pseudorapidity are derived based on these studies.
Abstract: A measurement of the calorimeter response to isolated charged hadrons in the ATLAS detector at the LHC is presented. This measurement is performed with 3.2 nb$^{-1}$ of proton--proton collision data at $\sqrt{s}=7$ TeV from 2010 and 0.1 nb$^{-1}$ of data at $\sqrt{s}=8$ TeV from 2012. A number of aspects of the calorimeter response to isolated hadrons are explored. After accounting for energy deposited by neutral particles, there is a 5\% discrepancy in the modelling, using Geant4 physics lists, of the calorimeter response to isolated charged hadrons in the central calorimeter region. The description of the response to anti-protons at low momenta is found to be improved with respect to previous analyses. The electromagnetic and hadronic calorimeters are also examined separately, and the detector simulation is found to describe the response in the hadronic calorimeter well. The jet energy scale uncertainty and correlations in scale between jets of different momenta are derived based on these studies. The uncertainty is 2--5\% for jets with transverse momenta above 2 TeV, where this method provides the jet energy scale uncertainty for ATLAS.
38 citations
TL;DR: A new computational model based on artificial neural network (ANN) for estimating battery heat generation rate with cell nominal capacity as one of its key inputs along with ambient temperature, discharge rate and depth of discharge is proposed.
38 citations
TL;DR: In this article, an overview of chemical kinetics on the thermal decomposition of di-tert-butyl peroxide (DTBP) has been performed in this study.
Abstract: An overview in the field of chemical kinetics on the thermal decomposition of di-tert-butyl peroxide (DTBP) has been performed in this study. Nowadays, DTBP has been a model compound for studying thermokinetics of organic peroxide and standardization of the DSC or adiabatic calorimeter. Thermal decompositions of DTBP in neat state or solution are conducted by heat flow or adiabatic calorimeters. Chemical kinetics on the thermal decomposition of DTBP obeyed n-th-order reaction and the type of Arrhenius equation. Order of reaction is first without any exception. DTBP in alkyl or aromatic hydrocarbon solvent behaves with excellent precision in activation energy with an averaged value of 157.0 (±4.1) and 159.7(±3.9) kJ mol−1 determined by DSC and adiabatic calorimeters, respectively. Frequency factors A (in s−1) in the form of logA are determined to be 15.8 (±1.1) and 16.3(±0.5) by DSC and adiabatic calorimeters, respectively. In the neat state of DTBP, activation energy and frequency factor in logA both possess the lower value of 128.4 (±6.2) kJ mol−1 and 12.2 (±0.8) determined by DSC. In ARC, these respective parameters are determined to be 142.0 (±17.7) kJ mol−1 and 15.5 (±1.3). Arrhenius parameters acquired from published literature with regard to the kinetics and mechanism on thermal decomposition of DTBP are summarized and discussed.
38 citations
TL;DR: In this paper, the performance of a shashlik calorimeter made up of 12 photomultipliers is discussed and the performance in terms of energy resolution, linearity, response to minimum ionizing particles, and reconstruction of the shower profile are discussed.
Abstract: Effective longitudinal segmentation of shashlik calorimeters can be achieved taking advantage of the compactness and reliability of silicon photomultipliers. These photosensors can be embedded in the bulk of the calorimeter and are employed to design very compact shashlik modules that sample electromagnetic and hadronic showers every few radiation lengths. In this paper, we discuss the performance of a calorimeter made up of 12 such modules and able to sample showers every $\sim 4X_{0}$ . In summer 2016, this prototype has been exposed to electrons, muons, and hadrons at CERN PS (East Area T9 beamline). The performances in terms of energy resolution, linearity, response to minimum ionizing particles, and reconstruction of the shower profile are discussed.
31 citations
TL;DR: In this paper, a high-temperature adsorption calorimeter was proposed for measuring pulse-to-pulse heat of half-reactions during atomic layer deposition (ALD) at 400 K.
Abstract: We introduce a new high-temperature adsorption calorimeter that approaches the ideal limit of a heat detector whereby the signal at any time is proportional to the heat power being delivered to the sample and prove its sensitivity for measuring pulse-to-pulse heats of half-reactions during atomic layer deposition (ALD) at 400 K. The heat dynamics of amorphous Al2O3 growth via sequential self-limiting surface reaction of trimethylaluminum (TMA) and H2O is clearly resolved. Calibration enables quantitation of the exothermic TMA and H2O half-reactions with high precision, −343 kJ/mol TMA and −251 kJ/mol H2O, respectively. A time resolution better than 1 ms is demonstrated, allowing for the deconvolution of at least two distinct surface reactions during TMA microdosing. It is further demonstrated that this method can provide the heat of reaction versus extent of reaction during each precursor’s half-reaction, thus providing even richer mechanistic information on the surface processes involved. The broad appli...
TL;DR: In this article, a detector module using two magnetic calorimeters was built to perform low-temperature measurements of heat and scintillation light generated by particle interaction in a 340 g 40Ca100MoO4 crystal.
Abstract: Metallic magnetic calorimeters (MMCs) are highly sensitive temperature sensors that use the paramagnetic nature of erbium in a metallic host and superconducting electronics usually composed of a superconducting niobium coil and a current sensing superconducting quantum interference device. This article discusses the applicability of MMCs in experimental searches for rare events in particle physics. A detector module using two MMCs was built to perform low-temperature measurements of heat and scintillation light generated by particle interaction in a 340 g 40Ca100MoO4 crystal. The energy transfer mechanism, from incident particles to the components of the heat and light sensors, is described through a thermal model. MMCs, with gold films collecting athermal phonons, can be used over wide ranges of operating temperature and crystal volume without a significant change in detector performances. Rare event searches could thus benefit from MMC-based detectors presenting such flexibility as well as excellent energy resolution and particle discrimination power.
TL;DR: In this paper, micro-scale combustion calorimeter was used to predict the time to ignition of two extruded polystyrene foam types, and the relationship between these two methods can be established with ignition temperature.
Abstract: Flammability of two kinds of two extruded polystyrene foam was tested by micro-scale combustion calorimeter and cone calorimeter. Maximum specific heat release rate, specific heat release, heat release temperature, combustion time and fire growth rates from micro-scale combustion calorimeter tests, and time to ignition, effective net heat of combustion, heat release rate from cone calorimeter tests, were used to compare the flammability of two foams. These two methods would draw different results in evaluating flammability of the foams. This confliction is due to the test scale and combustion condition. The relationship between these two methods can be established with ignition temperature; thus, micro-scale combustion calorimeter can be used to predict time to ignition in cone calorimeter tests. Joint using of micro-scale combustion calorimeter and cone calorimeter leads to a comprehensive evaluation of flammability of polymers.
TL;DR: In this paper, a custom amplifier board coupled to a large-format 16-channel Hamamatsu silicon photomultiplier device for use as the light sensor for the electromagnetic calorimeters in the Muon g - 2 experiment at Fermilab was developed.
Abstract: We have developed a custom amplifier board coupled to a large-format 16-channel Hamamatsu silicon photomultiplier device for use as the light sensor for the electromagnetic calorimeters in the Muon g - 2 experiment at Fermilab. The calorimeter absorber is an array of lead-fluoride crystals, which produces short-duration Cherenkov light. The detector sits in the high magnetic field of the muon storage ring. The SiPMs selected, and their accompanying custom electronics, must preserve the short pulse shape, have high quantum efficiency, be non-magnetic, exhibit gain stability under varying rate conditions, and cover a fairly large fraction of the crystal exit surface area. We describe an optimized design that employs the new-generation of thru-silicon via devices. The performance is documented in a series of bench and beam tests.
TL;DR: In this article, the authors compare the values of TMRad by using zero-order and intrinsic kinetic models, compared to the use of an intrinsic kinetic model, in the presence and absence of copper sulfate in an advanced reactive system screening tool.
Abstract: The thermal safety of chemical processes requires knowledge of the safety parameters that quantify the probability, such as time to maximum rate under adiabatic conditions (TMRad), and the severity, such as adiabatic temperature rise under adiabatic conditions (ΔTad). The zero-order approximation is used to ease the determination of TMRad values at different process temperatures; but how can one be sure that this approximation is acceptable, compared to the use of an intrinsic kinetic model? In the literature, there are no such studies that compare the values of TMRad by using zero-order and intrinsic kinetic models. For that, decomposition of hydrogen peroxide in the presence (and in the absence) of copper sulfate was studied in an advanced reactive system screening tool (ARSST) unit. This calorimeter operates under near-adiabatic conditions, based on heat loss compensation principle, and by using a background heating rate (β). In a first stage, a kinetic model was built to estimate the intrinsic kinetic...
TL;DR: In this article, a flexible microreactor and measurement setup for exothermic chemical reactions in plate-type microreactors is presented, where precise heat flux measurement is realized by means of Seebeck elements and allows for direct as well as space and time-resolved heat flux determination across the reactor.
Abstract: A flexible reactor and measurement setup to safely obtain thermokinetic data for exothermic chemical reactions in plate-type microreactors is presented. Precise heat flux measurement is realized by means of Seebeck elements and allows for direct as well as space- and time-resolved heat flux determination across the reactor. The microreactor used in this work is manufactured from poly(vinylidene fluoride) foils and consists of 11 SZ-shaped mixing channel elements. The Seebeck elements are calibrated by the Joule effect, while its performance is demonstrated in heat transfer and neutralization reaction experiments. Furthermore, the local resolution enables an estimation of mixing time scale for rapid reactions. A comparison of obtained results indicates good accordance with literature data and is the base of further investigations using the calorimeter.
TL;DR: The software compensation technique is described and its implementation in particle flow reconstruction with the Pandora Particle Flow Algorithm (PandoraPFA) is described, which results in a better overall jet energy resolution.
Abstract: The particle flow approach to calorimetry benefits from highly granular calorimeters and sophisticated software algorithms in order to reconstruct and identify individual particles in complex event topologies The high spatial granularity, together with analogue energy information, can be further exploited in software compensation In this approach, the local energy density is used to discriminate electromagnetic and purely hadronic sub-showers within hadron showers in the detector to improve the energy resolution for single particles by correcting for the intrinsic non-compensation of the calorimeter system This improvement in the single particle energy resolution also results in a better overall jet energy resolution by improving the energy measurement of identified neutral hadrons and improvements in the pattern recognition stage by a more accurate matching of calorimeter energies to tracker measurements This paper describes the software compensation technique and its implementation in particle flow reconstruction with the Pandora Particle Flow Algorithm (PandoraPFA) The impact of software compensation on the choice of optimal transverse granularity for the analogue hadronic calorimeter option of the International Large Detector (ILD) concept is also discussed
TL;DR: In this paper, the authors presented a novel setup to analyze the heat of reaction of different single-and multiphase reactions carried out in continuous flow, which is based on true heat flow measurements and therefore ensures precise calorimetric data within 10 mW resolution.
TL;DR: In this paper, the heat capacity of six n-alkanes, i.e. n-hexane, n-octane and n-decane, was determined with a Calvet type differential heat-flux calorimeter at 0.1 and 10 MPa in a broad temperature range.
11 Feb 2017-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, a radiation tolerance study after neutron irradiation of 300, 200, and 100μm n-onp and p-onn silicon pads irradiated to fluences up to 1.6×1016−nq/cm2 is presented.
Abstract: The high luminosity upgraded LHC or Phase-II is expected to increase the instantaneous luminosity by a factor of 10 beyond the LHC's design value, expecting to deliver 250 fb−1 per year for a further 10 years of operation. Under these conditions the performance degradation due to integrated radiation dose will need to be addressed. The CMS collaboration is planning to upgrade the forward calorimeters. The replacement is called the High Granularity Calorimeter (HGC) and it will be realized as a sampling calorimeter with layers of silicon detectors interleaved. The sensors will be realized as pad detectors with sizes of less that ∼1.0 cm2 and an active thickness between 100 and 300 μm depending on the position, respectively, the expected radiation levels. For an integrated luminosity of 3000 fb−1, the electromagnetic calorimetry will sustain integrated doses of 1.5 MGy (150 Mrads) and neutron fluences up to 1016 neq/cm2. A radiation tolerance study after neutron irradiation of 300, 200, and 100 μm n-on-p and p-on-n silicon pads irradiated to fluences up to 1.6×1016 neq/cm2 is presented. The properties of these diodes studied before and after irradiation were leakage current, capacitance, charge collection efficiency, annealing effects and timing capability. The results of these measurements validate these sensors as candidates for the HGC system.
TL;DR: In this article, the specific heat capacities of four absorbents (1,1,3,3-tetramethlylguanidinium lactate, monoethanolammonium and betaine-ethylene glycol) were measured by a Calvet BT 2.15 calorimeter.
Abstract: The specific heat capacities (Cp) of four absorbents (1,1,3,3-tetramethlylguanidinium lactate, monoethanolammonium lactate, betaine-ethylene glycol, and l-carnitine-ethylene glycol), which can chemically absorb sulfur dioxide (SO2) with low concentrations, were measured by a Calvet BT 2.15 calorimeter in a temperature range of 318.15 K–363.15 K. The measured specific heat capacities as a function of temperature were correlated with a second-order empirical polynomial equation. The result indicates that the equation can accurately fit the measured specific heat capacities. All the measured specific heat capacities increase with increasing temperature. 1,1,3,3-Tetramethlylguanidinium lactate has the lowest specific heat capacity. The measured specific heat capacities of the four absorbents are lower than that of water, which is beneficial to the desulfurization process.
TL;DR: The High Granularity Calorimeter (HGCAL) as mentioned in this paper uses transverse and longitudinal segmentation for both electromagnetic and hadronic compartments, where the fine structure of showers can be measured and used to enhance particle identification, energy resolution and pileup rejection.
Abstract: Calorimetry at the High Luminosity LHC (HL-LHC) faces two enormous challenges, particularly in the forward direction: radiation tolerance and unprecedented in-time event pileup. To meet these challenges, the CMS experiment has decided to construct a High Granularity Calorimeter (HGCAL), featuring a previously unrealized transverse and longitudinal segmentation, for both electromagnetic and hadronic compartments. This will facilitate particle-flow-type calorimetry, where the fine structure of showers can be measured and used to enhance particle identification, energy resolution and pileup rejection. The majority of the HGCAL will be based on robust and cost-effective hexagonal silicon sensors with 1 cm2 or 0.5 cm2 hexagonal cell size, with the final five interaction lengths of the hadronic compartment being based on highly segmented plastic scintillator with on-scintillator SiPM readout. We present an overview of the HGCAL project, including the motivation, engineering design, readout/trigger concept and simulated performance.
TL;DR: For natural plant raw materials and for artificial mixture samples with different lignin content, a comparison between empirical equations for the calculation of higher heating values was carried out relying on the data of ultimate analysis as mentioned in this paper.
Abstract: For natural plant raw materials and for artificial mixture samples with different lignin content, a comparison between empirical equations for the calculation of higher heating values was carried out relying on the data of ultimate analysis. Selection of tested equations from already known was carried out according to the criteria: equations should be intended for work with plant raw materials; the range of used materials should be rather wide; the data on element content (C, H, N, S) obtained experimentally and in routine mode, as well as ash value of the material, should be variables; ambiguous equations should be excluded. Only 8 from more than 150 published equations were chosen for testing, and 3 of these provide calculation of higher heating values with a less than 5–6% deviation from reference values obtained by means of combustion in an adiabatic calorimeter.
11 Feb 2017-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: The Calocube as discussed by the authors is a homogeneous calorimeter whose basic geometry is cubic and isotropic, so as to detect particles arriving from every direction in space, thus maximizing the acceptance; granularity is obtained by filling the cubic volume with small cubic scintillating crystals.
Abstract: The direct observation of high-energy cosmic rays, up to the PeV region, will increasingly rely on highly performing calorimeters, and the physics performance will be primarily determined by their geometrical acceptance and energy resolution. Thus, it is extremely important to optimize their geometrical design, granularity, and absorption depth, with respect to the total mass of the apparatus, which is among the most important constraints for a space mission. Calocube is a homogeneous calorimeter whose basic geometry is cubic and isotropic, so as to detect particles arriving from every direction in space, thus maximizing the acceptance; granularity is obtained by filling the cubic volume with small cubic scintillating crystals. This design forms the basis of a three-year R & D activity which has been approved and financed by INFN. A comparative study of different scintillating materials has been performed. Optimal values for the size of the crystals and spacing among them have been studied. Different geometries, besides the cubic one, and the possibility to implement dual-readout techniques have been investigated. A prototype, instrumented with CsI(Tl) cubic crystals, has been constructed and tested with particle beams. An overview of the obtained results will be presented and the perspectives for future space experiments will be discussed.
TL;DR: In this paper, the authors compare the results obtained in previous measurements of the TeO2 light yield with a detailed Monte Carlo simulation able to reproduce the number of Cherenkov photons produced in β/γ interactions within the calorimeter and their propagation in the experimental set-up.
TL;DR: In this paper, a sub-gigahertz Josephson parametric amplifier for the readout of nanoscale calorimeters which consist of normal-metal-superconductor heterostructures was designed.
Abstract: We design a sub-gigahertz Josephson parametric amplifier for the readout of nanoscale calorimeters which consist of normal-metal–superconductor heterostructures. We characterize the amplifier performance at two operating points, 605 and 655 MHz, corresponding to reproducible local frequency maxima with respect to the applied magnetic flux. At the 655 MHz operating point, the device displays its maximum small-signal gain of 32 dB and gain-bandwidth product of . The gain remains above 20 dB for incident powers up to −119 dBm. The added noise of the amplifier, determined by the hot/cold source method, assumes a minimum value of 0.2 K.
01 Jan 2017-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, the authors report the test of many of the key elements of the laser-based calibration system for muon g-2 experiment E989 at Fermilab and show results regarding the calorimeter's response calibration, the maximum equivalent electron energy which can be provided by the laser and the stability of the calibration system components.
Abstract: We report the test of many of the key elements of the laser-based calibration system for muon g - 2 experiment E989 at Fermilab. The test was performed at the Laboratori Nazionali di Frascati's Beam Test Facility using a 450 MeV electron beam impinging on a small subset of the final g - 2 lead-fluoride crystal calorimeter system. The calibration system was configured as planned for the E989 experiment and uses the same type of laser and most of the final optical elements. We show results regarding the calorimeter's response calibration, the maximum equivalent electron energy which can be provided by the laser and the stability of the calibration system components.
TL;DR: In this paper, a mechanical filter is installed to isolate the calorimeters from the vibration inside a cryogen-free dilution refrigerator while meeting thermal requirements, but the effect is significant in particular when the sensor is attached to a large absorber.
Abstract: Cryogen-free dilution refrigerators are getting popular for rare event searches underground due to their advantages. However, the application of a pulse tube refrigerator introduces mechanical vibration that can translate into temperature fluctuation for calorimeters. The effect is significant in particular when the sensor is attached to a large absorber. A mechanical filter is installed to isolate the calorimeters from the vibration inside a cryogen-free dilution refrigerator while meeting thermal requirements.
21 Aug 2017-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, a model for predicting the behaviour of holographic interferometry based calorimeters for radiation dosimetry is introduced using the variations of refractive index due to energy deposition of radiation has several considerable advantages such as extreme sensitivity and ability of working without normally used temperature sensors that disturb the radiation field.
Abstract: In this research work, a model for predicting the behaviour of holographic interferometry based calorimeters for radiation dosimetry is introduced Using this technique for radiation dosimetry via measuring the variations of refractive index due to energy deposition of radiation has several considerable advantages such as extreme sensitivity and ability of working without normally used temperature sensors that disturb the radiation field We have shown that the results of our model are in good agreement with the experiments performed by other researchers under the same conditions This model also reveals that these types of calorimeters have the additional and considerable merits of transforming the dose distribution to a set of discernible interference fringes