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Paper des Monats
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Remote gas sensors mounted on mobile robots enable the mapping of gas distributions in large or poorly accessible areas. A challenging task however, is the generation of three-dimensional distribution maps from these spatially sparse gas measurements. To obtain high-quality reconstructions, the choice of optimal measuring poses is of great importance. Remote gas sensors, that are commonly used in Robot Assisted Gas Tomography (RAGT), require reflecting surfaces within the sensor’s range, limiting the possible sensing geometries, regardless of whether the robots are ground-based or airborne. By combining ground and aerial robots into a heterogeneous swarm whose agents are equipped with reflectors and remote gas sensors, remote inter-robot gas measurements become available, taking RAGT to the next dimension – releasing those constraints. In this paper, we demonstrate the feasibility of drone-to-drone measurements under realistic conditions and highlight the resulting opportunities.
Die Integrität der Verstärkungsfasern in Komposit-Zahnstiften ist entscheidend für die Biegefestigkeit und die langfristige Haftung am Zement in den Wurzelkanälen. Es wurde vermutet, dass die Integrität von glasfaserverstärkten Zahnstiften durch das Beschleifen während der zahnmedizinischen Behandlung beeinträchtigt wird. Eine Beschädigung der Fasern führt zu einer erheblichen strukturellen Schwächung über den gesamten Stiftdurchmesser. Glasfragmente, die durch den Kontakt mit dem Zahnbohrer entstehen, können sich vom Stift lösen und die Haftfähigkeit erheblich verringern. Mit Hilfe hochauflösender Synchrotron-Röntgen-Refraktions-Radiographie (SXRR) konnte das Ausmaß der Schäden zuverlässig identifiziert und charakterisiert werden.
Dazu wurden die Glasfaserstifte sowohl im Herstellungszustand als auch nach der Bearbeitung mit einem Diamantbohrer untersucht. Die Datensätze wurden zur Visualisierung und Quantifizierung der morphologischen Charakteristika intakter und durch das Beschleifen beschädigter Regionen analysiert. Sie zeigen Schäden im bearbeiteten Bereich (z. B. Brüche, Splitter und Risse) sowie herstellungsbedingte Inhomogenitäten der Fasern mit einer signifikanten Zunahme der inneren Oberflächen in Probenregionen, die durch das Beschleifen beschädigt wurden.
Remote gas sensors mounted on mobile robots enable the mapping of gas distributions in large or poorly accessible areas. A challenging task however, is the generation of three-dimensional distribution maps from these spatially sparse gas measurements. To obtain high-quality reconstructions, the choice of optimal measuring poses is of great importance. Remote gas sensors, that are commonly used in Robot Assisted Gas Tomography (RAGT), require reflecting surfaces within the sensor’s range, limiting the possible sensing geometries, regardless of whether the robots are ground-based or airborne. By combining ground and aerial robots into a heterogeneous swarm whose agents are equipped with reflectors and remote gas sensors, remote inter-robot gas measurements become available, taking RAGT to the next dimension – releasing those constraints. In this paper, we demonstrate the feasibility of drone-to-drone measurements under realistic conditions and highlight the resulting opportunities.
Die Integrität der Verstärkungsfasern in Komposit-Zahnstiften ist entscheidend für die Biegefestigkeit und die langfristige Haftung am Zement in den Wurzelkanälen. Es wurde vermutet, dass die Integrität von glasfaserverstärkten Zahnstiften durch das Beschleifen während der zahnmedizinischen Behandlung beeinträchtigt wird. Eine Beschädigung der Fasern führt zu einer erheblichen strukturellen Schwächung über den gesamten Stiftdurchmesser. Glasfragmente, die durch den Kontakt mit dem Zahnbohrer entstehen, können sich vom Stift lösen und die Haftfähigkeit erheblich verringern. Mit Hilfe hochauflösender Synchrotron-Röntgen-Refraktions-Radiographie (SXRR) konnte das Ausmaß der Schäden zuverlässig identifiziert und charakterisiert werden.
Dazu wurden die Glasfaserstifte sowohl im Herstellungszustand als auch nach der Bearbeitung mit einem Diamantbohrer untersucht. Die Datensätze wurden zur Visualisierung und Quantifizierung der morphologischen Charakteristika intakter und durch das Beschleifen beschädigter Regionen analysiert. Sie zeigen Schäden im bearbeiteten Bereich (z. B. Brüche, Splitter und Risse) sowie herstellungsbedingte Inhomogenitäten der Fasern mit einer signifikanten Zunahme der inneren Oberflächen in Probenregionen, die durch das Beschleifen beschädigt wurden.
Due to the diffusive nature of heat propagation in solids, the detection and resolution of internal defects with active thermography based non-destructive testing is commonly limited to a defect-depth-to-defect-size ratio greater than or equal to one. In the more recent past, we have already demonstrated that this limitation can be overcome by using a spatially modulated illumination source and photothermal super resolution-based reconstruction. Furthermore, by relying on compressed sensing and computational imaging methods we were able to significantly reduce the experimental complexity to make the method viable for investigating larger regions of interest. In this work we share our progress on improving the defect/inhomogeneity characterization using fully 2D spatially structured illumination patterns instead of scanning with a single laser spot. The experimental approach is based on the repeated blind pseudo-random illumination using modern projector technology and a high-power laser. In the subsequent post-processing, several measurements are then combined by taking advantage of the joint sparsity of the defects within the sample applying 2D-photothermal super resolution reconstruction. Here, enhanced nonlinear convex optimization techniques are utilized for solving the underlying ill-determined inverse problem for typical simple defect geometries. As a result, a higher resolution defect/inhomogeneity map can be obtained at a fraction of the measurement time previously needed.
In the face of rising energy demand and the impending climate change the development of a sustainable, fossil-free fuel and chemical production is of global importance. One possible goal is the development of electrochemical conversion processes using catalysts. Porous materials play an important role in such energy applications. The activity and stability of each catalyst is highly dependent on the properties of the coating, i.e., phase composition, crystallinity, accessible surface area, and many other factors. The key to the development of improved catalysts is a better understanding of the relations between their performance, stability and physico-chemical properties. However, the complex morphology of such catalysts constitutes a challenge even for modern analytical techniques. Spectroscopic ellipsometry (SE) is a versatile method for studying material properties by using appropriate models (e.g., film thickness, optical and electronic properties). Ellipsometric models need to be validated in order to produce accurate results. In a first step, the model for the ellipsometric fit studies of a calcination series of mesoporous iridium oxide films (300 – 600 °C) was investigated and validated with respect to their material properties.[4] The information on electronic structure of the catalysts shows a direct correlation with electrochemical activities. The development of an environmental electrochemical cell offers the possibility of investigations under operando conditions. Thus, changes in optical and electronic properties can be induced and monitored during the electrocatalytic oxygen evolution reaction.
In this work, we present the recent in-situ imaging developments at the BAMline (of synchrotron BESSY II, HZB), focused on the in-situ characterization and understanding of microstructural evolution of additively manufactured materials subjected to different environments. Two show cases are presented. In the first, X-ray refraction radiography (SXRR) was combined with in-situ heat treatment to monitor the microstructural evolution as a function of temperature in a laser powder bed fusion (LPBF) manufactured AlSi10Mg alloy. We show that SXRR allows detecting the changes in the Si-phase morphology upon heating using statistically relevant volumes. SXRR also allows observing the growth of pores (i.e., thermally induced porosity), usually studied via X-ray computed tomography (XCT), but using much smaller fields-of-view. In the second case study, XCT was combined with in-situ tensile test to investigate the damage mechanism in a LPBF Aluminum Metal Matrix Composite (MMC). In-situ SXCT test disclosed the critical role of the defects in the failure mechanism along with pre-cracks in the reinforcement phase of MMC. We found that cracks were initiated from lack-of-fusion defects and propagated through coalescence with other defects.
Für die aktive Thermografie als zerstörungsfreie Prüfmethode galt lange Zeit die Faustformel, dass die Auflösung interner Defekte/Inhomogenitäten auf ein Verhältnis von Defekttiefe/Defektgröße ≤ 1 beschränkt ist. Die Ursache hierfür liegt in der diffusiven Natur der Wärmeleitung in Festkörpern. Sogenannte Super-Resolution-Ansätze erlauben seit Kurzem die Überwindung dieser physikalischen Grenze um ein Vielfaches. Damit ergibt sich die attraktive Möglichkeit die Thermografie von einem rein oberflächensensitiven Prüfverfahren hin zu einem Verfahren mit verbesserter Tiefenreichweite zu entwickeln. Wie weit diese Entwicklung getrieben werden kann, ist Gegenstand aktueller Forschung.
Wir konnten bereits zeigen, dass diese klassische Grenze für 1D- und 2D-Defektgeometrien mit Hilfe des Abscannens des Prüfkörpers mittels einzelner Laserspots und der anschließenden Anwendung von photothermischer Super-Resolution-Rekonstruktion überwunden werden kann. Bei dieser Methode wird eine Kombination aus sequenzieller räumlich strukturierter Beleuchtung und numerischen Optimierungsmethoden eingesetzt. Dies geschieht allerdings auf Kosten der experimentellen Komplexität, die zu einer langen Messdauer, großen Datensätzen und langwieriger numerischer Auswertung führt.
In dieser Arbeit berichten wir über einen neuen experimentellen Ansatz, bei dem räumlich strukturierte 2D-Beleuchtungsmuster in Verbindung mit Compressed-Sensing und Computational-Imaging-Methoden verwendet werden, um die experimentelle Komplexität deutlich zu verringern und die Methode für die Untersuchung größerer Prüfflächen nutzbar zu machen.
Der experimentelle Ansatz basiert dabei auf der wiederholten (blinden) photothermischen Anregung mit räumlich strukturierten 2D-Mustern unter Verwendung moderner Projektortechnik und eines Hochleistungslasers. In der anschließenden numerischen Rekonstruktion werden mehrere Messungen unter Ausnutzung der Joint-Sparsity der Defekte innerhalb des Prüfkörpers mittels nichtlinearer konvexer Optimierungsmethoden kombiniert. Als Ergebnis kann eine 2D-sparse Defekt-/Inhomogenitätskarte erstellt werden.
Hundreds of papyrus rolls, carbonized during the 79CE eruption of Mount Vesuvius, were discovered in 1754 at Herculaneum. Sophisticated mechanical methods for unrolling the best-preserved scrolls have been applied, with varying success. However, such processes have been abandoned, to prevent risk from irremediable damage or loss and to preserve the integrity of the extremely fragile rolls. Following the development of X-ray based non-invasive techniques, attempts to virtually unroll the scrolls were made. The most common ink in Antiquity was carbon-based, and the main element of carbonized papyrus is carbon, making these investigations difficult. However, some attempts with synchrotron X-ray phase-contrast tomography (XPCT) were successful. Recently, the identification of antique inks containing metals raised hope that if some of the inks contain metal the rolls can be virtually unrolled using conventional CT- technique. We investigated the inks of a selection of partially unrolled fragments stored at the Biblioteca Nazionale di Napoli with X-ray fluorescence in order to select the best candidates for tomography. Despite the many difficulties (analysis of several layers sticking together, letters barely visible, difficulty to separate contribution from the ink and from the papyrus, inhomogeneity of the support, fragility of the fragments…), encouraging results were found, with a number of inks from Greek fragments found to contain additions to the soot (Fe, Pb, Cu P).
Für die aktive Thermografie als zerstörungsfreie Prüfmethode galt lange Zeit die Faustformel, dass die Auflösung interner Defekte/Inhomogenitäten auf ein Verhältnis von Defekttiefe/Defektgröße ≤ 1 beschränkt ist. Die Ursache hierfür liegt in der diffusiven Natur der Wärmeleitung in Festkörpern. Sogenannte Super-Resolution-Ansätze erlauben seit Kurzem die Überwindung dieser physikalischen Grenze um ein Vielfaches. Damit ergibt sich die attraktive Möglichkeit die Thermografie von einem rein oberflächensensitiven Prüfverfahren hin zu einem Verfahren mit verbesserter Tiefenreichweite zu entwickeln. Wie weit diese Entwicklung getrieben werden kann, ist Gegenstand aktueller Forschung.
Wir konnten bereits zeigen, dass diese klassische Grenze für 1D- und 2D Defektgeometrien mit Hilfe des Abscannens des Prüfkörpers mittels einzelner Laserspots und der anschließenden Anwendung von photothermischer Super-Resolution-Rekonstruktion überwunden werden kann. Bei dieser Methode wird eine Kombination aus sequenzieller räumlich strukturierter Beleuchtung und numerischen Optimierungsmethoden eingesetzt. Dies geschieht allerdings auf Kosten der experimentellen Komplexität, die zu einer langen Messdauer, großen Datensätzen und langwieriger numerischer Auswertung führt.
In dieser Arbeit berichten wir über einen neuen experimentellen Ansatz, bei dem räumlich strukturierte 2D-Beleuchtungsmuster in Verbindung mit Compressed-Sensing und Computational-Imaging-Methoden verwendet werden, um die experimentelle Komplexität deutlich zu verringern und die Methode für die Untersuchung größerer Prüfflächen nutzbar zu machen.
Der experimentelle Ansatz basiert dabei auf der wiederholten (blinden) photothermischen Anregung mit räumlich strukturierten 2D-Mustern unter Verwendung moderner Projektortechnik und eines Hochleistungslasers. In der anschließenden numerischen Rekonstruktion werden mehrere Messungen unter Ausnutzung der Joint-Sparsity der Defekte innerhalb des Prüfkörpers mittels nichtlinearer konvexer Optimierungsmethoden kombiniert. Als Ergebnis kann eine 2D-sparse Defekt-/Inhomogenitätskarte erstellt werden.
Per- and polyfluoroalkyl substances (PFAS) are a large group of organofluorine surfactants used in the formulations of thousands of consumer goods, including aqueous film-forming foams (AFFF) used to suppress aviation fires in training scenarios, non-stick cookware, fast-food wrappers, water-repellent fabrics, medical equipment, and plastic and leather products. As a result of the perpetual use of PFAS containing products, effluents and sewage sludge from wastewater treatment plants (WWTPs) have been observed to be an important pathway for PFAS into the environment. In Germany, phosphorus and other nutrients from sewage sludge and wastewater should be recycled in WWTPs of cities with a large population. However, it is not clear if PFAS contamination from wastewater and sewage sludge end up in novel wastewater-based fertilizers. Normally, PFAS are analyzed using PFAS protocols typically with time-consuming extraction steps and LC-MS-MS quantification. However, for screening of PFAS contaminations in sewage sludge or wastewater-based fertilizers also passive sampler based on the Diffusive Gradients in Thin-films (DGT) technique can be used for the PFAS extraction. Afterwards, combustion ion chromatography (CIC) can be applied to analyse the “total” amount of PFAS on the passive sampler. Here, we show results from the DGT method in comparison to those of the extractable organic fluorine (EOF) method for a variety of wastewater-based fertilizers. Additionally, we analysed the adsorption of PFAS on the weak anion exchanger (WAX) based DGT passive sampler binding layer by infrared and fluorine K-edge X-ray adsorption near-edge structure (XANES) spectroscopy.
Equilibrium model of titanium laser induced plasma in air with reverse deposition of titanium oxides
(2022)
A chemical-hydrodynamic model of laser induced plasma is developed to study a process of deposition of titanium oxides from titanium laser induced plasma to the titanium target surface. The model is relevant to texturing and coating of titanium bone implants that is done by scanning the ablation laser across implant surfaces. Such the procedure improves the biocompatibility and durability of the implants. The model considers plasma chemical reactions, formation of condensed species inside the plasma plume, and deposition and accumulation of these species on the ablation surface. A chemical part of the model is based on minimization of Gibbs free energy of the chemical system; it is used to calculate the chemical composition of the plasma. A hydrodynamic part uses the 2D fluid-dynamic equations that model a 3D axisymmetric plasma plume and assumes the mass and energy exchange between the plasma and the surface. The initial parameters for the model are inferred from experiment.
The model shows that condensed titanium oxides, mostly TiO2, form in a peripheral plasma zone and gradually adhere to the surface during the plasma plume evolution. The model predicts the major component and thickness of the deposit and can be applied for the optimization of experiments aimed at surface modification.
Brillouin Optical Frequency Domain Analysis (BOFDA) is a powerful and well-established method for static distributed sensing of temperature and strain. Recently, we demonstrated a BOFDA system based on convolutional neural network which shortens the measurement time considerably. In this paper, we apply leave-one-out cross validation to evaluate the generalization performance and provide an unbiased and reliable machine learning model for a time-efficient BOFDA system.
In the last few years, the use of machine learning has emerged in the field of distributed fiber optic sensors as a promising approach to enhance their performance and provide new capabilities. In this study, we use machine learning for simultaneous measurements of temperature and humidity in polyimide (PI)-coated optical fibers based on Brillouin Brillouin optical frequency domain analysis (BOFDA). Different non-linear machine learning algorithms are employed, namely polynomial regression, decision trees and artificial neural networks (ANNs), and their discrimination performance is benchmarked against that of the conventional linear regression. The performance is evaluated using leave-one-out cross-validation to ensure that the models are reliable and able to generalize well on new data. We show that nonlinear machine learning algorithms outperform the conventional linear regression and thus could pave the way towards simultaneous cost-effective temperature and humidity distributed sensing, which has the potential to find attractive new applications in the field of civil and geotechnical engineering, from structural health monitoring of dikes and bridges to subsea cables and long pipelines corrosion detection.
The deposition of titanium oxides during titanium laser ablation in air has been experimentally and numerically investigated. A titanium sample was irradiated by nanosecond pulses from an Yb-fber laser with a beam scanned across the sample surface for its texturing. As a result, the hierarchical structure was observed consisting of a microrelief formed by the laser ablation and a nanoporous coating formed by the reverse deposition from the laser induced plasma plume. The chemical and phase composition of the nanoporous coating, as well as the morphology and structure of the surface, were studied using scanning electron microscopy, atomic force microscopy, and X-ray microanalysis. It was found that the deposit consists mostly of porous TiO2 with 26% porosity and inclusions of TiO, Ti2O3, and Ti2O3N. Optical emission spectroscopy was used to control the plasma composition and estimate the effective temperature of plasma plume. The chemical-hydrodynamic model of laser induced plasma was developed to get a deeper insight into the deposition process. The model predicts that condensed titanium oxides, formed in peripheral plasma
zones, gradually accumulate on the surface during the plasma plume evolution. A satisfactory agreement between the experimental and calculated chemical composition of the plasma plume as well as between the experimental and calculated composition and thickness of the deposited film was demonstrated. This allows a cautious conclusion that the formation of condensed oxides in the plasma and their consequent deposition onto the ablation surface are among the key mechanisms of formation of porous surface films.
Following the reviews of atomic-weight determinations and other cognate data in 2015, 2017, 2019 and 2021, the IUPAC (International Union of Pure and Applied Chemistry) Commission on Isotopic Abundances and Atomic Weights (CIAAW) reports changes of standard atomic weights. The symbol Ar(E) was selected for standard atomic weight of an element to distinguish it from the atomic weight of an element E in a specific substance P, designated Ar(E, P). The CIAAW has changed the values of the standard atomic weights of five elements based on recent determinations of terrestrial isotopic abundances:
Ar (argon): from 39.948 ± 0.001 to [39.792, 39.963]
Hf (hafnium): from 178.49 ± 0.02 to 178.486 ± 0.006
Ir (iridium): from 192.217 ± 0.003 to 192.217 ± 0.002
Pb (lead): from 207.2 ± 0.1 to [206.14, 207.94]
Yb (ytterbium): from 173.054 ± 0.005 to 173.045 ± 0.010
The standard atomic weight of argon and lead have changed to an interval to reflect that the natural variation in isotopic composition exceeds the measurement uncertainty of Ar(Ar) and Ar(Pb) in a specific substance. The standard atomic weights and/or the uncertainties of fourteen elements have been changed based on the Atomic Mass Evaluations 2016 and 2020 accomplished under the auspices of the International Union of Pure and Applied Physics (IUPAP). Ar of Ho, Tb, Tm and Y were changed in 2017 and again updated in 2021:
Al (aluminium), 2017: from 26.981 5385 ± 0.000 0007 to 26.981 5384 ± 0.000 0003
Au (gold), 2017: from 196.966 569 ± 0.000 005 to 196.966 570 ± 0.000 004
Co (cobalt), 2017: from 58.933 194 ± 0.000 004 to 58.933 194 ± 0.000 003
F (fluorine), 2021: from 18.998 403 163 ± 0.000 000 006 to 18.998 403 162 ± 0.000 000 005
(Ho (holmium), 2017: from 164.930 33 ± 0.000 02 to 164.930 328 ± 0.000 007)
Ho (holmium), 2021: from 164.930 328 ± 0.000 007 to 164.930 329 ± 0.000 005
Mn (manganese), 2017: from 54.938 044 ± 0.000 003 to 54.938 043 ± 0.000 002
Nb (niobium), 2017: from 92.906 37 ± 0.000 02 to 92.906 37 ± 0.000 01
Pa (protactinium), 2017: from 231.035 88 ± 0.000 02 to 231.035 88 ± 0.000 01
Pr (praseodymium), 2017: from 140.907 66 ± 0.000 02 to 140.907 66 ± 0.000 01
Rh (rhodium), 2017: from 102.905 50 ± 0.000 02 to 102.905 49 ± 0.000 02
Sc (scandium), 2021: from 44.955 908 ± 0.000 005 to 44.955 907 ± 0.000 004
(Tb (terbium), 2017: from 158.925 35 ± 0.000 02 to 158.925 354 ± 0.000 008)
Tb (terbium), 2021: from 158.925 354 ± 0.000 008 to 158.925 354 ± 0.000 007
(Tm (thulium), 2017: from 168.934 22 ± 0.000 02 to 168.934 218 ± 0.000 006)
Tm (thulium), 2021: from 168.934 218 ± 0.000 006 to 168.934 219 ± 0.000 005
(Y (yttrium), 2017: from 88.905 84 ± 0.000 02 to 88.905 84 ± 0.000 01)
Y (yttrium), 2021: from 88.905 84 ± 0.000 01 to 88.905 838 ± 0.000 002
Anear-infrared (NIR) light-triggered release method for nitric oxide (NO) was developed utilizing core/shell NaYF4: Tm/Yb/Ca@NaGdF4:Nd/Yb up-conversion nanoparticles (UCNPs) bearing a mesoporous silica (mSiO2) shell loaded with theNOdonor S-nitroso-N-acetyl-DL-penicillamine (SNAP). To avoid overheating in biological samples, Nd3+ was chosen as a sensitizer, Yb3+ ions as the bridging sensitizer, andTm3+ ions as UV-emissive activator while co-doping with Ca2+ was done to enhance the luminescence of the activatorTm3+.NOrelease from SNAP was triggered by an NIR-UV up-conversion process, initiated by 808nmlight absorbed by the Nd3+ ions.NOrelease was confirmed by the Griess method. Under 808nmirradiation, the viability of the liver cancer cell line HepG2 significantly decreased with increasing UCNPs@mSiO2-SNAP concentration. For a UCNPs@mSiO2-SNAP concentration of 200 μgml−1, the cell survival probability was 47%. These results demonstrate that UCNPs@mSiO2-SNAP can induce the release of apoptosis-inducingNOby NIR irradiation.
For more than 110 years, BAM has been producing reference materials for a wide range of application fields. With the development of new analytical methods and new applications as well as continuously emerging more stringent requirements of laboratory accreditation with regard to quality control and metrological traceability, the demand and requirements for reference materials are increasing. This trend article gives an overview of general developments in the field of reference materials as well as developments in selected fields of application in which BAM is active. This includes inorganic and metal analysis, gas analysis, food and consumer products, and geological samples. In addition to these more traditional fields of application, developments in the areas of optical spectroscopy, particulary fluorescence methods, and nanomaterials are considered.
Thermographic photothermal super resolution reconstruction enables the resolution of internal defects/inhomogeneities below the classical limit, which is governed by the diffusion properties of thermal wave propagation. Based on a combination of the application of special sampling strategies and a subsequent numerical optimization step in post-processing, thermographic super resolution has already proven to be superior to standard thermographic methods in the detection of one-dimensional defect/inhomogeneity structures. In our work, we report an extension of the capabilities of the method for efficient detection and resolution of defect cross sections with fully two-dimensional structured laser-based heating. The reconstruction is carried out using one of two different algorithms that are proposed within this work. Both algorithms utilize the combination of several coherent measurements using convex optimization and exploit the sparse nature of defects/inhomogeneities as is typical for most nondestructive testing scenarios. Finally, the performance of each algorithm is rated on reconstruction quality and algorithmic complexity. The presented experimental approach is based on repeated spatially structured heating by a high power laser. As a result, a two-dimensional sparse defect/inhomogeneity map can be obtained. In addition, the obtained results are compared with those of conventional thermographic inspection methods that make use of homogeneous illumination. Due to the sparse nature of the reconstructed defect/inhomogeneity map, this comparison is performed qualitatively.