Physikalisch-Technische Bundesanstalt

We analyze the effect of circuit parameter variation on the performance of Josephson traveling-wave parametric amplifiers (JTWPAs). Specifically, the JTWPA concept we investigate is using flux-biased nonhysteretic rf-SQUIDs in a transmission line configuration, which harnesses the three-wave mixing (3WM) regime. Dispersion engineering enables phase-matching to achieve power gain of $\sim$ 20 dB, while suppressing the generation of unwanted mixing processes. Two dispersion engineering concepts using a 3WM-JTWPA circuit model, i.e., resonant phase-matching (RPM) and periodic capacitance modulation (PCM), are discussed, with results potentially also applicable to four-wave-mixing (4WM) JTWPAs. We propose suitable circuit parameter sets and evaluate amplifier performance with and without circuit parameter variance using transient circuit simulations. This approach inherently takes into account microwave reflections, unwanted mixing products, imperfect phase-matching, pump depletion, etc. In the case of RPM the resonance frequency spread is critical, while PCM is much less sensitive to parameter spread. We discuss degrees of freedom to make the JTWPA circuits more tolerant to parameter spread. Finally, our analysis shows that the flux-bias point where rf-SQUIDs exhibit Kerr-free nonlinearity is close to the sweet spot regarding critical current spread.

Herein, we report a straightforward, scalable synthetic route towards poly(ionic liquid) (PIL) homopolymer nanovesicles (NVs) with a tunable particle size of 50 to 120 nm and a shell thickness of 15 to 60 nm via one-step free radical polymerization induced self-assembly. By increasing monomer concentration for polymerization, their nanoscopic morphology can evolve from hollow NVs to dense spheres, and finally to directional worms, in which a multilamellar packing of PIL chains occurred in all samples. The transformation mechanism of NVs' internal morphology is studied in detail by coarse-grained simulations, revealing a correlation between the PIL chain length and the shell thickness of NVs. To explore their potential applications, PIL NVs with varied shell thickness are in situ functionalized with ultra-small (1 ∼ 3 nm in size) copper nanoparticles (CuNPs) and employed as electrocatalysts for CO2 electroreduction. The composite electrocatalysts exhibit a 2.5-fold enhancement in selectivity towards C1 products (e.g., CH4), compared to the pristine CuNPs. This enhancement is attributed to the strong electronic interactions between the CuNPs and the surface functionalities of PIL NVs. This study casts new aspects on using nanostructured PILs as new electrocatalyst supports in CO2 conversion to C1 products.

Introduction: A long T2 relaxation time can reflect oedema, and myocardial inflammation when combined with increased plasma troponin levels. Cardiovascular magnetic resonance (CMR) T2 mapping therefore has potential to provide a key diagnostic and prognostic biomarkers. However, T2 varies by scanner, software, and sequence, highlighting the need for standardization and for a quality assurance system for T2 mapping in CMR. Aim: To fabricate and assess a phantom dedicated to the quality assurance of T2 mapping in CMR. Method: A T2 mapping phantom was manufactured to contain 9 T1 and T2 (T1|T2) tubes to mimic clinically relevant native and post-contrast T2 in myocardium across the health to inflammation spectrum (i.e., 43-74 ms) and across both field strengths (1.5 and 3 T). We evaluated the phantom's structural integrity, B0 and B1 uniformity using field maps, and temperature dependence. Baseline reference T1|T2 were measured using inversion recovery gradient echo and single-echo spin echo (SE) sequences respectively, both with long repetition times (10 s). Long-term reproducibility of T1|T2 was determined by repeated T1|T2 mapping of the phantom at baseline and at 12 months. Results: The phantom embodies 9 internal agarose-containing T1|T2 tubes doped with nickel di-chloride (NiCl2) as the paramagnetic relaxation modifier to cover the clinically relevant spectrum of myocardial T2. The tubes are surrounded by an agarose-gel matrix which is doped with NiCl2 and packed with high-density polyethylene (HDPE) beads. All tubes at both field strengths, showed measurement errors up to ≤ 7.2 ms [< 14.7%] for estimated T2 by balanced steady-state free precession T2 mapping compared to reference SE T2 with the exception of the post-contrast tube of ultra-low T1 where the deviance was up to 16 ms [40.0%]. At 12 months, the phantom remained free of air bubbles, susceptibility, and off-resonance artifacts. The inclusion of HDPE beads effectively flattened the B0 and B1 magnetic fields in the imaged slice. Independent temperature dependency experiments over the 13-38 °C range confirmed the greater stability of shorter vs longer T1|T2 tubes. Excellent long-term (12-month) reproducibility of measured T1|T2 was demonstrated across both field strengths (all coefficients of variation < 1.38%). Conclusion: The T2 mapping phantom demonstrates excellent structural integrity, B0 and B1 uniformity, and reproducibility of its internal tube T1|T2 out to 1 year. This device may now be mass-produced to support the quality assurance of T2 mapping in CMR.

In this paper, the efficiency of a 2.75 MW nacelle drivetrain on a test bench was determined traceably at various load points. For this purpose, so-called transfer standards for mechanical and electrical power measurement were additionally installed and integrated into the nacelle drivetrain. As torque measurement contributes greatly to the overall uncertainty, the static torque calibration was expanded to include additional influences present under rotation. An overall system efficiency of 89% was measured in the high torque and high speed range. The relative expanded measurement uncertainty for efficiency determination was between 0.30% and 0.72% over the entire operating range. Both the efficiency and the relative expanded measurement uncertainty were calculated for each operating point.

Decreasing the levelized cost of energy is a major design objective for wind turbines. Accordingly, the control is generally optimized to achieve a high energy production and a high-power coefficient. In partial load range, speed and torque are controlled via the generator torque but the rotor torque determines the power coefficient of the turbine. High uncertainties for the uncalibrated low-speed shaft torque measurement and varying drivetrain efficiencies which depend on the speed, load and temperature lead to a torque control error that reduces the power coefficient of the wind turbine. In this paper the rotor torque control error and the impact on the power coefficient of wind turbines is quantified. For this purpose, the variation of drivetrain efficiency is analyzed. An efficiency model for the wind turbine drivetrain is build and validated on the test bench. Then, the influence of the drivetrain speed, torque loads, non-torque loads, and temperature on the efficiency is quantified. Finally, the influence of the rotor torque control error on the power coefficient was simulated with an aerodynamic model. The results show that of all examined influences only torque and temperature significantly impacting the efficiency leading to rotor torque control errors that reduce the power coefficient and consequently increase the levelized cost of energy. Improved efficiency measurement on WT test benches or drivetrain efficiency modelling can reduce the rotor torque control error and therefore decrease the LCOE.

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows expert knowledge or physical constraints to be formulated in a probabilistic fashion and plays an important role for the success of the inference. Recently, Bayesian inverse problems were solved using generative models as highly informative priors. Generative models are a popular tool in machine learning to generate data whose properties closely resemble those of a given database. Typically, the generated distribution of data is embedded in a low-dimensional manifold. For the inverse problem, a generative model is trained on a database that reflects the properties of the sought solution, such as typical structures of the tissue in the human brain in magnetic resonance imaging. The inference is carried out in the low-dimensional manifold determined by the generative model that strongly reduces the dimensionality of the inverse problem. However, this procedure produces a posterior that does not admit a Lebesgue density in the actual variables and the accuracy attained can strongly depend on the quality of the generative model. For linear Gaussian models, we explore an alternative Bayesian inference based on probabilistic generative models; this inference is carried out in the original high-dimensional space. A Laplace approximation is employed to analytically derive the prior probability density function required, which is induced by the generative model. Properties of the resulting inference are investigated. Specifically, we show that derived Bayes estimates are consistent, in contrast to the approach in which the low-dimensional manifold of the generative model is employed. The MNIST data set is used to design numerical experiments that confirm our theoretical findings. It is shown that the approach proposed can be advantageous when the information contained in the data is high and a simple heuristic is considered for the detection of this case. Finally, the pros and cons of both approaches are discussed.

Objective: To examine the feasibility of human cardiac MR (CMR) at 14.0 T using high-density radiofrequency (RF) dipole transceiver arrays in conjunction with static and dynamic parallel transmission (pTx). Materials and methods: RF arrays comprised of self-grounded bow-tie (SGBT) antennas, bow-tie (BT) antennas, or fractionated dipole (FD) antennas were used in this simulation study. Static and dynamic pTx were applied to enhance transmission field (B1+) uniformity and efficiency in the heart of the human voxel model. B1+ distribution and maximum specific absorption rate averaged over 10 g tissue (SAR10g) were examined at 7.0 T and 14.0 T. Results: At 14.0 T static pTx revealed a minimum B1+ROI efficiency of 0.91 μT/√kW (SGBT), 0.73 μT/√kW (BT), and 0.56 μT/√kW (FD) and maximum SAR10g of 4.24 W/kg, 1.45 W/kg, and 2.04 W/kg. Dynamic pTx with 8 kT points indicate a balance between B1+ROI homogeneity (coefficient of variation < 14%) and efficiency (minimum B1+ROI > 1.11 µT/√kW) at 14.0 T with a maximum SAR10g < 5.25 W/kg. Discussion: MRI of the human heart at 14.0 T is feasible from an electrodynamic and theoretical standpoint, provided that multi-channel high-density antennas are arranged accordingly. These findings provide a technical foundation for further explorations into CMR at 14.0 T.

In 2020, the ICRU released a new report which includes the re-definition of the operational quantities used in radiation protection and new conversion coefficients from physical quantities to operational radiation protection quantities. An assessment of the ambient and personal dose conversion coefficients for the reference neutron fields of radionuclide sources at PTB is necessary based on these new definitions. In this work, a numerical estimation of the conversion coefficients of moderated and unmoderated 252Cf and 241Am-Be neutron sources based on ICRU57 and ICRU95 reports and using spectrum data available in the ISO 8529-1 standard and at PTB are discussed. Two numerical approaches are used for this estimation to ensure the reliability of the calculated values: a direct calculation using MCNP6, and cubic interpolation of conversion coefficients datasets written in Python. The results show large differences between the spectrum-averaged operational quantities for the current and new conversion coefficients of up to 23%. The choice of spectrum data affects conversion coefficient values by 6-8%.

Intramolecular or position-specific carbon isotope analysis of propane (13CH3-12CH2-12CH3 and 12CH3-13CH2-12CH3) provides unique insights into its formation mechanism and temperature history. The unambiguous detection of such carbon isotopic distributions with currently established methods is challenging due to the complexity of the technique and the tedious sample preparation. We present a direct and nondestructive analytical technique to quantify the two singly substituted, terminal (13Ct) and central (13Cc), propane isotopomers, based on quantum cascade laser absorption spectroscopy. The required spectral information on the propane isotopomers was first obtained using a high-resolution Fourier-transform infrared (FTIR) spectrometer and then used to select suitable mid-infrared regions with minimal spectral interference to obtain the optimum sensitivity and selectivity. We then measured high-resolution spectra around 1384 cm-1 of both singly substituted isotopomers by mid-IR quantum cascade laser absorption spectroscopy using a Stirling-cooled segmented circular multipass cell (SC-MPC). The spectra of the pure propane isotopomers were acquired at both 300 and 155 K and served as spectral templates to quantify samples with different levels of 13C at the central (c) and terminal (t) positions. A prerequisite for the precision using this reference template fitting method is a good match of amount fraction and pressure between the sample and templates. For samples at natural abundance, we achieved a precision of 0.33 ‰ for δ13Ct and 0.73 ‰ for δ13Cc values within 100 s integration time. This is the first demonstration of site-specific high-precision measurements of isotopically substituted non-methane hydrocarbons using laser absorption spectroscopy. The versatility of this analytical approach may open up new opportunities for the study of isotopic distribution of other organic compounds.

In this Perspective, we summarize the status of technological development for large-area and low-noise substrate-transferred GaAs/AlGaAs (AlGaAs) crystalline coatings for interferometric gravitational-wave (GW) detectors. These topics were originally presented as part of an AlGaAs Workshop held at American University, Washington, DC, from 15 August to 17 August 2022, bringing together members of the GW community from the laser interferometer gravitational-wave observatory (LIGO), Virgo, and KAGRA collaborations, along with scientists from the precision optical metrology community, and industry partners with extensive expertise in the manufacturing of said coatings. AlGaAs-based crystalline coatings present the possibility of GW observatories having significantly greater range than current systems employing ion-beam sputtered mirrors. Given the low thermal noise of AlGaAs at room temperature, GW detectors could realize these significant sensitivity gains while potentially avoiding cryogenic operation. However, the development of large-area AlGaAs coatings presents unique challenges. Herein, we describe recent research and development efforts relevant to crystalline coatings, covering characterization efforts on novel noise processes as well as optical metrology on large-area (∼10 cm diameter) mirrors. We further explore options to expand the maximum coating diameter to 20 cm and beyond, forging a path to produce low-noise mirrors amenable to future GW detector upgrades, while noting the unique requirements and prospective experimental testbeds for these semiconductor-based coatings.

Ammonia (NH3) is a promising fuel, because it is carbon-free and easier to store and transport than hydrogen (H2). However, an ignition enhancer such as H2 might be needed for technical applications, because of the rather poor ignition properties of NH3. The combustion of pure NH3 and H2 has been explored widely. However, for mixtures of both gases, mostly only global parameters such as ignition delay times or flame speeds were reported. Studies with extensive experimental species profiles are scarce. Therefore, we experimentally investigated the interactions in the oxidation of different NH3/H2 mixtures in the temperature range of 750-1173 K at 0.97 bar in a plug-flow reactor (PFR), as well as in the temperature range of 1615-2358 K with an average pressure of 3.16 bar in a shock tube. In the PFR, temperature-dependent mole fraction profiles of the main species were obtained via electron ionization molecular-beam mass spectrometry (EI-MBMS). Additionally, for the first time, tunable diode laser absorption spectroscopy (TDLAS) with a scanned-wavelength method was adapted to the PFR for the quantification of nitric oxide (NO). In the shock tube, time-resolved NO profiles were also measured by TDLAS using a fixed-wavelength approach. The experimental results both in PFR and shock tube reveal the reactivity enhancement by H2 on ammonia oxidation. The extensive sets of results were compared with predictions by four NH3-related reaction mechanisms. None of the mechanisms can well predict all experimental results, but the Stagni et al. [React. Chem. Eng. 2020, 5, 696-711] and Zhu et al. [Combust. Flame 2022, 246, 115389] mechanisms perform best for the PFR and shock tube conditions, respectively. Exploratory kinetic analysis was conducted to identify the effect of H2 addition on ammonia oxidation and NO formation, as well as sensitive reactions in different temperature regimes. The results presented in this study can provide valuable information for further model development and highlight relevant properties of H2-assisted NH3 combustion.

The methyl substitution along and among the polymer chains of methyl cellulose (MC) is commonly analyzed by ESI-MS after perdeuteromethylation of the free-OH groups and partial hydrolysis to cello-oligosaccharides (COS). This method requires a correct quantification of the molar ratios of the constituents belonging to a particular degree of polymerization (DP). However, isotopic effects are most pronounced for H/D since their mass difference is 100%. Therefore, we investigated whether more precise and accurate results could be obtained for the methyl distribution of MC by MS of ¹³ CH 3 instead of CD 3 -etherified O -Me-COS. Internal isotope labeling with ¹³ CH 3 makes the COS of each DP chemically and physically much more similar, reducing mass fractionation effects, but at the same time requires more complex isotopic correction for evaluation. Results from syringe pump infusion ESI-TOF-MS with ¹³ CH 3 and CD 3 as isotope label were equal. However, in the case of LC-MS with a gradient system, ¹³ CH 3 was superior to CD 3 . In the case of CD 3 , the occurrence of a partial separation of the isotopologs of a particular DP resulted in slight distortion of the methyl distribution since the signal response is significantly dependent on the solvent composition. Isocratic LC levels this problem, but one particular eluent-composition is not sufficient for a series of oligosaccharides with increasing DP due to peak broadening. In summary, ¹³ CH 3 is more robust to determine the methyl distribution of MCs. Both syringe pump and gradient-LC-MS measurements are possible, and the more complex isotope correction is not a disadvantage. Graphical abstract

Exploiting the outstanding performance of optical atomic clocks for improved timekeeping, relativistic geodesy, and for fundamental physics beyond the standard model demands comparing distant state-of-the-art optical clocks. Interferometric optical fiber links have been demonstrated as eminent method for such frequency comparisons over distances up to thousands of kilometers. However, the optical fiber attenuation mandates signal amplification. Fiber Brillouin amplification has been proven as an efficient technique for the coherent frequency transfer. Demonstrated FBAs have been designed based on costly narrow-linewidth pump lasers and analog pump-to-signal phase locking schemes. Furthermore, the high pump power requirement of these FBAs hinders the integration of FBA-based frequency dissemination on fiber connections shared telecommunication signals in the C-band. In this paper, we propose and experimentally demonstrate a novel FBA module (FBAM) employing cost-effective distributed feedback (DFB) pump lasers assisted by a digital phase locking scheme based on field programmable gated array. The new FBAM is compact, cost-effective, and directly applicable to different bands, which opens up new opportunities to establish a frequency metrology infrastructure within existing telecommunication fibers. The small-footprint of the DFB-FBAM allows for frequent amplification stages with lower pump power to reach continental scale optical metrology links with optimized signal-to-noise ratio. We characterized the DFB-FBAM's frequency transfer uncertainty using a two-way layout over an in-lab 100 km long optical fiber link and reach a fractional frequency instability of 9.3×10 ⁻²² at 10 ks integration time. The DFB-FBAM characterizations show uncertainty contributions of (-2.1{plus minus}3.3)×10 ⁻²² and below for averaging times >100 ks.

Abstract The prototype of a digital machine-readable and machine-actionable calibration certificate (DCC) Digital Calibration Certificate) was already published in 2017 in the PTB-Mitteilungen [S. Hackel, F. Härtig, J. Hornig, und T. Wiedenhöfer, The Digital Calibration Certificate, PTB-Mitteilungen, vol. 127, Bd. 4, S. 7, 2017 [Online]. Verfügbar unter: https://oar.ptb.de/resources/show/10.7795/310.20170403 [Zugegriffen: Jul. 2, 2019].]. The idea is based on the European research project SmartCom (17IND02) [,,Welcome to SmartCom”, 2021 [Online]. Verfügbar unter: https://www.ptb.de/empir2018/smartcom/project/ [Zugegriffen: Februar. 15, 2023]; EURAMET-European Association of National Metrology Institutes, ,,Communication and validation of smart data in IoT-networks”, EURAMET, 2023 [Online]. Verfügbar unter: https://www.euramet.org/research-innovation/search-research-projects/details/project/communication-and-validation-of-smart-data-in-iot- networks [Zugegriffen: Februar. 15, 2023.] by PTB in 2016 and has been an integral part of PTB’s digitization concept since 2017. The DCC offers the worldwide unambiguous identification and storage of the properties of any calibration object and thus does more than just prove metrological traceability. The prototype DCC developed by PTB is based on the XML exchange format and is therefore machine-readable and machine-actionable and future-proof. In addition, all requirements of DIN ISO 17025 [DIN EN ISO/IEC 17025:2018-03, Allgemeine Anforderungen an die Kompetenz von Prüf- und Kalibrierlaboratorien (ISO/IEC_17025:2017); Deutsche und Englische Fassung EN_ISO/IEC_17025:2017, Beuth Verlag GmbH [Online]. Verfügbar unter: https://www.beuth.de/de/-/-/278030106 [Zugegriffen: Sept. 24, 2021].] are considered. For the representation of measured values, a data model based on the SI Units was designed in the SmartCom project and a prototypical XML data exchange format was developed. This format, known as DSI (digital SI [D. Hutzschenreuter u.a., SmartCom Digital-SI (D-SI) XML Exchange Format for Metrological Data Version 2.0.0, 2021 [Online]. Verfügbar unter: https://zenodo.org/record/4709001 [Zugegriffen: Mär. 10, 2022].]) forms the basis for the specification of measurement data in the DCC, among other things. In addition, it can be used for any other exchange of metrological information. All information, including numerical calibration curves, can be transferred directly and automatically from the DCC to digital processes. Cryptographic signatures as a security method ensure the integrity and authenticity of a DCC. All concepts have been discussed, coordinated, and further developed with partners in Europe and the world.

The low reactivity of ammonia (NH3) is the main barrier to applying neat NH3 as fuel in technical applications, such as internal combustion engines and gas turbines. Introducing combustion promoters as additives in NH3-based fuel can be a feasible solution. In this work, the oxidation of ammonia by adding different reactivity promoters, i.e., hydrogen (H2), methane (CH4), and methanol (CH3OH), was investigated in a jet-stirred reactor (JSR) at temperatures between 700 and 1200 K and at a pressure of 1 bar. The effect of ozone (O3) was also studied, starting from an extremely low temperature (450 K). Species mole fraction profiles as a function of the temperature were measured by molecular-beam mass spectrometry (MBMS). With the help of the promoters, NH3 consumption can be triggered at lower temperatures than in the neat NH3 case. CH3OH has the most prominent effect on enhancing the reactivity, followed by H2 and CH4. Furthermore, two-stage NH3 consumption was observed in NH3/CH3OH blends, whereas no such phenomenon was found by adding H2 or CH4. The mechanism constructed in this work can reasonably reproduce the promoting effect of the additives on NH3 oxidation. The cyanide chemistry is validated by the measurement of HCN and HNCO. The reaction CH2O + NH2 ⇄ HCO + NH3 is responsible for the underestimation of CH2O in NH3/CH4 fuel blends. The discrepancies observed in the modeling of NH3 fuel blends are mainly due to the deviations in the neat NH3 case. The total rate coefficient and the branching ratio of NH2 + HO2 are still controversial. The high branching fraction of the chain-propagating channel NH2 + HO2 ⇄ H2NO + OH improves the model performance under low-pressure JSR conditions for neat NH3 but overestimates the reactivity for NH3 fuel blends. Based on this mechanism, the reaction pathway and rate of production analyses were conducted. The HONO-related reaction routine was found to be activated uniquely by adding CH3OH, which enhances the reactivity most significantly. It was observed from the experiment that adding ozone to the oxidant can effectively initiate NH3 consumption at temperatures below 450 K but unexpectedly inhibit the NH3 consumption at temperatures higher than 900 K. The preliminary mechanism reveals that adding the elementary reactions between NH3-related species and O3 is effective for improving the model performance, but their rate coefficients have to be refined.

The formation of surface relief gratings (SRGs) in thin azo-polymeric films is investigated using atomistic molecular dynamics simulations and compared to experimental results for the specific case of poly-disperse-orange3-methyl-methacrylate. For this purpose, the film is illuminated with a light pattern of alternating bright and dark stripes in both cases. The simulations use a molecular mechanics switching potential to explicitly describe the photoisomerization dynamics between the E and Z isomers of the azo-units and take into account the orientation of the transition dipole moment with respect to the light polarisation. Local heating and elevation of the illuminated regions with subsequent movement of molecules into the neighboring dark regions is observed. This leads to the formation of valleys in the bright areas after re-cooling and is independent of the polarisation direction. To verify these observations experimentally, the azopolymer film is illuminated with bright stripes of varying width using a spatial light modulator. Atomic force microscopy images confirm that the elevated areas correspond to the previously dark areas. In the experiment, the polarisation of the incident light makes only a small difference, since tiny grain-like structures form in the valleys only when the polarisation is parallel to the stripes.

We present a theoretical study of nondipole excitation of a single trapped atom by twisted light. Special emphasis is placed on effects that arise from the interplay between internal (electronic) and vibrational (center-of-mass) degrees of freedom of an atom. In order to provide a fully quantum mechanical understanding of the excitation, we used the density-matrix approach based on the Liouville–von Neumann equation. The developed theory has been applied to the particular case of the 4sS1/22→3dD5/22 electric quadrupole (E2) transition in a Ca+40 ion induced by Laguerre-Gaussian modes. It was found that the Rabi oscillations can show unconventional anharmonic behavior that is attributed to the strong coupling between vibrational levels of the trap. This effect is accompanied by the transfer of angular momentum to the center-of-mass motion and becomes most pronounced when the Rabi frequency is comparable to the trapping frequency.

Objective.T1 mapping of the liver is time consuming and can be challenging due to respiratory motion. Here we present a prospective slice tracking approach, which utilizes an external ultra-wide band radar signal and allows for efficient T1 mapping during free-breathing.Approach.The fast radar signal is calibrated to an MR-based motion signal to create a motion model. This motion model provides motion estimates, which are used to carry out slice tracking for any subsequent clinical scan. This approach was evaluated in simulations, phantom experiments and in-vivo scans.Main Results.Radar-based slice tracking was implemented on an MR system with a total latency of 77 ms. Moving phantom experiments showed accurate motion prediction with an error of 0.12 mm in anterior-posterior and 0.81 mm in head-feet direction. The model error remained stable for up to two hours. In vivo experiments showed visible image improvement with a motion model error three times smaller than with a respiratory bellow. For T1 mapping during free-breathing the proposed approach provided similar results compared to reference T1 mapping during a breathhold.Significance.The proposed radar-based approach achieves accurate slice tracking and enables efficient T1 mapping of the liver during free-breathing. This motion correction approach is independent from scanning parameters and could also be used for applications like MR guided radiotherapy or MR Elastography.