Martin Möddel

Magneto-mechanical resonators (MMRs) represent a recently proposed type of passive sensor that enables the estimation of its pose as well as sensing other parameters in its environment. The working principle of MMRs entails an excitation of the sensors by oscillating magnetic fields, followed by a readout process facilitated by inductive receiver coils. The sensing technology relies on real-time parameter estimation. This encompasses the solution of a nonlinear inverse problem, with the induced signals and a suitable forward model as inputs. The aim of this paper is twofold: first, to introduce a reference model and simplified models for the MMR dynamics and inductive readout, and second, to provide robust and real-time capable methods to estimate the model parameters. The effectiveness of the presented methods is evaluated in terms of their real-time potential, precision, and accuracy. All presented methods demonstrate the capacity to estimate the measured signal, with the simplified methods reducing the corresponding parameter estimation time by up to two orders of magnitude at the expense of less than 4% deviation for large maximum deflection angles.

Objective. High-resolution peripheral quantitative computed tomography enables the assessment of bone mineral density and three-dimensional microstructure of peripheral limbs. Due to its long scanning time, it is especially susceptible to patient induced motion artifacts. The goal of this study is to compensate for such artifacts without requiring excessive computation time, while still avoiding the hallucination of erroneous structures. Approach. This work proposes a machine learning-based approach for the rapid estimation of rigid motion parameters directly from raw projection data. The model is trained on patient scans with motion simulated as a single, instantaneous jump. We demonstrate the performance and generalization of the method on simulated and experimentally acquired data, benchmarking our results against two recent baselines. Main results. The proposed method greatly reduced the amount of motion artifacts in both simulated and experimental data. On the simulated test data, the median structural similarity index measure (SSIM) for the reconstruction results could be improved from 0.62 to 0.88. Similarly, the SSIM for the experimental data improved from 0.58–0.71 to 0.74–0.78. At the tibia site that was used for training, motion artifacts were successfully reduced to such an extent that 92 % of previously inaccessible scans could be reconsidered for clinical evaluation. For the unseen radius site, a clinical recovery rate of 56 % could be achieved. Predicting the motion parameters for a measurement required less than 200 ms on consumer hardware. Significance. The proposed approach has the potential to enable the reuse of scans that were previously discarded for clinical evaluation while preventing generative hallucinations by design. Consequently, eliminating the need for repeated scans would reduce patient radiation exposure and clinical workflow overhead.

Accurate and efficient volumetric magnetic field measurements are essential for a wide range of applications. Conventional methods are often limited in terms of measurement speed and applicability, or suffer from scaling problems at larger volumes. This work presents a proof-of-concept field camera designed to measure magnetic fields within a spherical volume at a frame rate of 10 Hz. The camera features an array of 3D Hall magnetometers positioned according to a spherical t-design, allowing simultaneous magnetic field data acquisition from the surface of the sphere. The approach enables the efficient representation of all three components of the magnetic field inside the sphere using a sixth-degree polynomial, significantly reducing measurement time compared to sequential methods. This work details the design, calibration, and measurement methods of the field camera. To evaluate its performance, we compare it to a sequential single-sensor measurement by examining a magnetic gradient field. The obtained measurement uncertainties of approx. 1% demonstrate the feasibility of the approach and its potential applicability to a variety of future applications.

The precise derivation of physical quantities like temperature or pressure at arbitrary locations is useful in numerous contexts, e.g. medical procedures or industrial process engineering. The novel sensor technology of magneto-mechanical resonators (MMR), based on the interaction of a rotor and stator permanent magnet, allows for the combined tracking of the sensor position and orientation while simultaneously sensing an external measurand. Thereby, the quantity is coupled to the torsional oscillation frequency, e.g. by varying the magnet distance. In this paper, we analyze the (deflection angle-independent) natural frequency dependency of MMR sensors on the rotor-stator distance, and evaluate the performance of theoretical models. The three presented sensors incorporate magnets of spherical and/or cylindrical geometry and can be operated at adjustable frequencies within the range of 61.9−307.3 Hz. Our proposed method to obtain the natural frequency demonstrates notable robustness to variations in the initial deflection amplitudes and quality factors resulting in statistical errors on the mean smaller than 0.05%. We find that the distance-frequency relationship is well described by an adapted dipole model accounting for material and manufacturing uncertainties. Their combined effect can be compensated by an adjustment of a single parameter which drives the median model deviation generally below 0.2%. Our depicted methods and results are important for the design and calibration process of new sensor types utilizing the MMR technique.

A custom-developed magneto-mechanical resonator (MMR) for wireless pressure measurement is investigated for potential applications in process engineering. The MMR sensor utilises changes in the resonance frequency caused by pressure on a flexible 3D printed membrane. The thickness of the printed membrane plays a crucial role in determining the performance and sensitivity of MMRs and can be tailored to meet the requirements of specific applications. The study includes static and dynamic measurements to determine the pressure sensitivity and temporal resolution of the sensor. The results show a minimum sensitivity of 0.06  Hz mbar − 1 and are in agreement with theoretical calculations and measurements. The maximum sensor readout frequency is 2 Hz in this study. Additionally, the temperature dependence of the sensor is investigated, revealing a significant dependence of the resonance frequency on temperature. The developed MMR offers a promising and versatile method for precise pressure measurements in process engineering environments.

Spherical harmonic expansions are well-established tools for estimating magnetic fields from surface measurements and are widely used in applications such as tomographic imaging, geomagnetism, and biomagnetism. Although the mathematical foundations of these expansions are well understood, the impact of real-world imperfections, on the uncertainty of the field model has received little attention. In this work, we present a systematic uncertainty propagation analysis for a magnetic field camera that estimates the field from surface measurements using a spherical array of Hall magnetometers arranged in a spherical t-design. A Monte Carlo-based approach is employed to quantify how sensor-related uncertainties, such as calibration errors and positioning inaccuracies, affect the spatial distribution of the estimated field's uncertainty. The results offer insights into the robustness of spherical harmonic methods and help identify the dominant sources of uncertainty in practical implementations.

Given the pivotal role of magnetic fields in modern medicine, there is an increasing necessity for a precise characterization of their strength and orientation at high spatial and temporal resolution. As source-free magnetic fields present in tomographic imaging can be described by harmonic polynomials, they can be efficiently represented using spherical harmonic expansions, which allows for measurement at a small set of points on a sphere surrounding the field of view. However, the majority of closed-bore systems possess a cylindrical field of view, making a sphere an inadequate choice for coverage. Ellipsoids represent a superior geometrical choice, and the theory of ellipsoidal harmonic expansions can be applied to magnetic fields in an analogous manner. Despite the mathematical principles underpinning ellipsoidal harmonics being well-established, their utilization in practical applications remains relatively limited. In this study, we present an effective and flexible approach to measuring and representing magnetic fields present in tomographic imaging, which draws upon the theory of ellipsoidal harmonic expansions.

Precise knowledge of magnetic fields is crucial in many medical imaging applications such as magnetic resonance imaging (MRI) or magnetic particle imaging (MPI), as they form the foundation of these imaging systems. Mathematical methods are essential for efficiently analysing the magnetic fields in the entire field-of-view. In this work, we propose a compact and unique representation of the magnetic fields using real solid spherical harmonic expansions, which can be obtained by spherical t-designs. To ensure a unique representation, the expansion point is shifted at the level of the expansion coefficients. As an application scenario, these methods are used to acquire and analyse the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as the unique expansion point.

The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the intensities of a complex wave-field are measured by the detector and the phase information is lost. For the reconstruction of sharp images from holograms in a near-field experimental setting, it is crucial to solve the autofocus problem, i.e., to precisely estimate the Fresnel number of the forward model. Otherwise, blurred out-of focus images that also can contain artifacts are the result. In general, a simple distance measurement at the experiment is not sufficiently accurate, thus the fine-tuning of the Fresnel number has to be done prior to the actual reconstructions. This can be done manually or automatically by an estimation algorithm. To automatize the process, as needed, e.g., for in-situ/operando experiments, different focus criteria have been widely studied in literature but are subjected to certain restrictions. The methods often rely on image analysis of the reconstructed image, making them sensitive to image noise and also neglecting algorithmic properties of the applied phase retrieval. In this paper, we propose a novel criterion, based on a model-matching approach, which improves autofocusing by also taking the underlying reconstruction algorithm, the forward model and the measured hologram into account. We derive a common autofocusing framework, based on a recent phase-retrieval approach and a downhill-simplex method for the automatic optimization of the Fresnel number. We further demonstrate the robustness of the framework on different data sets obtained at the nano imaging endstation of P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon.