Electrostatic sensor modeling for torque measurements

Torque load measurements play an important part in various engineering applications, as for automotive industry, in which the drive torque of a motor has to be determined. A widely used measuring method are strain gauges. A thin flexible foil, which supports a metallic pattern, is glued to the surface of the object the torque is being applied to. In case of a deformation due to the torque load, the change in the electrical resistance is measured. With the combination of constitutive equations the applied torque load is determined by the change of electrical resistance. The creep of the glue and the foil material, together with the temperature and humidity dependence, may become an obstacle for some applications Kapralov and Fesenko(1984). Thus, there have been optical and magnetical, as well as capacitive sensors introduced ). This paper discusses the general idea behind an electrostatic capacitive sensor based on a simple draft of an exemplary measurement setup. For better understanding an own electrostatical, geometrical and mechanical model of this setup has been developed

Comparing Apples with Apples: Robust Detection Limits for Exoplanet High-Contrast Imaging in the Presence of non-Gaussian Noise

Over the past decade, hundreds of nights have been spent on the worlds largest telescopes to search for and directly detect new exoplanets using high-contrast imaging (HCI). Thereby, two scientific goals are of central interest: First, to study the characteristics of the underlying planet population and distinguish between different planet formation and evolution theories. Second, to find and characterize planets in our immediate Solar neighborhood. Both goals heavily rely on the metric used to quantify planet detections and non-detections. Current standards often rely on several explicit or implicit assumptions about the noise. For example, it is often assumed that the residual noise after data post-processing is Gaussian. While being an inseparable part of the metric, these assumptions are rarely verified. This is problematic as any violation of these assumptions can lead to systematic biases. This makes it hard, if not impossible, to compare results across datasets or instruments with different noise characteristics. We revisit the fundamental question of how to quantify detection limits in HCI. We focus our analysis on the error budget resulting from violated assumptions. To this end, we propose a new metric based on bootstrapping that generalizes current standards to non-Gaussian noise. We apply our method to archival HCI data from the NACO-VLT instrument and derive detection limits for different types of noise. Our analysis shows that current standards tend to give detection limit that are about one magnitude too optimistic in the speckle-dominated regime. That is, HCI surveys may have excluded planets that can still exist.Comment: After first iteration with the referee, resubmitted to AJ. Comments welcome

CROCODILE \\ Incorporating medium-resolution spectroscopy of close-in directly imaged exoplanets into atmospheric retrievals via cross-correlation

The investigation of the atmospheres of closely separated, directly imaged gas giant exoplanets is challenging due to the presence of stellar speckles that pollute their spectrum. To remedy this, the analysis of medium- to high-resolution spectroscopic data via cross-correlation with spectral templates (cross-correlation spectroscopy) is emerging as a leading technique. We aim to define a robust Bayesian framework combining, for the first time, three widespread direct-imaging techniques, namely photometry, low-resolution spectroscopy, and medium-resolution cross-correlation spectroscopy in order to derive the atmospheric properties of close-in directly imaged exoplanets. Our framework CROCODILE (cross-correlation retrievals of directly imaged self-luminous exoplanets) naturally combines the three techniques by adopting adequate likelihood functions. To validate our routine, we simulated observations of gas giants similar to the well-studied $\beta$~Pictoris~b planet and we explored the parameter space of their atmospheres to search for potential biases. We obtain more accurate measurements of atmospheric properties when combining photometry, low- and medium-resolution spectroscopy into atmospheric retrievals than when using the techniques separately as is usually done in the literature. We find that medium-resolution ($R \approx 4000$) K-band cross-correlation spectroscopy alone is not suitable to constrain the atmospheric properties of our synthetic datasets; however, this problem disappears when simultaneously fitting photometry and low-resolution ($R \approx 60$) spectroscopy between the Y and M bands. Our framework allows the atmospheric characterisation of directly imaged exoplanets using the high-quality spectral data that will be provided by the new generation of instruments such as VLT/ERIS, JWST/MIRI, and ELT/METIS

The expected performance of nulling at the VLTI down to 5 mas

While VLTI offers the recombination of four 8-m telescopes with baselines of more than 100m, it has never hosted a dedicated high-contrast nulling beam-combiner. The SCIFY project aims to design, build and commission Hi- 5, the first nulling beam-combiner of the VLTI, optimized for the detection and characterization of young giant exoplanets near the snow line, with spectroscopy up to R=2000 in the L’ band. It will make use of advanced four-beam nulling combination schemes, like double-Bracewell and kernel-nulling implemented in a single-mode photonic device to produce differential nulled outputs with self-calibrating properties. In the wavelength range of interest, both instrumental errors and background noise are significant. In order to estimate the practical performance of these different configurations in the presence of instrumental errors and further optimize the instrumental design, we have developed SCIFYsim. SCIFYsim is an end-to-end simulator geared towards single- mode beam combiners with of a wide variety of instrumental errors, like optical path difference residuals from fringe tracking, wavefront error at the injection, longitudinal dispersion, chromaticity of the combiner chip, and more. In order to evaluate the performance of the combined spectral channels, we use statistical tests based on likelihood ratios, and account for the covariance in the data. In this paper, we present the expected performance of Hi-5 with a few examples and discuss the main technical limitations to reach the contrast required to image young giant exoplanets.SCIF

Asgard/NOTT: L-band nulling interferometry at the VLTI I. Simulating the expected high-contrast performance

Context: NOTT (formerly Hi-5) is a new high-contrast L' band (3.5-4.0 \textmu m) beam combiner for the VLTI with the ambitious goal to be sensitive to young giant exoplanets down to 5 mas separation around nearby stars. The performance of nulling interferometers in these wavelengths is affected both by fundamental noise from the background and by the contributions of instrumental noises. This motivates the development of end-to-end simulations to optimize these instruments. Aims: To enable the performance evaluation and inform the design of such instruments on the current and future infrastructures, taking into account the different sources of noise, and their correlation. Methods: SCIFYsim is an end-to-end simulator for single mode filtered beam combiners, with an emphasis on nulling interferometers. It is used to compute a covariance matrix of the errors. Statistical detection tests based on likelihood ratios are then used to compute compound detection limits for the instrument. Results: With the current assumptions on the performance of the wavefront correction systems, the errors are dominated by correlated instrumental errors down to stars of magnitude 6-7 in the L band, beyond which thermal background from the telescopes and relay system becomes dominant. Conclusions: SCIFYsim is suited to anticipate some of the challenges of design, tuning, operation and signal processing for integrated optics beam combiners. The detection limits found for this early version of NOTT simulation with the unit telescopes are compatible with detections at contrasts up to $10^5$ in the L band at separations of 5 to 80 mas around bright stars

Large Interferometer For Exoplanets (LIFE): II. Signal simulation, signal extraction, and fundamental exoplanet parameters from single-epoch observations

peer reviewedContext. The Large Interferometer For Exoplanets (LIFE) initiative is developing the science and a technology road map for an ambitious space mission featuring a space-based mid-infrared (MIR) nulling interferometer in order to detect the thermal emission of hundreds of exoplanets and characterize their atmospheres. Aims. In order to quantify the science potential of such a mission, in particular in the context of technical trade-offs, an instrument simulator is required. In addition, signal extraction algorithms are needed to verify that exoplanet properties (e.g., angular separation and spectral flux) contained in simulated exoplanet data sets can be accurately retrieved. Methods. We present LIFEsim, a software tool developed for simulating observations of exoplanetary systems with an MIR space-based nulling interferometer. It includes astrophysical noise sources (i.e., stellar leakage and thermal emission from local zodiacal and exozodiacal dust) and offers the flexibility to include instrumental noise terms in the future. Here, we provide some first quantitative limits on instrumental effects that would allow the measurements to remain in the fundamental noise limited regime. We demonstrate updated signal extraction approaches to validating signal-to-noise ratio (S/N) estimates from the simulator. Monte Carlo simulations are used to generate a mock survey of nearby terrestrial exoplanets and determine to which accuracy fundamental planet properties can be retrieved. Results. LIFEsim provides an accessible way to predict the expected S/N of future observations as a function of various key instrument and target parameters. The S/Ns of the extracted spectra are photon noise dominated, as expected from our current simulations. Signals from multi-planet systems can be reliably extracted. From single-epoch observations in our mock survey of small (R < 1.5 REarth) planets orbiting within the habitable zones of their stars, we find that typical uncertainties in the estimated effective temperature of the exoplanets are ≲10%, for the exoplanet radius ≲20%, and for the separation from the host star ≲2%. Signal-to-noise-ratio values obtained in the signal extraction process deviate by less than 10% from purely photon-counting statistics-based S/Ns. Conclusions. LIFEsim has been sufficiently well validated so that it can be shared with a broader community interested in quantifying various exoplanet science cases that a future space-based MIR nulling interferometer could address. Reliable signal extraction algorithms exist, and our results underline the power of the MIR wavelength range for deriving fundamental exoplanet properties from single-epoch observations.Large Interferometer For Exoplanets (LIFE

Monte-Carlo simulations of defect-rich tilings of polydisperse squares

Two-dimensional systems have long been a subject of research, as they exhibit interesting behavior not found in three dimensions. The thesis presented here examines two-dimensional, hard core potential systems of squares. These squares are anisotropic and exclusively driven by entropic forces. Their equilibrium behavior is accessed through Monte-Carlo simulations. The different thermodynamic phases of this system are analyzed and the thesis reports an intermediate phase between the solid and the fluid called the tetratic phase [1]. Defects in the system are evaluated. It is found that the point defect density increases with the packing fraction to values of up to 1.4%. Finally, the dispersion relations of the lattice vibrations are calculated via an elasticity theory for real crystals [2]. Most interestingly the frequency of the angular vibrations in the solid phase does not tend to zero in the hydrodynamic limit. In the tetratic phase however, the same branch tends to zero in this limit case.publishe

Large Interferometer For Exoplanets (LIFE): VI. Detecting rocky exoplanets in the habitable zones of Sun-like stars

Context. Identifying and characterizing habitable and potentially inhabited worlds is one of the main goals of future exoplanet directimaging missions. The number of planets within the habitable zone (HZ) that are accessible to such missions is a key metric to quantify their scientific potential, and it can drive the mission and instrument design. Aims. While previous studies have shown a strong preference for a future mid-infrared nulling interferometer space mission, such as LIFE, to detect planets within the HZ around M dwarfs, we here focus on a more conservative approach toward the concept of habitability and present yield estimates for two stellar samples consisting of nearby (d < 20 pc) Sun-like stars (4800 K = Teff= 6300 K) and nearby FGK-type stars (3940 K = Teff= 7220 K) accessible to such a mission. Methods. Our yield estimates are based on recently derived occurrence rates of rocky planets from the Kepler mission and our LIFE exoplanet observation simulation tool LIFEsim, which includes all main astrophysical noise sources, but no instrumental noise sources as yet. In a Monte Carlo-like approach, we marginalized over 1000 synthetic planet populations simulated around single and wide binary stars from our two samples. We use new occurrence rates for rocky planets that cover the entire HZ around FGK-type stars, marginalize over the uncertainties in the underlying occurrence rate model, present a parameter study investigating the dependence of the planet yield on different instrumental and astrophysical parameters, and estimate the number of detectable HZ planets that might indeed harbor liquid surface water. Results. Depending on a pessimistic or optimistic extrapolation of the Kepler results, we find that during a 2.5-yr search phase, LIFE could detect between ∼ 1016(average) or ∼ 5 34 (including 1s uncertainties) rocky planets (0.5 R = Rp = 1.5 R) within the optimistic HZ of Sun-like stars and between ∼4 6 (average) or ∼1 13 (including 1s uncertainties) exo-Earth candidates (EECs) assuming four collector spacecraft equipped with 2 m mirrors and a conservative instrument throughput of 5%. The error bars are dominated by uncertainties in the underlying planet occurrence rates and the extrapolation of the Kepler results. With D = 3.5 m or 1 m mirrors, the yield Y changes strongly, following approximately Y D3/2. With the larger sample of FGK-type stars, the yield increases to ∼16 22 (average) rocky planets within the optimistic HZ and ∼5 8 (average) EECs, which corresponds to ∼50% of the yield predicted for M dwarfs in LIFE paper I. Furthermore, we find that in addition to the mirror diameter, the yield depends strongly on the total throughput, but only weakly on the exozodiacal dust level and the accessible wavelength range of the mission. Conclusions. When the focus lies entirely on Sun-like stars, larger mirrors (∼3 m with 5% total throughput) or a better total throughput (∼20% with 2 m mirrors) are required to detect a statistically relevant sample of ∼30 rocky planets within the optimistic HZ. When the scope is extended to FGK-type stars, and especially when M dwarfs are included, a significant increase in the number of detectable rocky HZ planets is obtained, which relaxes the requirements on mirror size and total throughput. Observational insight into the habitability of planets orbiting M dwarfs, for example, from the James Webb Space Telescope, is crucial for guiding the target selection and observing sequence optimization for a mission such as LIFE.ISSN:0004-6361ISSN:1432-074

LIFEsim: Methods for predicting the exoplanet yield of the future LIFE mission

ISSN:0002-753