This thesis studies Lie group methods for inertial navigation. One seeks to find the orientation, position and velocity of a rigid body using measurements of angular velocity and specific force made by an inertial measurement unit (IMU). The orientation and states combining orientation with position and velocity do not live in vector spaces, but in nonlinear spaces like SO(3), SE(3) and SE2(3). These spaces are Lie groups, i.e. both groups and smooth manifolds.

The first part of this thesis develops the mathematical foundations of smooth manifolds and Lie groups. We also explain some important maps on Lie groups, the Lie algebra, how to formulate errors and perturbations on Lie groups, and how to describe a state on a Lie group that evolves with time due to IMU measurements.

In the second part of the thesis we use this foundation to analyze how existing estimation errors propagate and how new errors are introduced by noise. Here we study concepts such as group-affine dynamics, log-linear error behavior and covariance propagation. We also study a technique called preintegration: summarizing the motion implied by high-frequency IMU data in preintegrated increments, which are independent of the initial state. Using these increments, an optimizer can change its estimate of the initial state without having to reintegrate the IMU data to find the final state.

Finally, some numerical experiments on the EuRoC MAV V1_01 easy dataset illustrate that IMU dead reckoning is not reliable as a global estimator and that the accuracy and reliability of preintegrated increments decrease as more IMU data is summarized in them.

Overall, this thesis aims to give a mathematically rigorous but accessible overview of Lie group methods for inertial navigation, connecting the underlying theory with practical implementations while starting from the level of a bachelor’s student in mathematics. ... Read more

The goal of this thesis is to investigate the viability of reflection-based biphoton Hong-Ou-Mandel Interferometry (HOMI) for measuring a sub-nanometer step size. We attempt to push this technology forward by designing for larger separation than has been done before in the literature, resulting in higher possible precision.
This is a Fisher-information-based estimation method. We show that the Quantum Cramér-Rao (QCR) bound can be saturated with our proposed measurement. We propose a mostly common-path interferometer design, where the two optical paths are distinct in polarization instead of spatial mode. This reduces the risk of creating accidental which-path information.
For the production of the photon superposition, we propose a novel biphoton source design specialized for large detuning between the two downconverted wavelengths, similar to the more common beamdisplacer entangled photon sources. The proposed photon source can be designed for type-0 and type-II SPDC.
We suggest a detection system based on a combination of visible and NIR single-photon detectors to handle larger detunings than is possible with a single type of detector. The best combination of detectors and type of SPDC was Si-SPAD (visible) and SNSPD (NIR) with weak downconversion focusing (ξ ≪ 1).
This experiment has an expected measurement time of 7.4 seconds for 0.1 nm precision. We conclude that biphoton HOMI is indeed feasible for high-precision metrology. ... Read more

The analysis of equilibria of complex systems is challenging due to the high dimensionality and non-linear interactions. There are different kinds of complex systems such as cooperative systems in which all interactions help growth and mixed-weight systems, in which some interactions help growth, while others hinder it. In this thesis, we focus on the correlation between the equilibria of cooperative and mixed-weight systems. We simplified the equilibrium equations by combining the attributes of a system into a one-dimensional equation. This reduced equation is easy to compute and provides an upper bound on the equilibrium value of each node. Although this bound may exceed many actual equilibrium values, it still defines the subspace in which all equilibria must lie. For cooperative systems, we presented a theorem that provides constraints on two vectors. If these vectors satisfy the given conditions, then there exists an equilibrium between the components. We also discussed methods to find such vector pairs. We applied this theorem to relate the equilibria of mixed-weight and cooperative systems. The equilibria of the mixed-weight system are always less than or equal to some equilibrium in the cooperative system. We introduced a framework for classifying cooperative equilibria. On any subset of nodes, an equilibrium may have entries that are maximal compared to all other equilibria on that subset. This leads to a single equilibrium that is the largest at every entry, called the principal equilibrium, which is component-wise maximal. The principal equilibrium upper bounds all equilibria of the mixed-weight system. Finally, we discussed the inherent difficulty of translating cooperative equilibria into the mixed-weight system, which stems from high dimensionality and non-linearity. We stated the conditions that mixedweight equilibria must satisfy and provided constraints determining if a cooperative-system equilibrium remains valid when competitive interactions are added. This concludes the comparison by showing that the principal equilibrium provides a component-wise upper bound for all equilibria of the mixed-weight system. ... Read more

Finding signs of life on planets outside of Earth is an ongoing challenge in astronomy. Nulling interferometry is a promising method to not only detect exoplanets, but also allow for characterization of their atmospheres. Nulling interferometry has been demonstrated on ground, but with limited success, due to atmospheric turbulence. To maximize the potential, a space-based observatory is needed. In the early 2000s, several space based missions were proposed, which marked the start of many system studies. Nonetheless, considerations on the telescope design are lacking in the literature. To gain new insights in the behavior of a space-based nulling interferometer under operational conditions, several designs were made in Code V for this study, including an off-axis Cassegrain, Ritchey-Chretien (RC) and Gregorian. By means of a numerical perturbation analysis, the RC was shown to be the most promising. ... Read more

The Kuramoto model (KM) is a well known mathematical model of coupled oscillators that is frequently used to study synchronization phenomena. In this bachelor thesis we investigate the effects of noise on synchronization in Kuramoto-type networks.

In the first part we follow the methods of Maggi and Paoluzzi [1], but include detailed in between steps, to obtain an analytical expression for the critical coupling strength, $k_c$, of the KM in the thermodynamic limit under the influence of time-correlated noise (i.e non-white noise). The coupling strength, $k$, is a parameter in the KM that essentially determines to what extent oscillators influence each other. When $k > k_c$ we start to see synchronization. Our numerical simulations agree with the results found in [1], in that the analytical expression for $k_c$ holds up for low values of correlation time, but quickly breaks down as correlation time increases.

In the second part of this thesis we consider a Kuramoto-type adaptive dynamical network that is also investigated in Fialkowski et al. [2]. The dynamical phenomena that are observed in [2] are also present in our simulations. We explain these dynamical phenomena with the help of a variety of plots. Subsequently, the Kuramoto-type adaptive dynamical network is expanded to include white noise terms in the coupling dynamics. We find, through the use of simulation, that under the same conditions as in [2], synchronization is observed for significantly lower values of coupling strength. This result is explained qualitatively. Simulations also show, that for specific values of noise strength, the
hysteric behaviour observed in [2] is not present.

Other conclusions, like the degree to which the noise can reduce the coupling strength required for full synchronization, or beyond what value of noise strength full synchronization can no longer occur, are unable to be drawn. Additional simulation work and a further analytical work is recommended for an ensuing study.
... Read more

Extremely large telescopes (ELTs) are expected to be one of the most promising astronomical observation instruments when it comes to observing exoplanets. During observations, however, Earth’s atmosphere introduces optical distortion, which needs to be corrected. For this reason, a wavefront sensor (WFS) will be developed that comprises a 100 ⇥ 100 array of kinetic inductance detectors (KID), superconductor-based photodetectors. The main advantage of KIDs in an array is their ability to be multiplexed on a single read out line by designing each KID to operate at a different frequency. The signal of an individual KID can essentially be described as a dip in the transmission signal of the readout signal. Upon the fabrication of these KID arrays, however, these dips may have shifted as so-called frequency scatter (or f-scatter), which severely disorders the readout signal. The f-scatter cannot be determined based solely on the readout signal as it contains no information about which KID each individual signal originates from.
This paper manages to provide a solution in the form of an experimental method in which the KID array is scanned along the x- and y-axis to produce a spatial map. To realize this, an optical setup was designed and constructed, based on a single-lens system with a magnification of M = 1.22. By implementing a CCD camera, the KID array could be live imaged to align the setup accordingly. Thanks to numerous other alignment measures, the setup was able to scan the entire KID array along the x- and y-axis in 45 scans per axis. Based on the difference in transmission, a 45x45 spatial map was constructed, which was manually scaled down to 20x20. This 20x20 spatial map presented the location of KIDs on the fabricated detector array based on their measured operating frequency. By comparing this with the spatial map of the KID array design, the standard deviation in the fractional frequency deviation was determined, σ_δf/f = 5.92 · 10^-3. This result shows the experimental method is able to effectively unveil the severity of the f-scatter in the studied 20x20 KID array.
Despite the potency of the presented method, the biggest giveaway of its flaws is a reduced pixel yield on the 20x20 spatial map from 400 to 374 pixels. The developed data analysis is able recognize multiple complications, which can be mitigated by optimizing readout parameters to improve the quality of the signal. Additionally, one-to-one imaging is far too restricting for advanced scanning techniques due to its fixed M. Appropriate suggestions for improving the lens systems would be implementing the Cooke triplet or a two-lens system that utilizes the principle of virtual imaging. ... Read more

In this thesis we are interested in distinguishing patterns of mesoscale cloud patterns in the trades. Specifically, whether Sugar, Gravel, Fish and Flowers patterns can objectively be identified using physical quantities. For this purpose, we use cloud fraction data attained by the CORAL Ka-Band cloud radar at the Barbados Cloud Observatory during the boreal winter seasons of 2018, 2019 and 2020. These cloud fraction data represents the curves up until a height of 4 km for a given 6-hour interval of time. We do this to see if these clusters match up with the labels assigned to each cloud fraction curve obtained from a classification model used in Schulz (2021). Firstly, we map the cloud fraction curves onto points on a finite dimensional space using functional principal component analysis. We subsequently apply K-means, Gaussian Mixture Models and Mean Shift clustering onto the pre-processed dataset to identify any robust clusters. We have been able to attain robust Sugar-like clusters for K-means for 3 and 4 partitions and Mean Shift with bandwidth λ ≈ 585. This provides evidence that we are able to use cloud fraction data to distinguish Sugar. However, the same can not be said for Gravel, Fish and Flowers as we have not been able to identify them in our analysis. It is suggested for future research to do sensitivity analysis in the height interval of the cloud fraction data, that outliers are omitted and that the labeled data from Schulz (2021) are used instead of the mean and spread of the data pertaining to those labels. ... Read more

Context. In the near-future, exoplanets can be observed directly through telescopes. Although the resolution of the planet's image will only be one pixel at first, the intensity of this pixel will change over time because of the orbit around its host star and its diurnal rotation. This intensity as a function of time is called the light curve of an exoplanet. The changes in the light curve as a result of annual and diurnal rotation can in turn be used to obtain information about the surface of the planet, this is called spin-orbit tomography.

Aims. The aim of this study is to determine if an exoplanet's surface can be retrieved from its light curve for planet surfaces that can be described by Lambertian, Lommel-Seeliger or Fresnel reflection, or a combination of these. The variation in the light curve due to differences in the planet's surface will be used to find a map of its continents and oceans and to determine what surface types the planet is made of.

Methods. This thesis starts by composing a near-equal area segmentation of a sphere to maximize the retrieval of information per pixel of the exoplanet's surface. Additionally, a method for generating artificial planets is described, such that the following method can be tested on light curves, since the current telescopes are not powerful enough to measure an exoplanet's light curve. A linear transformation from the surface to the light curve is constructed to obtain the light curve from the surface. Consequently, this transformation is inverted in order to obtain information about the surface from the light curve. This method is applied to exoplanets with a stationary surface, i.e. no clouds or changing ice caps and is consistent of the following surfaces: water, vegetation, sand and snow, each described by a different reflection model. Lastly, surface retrieval is tested from a light curve with a realistic amount of photon shot noise (SNR ≈ 14).

Results. The composed near-equal area segmentation of a sphere is the Voronoi diagram of the Fibonacci lattice. It is a very appropriate near-equal area segmentation, because the maximum difference in facet area is 12% for 1001 points. Furthermore, the retrieval of an exoplanet's surface from its reflected light curve is close to perfect for exoplanets that are described by a combination of the three reflection models if the light curve does not contain noise and there are a sufficient number of data points. If the light curve does contain shot noise, parts of the surface that are described by the Lommel-Seeliger law, are not retrieved correctly. However, the general shape of the surface that is described by Lambertian or Fresnel reflection is still retrieved correctly. If the surface can be described by one single reflection model, the planet's features are retrieved correctly from a light curve with shot noise regardless of the reflection model.

Conclusions. Spin-orbit tomography in the form of a linear transformation between the light curve and albedo map of an exoplanet is a very accurate method to retrieve the albedo map from a single observed pixel, even with a realistic amount of shot noise. ... Read more

A gas-cell-based calibration setup was designed to evaluate the wideband response of sub-millimeter spectrometers like DESHIMA (DEep Spectroscopic High-redshift MApper). The use of low pressure gas emission spectra allowed for accurate calibration of the absolute frequency response, and to test the detectability of faint emission spectra with long integration times. This is important to understand and evaluate systematic errors and noise profiles of sub-millimeter astronomical spectrometers before their telescope campaigns.

The setup consisted of a low pressure (~mbar) gas at room temperature in a high vacuum (<10^-3 mbar) chamber in front of a 77K N₂ background. A double-winged rotating chopper was used for signal modulation of the on- and off-source paths to reduce the low-frequency noise profile. The setup has been able to successfully detect the emission spectra of nitrous oxide at 30 mbar and methanol at 1 mbar in the frequency range of 332 to 377 GHz with the prototype DESHIMA spectrometer. Our models showed that lower pressures should be detectable over similar averaging times. The standing spectrum showed to be too irregular for detecting spectral lines in a single measurement. A second measurement was required to subtract the standing features, which extended the total time required beyond the current system stability.

Detailed analysis into optical resonances has shown the importance of anti-reflective (AR) coatings on the main optical interfaces to improve the detectability of the emission spectra. We adapted sub-wavelength pyramid gratings milled into TOPAS windows to reduce a standing wave in the output spectrum of the gas cell setup. Stability of the setup was shown for observation times of up to ~10³ seconds before environmental
noises became dominant. Extensive stability testing has shown the impact of key components in the setup. A two-stage post-processing algorithm was developed to successfully reduce instabilities in the data by removing linear drifts and by removing the common profile over simultaneous read-out data.
... Read more

Suppose we have a target radiance distribution, a light source, and a plane for receiving light. How do we design a reflector that can give a similar result as the target radiance distribution? The inverse reflector problem is of high interest for light designers and related industries, such as lamp manufacture, headlight and street light design, and interior designs. There have been some researches on this specific topic. Nevertheless, the existing algorithms are either not fully compatible with parallel acceleration or have a narrow application scope (can only handle the far-field problem). This thesis's goal is to design a method that can have a fast approximation of the inverse reflector problem and handle different application scenarios. The core of the proposed method in this thesis is a modified simulated annealing algorithm. I first give the definition of the inverse reflector problem and explain why I choose simulated annealing in the proposed method by analysing the related works and various optimisation algorithms. Then, I detail what issues the plain simulated annealing algorithm will have and why it cannot achieve satisfactory results. Moreover, to solve the issues and improve performance, I propose additional strategies, such as Phong tessellation, randomisation strategy, multi-level strategy, history-decision strategy and penalising strategy. I also discuss the system design based on the proposed method and how to accelerate the optimisation process in this system. I evaluate and validate the proposed method by running test cases in different scenarios and compare the results with other algorithms. The results show that the method, as a general optimisation algorithm, can achieve good results in different application scenarios. The compatibility, speed and accuracy are the main advantages. The result of the proposed method can also serve as the initial guess for a finer optimisation. ... Read more

In this report, we will focus on simulating galaxy observations with the Deep Spectroscopic High-redshift Mapper (DESHIMA). To do so, we will discuss and evaluate two main parts needed to accurately perform such a simulation:

Firstly, we will answer the question whether Time-dependent End-to-end Model for Post-process Optimization (TiEMPO), the modelling software used for DESHIMA observation simulations, is able to accurately simulate real life galaxy observations conditions. To do so, the simulation program is fed artificially created atmospheric data and its output is compared with sky brightness data of real measurements. More specifically, the time signal, power spectral density and noise equivalent flux density of both the simulation and the measurement data are derived and compared. This comparison showed, apart from a linear drift of the time signal data and a small offset of the power spectral density, good agreement between the simulation and the measurement.

The second part of this thesis discusses whether we can detect an artificially created galaxy, using the already verified atmospheric model of TiEMPO. To do so, the output of the simulation is run through a series of algorithms that calculate the observation spectrum of the telescope, as if it were a real measurement. In addition, the application of different observation tactics and telescope parameters are tested and visualised. Most importantly, two observational position-switching (chopping) techniques are applied and compared: the dual point and ABBA chopping techniques. To test the effectiveness of the two chopping techniques, both will be used to simulate atmospheric filtration using stationary, i.e. without telescope movement, simulation and measurement data, which do not contain the (to be detected) galactic data. As there is no telescope movement, nor galactic data, the spectra should ideally fluctuate around zero. However, as we will see in this report, this is not obtained in all cases. After further analysis, two main types of offsets could be identified: the first one originating from the linear drift of the measurement's time signal data, whereas the second one is due to the spatial displacement of the chopping positions. The former can be corrected by applying the ABBA chopping technique rather than the dual chopping method, whereas the latter cannot with either of the two.

Using the insights we acquire from running these simulations with observation conditions for DESHIMA, we are able to perform an actual galaxy observation simulation. The galactic data acquired from this observation simulation shows good agreement with the input values of the galaxy data of TiEMPO, assuring that TiEMPO can be used for galaxy observation simulations.
... Read more

The Deep Spectroscopic High-redshift Mapper, or DESHIMA, is an integrated superconducting spectrometer which measures the redshift of photons originating from submillimeter galaxies. These photons have to travel through the Earth's atmosphere before arriving at DESHIMA, but this atmosphere adds noise to the signal. Using a principal component analysis on still-sky measurement data, the influence of the atmospheric noise on these observations is analyzed. To achieve this, several principal component analyses are performed on still-sky observations, which are measurements of the brightness temperature of the sky, Tsky. These observations are assumed to be governed by three noise types: atmospheric noise, photon noise, and detector 1=f noise. A PCA on a still-sky observation reveals the effect of the most dominant noise sources. By creating an artificial data set, the physical origin of these noise sources can be found. This data set was produced by using an existing atmospheric model, based on the fluctuation of the precipitable water vapour, or PWV, in the atmosphere. A principal component analysis on this artificial data set reveals the effect of this PWV fluctuation on the data. The first principal component of the artificial data is found to represent the derivatives of the Tsky-PWV relations for every channel. The second principal component has a non-zero explained variance and is found to represent the second-order derivatives of the
Tsky-PWV relations for every channel, indicating that these relations are not linear. This can be explained by performing a Taylor expansion on the Tsky-PWV relation. Comparing the principal components of the real data to those of the artificial data shows that the first principal component generally has the same shape as the fist principal component of the artificial data, which represents the first-order PWV fluctuation, confirming that PWV fluctuation is the most dominant noise source for still-sky observations. It is also found that, when the PWV fluctuation is large, the second-order Taylor expansion term of the Tsky-PWV generally becomes more important in the real data. In this case, the first
principal component has a very high explained variance, and the second-order term is usually represented by the second principal component. Conversely, when the PWV range is small, the first-order term explains significantly less variance, and random noise like the photon noise becomes more dominant than the higher-order terms. The results show a few exceptions to this interpretation, so further research on these systematic errors is strongly recommended. In order to achieve better results, the experimental method can be improved by including the bandwidths of the channels and better estimation of the PWV fluctuation. This research can also be extended into a design of a random noise level and ultimately, the design of a better atmosphere calibration method for DESHIMA. ... Read more

In this thesis we consider the reconstruction of albedo maps of exoplanets. This is done with a new variant of spin-orbit tomography that has been described in [Cowan and Agol, 2008] and more in depth in [Fujii and Kawahara, 2012]. This method reconstructs the albedo map from the reflected-light curve, the total intensity of the light that originates from the host star and is reflected by the planet. In the mentioned papers, the surface map of the planet is modeled as a sum of finite sized surface elements with constant albedo, and the relation between this approximation of the map and the light-curve in the time domain is determined. In this report, we use that the signal is quasi periodic due to diurnal and annual motion, and work with the Fourier peaks of the light-curve. We also approximate the map in a different way, writing it as the sum of spherical harmonics, and neglecting spherical harmonics with high spatial frequencies. This has the advantage that the relation can be worked out analytically (for edge-on and face-on observations) without the use of complex mathematics, and that both the surface map and the light-curve contain a daily frequency. We derive an equation for the reflective light-curve under the assumption that the surface map is not a function of time (no clouds), and that the reflection is Lambertian (equal in magnitude in all directions). This transformation is found to be a linear function of the surface map. This equation is worked out for edge-on and face-on observations with arbitrary axial tilt, which describes the orientation of the spin axis with respect to the observer and the orbital plane. Furthermore, we describe how to invert this relation if the axial tilt is known to the observer. We also aimed at recovering the map if the axial tilt is unknown to the observer, since this would make sure that the reconstruction does not rely on other observations. In contrast to what was found in papers like [Fujii and Kawahara, 2010] and [Fujii and Kawahara, 2012], we did not succeed in this. A number of methods were used for this. The first two looked at the problem from a mathematical perspective: the minimization of the distance between the measured light-curve and the light-curve from the reconstructed map, and Tikhonov regularization. The two failed because both the column space and the singular values respectively are not a function of the axial tilt. The third method that has been treated and tested involved the maximization of the ‘amount’ of positive albedo on the reconstructed map, but a test showed that the distinction that this method makes is in the same order of magnitude as the numerical error, thus proving that this method was not useful as well. Further study might show what causes the results of the two methods to differ in this respect ... Read more

The idea of having a smart environment to automate day to day tasks appeals to us all. To enable this, we need objects with embedded electronics to communicate with each other in a network known as the Internet of Things (IoT). The IoT communication infrastructure is built on top of existing Radio Frequency (RF) technologies such as Bluetooth Low Energy (BLE), WiFi, and cellular protocols. The RF technology is bandlimited and power hungry, making it unfeasible to support the growing demand of IoT networks. The number of IoT devices in the year 2020 is expected to be around 20 billion, making it essential to explore other areas of sustainable communication technology. Visible light communication (VLC) in the optical domain is being explored to meet the surge in connected devices and to enable sustainability in the energy consumed. The idea behind a VLC system is to toggle a Light Emitting Diode (LED) at high speed to transmit information which ensures that users are not subjected to visual interruptions. Even sunlight - the biggest source of illumination - can be used to transmit information. However, it is not possible to toggle the sun like LEDs. Hence, the objective of this thesis is to use sunlight to setup a green communication channel. In the 1800s, sunlight was used to communicate over long distances by using mirrors to reflect light to send signals. Taking inspiration from this method, I propose using smart materials to toggle sunlight and use it for wireless communication. My aim in this thesis is to analyze the behavior of smart materials, develop a modulation scheme suitable to send information using sunlight, and evaluate the system's performance. ... Read more

The concept of optical refrigeration dates back to 1929, when Pringsheim recognized that thermal energy associated with the translational degrees of freedom of isolated atoms could be reduced by the process of anti-Stokes fluorescence. Optical refrigeration of a solid was first experimentally demonstrated in 1995 with the Ytterbium-doped fluorozirconate glass by Epstein and his team and since then this invigorating field has garnered much scientific interest for development of an all optical refrigerator. The present works discusses the recent candidate materials including crystals, semiconductors, and ionically doped glasses. Cooling processes and necessary conditions for cooling are outlined, and general thermodynamic limitations are discussed.

10% wt. Ytterbium doped Yttrium Lithium Fluoride (Yb+3:YLF) is chosen as the candidate active material. The Carnot efficiency for laser and sun-light as a pump source is evaluated using a narrow-band approximation outlined by Stephen and his team. A quantum-mechanical cooling model based on Epstein and his team, is developed. In the proposed system, the candidate material is placed on a magnetically suspended platform inside a vacuum chamber and illuminated with laser light with the appropriate wavelength in the near infrared region. The dynamics of important cooling parameters are simulated and studied. The cooling effects due to radiative relaxation compete with the heating effects due to parasitic absorption and non-radiative relaxation but net cooling is observed confirming validity of light source and material parameter selection.

In addition to laser, the conventional source of pump radiation, sun-light as a pump input to the quantum-mechanical model is simulated and the effects on the cooling power and efficiency are studied. To enhance the energy efficiency of the system, fluorescence recovery schemes using photovoltaics are built and studied. Suggestions for experimental realization are given. The developed model can be base for designing a practical optical refrigeration system for laser and sun-light based optical sources.
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Sub-mm astronomy in space calls for an array of photon noise limited detectors, both for imaging and broadband spectroscopy. Microwave Kinetic Inductance Detectors (MKIDs), superconducting resonance circuits, are a suitable candidate for this purpose due to its multiplexing potential, but in literature excess noise in phase readout is encountered and attributed to so-called two-level systems (TLSs). Reduction in TLS induced noise and loss will provide greater flexibility in design and a route towards background limited detector performance.
In this thesis, TLSs from surface and bulk sources are modelled, so that their behaviour can be predicted through numerical computations of the field distributions inside the resonators. These calculations not only provide a guide for sensible chip designs, but allow for interpretation of experimental data and determination of dominant TLS sources.
It is found that for Al CPW resonators on Si or SiN, the noise is surface dominated but with a non-negligible bulk contribution, while for microstrips on a SiN membrane, the noise is bulk dominated. As the loss in microstrips for narrow microstrips is dominated by the substrate-air interface, the dominant TLS loss and noise sources do not necessarily coincide and should be treated independently. This makes it impossible to determine the dominant CPW surface noise contribution. Additionally, microstrips and CPWs on the same dielectric perform similarly, while Si is better than SiN, both in terms of loss and noise, due to a combination of SiN interface and bulk effects. Finally, material dependent loss and noise parameters have been determined and the importance of thorough Si surface cleaning has been established, yielding the best Al CPW noise ever encountered.
For sub-mm astronomy in space, the logical path to improvement would be the use of thorough cleaned Si as a dielectric, overetching and the use of LEKIDS and hybrid resonators, where microstrips are still viable for use. Importantly, having located the important TLS locations for various cases, tackling these problems areas further could provide the step towards background limited performance in space. ... Read more