An electrostatic actuator driven by conventional voltage control and charge control requires high actuation voltage and suffers from the pull-in phenomenon that limits its operation range, much less than its entire gap. To provide effective solutions to these problems, we present complete analytical and numerical models of various electrostatic actuators coupled with resonant drive circuits that are able to drive electrostatic actuators at much lower input voltage than that of conventional actuation methods and to extend their operation range beyond their conventional pull-in points in the presence of high parasitic capacitance. Moreover, in order to validate the analytical and numerical models of various electrostatic actuators coupled with the resonant drive circuits, we perform the experiment on the microplate and the micromirror coupled with the resonant drive circuit. For instance, using a high voltage amplifier, we manage to rotate the micromirror with sidewall electrodes by 6 ° at 180 V. However, using the resonant drive circuit, we are able to rotate the same micromirror by 6 ° at much lower input voltage, 8.5 V. In addition, the presented work also facilitates the stability analysis of electrostatic actuators coupled with the resonant drive circuits and provides how the effect of the parasitic capacitance can be minimized. For example, the resonant drive circuit placed within a positive feedback loop of a variable gain amplifier is able to extend the operation range much further even in the presence of very high parasitic capacitance. The resonant drive circuit with the proposed feedback controllers is also able to minimize the detrimental effects of the parasitic capacitance and to displace a parallel-plate actuator over its entire gap without the saddle-node bifurcation. Finally, we present a new displacement measurement method of electrostatic actuators coupled with the resonant drive circuits by sensing the phase delay of an actuation voltage with respect to an input voltage. This new measurement method allows us to easily implement feedback control into existent systems employing an electrostatic actuator without any modification or alteration to the electrostatic actuator itself. Hence, this research work presents the feasibility of electrostatic actuators coupled with the resonant drive circuit in various industrial and medical applications, in which the advantages of miniaturization, low supply voltage, and low power consumption are greatly appreciated.

Imaging mass spectrometry (MS) analysis allows scientists the ability to obtain spatial and chemical information of analytes on a wide variety of surfaces. The ability to image biological analytes is an important tool in many areas of life science research, including: the ability to map pharmaceutical drugs in targeted tissue, to spatially determine the expression profile of specific proteins in healthy vs. diseased tissue states, and to rapidly interrogate biomolecular microarrays. However, there are several avenues for improving the imaging MS experiment for biological samples. Three significant directions this work addresses include: (1) reducing chemical noise and increasing analyte identification by developing sample preparation methodologies, (2) improving the analytical figures of merit (i.e., spatial resolution, analysis time) by implementing a spatially dynamic optical system, and (3) increasing both mass spectral resolution and ion detection sensitivity by modifying a commercial time-of-flight (TOF) MS. Firstly, sample methodology schemes presented in these studies consist of obtaining both ?top-down? and ?bottom-up? information. In that, both intact mass and peptide mass fingerprinting data can be obtained to increase protein identification. This sample methodology was optimized on protein microarrays in preparation for bio tissue analysis. Other work consists of optimizing novel sample preparation strategies for hydrated solid-supported lipid bilayer studies. Sample methods incorporating nanomaterials for laser desorption/ionization illustrate the ability to perform selective ionization of specific analytes. Specifically, our results suggest that silver nanoparticles facilitate the selective ionization of olefin containing species (e.g., steroids, vitamins). Secondly, an advanced optical design incorporating a spatially dynamic optical scheme allows for laser beam expansion, homogenization, collimation, shaping, and imaging. This spatially dynamic optical system allows user defined beam shapes, decreases analysis times associated with mechanical movement of the sample stage, and is capable of increasing the MS limits of detection by simultaneously irradiating multiple spots. Lastly, new data acquisition strategies (multiple anode detection schemes) were incorporated into a commercial time-of-flight mass spectrometer to increase both sensitivity and resolution in a matrix assisted laser desorption/ionization mass spectrometer. The utility of this technique can be applied to many different samples, where high mass spectral resolution allows for increased mass measurement accuracy.

An electrostatic actuator driven by conventional voltage control and charge control requires high actuation voltage and suffers from the pull-in phenomenon that limits its operation range, much less than its entire gap. To provide effective solutions to these problems, we present complete analytical and numerical models of various electrostatic actuators coupled with resonant drive circuits that are able to drive electrostatic actuators at much lower input voltage than that of conventional actuation methods and to extend their operation range beyond their conventional pull-in points in the presence of high parasitic capacitance. Moreover, in order to validate the analytical and numerical models of various electrostatic actuators coupled with the resonant drive circuits, we perform the experiment on the microplate and the micromirror coupled with the resonant drive circuit. For instance, using a high voltage amplifier, we manage to rotate the micromirror with sidewall electrodes by 6 ° at 180 V. However, using the resonant drive circuit, we are able to rotate the same micromirror by 6 ° at much lower input voltage, 8.5 V. In addition, the presented work also facilitates the stability analysis of electrostatic actuators coupled with the resonant drive circuits and provides how the effect of the parasitic capacitance can be minimized. For example, the resonant drive circuit placed within a positive feedback loop of a variable gain amplifier is able to extend the operation range much further even in the presence of very high parasitic capacitance. The resonant drive circuit with the proposed feedback controllers is also able to minimize the detrimental effects of the parasitic capacitance and to displace a parallel-plate actuator over its entire gap without the saddle-node bifurcation. Finally, we present a new displacement measurement method of electrostatic actuators coupled with the resonant drive circuits by sensing the phase delay of an actuation voltage with respect to an input voltage. This new measurement method allows us to easily implement feedback control into existent systems employing an electrostatic actuator without any modification or alteration to the electrostatic actuator itself. Hence, this research work presents the feasibility of electrostatic actuators coupled with the resonant drive circuit in various industrial and medical applications, in which the advantages of miniaturization, low supply voltage, and low power consumption are greatly appreciated.

The Coherence Controlled Holographic Microscope (CCHM) was developed at BUT Brno for a quantitative phase imaging of living cells. Nowadays it ocurres that its imaging properties are enhanced by the use of additional modules. In the present the microscope is equipped with the epifluorescence module, which allows observation of fluorescently marked living cells. This thesis is going to follow up on the development of this module and is going to extend its options by confocal imaging. The disadvantage of current multi-channel confocal microscopes is a mechanical rotation of the Nipkow discs, which causes undesired mechanical vibrations. That is why in this thesis it is replaced by Digital Micromirror Device. With its use was developed optical system of the whole confocal model, whose correct funcion was simulated in optical CAD. The experimentally verified prototype serves to test the imaging properties. On this basis is designed an application idea of the fluorescence confocal module, which will be possible to connect to the CCHM microscope.

Diffraktive Mikrospiegelarrays sind eine seit Jahren etablierte innovative Lösung zur ortsaufgelösten Beleuchtungsmodulation im UV-Spektralbereich. Sie werden hauptsächlich als Schlüsselbauelement in mikrolithografischen Industrieanlagen eingesetzt. Gegenwärtige Untersuchungen befassen sich mit der Erweiterung der Technologie hin zu multispektralen Anwendungen, beispielsweise in der Mikroskopie zur strukturierten Objektausleuchtung. Aufgrund des diffraktiven Arbeitsprinzips mit Phasenmodulationen im Nanometerbereich sowie der Vielzahl von Einzelspiegeln mit individuellem Auslenkverhalten stellt die präzise Ansteuerung der Bauelemente eine wesentliche Herausforderung dar. In diesem Kontext steht die Entwicklung und Validierung eines Verfahrens im Fokus dieser Arbeit, das die Gesamtheit von mehreren Tausend oder auch Millionen Mikrospiegeln abhängig von gewünschtem Beleuchtungsmuster und -wellenlänge auf korrekte Kippwinkel einstellen kann. Der gewählte Ansatz liegt in einem Mess- und Korrekturverfahren aller Einzelspiegelverkippungen. Die als Kalibrierung bezeichnete Methode nutzt ein Weißlichtinterferometer zur profilometrischen Charakterisierung der elektro-mechanischen Übertragungsfunktionen der Aktuatoren, wodurch erstmalig auf diesem Themengebiet der multispektrale Bauelementeinsatz gewährleistet werden kann. Zentrales Ergebnis der Kalibrierroutine ist eine Reduzierung der Streuung der Spiegelverkippungen um einen Faktor größer fünf. Direkte Folge sind erheblich verbesserte optische Projektionsmuster, aufgenommen an einem parallel entwickelten optischen Lasermessplatz mit spektral verschiedenen Quellen. Nachgewiesen wurden im Vergleich zum unkalibrierten Ausgangszustand Kontrastverdoppelungen, Homogenitätssteigerungen und die Sicherstellung der Abbildung von mindestens 64 Graustufen. Die Ergebnisse dokumentieren einerseits die Leistungsfähigkeit von diffraktiven Mikrospiegelarrays in multispektralen Umgebungen mit sehr guten Abbildungseigenschaften. Gleichzeitig konnte die wesentliche Grundlage für einen deutlich erweiterten Einsatz optischer Mikrosysteme im stark wachsenden Anwendungsbereich der diffraktiven Optik bzw. der Ultrapräzisionsoptik geschaffen werden.

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Photos captured in the shortwave infrared (SWIR) spectrum are interesting in military applications because they are independent of what time of day the pic- ture is captured because the sun, moon, stars and night glow illuminate the earth with short-wave infrared radiation constantly. A major problem with today’s SWIR cameras is that they are very expensive to produce and hence not broadly available either within the military or to civilians. Using a relatively new tech- nology called compressive sensing (CS), enables a new type of camera with only a single pixel sensor in the sensor (a SPC). This new type of camera only needs a fraction of measurements relative to the number of pixels to be reconstructed and reduces the cost of a short-wave infrared camera with a factor of 20. The camera uses a micromirror array (DMD) to select which mirrors (pixels) to be measured in the scene, thus creating an underdetermined linear equation system that can be solved using the techniques described in CS to reconstruct the im- age. Given the new technology, it is in the Swedish Defence Research Agency (FOI) interest to evaluate the potential of a single pixel camera. With a SPC ar- chitecture developed by FOI, the goal of this thesis was to develop methods for sampling, reconstructing images and evaluating their quality. This thesis shows that structured random matrices and fast transforms have to be used to enable high resolution images and speed up the process of reconstructing images signifi- cantly. The evaluation of the images could be done with standard measurements associated with camera evaluation and showed that the camera can reproduce high resolution images with relative high image quality in daylight.

Scannende MEMS-Mikrospiegel stellen eine vielversprechende technologische Entwicklung mit potentiellen Anwendungen im Bereich der miniaturisierten Bildprojektion und Umgebungssensierung dar. Im Regelfall oszilliert das Spiegelelement hierbei resonant um die horizontale Achse, während die vertikale Achse statisch ausgelenkt wird. Somit ergibt sich ein sogenannter Raster-Scan. Während eine resonante Aktuierung in MEMS-Technologie im Frequenzbereich mehrerer kHz effizient umgesetzt werden kann, stellt die Implementierung statischer Antriebe eine Herausforderung dar. In dieser Arbeit wird ein neuartiges Aktuierungskonzept vorgestellt, das effizientere quasi-statische Auslenkung ermöglicht. Hierfür wird der Drehimpuls, der durch die hochfrequente horizontale Schwingung erzeugt wird, durch eine weitere resonante Oszillation ähnlicher Frequenz gestört, wodurch sich ein für die quasi-statische Auslenkung nutzbares Drehmoment ergibt. Da gyroskopische Effekte ausgenutzt werden, die nicht in aktuellen auf Modalanalyse basierenden Simulationsmethoden berücksichtigt sind, werden Starrkörper- und transiente FEM-Modelle entwickelt, um die Realisierbarkeit des Antriebskonzepts simulatorisch zu verifizieren. Im Rahmen der durch den genutzten Prozess gegebenen Randbedingungen werden daraufhin Aktuierungselemente für die resonanten Achsen erarbeitet und mit diesen zwei Designvarianten eines 2D-Mikrospiegels erstellt. Nach modellbasierter Verifikation werden diese in einer MEMS-Fertigungslinie prozessiert. Mit den generierten Mustern wird dann eine vollständige experimentelle Charakterisierung unter Nutzung eines speziell erstellten FPGA-basierten Evaluations-Boards durchgeführt. Beide Design-Varianten zeigen hierbei voll funktionsfähige Sensierungs- und Aktuierungselemente. Es kann ein erfolgreicher Nachweis der Funktionsfähigkeit des neuartigen Antriebskonzepts vollbracht werden. Die dabei gezeigte 2D-Projektion erreicht Winkel von 12° x 1.8° / Scanning MEMS micromirrors are an emergent technology for compact form factor image projection and environment sensing applications. Commonly the mirror element oscillates resonantly along the horizontal axis, whereas it is deflected statically along the vertical axis, performing a so called raster scan. While resonant actuation can be implemented efficiently in MEMS, static deflection however remains challenging. In this thesis a novel actuation concept for 2D MEMS micromirrors is introduced that potentially enables efficient quasi-static actuation. Therefore the angular momentum that is generated by the high frequency resonant axis is disturbed by an orthogonal resonant oscillation of similar frequency, leading to a torque that can be utilized to achieve an indirect quasi-static deflection. As in this case gyroscopic effects are exploited that are usually not considered in state of the art modal finite element based MEMS simulation, in order to validate the feasibility of the actuation concept rigid body and transient finite element based models are developed and simulation studies conducted. Using an existing manufacturing process as a framework, actuation schemes for the resonant axes are introduced and two distinct micromirror designs are developed and verified by simulation. These are processed in a MEMS manufacturing line. A thorough characterization study is then carried out using a custom FPGA based evaluation board with closed loop control capabilities. Both design variants are functional with regard to all actuation and tilt angle detection elements. A successful implementation of the proposed actuation concept is shown achieving 2D projection of a laser beam with tilt angles of 12 ◦ × 1.8 ◦ in frequency and amplitude controlled operation.

The physics of ultracold quantum gases has been the subject of a long-lasting and intense research activity, which started almost a century ago with purely theoretical studies and had a fluorishing experimental development after the implementation of laser and evaporative cooling techniques that led to the first realization of a Bose Einstein condensate (BEC) over 25 years ago. In recent years, a great interest in ultracold atoms has developed for their use as platforms for quantum technologies, given the high degree of control and tunability offered by ultracold atom systems. These features make ultracold atoms an ideal test bench for simulating and studying experimentally, in a controlled environment, physical phenomena analogous to those occurring in other, more complicated, or even inaccessible systems, which is the idea at the heart of quantum simulation. In the rapidly developing field of quantum technologies, it is highly important to acquire an in-depth understanding of the state of the quantum many-body system that is used, and of the processes needed to reach the desired state. The preparation of the system in a given target state often involves the crossing of second order phase transitions, bringing the system strongly out-of-equilibrium. A better understanding of the out-of-equilibrium processes occurring in the vicinity of the transition, and of the relaxation dynamics towards the final equilibrium condition, is crucial in order to produce well-controlled quantum states in an efficient way. In this thesis I present the results of the research activity that I performed during my PhD at the BEC1 laboratory of the BEC center, working on ultracold gases of 23Na atoms in an elongated harmonic trap. This work had two main goals: the accurate determination of the equilibrium properties of a Bose gas at finite temperature, by the measurement of its equation of state, and the investigation of the out-of-equilibrium dynamics occurring when a Bose Einstein condensate is prepared by cooling a thermal cloud at a finite rate across the BEC phase transition.To study the equilibrium physics of a trapped atomic cloud, it is crucial to be able to observe its density distribution in situ. This requires a high optical resolution to accurately obtain the density profile of the atomic distribution, from which thermodynamic quantities can then be extracted. In particular, in a partially condensed atomic cloud at finite temperature, it is challenging to resolve well also the boundaries of the BEC, where the condensate fraction rapidly drops in a narrow spatial region. This required an upgrade of the experimental apparatus in order to obtain a high enough resolution. I designed, tested and implemented in the experimental setup new imaging systems for all main directions of view. Particular attention was paid for the vertical imaging system, which was designed to image the condensates in trap with a resolution below 2 μm, with about a factor 4 improvement compared to the previous setup. The implementation of the new imaging systems involved a partial rebuilding of the experimental apparatus used for cooling the atoms. This created the occasion for an optimization of the whole system to obtain more stable working conditions. Concurrently I also realized and included in the experiment an optical setup for the use of a Digital Micromirror Device (DMD) to project time-dependent arbitrary light patterns on the atoms, creating optical potentials that can be controlled at will. The use of this device opens up exciting future scenarios where it will be possible to locally modify the trapping potential and to create well-controlled barriers moving through the atomic cloud. Another challenge in imaging the density distribution in situ is determined by the fact that the maximum optical density (OD) of the BEC, in the trap center, exceeds the low OD of the thermal tails by several orders of magnitude. In order to obtain an accurate image of the whole density profile, we developed a minimally destructive, multi-shot imaging technique, based on the partial transfer of a fraction of atoms to an auxiliary state, which is then probed. Taking multiple images at different extraction fractions, we are able to reconstruct the whole density profile of the atomic cloud avoiding saturation and maintaining a good signal to noise ratio. This technique, together with the improvements in the imaging resolution, has allowed us to accurately obtain the optical density profile of the Bose gas in trap, from which the 3D density profile was then calculated applying an inverse Abel transform, taking advantage of the symmetry of the trap. From images of the same cloud after a time-of-flight expansion, we measured the temperature of the gas. From these quantities we could find the pressure as a function of the density and temperature, determining the canonical equation of state of the weakly interacting Bose gas in equilibrium at finite temperature. These measurements also allowed us to clearly observe the non-monotonic temperature behavior of the chemical potential near the critical point for the phase transition, a feature that characterizes also other superfluid systems, but that had never been observed before in weakly interacting Bose gases. The second part of this thesis work is devoted to the study of the dynamical processes that occur during the formation of the BEC order parameter within a thermal cloud. The cooling at finite rate across the Bose-Einstein condensation transition brings the system in a strongly out-of-equilibrium state, which is worth investigating, together with the subsequent relaxation towards an equilibrium state. This is of interest also in view of achieving a better understanding of second order phase transitions in general, since such phenomena are ubiquitous in nature and relevant also in other platforms for quantum technologies. A milestone result in the study of second order phase transitions is given by the Kibble-Zurek mechanism, which provides a simple model capturing important aspects of the evolution of a system that crosses a second-order phase transition at finite rate. It is based on the principle that in an extended system the symmetry breaking associated with a continuous phase transition can take place only locally. This causes the formation of causally disconnected domains of the order parameter, at the boundaries of which topological defects can form, whose number and size scale with the rate at which the transition is crossed, following a universal power law. It was originally developed in the context of cosmology, but was later successfully tested in a variety of systems, including superfluid helium, superconductors, trapped ions and ultracold atoms. The BEC phase transition represents in this context a paradigmatic test-bench, given the high degree of control at which this second-order phase transition can be crossed by means of cooling ramps at different rates. Already early experiments investigated the formation of the BEC order parameter within a thermal cloud, after quasi-instantaneous temperature quenches or very slow evaporative cooling. In the framework of directly testing the Kibble-Zurek mechanism, further experiments were performed, both in 2D and 3D systems, focusing on the emergence of coherence and on the statistics of the spontaneously generated topological defects as a function of the cooling rate. The Kibble-Zurek mechanism, however, does not fully describe the out-of-equilibrium dynamics of the system at the transition, nor the post-quench interaction mechanisms between domains that lead to coarse-graining. Most theoretical models are based on a direct linear variation of a single control parameter, e.g. the temperature, across the transition. In real experiments, the cooling process is controlled by the tuning of other experimental parameters and a global temperature might not even be well defined, in a thermodynamic sense, during the whole process. Moreover, the temperature variation is usually accompanied by the variation of other quantities, such as the number of atoms and the collisional rate, making it difficult to accurately describe the system and predict the post-quench properties. Recent works included effects going beyond the Kibble-Zurek mechanism, such as the inhomogeneity introduced by the trapping potential, the role of atom number losses, and the saturation of the number of defects for high cooling rates. These works motivate further studies, in particular of the dynamics taking place at early times, close to the crossing of the critical point. The aim of the work presented in this thesis is to further investigate the timescales associated to the formation and evolution of the BEC order parameter and its spatial fluctuations, as a function of the rate at which the transition point is crossed. We performed experiments producing BECs by means of cooling protocols that are commonly used in cold-atom laboratories, involving evaporative cooling in a magnetic trap. We explored a wide range of cooling rates across the transition and found a universal scaling for the growth of the BEC order parameter with the cooling rate and a finite delay in its formation. The latter was already observed in earlier works, but for a much more limited range of cooling rates. The evolution of the fluctuations of the order parameter was also investigated, with an analysis of the timescale of their decay during the relaxation of the system, from an initial strongly out-of-equilibrium condition to a final equilibrium state. This thesis is structured as follows: The first chapter presents the theoretical background, starting with a brief introduction to the concept of Bose Einstein condensation and a presentation of different models describing the thermodynamics of an equilibrium Bose gas. The second part of this chapter then deals with the out-of-equilibrium dynamics that is inevitably involved in the crossing of a second-order phase transition such as the one for Bose-Einstein condensation. The Kibble-Zurek mechanism is briefly reviewed and beyond KZ effects are pointed out, motivating a more detailed investigation of the timescales involved in the BEC formation. In the second chapter, I describe the experimental apparatus that we use to cool and confine the atoms. Particular detail is dedicated to the parts that have been upgraded during my PhD, such as the imaging system. In the third chapter I show our experimental results on the measurement of the equation of state of the weakly interacting uniform Bose gas at finite temperature. In the fourth chapter I present our results on the out-of-equilibrium dynamics in the formation of the condensate order parameter and its spatial fluctuations, as a function of different cooling rates.