This thesis addresses particular topics in the field of the length metrology for nanometrology. Nanometrology deals with dimensional measurements of micro- and nanostructures with a high spatial resolution. It typically combines a microscope imaging with a precise coordinate measurement, usually capable of nanometre resolution using the state-of-art laser interferometry techniques. The development in this field is driven, among others, by emerging advanced nanotechnologies that demand to push further the capabilities and limits of the interferometric techniques to make the nanometre-level dimensional measurement of nanostructures possible. The principal limitations of current systems are the environmental conditions and especially the fluctuations in the refractive index of air. The theoretical part of this thesis aim at analysis of individual parts of laser interferometer. I oriented myself on the study of their advantages/disadvantages and further also the possibilities of their industrial applications. The second part of the thesis presents my work that focused on the influence of the refractive index of air (RIA) on the measurement uncertainty. I experimentally demonstrated an interferometric system with a self-cancellation RIA fluctuations: a transparent photodetector is used for the measurement of the standing wave along the axis of a passive resonator, where the resonator also serves as a reference for the laser wavelength stabilisation. Another optical arrangement, based on a setup of several Michelson interferometers, represents a combination of an interferometer and a refractometer into a single system. This setup was used to study the behaviour of the ambient airflow with respect to the optical path difference and physical separation of the interferometer’s and refractometer’s path. Based on the experimental results I proposed new arrangements for shape measuring interferometers, which combine length interferometry and a tracking refractometer for the direct compensation of RIA fluctuations with geometrically adjacent optical beams. The results indicate an improvement in RIA fluctuation induced uncertainty by a factor of 100. Third part describes the design and implementation of interferometric systems for specific applications. For the industrial environment I developed a compact interferometric displacement gauge which is designed to allow nanometre level measurement using a simplified interferometer construction. For coordinate measurement of the position of the sample up to six degrees of freedom, I realised a compact modular interferometric system, which represents a unique setup together with a stabilised laser source. To measure the position of the sample in an electron beam writer chamber, I designed and implemented a differential interferometer that works in the near infrared domain and uses a new detection method developed for this system. In the fourth part I describe the realisation of a high-speed interferometer with a differential arrangement, which allows evaluation of high-cycle fatigue in material engineering. This method of studying high-cycle fatigue should be beneficial for both the basic research and the engineering practice.

This diploma thesis deals with assessment of geometric accuracy of machining center MCV 754 QUICK. BlueSYSTEM digital inclinometers from WYLER AG, XL-80 laser interferometer from RENISHAW, Ballbar QC20-W from RENISHAW and LaserTRACER self-guiding laser interferometer from ETALON AG were used to measure accuracy. Error of the X straightness in the direction of the Z axis was assessed. The first part of the paper describes the geometric accuracy of the machine, currently available instruments for measuring geometric accuracy and an explanation of straightness. The second part consists of the design of measurements, experiment, evaluation and comparison of results and recommendations for teaching.

This diploma thesis deals with uncertainties of interferometric measurements and methods for their evaluation. In the theoretical part of the thesis, are described interferometers and interferometric measurement techniques. Furthermore, there is presented process of determining the measurement uncertainty using methods GUM and Monte Carlo. In the practical part of the thesis, there are these two methods are used for qualification of measurement uncertainty calculated for the specific interferometer.

Gravitational-wave astronomy is an emerging field in observational astrophysics concerned with the study of gravitational signals proposed to exist nearly a century ago by Albert Einstein but only recently confirmed to exist. Such signals were theorized to result from astronomical events such as the collisions of black holes, but they were long thought to be too faint to measure on Earth. In recent years, the construction of extremely sensitive detectors—including the Laser Interferometer Gravitational-Wave Observatory (LIGO) project—has enabled the first direct detections of these gravitational waves, corroborating the theory of general relativity and heralding a new era of astrophysics research. As a result of their extraordinary sensitivity, the instruments used to study gravitational waves are also subject to noise that can significantly limit their ability to detect the signals of interest with sufficient confidence. The detectors continuously record more than 200,000 time series of auxiliary data describing the state of a vast array of internal components and sensors, the environmental state in and around the detector, and so on. This data offers significant value for understanding the nearly innumerable potential sources of noise and ultimately reducing or eliminating them, but it is clearly impossible to monitor, let alone understand, so much information manually. The field of machine learning offers a variety of techniques well-suited to problems of this nature. In this thesis, we develop and present several machine learning–based approaches to automate the process of extracting insights from the vast, complex collection of data recorded by LIGO detectors. We introduce a novel problem formulation for transient noise detection and show for the first time how an efficient and interpretable machine learning method can accurately identify detector noise using all of these auxiliary data channels but without observing the noise itself. We present further work employing more sophisticated neural network–based models, demonstrating how they can reduce error rates by over 60% while also providing LIGO scientists with interpretable insights into the detector’s behavior. We also illustrate the methods’ utility by demonstrating their application to a specific, recurring type of transient noise; we show how we can achieve a classification accuracy of over 97% while also independently corroborating the results of previous manual investigations into the origins of this type of noise. The methods and results presented in the following chapters are applicable not only to the specific gravitational-wave data considered but also to a broader family of machine learning problems involving prediction from similarly complex, high-dimensional data containing only a few relevant components in a sea of irrelevant information. We hope this work proves useful to astrophysicists and other machine learning practitioners seeking to better understand gravitational waves, extremely complex and precise engineered systems, or any of the innumerable extraordinary phenomena of our civilization and universe.

The two main themes in this thesis are the implementation of interference methods with optically trapped particles for measurements of position and optical phase (optical interferometric metrology) and the optical manipulation of nanoparticles for studies in the assembly of nanostructures, nanoscale heating and nonlinear optics (nanophotonics). The first part of the thesis (chapter 1, 2) provides an introductory overview to optical trapping and describes the basic experimental instrument used in the thesis respectively. The second part of the thesis (chapters 3 to 5) investigates the use of optical interferometric patterns of the diffracting light fields from optically trapped microparticles for three types of measurements: calibrating particle positions in an optical trap, determining the stiffness of an optical trap and measuring the change in phase or coherence of a given light field. The third part of the thesis (chapters 6 to 8) studies the interactions between optical traps and nanoparticles in three separate experiments: the optical manipulation of dielectric enhanced semiconductor nanoparticles, heating of optically trapped gold nanoparticles and collective optical response from an ensemble of optically trapped dielectric nanoparticles.

Neste trabalho, medimos o perfil 3D de superfícies (microtopografia) utilizando uma técnica de interferometria óptica: Phase-Shi,ftzng (Deslocamento de Fase). Utilizamos um interferômetro do tipo Twyman-Green para produzir fi.guras de interferência da superfície analisada. Essas imagens foram armazenadas usando-se uma câmera CCD ligada à um microcomputador. Para obter a microtopografia, calculamos o Mapa de Fase a partir das imagens digitalizadas usando um programa de microcomputador. Posteriormente um outro programa removeu a ambiguidade da função tangente (unwrapping), pela Técnica do Autômato Celular, usada no cáiculo do Mapa de Fase. Então efetuamos os cálculos para determinar a microtopografia da superfície. Depois fizemos a análise da microtopografia, levantando informações relevantes para a sua caracterização. Analisamos objetos com alta refletividade (espelhos planos e redes de Ronchi) e obtivemos bons resultados. Também comparamos alguns dos resultados obtidos com a técnica de Deslocamento de Fase com os resultados obtidos pela análise de Franjas de Igual Espessura. / In this work we measured the 3D profile of surfaces (microtopography) using a optical interferometric technique: Phase-Shifting. We used a interferometer of type Twyman-Green to produce interferograms from analyzed surface. These images was captured using a CCD camera that was linked to a microcomputer. To obtain a microtopography, we calculated the Phase Map using the digitalized images and a software of microcomputer. Then another program removed the wrapping of tangent fuction, using the Cellular-Automata Technique, that was used to calculate the Phase Map. So we calculated the microtopography of the surface. After we did the analyses of the microtopography, find out some important informations of its description. We studied objects with high reflectivity (plane mirrors and Ronchi ruting) and we obtained good results. Also we compared some results with that obtained by analyses of Fringes of Equal Thickness\'

Neste trabalho, medimos o perfil 3D de superfícies (microtopografia) utilizando uma técnica de interferometria óptica: Phase-Shi,ftzng (Deslocamento de Fase). Utilizamos um interferômetro do tipo Twyman-Green para produzir fi.guras de interferência da superfície analisada. Essas imagens foram armazenadas usando-se uma câmera CCD ligada à um microcomputador. Para obter a microtopografia, calculamos o Mapa de Fase a partir das imagens digitalizadas usando um programa de microcomputador. Posteriormente um outro programa removeu a ambiguidade da função tangente (unwrapping), pela Técnica do Autômato Celular, usada no cáiculo do Mapa de Fase. Então efetuamos os cálculos para determinar a microtopografia da superfície. Depois fizemos a análise da microtopografia, levantando informações relevantes para a sua caracterização. Analisamos objetos com alta refletividade (espelhos planos e redes de Ronchi) e obtivemos bons resultados. Também comparamos alguns dos resultados obtidos com a técnica de Deslocamento de Fase com os resultados obtidos pela análise de Franjas de Igual Espessura. / In this work we measured the 3D profile of surfaces (microtopography) using a optical interferometric technique: Phase-Shifting. We used a interferometer of type Twyman-Green to produce interferograms from analyzed surface. These images was captured using a CCD camera that was linked to a microcomputer. To obtain a microtopography, we calculated the Phase Map using the digitalized images and a software of microcomputer. Then another program removed the wrapping of tangent fuction, using the Cellular-Automata Technique, that was used to calculate the Phase Map. So we calculated the microtopography of the surface. After we did the analyses of the microtopography, find out some important informations of its description. We studied objects with high reflectivity (plane mirrors and Ronchi ruting) and we obtained good results. Also we compared some results with that obtained by analyses of Fringes of Equal Thickness\'

This thesis deals with a theoretical analysis and experimental verification of a new method for the refractive index of air measurement. This method uses a combination of laser and low-coherence interferometry. The experimental setup is based on the Michelson interferometer equipped with a double-spaced glass cell. The optical path difference between the inner and outer part of the cell that is proportional to air refractivity is estimated using two low-coherence interference signals. These signals are analysed in the frequency domain which results in the dependence of the phase change caused the by air on vacuum wavelength. This dependency is fitted by a theoretical function based on Edlén's equations in order to calculate the phase difference for laser wavelength. This value is then made more accurate utilising two laser interference signals and used for the air refractive index calculation. The new method was experimentally verified and compared to two different techniques. Moreover, the measurement uncertainty was evaluated.

Le suivi de la déformation de la croûte terrestre durant la phase intersismique pour la recherche des transitoires nécessite des instruments précis capables d'opérer pour de très longues durées. Le projet ANR-LINES a visé le développement de trois nouveaux instruments : un sismomètre mono-axial, un inclinomètre hydrostatique à longue base et un inclinomètre de forage pendulaire. Ces trois instruments profitent d'un capteur interférométrique de déplacement à longues fibres optiques du type Fabry-Pérot Extrinsèque (EFFPI). Leurs architectures mécaniques et l'utilisation de longues fibres permettent à ces instruments géophysiques nouvellement fabriqués d'atteindre les objectifs fixés.Le premier objectif de cette étude est de proposer des méthodes adaptées à l'estimation de la phase du chemin optique dans les cavités Fabry-Pérot. Une modulation du courant de la diode laser, suivie par une démodulation homodyne du signal d'interférence et un filtre de Kalman permettent de déterminer la phase en temps réel. Les résultats sont convaincants pour des mesures de courtes durées mais exigent des solutions complémentaires pour se prémunir des effets de la variation des phénomènes environnementaux.Le capteur EFFPI intégré dans l'inclinomètre de forage LINES lui offre l'opportunité d'établir une mesure différentielle de l'oscillation de la masselotte pendulée grâce à trois cavités Fabry-Pérot. Le sismomètre LINES utilise lui aussi le capteur de déplacement EFFPI pour la mesure du déplacement de sa bobine. Une description de l'architecture mécanique de ces instruments et une analyse des phénomènes détectés (mouvements lents, marées, séismes, microséismes . . . ) font partie de cette thèse. / Monitoring crustal deformation during the interseismic phase when searching for earth transients requires precise instruments able to operate for very long periods. The ANR-LINES project aimed to develop three new instruments: a single-axis seismometer, a hydrostatic long base tiltmeter and a borehole pendulum tiltmeter. These three instruments benefit of an extrinsic Fabry-Pérot interferometer (EFFPI) with long optic fibers for displacement detections. Their mechanical architectures and their disposal of long fibers help these newly manufactured geophysical instruments complete their goals.The first objective of this study is to propose appropriate methods for estimating the phase of the optical path in the Fabry-Pérot cavities. A modulation of the laser diode current, followed by a homodyne demodulation of the interference signal and a Kalman filter, allow determining the phase in real time. The results are convincing while taking short periods measurements but require additional solutions for protection against environmental phenomena variations. The EFFPI sensor integrated in the LINES borehole tiltmeter gives it the opportunity to establish a differential measurement of the bob's oscillation thanks to three Fabry-Perot cavities. The LINES seismometer also uses the EFFPI displacement sensor to measure its coil's displacement. A description of the two instruments' mechanical structures and an analysis of the detected phenomena (slow movements, tides, earthquakes, microseisms . . . ) are part of this thesis.Keywords: Laser interferometry, wavelength modulation, synchronous homodyne demodulation, ellipse fitting, Kalman filter, temperature compensation, borehole tiltmeter, simple pendulum, differential measurements, slow drift, seismicobservations, seismometer.

Der weltraumgestützte Gravitationswellendetektor LISA (Laser Interferometer Space Antenna) besteht aus drei identischen Satelliten an Bord derer sich jeweils zwei frei schwebende Testmassen befinden. Die Lage der einzelnen Testmassen in Bezug auf die zugehörige optische Bank muss mit einer Genauigkeit besser 1 pm/sqrt(Hz) in der Abstands- und besser 10 nrad/sqrt(Hz) in der Winkelmessung erfolgen. In der vorliegenden Arbeit wird ein kompaktes optisches Auslesesystem präsentiert, welches als Prototyp für diese Abstands- und Winkelmetrologie dient. Das dafür entwickelte polarisierende Heterodyn-Interferometer mit räumlich getrennten Frequenzen basiert auf einem hoch-symmetrischen Design, bei dem zur optimalen Gleichtakt-Unterdrückung Mess- und Referenzarm die gleiche Polarisation und Frequenz sowie annähernd gleiche optische Pfade haben. Für die Winkelmessung wird die Methode der differentiellen Wellenfrontmessung eingesetzt. In einem ersten Prototyp-Aufbau wird ein Rauschniveau von weniger als 100 pm/sqrt(Hz) in der Translations- und von weniger als 100 nrad/sqrt(Hz) in der Winkelmessung (beides für Frequenzen oberhalb 0.1 Hz) demonstriert. In einem zweiten Prototyp-Aufbau werden zusätzlich eine Intensitätsstabilisierung und ein Phasenlock der beiden Frequenzen implementiert. Die analoge Phasenmessung ist durch eine digitale, FPGA basierte, ersetzt. Mit diesem Aufbau wird ein Rauschen kleiner 5 pm/sqrt(Hz) in der Translationsmessung und kleiner 10 nrad/sqrt(Hz) in der Winkelmessung, beides für Frequenzen größer 0.01 Hz, erreicht. Eine Rausch-Analyse wurde durchgeführt und die Nichtlinearitäten des Interferometers bestimmt. Das Interferometer wurde im Hinblick auf die LISA Mission entwickelt, findet seine Anwendung aber auch bei der Charakterisierung der dimensionalen Stabilität von ultra-stabilen Materialien sowie in der optischen Profilometrie. Die Adaptierung des Interferometers dazu sowie erste Resultate zu beiden Anwendungen werden in dieser Arbeit präsentiert. / The space-based gravitational wave detector LISA (Laser Interferometer Space Antenna) consists of three identical satellites. Each satellite accommodates two free-flying proof masses whose distance and tilt with respect to its corresponding optical bench must be measured with at least 1 pm/sqrt(Hz) sensitivity in translation and at least 10 nrad/sqrt(Hz) sensitivity in tilt measurement. In this thesis, a compact optical readout system is presented, which serves as a prototype for the LISA proof mass attitude metrology. We developed a polarizing heterodyne interferometer with spatially separated frequencies. For optimum common mode rejection, it is based on a highly symmetric design, where measurement and reference beam have the same frequency and polarization, and similar optical pathlengths. The method of differential wavefront sensing (DWS) is utilized for the tilt measurement. In a first prototype setup noise levels below 100 pm/sqrt(Hz) in translation and below 100 nrad/sqrt(Hz) in tilt measurement (both for frequencies above 0.1 Hz) are achieved. A second prototype was developed with additional intensity stabilization and phaselock of the two heterodyne frequencies. The analog phase measurement is replaced by a digital one, based on a Field Programmable Gate Array (FPGA). With this setup, noise levels below 5 pm/sqrt(Hz) in translation measurement and below 10 nrad/sqrt(Hz) in tilt measurement, both for frequencies above 0.01Hz, are demonstrated. A noise analysis was carried out and the nonlinearities of the interferometer were measured. The interferometer was developed for the LISA mission, but it also finds its application in characterizing the dimensional stability of ultra-stable materials such as carbon-fiber reinforced plastic (CFRP) and in optical profilometry. The adaptation of the interferometer and first results in both applications are presented in this work.