This thesis describes and evaluates two new interferometric distance measurement methods based upon the well known method of Frequency Scanning Interferometry (FSI). These new methods are known as Dynamic FSI and Cascaded FSI. Dynamic FSI addresses the two problems, commonly seen in previous FSI implementa- tions, of not being able to measure a moving target and having a slow measurement rate. This method measures stationary and moving targets equally well, and can determine the distance to the target at all times during the measurement, in contrast to previous methods, which obtain only a single measured length from a measurement process which can take up to a second to make. Cascaded FSI was developed with the aim of increasing the accuracy and precision of FSI. This method allows for measurements with precision equal to that of displacement interferometry, and also provides a way of measuring length relative to the frequencies of atomic absorption lines, which are inherently more stable length references than a physical length artefact.

A acuracidade dos processos de medição e de montagem que utilizam os desempenos como referência depende principalmente da planicidade dessas superfícies. Se a referência está fora das especificações é inútil utilizar instrumentos sofisticados e de alta acuracidade. Neste trabalho é apresentado um sistema para medição de desvios de planicidade de desempenos. O sistema é constituído por dois transdutores de deslocamento do tipo LVDT fixados no eixo z de uma máquina de medir a três coordenadas (MM3C). Durante a medição a intenção é avaliar apenas os desvios da superfície, no entanto os mancais das MM3C não se deslocam perfeitamente e as leituras obtidas são as componentes dos desvios da superfície e do movimento dos mancais. Para eliminar os componentes de erros da máquina dos dados medidos, pode-se usar as técnicas de separação de erros, e então, o desvio da superfície pode ser determinado. O sistema de medição proposto possui uma interface eletrônica que possibilita a aquisição dos sinais da régua óptica da MM3C e dos transdutores de deslocamento do tipo LVDT. Possui, também, um programa computacional que utiliza as técnicas de separação de erros para determinar o desvio de planicidade do mensurando. O sistema desenvolvido foi utilizado para medir o desvio de planicidade de uma superfície. Para verificar a eficiência do mesmo foi realizada uma comparação entre os valores de erro de planicidade obtidos através de medição com o sistema proposto e aqueles obtidos com interferômetro a laser e nível eletrônico. / The accuracy of measurement and assembly process using surface plates depends mainly on these surfaces flatness. If the surface plate does not meet the flatness specification, it is ineffective to apply high technology instruments of measurement. This research proposes is to develop a flatness measurement system for surface plates using two electronic comparators attached to the coordinate measuring machine (CMM). During a measurement process, the purpose is to evaluate the workpiece profile. However, the signals picked up by sensors include the workpiece profile and component motion error. In order to separate these errors, error separation techniques can be applied. The proposed measurement system has an electronic interface to collect data from the CMM optical scale and from the electronic comparators. The collected data are sent to a computer prepared with an algorithm for applying the error separation equations and for compute the flatness error. A surface was measured using the proposed measurement system. To evaluate its efficiency, the results were compared to the measurements made using electronic level and laser interferometric system.

A acuracidade dos processos de medição e de montagem que utilizam os desempenos como referência depende principalmente da planicidade dessas superfícies. Se a referência está fora das especificações é inútil utilizar instrumentos sofisticados e de alta acuracidade. Neste trabalho é apresentado um sistema para medição de desvios de planicidade de desempenos. O sistema é constituído por dois transdutores de deslocamento do tipo LVDT fixados no eixo z de uma máquina de medir a três coordenadas (MM3C). Durante a medição a intenção é avaliar apenas os desvios da superfície, no entanto os mancais das MM3C não se deslocam perfeitamente e as leituras obtidas são as componentes dos desvios da superfície e do movimento dos mancais. Para eliminar os componentes de erros da máquina dos dados medidos, pode-se usar as técnicas de separação de erros, e então, o desvio da superfície pode ser determinado. O sistema de medição proposto possui uma interface eletrônica que possibilita a aquisição dos sinais da régua óptica da MM3C e dos transdutores de deslocamento do tipo LVDT. Possui, também, um programa computacional que utiliza as técnicas de separação de erros para determinar o desvio de planicidade do mensurando. O sistema desenvolvido foi utilizado para medir o desvio de planicidade de uma superfície. Para verificar a eficiência do mesmo foi realizada uma comparação entre os valores de erro de planicidade obtidos através de medição com o sistema proposto e aqueles obtidos com interferômetro a laser e nível eletrônico. / The accuracy of measurement and assembly process using surface plates depends mainly on these surfaces flatness. If the surface plate does not meet the flatness specification, it is ineffective to apply high technology instruments of measurement. This research proposes is to develop a flatness measurement system for surface plates using two electronic comparators attached to the coordinate measuring machine (CMM). During a measurement process, the purpose is to evaluate the workpiece profile. However, the signals picked up by sensors include the workpiece profile and component motion error. In order to separate these errors, error separation techniques can be applied. The proposed measurement system has an electronic interface to collect data from the CMM optical scale and from the electronic comparators. The collected data are sent to a computer prepared with an algorithm for applying the error separation equations and for compute the flatness error. A surface was measured using the proposed measurement system. To evaluate its efficiency, the results were compared to the measurements made using electronic level and laser interferometric system.

MScEng / Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Accurate dimensional measurement devices are critical for international industrial competitiveness for South Africa. An overview of all the necessary components of a laser tracking system using a multilateration technique for very accurate dimensional metrology is presented. A prototype laser tracker station was built to further investigate this type of system. The prototype successfully tracks a target within a volume of at least 200 200 200 mm3, approximately 300 mm away from the tracker. This system includes the mechanical design of a prototype tracker station, electronic implementation of ampli cation and motor control circuits, a tracking control algorithm, microcontroller programming and interfacing, as well as a user interface. Kinematic modelling along with Monte Carlo analyses nd the main error source of such a tracker as the beam steering mechanism gimbal axes misalignment. Multilateration is also motivated by the results found by the analysis. Furthermore, an initial sequential multilateration algorithm is developed and tested. The results of these tests are promising and motivate the use of multilateration over a single beam laser tracking system. / AFRIKAANSE OPSOMMING: Dit is van kritieke belang dat Suid-Afrika akkurate dimensionele metingstoestelle ontwikkel vir internasionale industriële medinging. 'n Oorsig van al die nodige komponente vir 'n Laser-Volgsisteem, wat slegs van multilaterasie gebruik maak om baie akkurate drie dimensionele metings te kan neem, word in hierdie projek voorgestel. 'n Prototipe Laser-Volgsisteem-stasie word gebou om so 'n sisteem verder te ondersoek. Die prototipe slaag wel daarin om 'n teiken, binne 'n volume van 200 200 200 mm3 op 'n afstand van omtrent 300 mm te volg. Die sisteem sluit die meganiese ontwerp van die sodanige stasie, elektroniese seinversterking, motorbeheer, 'n volgingsbeheer algoritme, mikroverwerker programeering en intergrasie, asook 'n gebruikerskoppelvlak program in. Kinematiese modelering, tesame met Monte Carlo simulasies, toon aan dat die hoof oorsaak van metingsfoute by so 'n stasie by die rotasie-asse van die laserstraal-stuurmeganisme, wat nie haaks is nie, lê. Die multilaterasie metode word ook verder ondersteun deur dié modelering. 'n Algoritme wat sekwensiële multilateratsie toepas word boonop ontwikkel en getoets. Die resultate van die toetse dui daarop dat die algoritme funksioneer en dat daar voordele daarin kan wees om so 'n metode in plaas van 'n Enkelstraal-Volgsisteem te gebruik.

[pt] O presente trabalho tem por objetivo implantar um método para calibração de sistema de medição linear por interferometria laser por meio de comparação a um outro sistema laser de referência. O referido método é considerado mais simples que a calibração por componentes realizada atualmente e, conforme demonstrado no trabalho, apresenta confiabilidade metrológica que atende a exatidão necessária para as aplicações dos laseres em metrologia dimensional, vindo suprir uma necessidade metrológica dos laboratórios credenciados pelo Instituto Nacional de Metrologia, Normalização e Qualidade Industrial (Inmetro) e do parque industrial brasileiro, usuários destes sistemas de medição. A implantação do sistema para calibração de lasers de medição foi baseada em normas internacionais de calibração e de cálculo da incerteza de medição e utilizou um sistema laser de referência calibrado no Inmetro, com rastreabilidade a padrões nacionais, com as menores incertezas possíveis. O método de medição implantado realiza a calibração de um sistema laser por comparação a outro utilizando medições feitas a partir do deslocamento da mesa onde é a apoiado o prisma óptico. O que é de fato analisado é a diferença das medições dos dois sistemas laser para um mesmo deslocamento. Foram registradas as diferenças das indicações de 200 mm em 200 mm de deslocamento, em um total de 2000 mm, que variaram de 0,027 µm a 0,690 µm. Foram realizadas três medições para cada deslocamento e quatro repetições completas do procedimento em dias diferentes, com variação do desvio padrão de 0,009 µm a 0,098 µm e incertezas expandidas que variaram de 0,109 µm a 0,306 µm. São apresentadas a metodologia de calibração, cálculos das correções, fontes de erros e cálculos da incerteza de medição para a comparação de sistemas laseres de medição linear. / [en] The present work aims at the implementation of a calibration method for interferometric linear laser measurement systems by comparison to another reference system. The proposed method is considered simpler than the calibration by components that is carried out today at Inmetro (National Institute of Metrology, Standardization and Industrial Quality) and, as demonstrated along this work, presents the metrological reliability and accuracy necessary for several applications of lasers in dimensional metrology. This approach will supply the metrological needs of several laboratories accredited by Inmetro and of the Brazilian industry in general, users of such measurement systems, regarding cost and time of calibration. The method implemented was based on international technical standards related to calibration and uncertainty calculation and used a reference system calibrated at Inmetro, with traceability to national standards, with the lowest uncertainties that could be achieved. The said method performs the calibration of a laser system by comparison to another through measurements of the displacement of the table where the optical prism rests. What is indeed analyzed is the difference of the measurements obtained by the two laser systems for the same table displacement. The differences were recorded for each displacement of 200 mm, in a total of 2,000 mm, their variation being from 0.027 µm to 0.690 µm. The whole procedure was repeated four times, in different days, with three measurements for each displacement. Their standard deviation varied from 0.009 µm to 0.098 µm while their expanded uncertainties varied from 0.109 µm to 0.306 µm depending on the value of the displacement. The calibration methodology, correction calculation, errors sources and measurement uncertainty calculations for the linear measurement laser systems comparison are presented in this dissertation.

Les formes asphériques et les surfaces complexes sont une classe très avancée d'éléments optiques. Leur application a considérablement augmenté au cours des dernières années dans les systèmes d'imagerie, l'astronomie, la lithographie, etc. La métrologie de ces pièces est très difficile, en raison de la grande gamme dynamique d'information acquise et la traçabilité à l'unité SI mètre. Elle devrait faire usage de la norme infinie; (Méthode de zone minimum ou la méthode Min-Max) pour calculer l'enveloppe entourant les points dans le jeu de données en réduisant au minimum la différence entre l'écart maximum et l'écart minimal entre la surface et l'ensemble de données. Cette méthode a une grande complexité en fonction du nombre de points, enplus, les algorithmes impliqués sont non-déterministes. Bien que cette méthode fonctionne pour des géométries simples (lignes, plans, cercles, cylindres, cônes et sphères), elle est encore un défi majeur lorsqu' utilisée pour des géométries complexes (asphérique et surfaces complexes). Par conséquent, l'objectif de la thèse est le développement des algorithmes d'ajustement Min-Max pour les deux surfaces asphériques et complexes, afin de fournir des algorithmes de référence robustes pour la grande communauté impliquée dans ce domaine. Les algorithmes de référence à développer devraient être évalués et validés sur plusieurs données de référence (Softgauges) qui seront générées par la suite. / Aspheres and freeform surfaces are a very challenging class of optical elements. Their application has grown considerably in the last few years in imaging systems, astronomy, lithography, etc. The metrology for aspheres is very challenging, because of the high dynamic range of the acquired information and the traceability to the SI unit meter. Metrology should make use of the infinite norm; (Minimum Zone Method or Min-Max method) to calculate the envelope enclosing the points in the dataset by minimizing the difference between the maximum deviation and the minimum deviation between the surface and the dataset. This method grows in complexity as the number of points in the dataset increases, and the involved algorithms are non-deterministic. Despite the fact that this method works for simple geometries (lines, planes, circles, cylinders, cones and spheres) it is still a major challenge when used on complex geometries (asphere and freeform surfaces). Therefore, the main objective is to address this key challenge about the development of Min-Max fitting algorithms for both aspherical and freeform surfaces as well as least squares fitting algorithms, in order to provide robust reference algorithms for the large community involved in this domain. The reference algorithms to be developed should be evaluated and validated on several reference data (softgauges) that will be generated using reference data generators.

Le Laboratoire Commun de Métrologie LNE-CNAM (LCM) souhaite affiner sa maîtrise des références de pression afin de réaliser des appareillages de tout premier rang au niveau international. L'incertitude relative visée sur les références de pression est de l'ordre de 10-6. Cet objectif se traduit par une problématique de métrologie dimensionnelle où une mesure de la forme des pistons/cylindres utilisés dans les balances manométriques doit être menée. La mesure de cylindricité est également impliquée dans un très grand nombre d'applications industrielles comme la qualification d'étalons de référence destinés à la qualification d'appareillages de mesure. Notre travail de recherche, réalisé dans le cadre d'une convention CIFRE avec la SAS GEOMNIA, concerne la réalisation d'un instrument de référence de très haute précision permettant la mesure de forme de cylindres creux ou pleins. Nous proposons un saut technologique pour satisfaire un niveau d'incertitude sur la mesure de l'écart de cylindricité de l'ordre de 10 nanomètres dans un volume de mesure cylindrique de Ø350 mm et de hauteur 150 mm. La mesure de forme est habituellement pratiquée en déplaçant un capteur par rapport à la surface à mesurer par un guidage de haute précision. Il n'est cependant pas possible de réaliser un guidage entre deux solides d'un niveau de précision permettant de garantir les incertitudes souhaitées, même en utilisant les techniques de correction d'erreurs dont la précision est limitée par le défaut de répétabilité des guidages. Pour satisfaire à ce niveau d'incertitude, nous proposons une démarche basée sur le concept de structure métrologique dissociée. La mesure d'une pièce consiste alors à comparer sa forme à celle d'une pièce cylindrique de référence. Cette dernière doit seulement présenter une stabilité de forme parfaite. La cartographie d'écart de forme de la référence cylindrique doit cependant être identifiée au même niveau d'incertitude visé.Le travail de recherche développé propose une analyse détaillée des machines actuelles et de leurs limitations. Suite à cette analyse, une architecture de machine a été proposée pour lever ces limitations. Cette architecture tient compte des écarts « secondaires » liés à la position des capteurs et des effets de second ordre, pour satisfaire le niveau de précision visé. Une procédure complète d'étalonnage de la machine a été élaborée en s'inspirant des méthodes de séparation d'erreurs. Cette procédure originale permet de séparer les défauts de forme du cylindre de référence de ceux d'une pièce de qualification cylindrique mesurée simultanément. La méthode employée ne présente pas de limitations en termes d'exactitude. Cette procédure a été expérimentalement validée. Une analyse des effets liés à la mesure de surfaces cylindriques par des capteurs capacitifs a été menée. Ces essais ont conduit au développement de stratégies d'étalonnage de ces capteurs in situ utilisant des interféromètres à laser intégrés dans la machine. La traçabilité métrologique des résultats des mesures est ainsi garantie. Deux bancs de tests ont été développés pour caractériser les diverses influences et valider les procédures d'étalonnage des capteurs. La conception détaillée de l'instrument est issue de la synthèse des réflexions menées sur l'architecture, sur l'étalonnage et sur la maîtrise de la mesure de déplacements par capteurs capacitifs. Ce travail a abouti à la réalisation de ce nouvel instrument de référence ; sa conception, son montage et son réglage sont présentés. / The “Laboratoire Commun de Métrologie LNE-CNAM (LCM)” seeks to improve the measurement of primary pressure standards done using pressure balances, to an order of 10-6 relative uncertainty. Therefore, it is appropriate to back-up these pressure balances with a measurement of the topology of the piston-cylinder devices used on these balances. Cylindricity measurement is also found in many industrial applications such as the measurement of standards used for the calibration of measuring machines. This research project, conducted in collaboration with SAS GEOMNIA under a CIFRE agreement, has a main objet to develop a new ultra-high precision machine for cylinders form measurement. We pushes with this project the leading edge of the cylinders form measurement area; we propose indeed a technological leap which leads to reduce the uncertainty associated to cylindricity errors up to 10 nm in a cylindrical working volume of 350 mm diameter rand 150 mm height. Form measurement is usually done using a measurement probe moved about the surface to be measured with high precision guiding systems. Nonetheless, these guiding systems are not precise enough to offer the low uncertainty required even when error correction techniques are used. This is because the precision of the guides is limited by their low repeatability. To meet this uncertainty level, we propose an approach based on the “dissociated metrological structure” concept. The measurement consists of comparing the artifact's form with the form of a cylindrical reference which should have perfect form stability. However, the mapping form deviation of this cylindrical reference needs to be identified at the same level of uncertainty referred.The present work exposes a detailed analysis of the existing measuring machines and their limitations. Consequently, an optimized machine architecture is proposed in order to overcome the present limitations. The proposed machine architecture takes into account the "secondary" error terms relative to the probes positions and second order effects in order to satisfy the level of accuracy sought. A complete calibration procedure of the machine has been elaborated based on the error separation methods; it allows the separation of the form errors of each of the reference cylinder and a qualification cylindrical part simultaneously measured. This procedure does not present any accuracy limitations and has been experimentally verified. An analysis of the effects related to the measurement of cylindrical artifacts using capacitive sensors has also been investigated. These experiments have led to the development of in-situ calibration strategies using laser interferometers integrated in the machine. Thus, the metrological traceability of the measurements is guaranteed. Two test benches have been developed to characterize the error sources that influence the measurement and to validate the calibration procedures of the probes used. The detailed design of the instrument synthesizes all the conceptual thoughts about the architecture, the calibration and the displacement measurement of the capacitive probes. This work has resulted in the development of this new reference instrument; its design, installation and adjustment are detailed.