L’arrivée du spectromètre imageur à transformée de Fourier SITELLE au télescope Canada-France-Hawaï souligne la nécessité d’un calculateur de temps d’exposition permettant aux utilisateurs de l’instrument de planifier leurs observations et leurs demandes de temps de télescope. Une grande partie de mon projet est ainsi le développement d’un code de simulation capable de reproduire les résultats de SITELLE et de son prédecesseur SpIOMM, installé à l’Observatoire du Mont-Mégantic. La précision des simulations est confirmée par une comparaison avec des données SpIOMM et les premières observations de SITELLE. La seconde partie de mon projet consiste en une analyse spectrale de données observationelles. Prenant avantage du grand champ de vue de SpIOMM, les caractéristiques du gaz ionisé (vitesse radiale et intensité) sont étudiées pour l’ensemble de la paire de galaxies en interaction Arp 72. La courbe de rotation dans le visible ainsi que le gradient de métallicité de NGC 5996, la galaxie principale d’Arp 72, sont obtenues ici pour la première fois. La galaxie spirale NGC 7320 est également étudiée à partir d’observations faites à la fois avec SpIOMM et SITELLE. / The arrival of the Fourier-transform imaging spectrometer SITELLE at the Canada-France-Hawaii telescope highlights the importance of having an exposure time calculator allowing the instrument’s users to plan ahead their observing proposals. A large part of my project is the development of a simulator able to reproduce the results obtained with SITELLE and its predecessor SpIOMM. The accuracy of the simulations is confirmed through comparison with SpIOMM data and SITELLE’s first observations. The second part of my project is the spectral analysis of observational data. SpIOMM’s large field of view allows us to study the properties (radial velocities and line intensities) of the ionized gas through the entirety of Arp 72, a pair of interacting galaxies. For the first time, the rotation curve in the optical and the metallicity gradient are obtained for NGC 5996, the main galaxy in Arp 72. Both SpIOMM and SITELLE results are also shown for the dwarf spiral galaxy NGC 7320.

Afin d’obtenir un spectre de haute résolution avec un spectromètre-imageur par transformation de Fourier (IFTS), il est nécessaire que la scène demeure statique pendant l’acquisition. Dans de nombreux cas, cette hypothèse ne peut pas être respecter simplement à cause de la présente d’un mouvement relatif entre la scène et l’instrument pendant l’acquisition. À cause de ce mouvement relatif, les échantillons obtenus à un pixel capturent différentes régions de la scène observée. Dans le meilleurs des cas, le spectre obtenu de ces échantillons sera peu précis et aura une faible résolution. Après une brève description des IFTS, nous présentons des algorithmes de d’estimation du mouvement pour recaler les trames des cubes de données acquises avec un IFTS, et desquelles il sera ensuite possible d’obtenir des spectres avec une précision et une résolution élevées. Nous utilisons des algorithmes d’estimation du mouvement qui sont robustes aux variations d’illumination, ce qui les rend appropriés pour traiter des interferogrammes. Deux scénarios sont étudiés. Pour le premier, nous observons un mouvement relatif unique entre la scène qui est imagée et l’instrument. Pour le second, plusieurs cibles d’intérêts se déplacent dans des directions différentes à l’intérieur de la scène imagée. Après le recalage des trames, nous devons ensuite résoudre un nouveau problème lié à la correction de l’effet hors-axe. Les échantillons qui sont associés à un interférogramme ont été acquis par différents pixels du senseur et leurs paramètres hors-axe sont donc différents. Nous proposons un algorithme de rééchantillonnage qui tient compte de la variation des paramètres de l’effet hors-axe. Finalement, la calibration des données obtenues avec un IFTS lorsque la scène imagée varie dans le temps est traitée dans la dernière partie de la thèse. Nous y proposons un algorithme de calibration apropriée des trames, qui précède le recalage des trames et la correction de l’effet hors-axe. Cette chaine de traitement nous permet d’obtenir des spectres avec une résolution élevée. Les algorithmes proposés ont été testés sur des données expérimentales et d’autres provenant d’un simulateur. La comparaison des résultats obtenus avec la réalité-terrain démontre la valeur de nos algorithmes: nous pouvons obtenir des spectres avec une résolution comparable à celle qui peut être obtenue lorsqu’il n’y aucun mouvement entre l’instrument (IFTS) et la scène qui est imagée. / To obtain a useful or high resolution spectrum from an Imaging Fourier Transform Spectrometer (IFTS), the scene must be stationary for the duration of the scan. This condition is hard to achieve in many cases due to the relative motion between the instrument and the scene during the scan. This relative motion results in multiple data samples at a given pixel being taken from different sub-areas of the scene, and from which (at best) spectra with low accuracy and resolution can be computed. After a review of IFTS, we present motion estimation algorithms to register the frames of data cubes acquired with a moving IFTS, and from which high accuracy and resolution spectra can be retrieved. We use motion estimation algorithms robust to illumination variations, which are suitable for interferograms. Two scenarios are examined. In the first, there is a global motion between the IFTS and the target. In the second, there are multiple targets moving in different directions in the field of view of the IFTS. After motion compensation, we face an off-axis correction problem. The samples placed on the motion corrected optical path difference (OPD) are coming from different spatial locations of the sensor. As a consequence, each sample does not have the same off-axis distortion. We propose a resampling algorithm to address this issue. Finally the calibration problem in the case of moving IFTS is addressed in the last part of the thesis. A calibration algorithm suitable for data cube of moving IFTS is proposed and discussed. We then register the frames and perform the off-axis correction to obtain high resolution spectra. To verify our results, we apply the algorithms on simulated and experimental data. The comparison between the results with the ground-truth shows promising performance. We obtain spectra with resolution similar to the ground truth spectra (i.e., with data acquired when the IFTS and the scene are stationary).

We describe an implementation of a multi-threaded NFFT (nonequispaced fast Fourier transform) software library and present the used parallelization approaches. Besides the NFFT kernel, the NFFT on the two-sphere and the fast summation based on NFFT are also parallelized. Thereby, the parallelization is based on OpenMP and the multi-threaded FFTW library. Furthermore, benchmarks for various cases are performed. The results show that an efficiency higher than 0.50 and up to 0.79 can still be achieved at 12 threads.

En plus de 40 ans d’existence, la spectroscopie de Fourier, basée sur l’interféromètre de Michelson,a permis des progrès considérables dans notre connaissance de la structure des atomes et des molécules s’imposant peu à peu comme un outil de base pour le diagnostic optique. Aujourd’hui, dépasser ses performances en terme de limite de résolution, rapidité, sensibilité et exactitude permettrait de répondre à de nouveaux enjeux. Cette thèse porte sur le développement expérimental de la spectroscopie de Fourier par peignes de fréquences femtosecondes. Deux peignes de fréquences, lasers composés de centaines de milliers de raies fines dont la position est parfaitement contrôlée, sondent l’échantillon et la transformation de Fourier de leurs interférences temporelles fournit le spectre. Trois dispositifs basés sur des lasers femtosecondes à fibres dopées (à 1 μm et 1.5 μm) ou à solides (à 2.4 μm) illustrent les performances de la méthode. Par comparaison à la spectroscopie de Fourier traditionnelle, les temps de mesure ont été réduits de la seconde à la microseconde, pour des spectres de molécules en phase gazeuse couvrant une centaine de nanomètres à des limites de résolution du GHz. La sensibilité atteint celle des spectromètres par laser accordable les plus performants grâce à des méthodes de détection différentielle ou d’utilisation de cavités multipassages ou résonnantes. Augmenter le temps de mesure et résoudre les raies individuelles du peigne permet une spectroscopie de précision à large bande spectrale, car la fréquence absolue de chaque raie de peigne peut être connue avec l’exactitude d’une horloge atomique. / For four decades, Fourier transform spectroscopy has greatly improved our atomes and molecules structures knowledges, and thus became a widely used tool for optical diagnosis. However, today it is useful to overcome some of its limitations in order to address new challenges. This thesis is about experimental developpement concerning frequency comb fourier transform spectroscopy. Two frequency combs, made of thousands of very narrow frequency lines perfectly known and controlled, are probing an absorbing sample. The fourier transform of their temporal interference pattern provides the optical spectrum. Three devices based on fiber doped lasers (emitting at 1μm and 1.5 μm) and solid lasers (at 2.4 μm) are used to demonstrate the method advantages. Compared to traditional Fourier transform spectroscopy the recording time has shrunk by one million for the acquisition of spectra spreading on a hundred of nanometers at GHz resolution. Using multipass cells of differential detection devices, the sensitivity reached is comparable to that provided by the most efficient laser based methods. Increasing the resolution allows for clear observation of the comb individual tooth which position can be measured with the accuracy of an atomic clock, providing thus a simple and accurate method for auto calibrated spectra.

We present a MPI based software library for computing the fast Fourier transforms on massively parallel, distributed memory architectures. Similar to established transpose FFT algorithms, we propose a parallel FFT framework that is based on a combination of local FFTs, local data permutations and global data transpositions. This framework can be generalized to arbitrary multi-dimensional data and process meshes. All performance relevant building blocks can be implemented with the help of the FFTW software library. Therefore, our library offers great flexibility and portable performance. Likewise FFTW, we are able to compute FFTs of complex data, real data and even- or odd-symmetric real data. All the transforms can be performed completely in place. Furthermore, we propose an algorithm to calculate pruned FFTs more efficiently on distributed memory architectures. For example, we provide performance measurements of FFTs of size 512^3 and 1024^3 up to 262144 cores on a BlueGene/P architecture.

We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

In flexible fitting, the high-resolution crystal structure of a molecule is deformed to optimize its position with respect to a low-resolution density map. Solving the flexible fitting problem entails answering the following questions: (A) How can the crystal structure be deformed? (B) How can the term "optimum" be defined? and (C) How can the optimization problem be solved? In this dissertation, we answer the above questions in reverse order. (C) We develop PFCorr, a non-uniform SO(3)-Fourier-based tool to efficiently conduct rigid-body correlations over arbitrary subsets of the space of rigid-body motions. (B) We develop PF2Fit, a rigid-body fitting tool that provides several useful definitions of the optimal fit between the crystal structure and the density map while using PFCorr to search over the space of rigid-body motions (A) We develop PF3Fit, a flexible fitting tool that deforms the crystal structure with a hierarchical domain-based flexibility model while using PF2Fit to optimize the fit with the density map. Our contributions help us solve the rigid-body and flexible fitting problems in unique and advantageous ways. They also allow us to develop a generalized framework that extends, breadth-wise, to other problems in computational structural biology, including rigid-body and flexible docking, and depth-wise, to the question of interpreting the motions inherent to the crystal structure. Publicly-available implementations of each of the above tools additionally provide a window into the technically diverse fields of applied mathematics, structural biology, and 3D image processing, fields that we attempt, in this dissertation, to span. / text

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.

No description available.

Published Article / The reproductive status of animals is of utmost importance to the modern farmer. Decisions concerning the management of the flock are influenced by the knowledge of the percentage of animals that are pregnant at any specific time. The aim of the project was to gain knowledge for the development of an instrument that is affordable and with which a farmer can do pregnancy determination himself/herself, thereby enabling him/her to make the correct management decisions. Experimental data were obtained from pregnant Dorper ewes with the aid of a portable Doppler instrument. Using real data as input, simulations of Wavelet and Short Time Fourier Transforms (STF) were done in MathCAD. In the simulations known levels of noise were added to the Doppler signals. Satisfactory results were obtained from the simulations of Wavelet Transforms. In the simulation of the Wavelet Transforms, signals with a SNR of -6.5 dB were successfully identified. It can thus be concluded that Wavelet Transforms can be used successfully for the detection of the fetal heartbeat in noisy ultrasonic Doppler signals.