Physics – Optics
Scientific paper
May 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006phdt.........2v&link_type=abstract
PhD Thesis, TU Delft, 2006
Physics
Optics
Interferometry, Aperture Synthesis
Scientific paper
Optical long baseline stellar interferometry is an observational technique in astronomy that already exists for over a century, but is truly blooming during the last decades. The undoubted value of stellar interferometry as a technique to measure stellar parameters beyond the classical resolution limit is more and more spreading to the regime of synthesis imaging. With optical aperture synthesis imaging, the measurement of parameters is extended to the reconstruction of high resolution stellar images. A number of optical telescope arrays for synthesis imaging are operational on Earth, while space-based telescope arrays are being designed. For all imaging arrays, the combination of the light collected by the telescopes in the array can be performed in a number of ways. In this thesis, methods are introduced to model these methods of beam combination and compare their effectiveness in the generation of data to be used to reconstruct the image of a stellar object. One of these methods of beam combination is to be applied in a future space telescope. The European Space Agency is developing a mission that can valuably be extended with an imaging beam combiner. This mission is labeled Darwin, as its main goal is to provide information on the origin of life. The primary objective is the detection of planets around nearby stars - called exoplanets- and more precisely, Earth-like exoplanets. This detection is based on a signal, rather than an image. With an imaging mode, designed as described in this thesis, Darwin can make images of, for example, the planetary system to which the detected exoplanet belongs or, as another example, of the dust disk around a star out of which planets form. Such images will greatly contribute to the understanding of the formation of our own planetary system and of how and when life became possible on Earth. The comparison of beam combination methods for interferometric imaging occupies most of the pages of this thesis. Additional chapters will treat related subjects, being experimental work on beam combination optics, a description of a novel formalism for aberration retrieval and experimental work on nulling interferometry. The Chapters on interferometric imaging are organized in such a way that not only the physical principles behind a stellar interferometer are clear, but these chapters also form a basis for the method of analysis applied to the interferometers - -or rather beam combination methods- under consideration. The imaging process in a stellar interferometer will be treated as the inversion of a linear system of equations. The definition of interferometric imaging in this thesis can be stated to be the reconstruction of a luminosity distribution function on the sky, that is, in angular measure, larger than the angular diffraction limited spot size -or Point-Spread Function (PSF)- of a single telescope in the array and that contains, again in angular measure, spatial structure that is much smaller than the PSF of a single telescope. This reconstruction has to be based on knowledge of the dimensions of the telescope array and the detector. The detector collects intensity data that is formed by observation of the polychromatic luminosity distribution on the sky and is deteriorated by the quantum-nature of light and an imperfect electronic detection process. Therefore, the imaging study presented in this thesis can be regarded to be a study on the signal characteristics of various interferometers while imaging a polychromatic wide-field stellar source. The collection of beam combination methods under consideration consists of four types. Among these are two well-known types, having either co-axially combined beams as in the Michelson-Morley experiment to demonstrate the existence of ether, or beams that follow optical paths as if an aperture mask were placed in front of a telescope, making the beams combine in the focus of that telescope, as suggested by Fizeau. For separated apertures rather than an aperture mask, these optical paths are stated to be homothetic. In short, these two types will be addressed as the Michelson or the Homothetic type. The other two types are addressed as Densified and Staircase. The first one is short for densified pupil imaging, an imaging technique very similar to the Homothetic type, be it that the natural course of light after the aperture mask is altered. However, the combination of the beams of light is again in focus. The Staircase method is an alternative to the co-axial Michelson method and lends its name from the fact that a staircase-shaped mirror is placed in an intermediate focal plane after each telescope in the array, before combining the beams of light co-axially. This addition allows stellar imaging as with the Michelson type, with the advantage of covering a large field-of-view. The details of these methods will intensively be discussed in this thesis, but the introduction of them at this point allows a short list of results, found by comparing them for equal imaging tasks. Homothetic imagers are best suited for covering a wide field-of-view, considering the information content of the interferometric signals these arrays produce. The large number of detectors does not seem to limit the imaging performance in the presence of noise, due to the high ratio of coherent versus incoherent information in the detector signal. The imaging efficiency of a Michelson type array is also high, although -considering only polychromatic wide-field imaging tasks- the ratio of coherent versus incoherent information in the detected signals is very low. This results in very large observation times needed to produce images comparable to those obtained with a Homothetic array. A detailed presentation of the characteristics of the detected signals in a co-axial Michelson array reveal that such signals, obtained by polychromatic observation of extended sources, have fringe envelope functions that do not allow Fourier-spectroscopy to obtain high-resolution spectroscopic information about such a source.
For the Densified case, it is found that this method can indeed provide an interferometric PSF that is more favorable than a homothetic PSF, but only for narrow-angle observations. For polychromatic wide-field observations, the Densified-PSF is field-dependent, for which the image reconstruction process can account. Wide-field imaging using the favorable properties of the Densified-PSF can be performed, by using special settings of the delay or optical path length difference between interferometer arms and including observations with several settings of delay in the observation data. The Staircase method is the second best method for the imaging task under consideration. The discontinuous nature of the staircase-shaped mirrors does not give rise to a discontinuous reconstructed luminosity distribution or non-uniformly covered spatial frequencies. The intrinsic efficiency of the interferometric signal in this type of interferometer is worse than that of the other co-axial method, although the ratio of coherent versus incoherent signal in the data -the length of the fringe packet in one intensity trace-e- is nearly ultimate. The inefficiency is overwhelmingly compensated for by the very short observation time needed. Besides numerical studies of interferometer arrays, one interferometric imager was also studied experimentally. A homothetic imager was built, comprising three telescopes with fully separated beam relay optics. The pointing direction, the location and the optical path length of two of the three beams are electronically controllable. The beams can be focused together to interfere, via a beam combiner consisting of curved surfaces. This set-up allows to measure the required accuracies at which certain optical elements have to be positioned. Moreover, this set-up demonstrates that without knowledge of the initial pointing directions, locations and optical path lengths of the beams, the situation of homothesis can be attained, solely based on information from the focal plane of the set-up. Further experiments show that the approxi
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