A worldwide collaboration attempts to confirm the existence of gravitational waves predicted by Einstein's theory
of General Relativity, through direct observation with a network of large-scale laser interferometric antennas.
This paper is a contribution to the methodologies used to scrutinize the data in order to reveal the tiny signature
of a gravitational wave from rare cataclysmic events of astrophysical origin. More specifically, we are interested
in the detection of short frequency modulated transients or gravitational wave chirps. The amount of information
about the frequency vs. time evolution is limited: we only know that it is smooth. The detection problem is
thus non-parametric. We introduce a finite family of "template waveforms" which accurately samples the set of
admissible chirps. The templates are constructed as a puzzle, by assembling elementary bricks (the chirplets)
taken a dictionary. The detection amounts to testing the correlation between the data and the template family.
With an adequate time-frequency mapping, we establish a connection between this correlation measurement and
combinatorial optimization problems of graph theory, from which we obtain efficient algorithms to perform the
calculation. We present two variants. A first one addresses the case of amplitude modulated chirps and the
second allows the joint analysis of the data from several antennas. Those methods are not limited to the specific
context for which they have been developed. We pay a particular attention to the aspects that can be source of
inspiration for other applications.
The French-Italian interferometric gravitational wave detector VIRGO is currently being commissioned. Its principal instrument is a Michelson interferometer with 3 km long optical cavities in the arms and a power-recycling mirror. This paper gives an overview of the present status of the system. We report on the presently attained sensitivity and the system’s performance during the recent commissioning runs.
The goal of the VIRGO program is to build a giant Michelson type interferometer (3 kilometer long arms) to detect gravitational waves. Large optical components (350 mm in diameter), having extremely low loss at 1064 nm, are needed. Today, the Ion beam Sputtering is the only deposition technique able to produce optical components with such performances.
Consequently, a large ion beam sputtering deposition system was built to coat large optics up to 700 mm in diameter. The performances of this coater are described in term of layer uniformity on large scale and optical losses (absorption and scattering characterization).
The VIRGO interferometer needs six main mirrors. The first set was ready in June 2002 and its installation is in progress on the VIRGO site (Italy). The optical performances of this first set are discussed. The requirements at 1064 nm are all satisfied. Indeed, the absorption level is close to 1 ppm (part per million), the scattering is lower than 5 ppm and the R.M.S. wavefront of these optics is lower than 8 nm on 150 mm in diameter. Finally, some solutions are proposed to further improve these performance, especially the absorption level (lower than 0.1 ppm) and the mechanical quality factor Q of the mirrors (thermal noise reduction).
Reassignment is a technique which consists in moving the computed value of a time-frequency or time-scale energy distribution to a different location in the plane, so as to increase its readability. In the case of scalograms (squared modulus of wavelet transforms), a general form is given for the reassignment operators and their properties are discussed with respect to the chosen wavelet. Characterization of local singularities after reassignment is investigated by simulation and some examples (from mathematics and physics) are presented in order to support the usefulness of the approach. Since reassigning a scalogram amounts to compute two extra wavelet transforms, it is finally shown how this can be achieved in a fast and efficient way within a multiresolution framework.