Mario Gai

Gravitation astrometric measurement experiment

The Gravitation Astrometric Measurement Experiment (GAME) is a mission concept based on astronomical techniques (astrometry and coronagraphy) for Fundamental Physics measurements, namely the γ and β parameters of the Parametrized Post-Newtonian formulation of gravitation theories extending the General Relativity. The science case also addresses cosmology, extra-solar planets, Solar System objects and fundamental stellar parameters. The mission concept is described, including the measurement approach and the instrument design.

Fizeau interferometer for global astrometry in space

We discuss the design and the performance of a Fizeau interferometer with a long focal length and a large field of view that is well suited for a global astrometry space mission. Our work focuses on the geometric optimization and minimization of aberration of such an astrometric interferometer, which is able to observe astronomical targets down to the visual magnitude (mag) mv = 20 mag, with an accuracy in the measurements of 10 micro-arcseconds at mv = 15 mag. We assume a mission profile similar to that of the Global Astrometric Interferometer for Astrophysics mission of the European Space Agency. In this framework, data acquisition is performed by an array of CCDs working in time-delay integration mode. Optical aberrations, particularly distortion and coma, play a crucial role in the efficiency of this technique. We present a design solution that meets the requirements for the best possible exploitation of the time-delay integration mode over a field of view of 0.7 degrees x 0.7 degrees.

Matrix pseudoinversion for image neural processing

Recently some novel strategies have been proposed for training of Single Hidden Layer Feedforward Networks, that set randomly the weights from input to hidden layer, while weights from hidden to output layer are analytically determined by Moore-Penrose generalised inverse. Such non-iterative strategies are appealing since they allow fast learning, but some care may be required to achieve good results, mainly concerning the procedure used for matrix pseudoinversion. This paper proposes a novel approach based on original determination of the initialization interval for input weights, a careful choice of hidden layer activation functions and on critical use of generalised inverse to determine output weights. We show that this key step suffers from numerical problems related to matrix invertibility, and we propose a heuristic procedure for bringing more robustness to the method. We report results on a difficult astronomical image analysis problem of chromaticity diagnosis to illustrate the various points under study.

OCReP: An Optimally Conditioned Regularization for pseudoinversion based neural training.

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimization of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.

GAME: Gamma Astrometric Measurement Experiment

The GAME mission concept aims at the very precise measurement of the gravitational deflection of light by the Sun, by means of an optimised telescope operating in the visible and launched in orbit on a small class satellite. The targeted precision on the γ parameter of the Parametrised Post-Newtonian formulation of General Relativity is 10-6 or better, i.e. one to two orders of magnitude better than the best currently available results. Such precision is suitable to detect possible deviations from the unity value, associated to generalised Einstein models for gravitation, with potentially huge impacts on the cosmological distribution of dark matter and dark energy. The measurement principle is based on the differential astrometric signature on the stellar positions, i.e., based on the spatial component of the effect rather than the temporal component as in the most recent experiments using radio link delay timing. The observation strategy also allows some additional scientific objectives related to other tests of General Relativity and to the study of exo-planetary field, multiple aperture Fizeau interferometer, observing simultaneously two regions close to the Solar limb. The diluted optics approach is selected for achieving an efficient rejection of the scattered solar radiation, while retaining an acceptable angular resolution on the science targets. We describe the science motivation, the proposed mission profile, the possible payload implementation and the expected performance.

A Fizeau interferometer for astrometry in space : the metrology point of view

In space astrometry one seeks to determine positions, parallaxes and proper motions of stars to within 50 prad. The proposed GAIA mission is based on a rotating instrument made up of two telescopes set at a large base angle to each other and scanning the same great circle in the sky. Since the intended performances impose very strict stability requirements, a sophisticated metrological system is needed, whose actual implementation requires an integrated design of telescopes and laser interferometers. This paper examines the response of the instrument to small perturbations, special emphasis being placed on the location of star images. In order to exploit laser interferometry as much as possible, the original design was reconsidered, the base-angle implementation was improved, the number of degrees of freedom was reduced and the critical parameters were factorized. Although the present paper considers only the original proposal, in which each telescope was designed as a Fizeau interferometer, the results can be readily extended to other configurations.

Drift Scanning from Ground and in Space

The drift scanning technique offers, in principle, a simple and efficientmethod for imaging wide regions of the sky with intrinsic high astrometricaccuracy. Its performance is analyzed in two distinct environments, namelyfrom a small class ground based telescope and a spaceborne interferometer. Inparticular, the study is referred to the proposed ESA cornerstone missionGAIA (Global Astrometric Interferometer for Astrophysics).The constant clock rate of a CCD, due to the declination dependentsidereal speed variation, results in a systematic image smearing, whichlimits the positional accuracy. Moreover, the readout timing accuracyprovides an additional random noise corresponding to a drift speed jitter.Stability requirements on the order of 10-6 or better have to be fulfilledfor the space option.Both effects can be addressed by proper system design; provisionalimplementation strategies are discussed for both applications.

Performance of an Algorithm for Estimation of Flux, Background, and Location on One-dimensional Signals

Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional measurements performed by Gaia on intermediate to faint magnitude stars. Our goal is to define a convenient maximum likelihood framework, suited to efficient iterative implementation and to assessment of noise level, bias, and correlation among variables. The analytical model is investigated numerically and verified by simulation over a range of magnitude and background values. The estimates are unbiased, with a well-understood correlation between amplitude and background, and with a much lower correlation of either of them with location, further alleviated in case of signal symmetry. Two versions of the algorithm are implemented and tested against each other, respectively, for independent and combined parameter estimation. Both are effective and provide consistent results, but the latter is more efficient because it takes into account the flux-background estimate correlation.

Gravitation Astrometric Measurement Experiment (GAME)

GAME (Gravitation Astrometric Measurement Experiment) is a mission concept based on astronomical techniques for high precision measurements of interest to Fundamental Physics and cosmology, in particular the γ and β parameters of the Parameterized Post-Newtonian formulation of gravitation theories extending the General Relativity. High precision astrometry also provides the light deflection induced by the quadrupole moment of Jupiter and Saturn, and, by high precision determination of the orbits of Mercury and high elongation asteroids, the PPN parameter β. The astrometric and photometric capabilities of GAME may also provide crucial complementary information on a selected set of known exo-planets.

Multiple Anamorphic Beam Combination

We suggest a new approach to the problem of simultaneous combination of many beams in an optical or infra-red stellar pupil-plane interferometer. All the beams are combined with all other beams. First all beams are stretched anamorphically to create a comb of light, then this comb is interfered with itself rotated at right angle. The diagonal, with self-interfering beams, provides also the individual intensity calibration.