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Abstract
The light coming from a star travels undisturbed for billions of kilometers until it reaches the boundaries of the Earth atmosphere: there small differences in the refraction index distort the spherical wavefront, creating phase errors in the image-forming ray paths. Even at the best sites, ground-based telescopes observing at visible wavelengths cannot, because of atmospheric turbulence alone, achieve an angular resolution better than telescopes of 10- to 20-cm diameter. Adaptive Optics (AO) is a technique to remove the effects of these distortions in real-time by operating a deformable mirror that rapidly adapts its shape to the atmospheric disturbance canceling it. ESO now operates several AO systems in the Paranal observatory, where the four telescopes of the VLT (Very Large Telescope) are installed. Several of them are the result of a common project called MACAO, for Multi Application Curvature Adaptive Optics. Four MACAO systems, one for each VLT telescope, are now serving the VLT-Interferometer (VLTI) increasing the capability of the interferometer. In this paper we will present the main concept of adaptive optics and then we will derive a model for a generic AO system. We will then tailor the model to MACAO and study some interesting features of MACAO as the control of the piston mode and the control of the tip/tilt modes.