  We investigate the possiblity to detect Earth-like planets, in the visible
and the near infrared domains, with ground based Extremely Large Telescopes
equipped with adaptive systems capable of providing high Strehl ratios. From a
detailed analysis of the speckle noise, we derive analytical expressions of the
signal to noise ratio on the planet flux, for direct and differential imaging,
in the presence of the speckle noise and the photon noise of the residual
stellar halo. We find that a 100m telescope would detect an Earth at a distance
of 10pc, with a signal to noise ratio of 5, in an integration time of 12 hours.
This requires to control the instrumental aberrations with a precision better
than 1 nanometer rms, and to reach an image dynamics of $1.2{\rm x}10^{6}$ at
$0\farcs 1$ radius. Under the same conditions, a telescope of 30m would require
a dynamics of $1.3{\rm x}10^{7}$ for a positive detection
