  The accuracy of ground-based astronomical photometry is limited by two
factors: photon statistics and stellar scintillation arising when star light
passes through Earth's atmosphere. This paper examines the theoretical role of
the outer scale $L_0$ of the optical turbulence (OT) which suppresses the
low-frequency component of scintillation. It is shown that for typical values
of $L_0 \sim 25 - 50$ m, this effect becomes noticeable for a telescopes of
diameter around 4 m. On extremely large, $30 - 40$ m, telescopes with exposures
longer than a few seconds, the inclusion of the outer scale in the calculation
reduces the scintillation power by more than a factor of 10 relative to
conventional estimates. The details of this phenomenon are discussed for
various models of non-Kolmogorov turbulence. Also, a quantitative description
of the influence of the telescope central obscuration on the measured
scintillation noise is introduced and combined with the effect of the outer
scale. Evaluation of the scintillation noise on the future TMT and E-ELT
telescopes, predicts an amplitude of approximately $10 \mumag$ for a 60 s
exposures.
