  High precision fast photometry from ground-based observatories is a challenge
due to intensity fluctuations (scintillation) produced by the Earth's
atmosphere. Here we describe a method to reduce the effects of scintillation by
a combination of pupil reconjugation and calibration using a comparison star.
Because scintillation is produced by high altitude turbulence, the range of
angles over which the scintillation is correlated is small and therefore simple
correction by a comparison star is normally impossible. We propose
reconjugating the telescope pupil to a high dominant layer of turbulence, then
apodizing it before calibration with a comparison star. We find by simulation
that given a simple atmosphere with a single high altitude turbulent layer and
a strong surface layer a reduction in the intensity variance by a factor of ~30
is possible. Given a more realistic atmosphere as measured by SCIDAR at San
Pedro M\'artir we find that on a night with a strong high altitude layer we can
expect the median variance to be reduced by a factor of 11. By reducing the
scintillation noise we will be able to detect much smaller changes in
brightness. If we assume a 2 m telescope and an exposure time of 30 seconds a
reduction in the scintillation noise from 0.78 mmag to 0.21 mmag is possible,
which will enable the routine detection of, for example, the secondary transits
of extrasolar planets from the ground.
