  This paper provides a framework for the incorporation of the wavefront sensor
measurements in the context of observing modes in which the science camera
takes millisecond exposures. In this formulation, the wavefront sensor
measurements provide a means to jointly estimate the static speckle and the
planetary signal. The ability to estimate planetary intensities in as little as
few seconds has the potential to greatly improve the efficiency of exoplanet
search surveys. Unlike currently used methods, in which increasing the
observation time beyond a certain threshold is useless, this method produces
estimates whose error covariances decrease more quickly than inversely
proportional to the observation time. This is due to the fact that the
estimates of the quasi-static aberrations are informed by a new random (but
approximately known) wavefront every millisecond. The method can be extended to
include angular (due to diurnal field rotation) and spectral diversity.
Numerical experiments are performed with wavefront data from the AEOS Adaptive
Optics System sensing at 850 nm. These experiments assume a science camera
wavelength $\lambda$\ of $1.1 \, \mu$, that the measured wavefronts are exact,
and a Gaussian approximation of shot-noise. The effects of detector read-out
noise and other issues are left to future investigations. A number of static
aberrations are introduced, including one with a spatial frequency exactly
corresponding the planet location, which was at a distance of $\approx
3\lambda/D$\ from the star. Using only 4 seconds of simulated observation time,
a planetary intensity, of $\approx 1$ photon/ms, a stellar intensity of
$\approx 10^5$\ photons/ms (contrast ratio $10^5$), the short-exposure
estimation method recovers the amplitudes static aberrations with a 1%
accuracy, and the planet brightness with a with 20% accuracy.
