  Ground-based ultra-high contrast imaging, as required for direct imaging of
exoplanets and other solar systems, is limited by difficulty of separating the
planetary emission from the effects of optical aberrations that are not
compensated by the adaptive optics (AO) system, so-called "non-common path
aberrations" (NCPAs). Simultaneous ($\sim$ millisecond) exposures by the
science camera and the AO system enable the use of "phase diversity" to
estimate both the NCPAs and the scene via a processing procedure first
described by the author (R. Frazin 2013, ApJ, 767, article id. 21). This method
is fully compatible with more standard concepts used in long-exposure
high-contrast imaging, such as angular differential imaging and spectral
deconvolution. Long-exposure methods find time-dependent NCPAs, such as those
caused by vibrations, particularly challenging. Here, an NCPA of the form of
$\alpha \cos(k \cdot r - \omega t + \vartheta)$ is considered. It is shown
that, when sampled at millisecond time-scales, the image plane data are
sensitive to $\mbox{arg}(\alpha)$, $\vartheta$ and $\omega$, and, therefore
such NCPAs can be simultaneously estimated with the scene. Simulations of
observations with ms exposure times are reported. These simulations include
substantial detector noise and a sinusoidal NCPA that places a speckle exactly
at the location of a planet. Simulations show that the effects of detector
noise can be mitigated by mixing exposures of various lengths, allowing
estimation of the planet's brightness.
