  In direct imaging of exoplanets from space, achieving the required dynamic
range (i.e., planet-to-star contrast in brightness) currently relies on
coronagraphic technology combined with active control of one or more deformable
mirrors (DMs) to create a dark region in the image plane, sometimes called a
"dark hole." While many algorithms have been proposed for this purpose, all of
them employ focal plane wavefront sensing (FPWS) in order to calculate the
optimal DM configuration to create the desired dark hole. All current
algorithms are limited by their own success in that, as the dark hole is
achieved, the FPWS procedure becomes shot-noise limited due to he low intensity
in the dark hole. This article proposes a FPWS procedure that allows
determination of the optimal DM configuration without relying on information
obtained when the DM is near the optimal configuration. This article gives
regression procedures for FPWS that do not assume the DM step size is small,
which should allow two important improvements to the control loop: 1)
performing informative FPWS observations with DM configurations that are
sufficiently distant from the optimal dark hole configuration to mitigate
shot-noise limitations, and 2) more accurately predicting the DM configuration
that will achieve the desired objective in the dark hole control loop. In order
to treat this more challenging FPWS problem, two different representations are
presented. The first of these, is called the empirical Green's function (EGF),
is easy to implement, and has a block-diagonal matrix structure that is
well-suited to parallel processing. The other representation, based on an
explicit aberration expansion (EAE) requires the regression to estimate a
smaller number of parameters than the EGF, but leads to a dense matrix
structure. The EGF and EAE methods both simultaneously estimate the planetary
image.
