  Wavefront stabilization is a fundamental challenge to high contrast imaging
of exoplanets. For both space and ground observations, wavefront control
performance is ultimately limited by the finite amount of starlight available
for sensing, so wavefront measurements must be as efficient as possible. To
meet this challenge, we propose to sense residual errors using bright
focal-plane speckles at wavelengths outside the high contrast spectral
bandwidth. We show that a linear relationship exists between the intensity of
the bright out-of-band speckles and residual wavefront aberrations. An
efficient linear control loop can exploit this relationship. The proposed
scheme, referred to as Spectral Linear Dark Field Control (spectral LDFC), is
more sensitive than conventional approaches for ultra-high contrast imaging.
Spectral LDFC is closely related to, and can be combined with, the recently
proposed spatial LDFC which uses light at the observation wavelength but
located outside of the high contrast area in the focal plane image. Both LDFC
techniques do not require starlight to be mixed with the high contrast speckle
field, so full-sensitivity uninterrupted high contrast observations can be
conducted simultaneously with wavefront correction iterations. We also show
that LDFC is robust against deformable mirror calibration errors and drifts, as
it relies on detector response stability instead of deformable mirror
stability. LDFC is particularly advantageous when science acquisition is
performed at a non-optimal wavefront sensing wavelength, such as nearIR
observations of planets around solar-type stars, for which visible-light
speckle sensing is ideal. We describe the approach at a fundamental level and
provide an algorithm for its implementation. We demonstrate, through numerical
simulation, that spectral LDFC is well-suited for picometer-level cophasing of
a large segmented space telescope.
