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.
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