On representing and correcting wavefront errors in high-contrast imaging systems

Conventional adaptive-optics systems correct the wavefront by adjusting a deformable mirror (DM) based on measurements of the phase aberration taken in a pupil plane. The ability of this technique, known as phase conjugation, to correct aberrations is normally limited by the maximum spatial frequency of the DM. In this paper we show that conventional phase conjugation is not able to achieve the dark nulls needed for high-contrast imaging. Linear combinations of high frequencies in the aberration at the pupil plane "fold" and appear as low-frequency aberrations at the image plane. After describing the frequency-folding phenomenon, we present an alternative optimized solution for the shape of the deformable mirror based on the Fourier decomposition of the effective phase and amplitude aberrations.