Polychromatic compensation of propagated aberrations for high-contrast imaging

We describe the influence of Fresnel propagation in apodized-pupil coronagraphs and introduce a methodology to compensate for propagated wavefront aberrations. We start from the Fresnel integral and derive an analytical closed form for the propagated field at an arbitrary distance from a pupil. In a second part, we show that the propagation of the coronagraphic term can be neglected with sufficiently oversized optics. Then we derive a λ-Fourier expansion of the aberration at an arbitrary plane in the optical train of a telescope. Finally, we present a series of wavefront actuators, based on multiple deformable mirrors, that possess adequate chromatic behavior to correct for the dominant terms of this expansion.