Extremely fast focal-plane wavefront sensing for extreme adaptive optics

Abstract

We present a promising approach to the extremely fast sensing and correction of small wavefront errors in adaptive optics systems. As our algorithm's computational complexity is roughly proportional to the number of actuators, it is particularly suitable to systems with 10,000 to 100,000 actuators. Our approach is based on sequential phase diversity and simple relations between the point-spread function and the wavefront error in the case of small aberrations. The particular choice of phase diversity, introduced by the deformable mirror itself, minimizes the wavefront error as well as the computational complexity. The method is well suited for highcontrast astronomical imaging of point sources such as the direct detection and characterization of exoplanets around stars, and it works even in the presence of a coronagraph that suppresses the diffraction pattern. The accompanying paper in these proceedings by Korkiakoski et al. describes the performance of the algorithm using numerical simulations and laboratory tests.

Focal-plane wavefront estimation and control using the extended Kalman filter

“…The classical approximation used to obtain this quadratic form is the Born approximation [4]. We use a more accurate approximation, that is the second order Taylor expansion of the PSF [10]. This has also the advantage of allowing us to use larger diversities than the classical approach.…”

Iterative linear focal-plane wavefront correction

“…It has been shown in [6] that an additional quadratic term leads to a more accurate PSF approximation than using the Born approximation. This term is obtained using a secondorder Taylor expansion of the GPF in ϕ 0 and neglecting the third and the fourth orders of the resulting PSF.…”

“…Spatial domain techniques make use of a local model for the PSF, but do not use the Fourier transform. The common idea in decreasing the computational complexity is the approximation of the PSF based on the assumption that the total aberration is small [5,6,10]. This small-phase assumption is associated in the literature with the Born approximation [5,11,12], which implicitly assumes that the diversity used is small.…”

“…Recently, in [6], it was shown that using a second-order expansion of the generalized pupil function (GPF), wavefront retrieval algorithms give more accurate results than using the Born approximation, which results from a linear expansion of the GPF. The key assumption of these methods is that the sum of the diversity and the aberration is small.…”

“…As a consequence, nonlinear PD has a limited usage in real-time correction algorithms [2], and different ideas have been presented to decrease the complexity of the calculations. These ideas can be split up into Fourier domain [4][5][6][7] and spatial domain [8,9] techniques. The Gerchberg-Saxton [4] algorithm is one of the oldest and best known Fourier domain techniques, which is an iterative algorithm for retrieving the phase from intensity measurements.…”