A Multifractal-Based Wavefront Phase Estimation Technique for Ground-Based Astronomical Observations

Turbulence in the Earth's atmosphere interferes with the propagation of planar wavefronts from outer space, resulting in a phase-distorted nonplanar wavefront. This phase distortion is responsible for the refractive blurring of images accounting to the loss in spatial resolution power of ground-based telescopes. The technology widely used to remove this phase distortion is adaptive optics (AO). In AO, an estimate of the distorted phase is provided by a wavefront sensor (WFS) in the form of low-resolution slope measurements of the wavefront. The estimate is then used to create a corrected wavefront that (approximately) removes the phase distortion from the incoming wavefronts. Phase reconstruction from WFS measurements is done by solving large linear systems, followed by interpolating the low-resolution phase to its desired high resolution. In this paper, we propose an alternate technique to wavefront phase reconstruction using concepts derived from the microcanonical multiscale formalism, which is a specific approach to multifractality. We take into account an a priori information of the wavefront phase, provided by the multifractal exponents. Then, through the framework of multiresolution analysis and wavelet transform, we address the problem of phase reconstruction from low-resolution WFS measurements. Comparison, in terms of reconstruction quality, with classical techniques in AO proves the superiority of our approach.