Reconstruction of Optical Phase from Acquired Sub-image Gradients Using Non-linear and Multiscale Approach in the Analysis of Complex Signals

Turbulences in the Earths atmosphere lead to the loss in spatial resolution power of ground based telescopes. The common mechanism used to deal with this phenomenon is Adaptive Optics (AO), which compensates for the loss in resolution power, in real time, by means of a servo-control loop. In this paper, we propose a new approach to phase reconstruction of astronomical images using Microcanonical Multiscale Formalism (herein referred to as MMF) and also check the performance of the reconstruction under noise. In fact, turbulent flows, although chaotic in nature, possess a complex arrangement of geometrical structures related to the cascading properties of physical variables; the properties of these variables reflect the transfer of energy taking place from large scales to smaller ones. The geometrical representation of the cascade process can be exploited by the use of an appropriate wavelet (here Battle-Lemarié of order 3) decomposition which leads to a proper reconstruction of the turbulent phase. Keywords—adaptive optics, atmospheric turbulence, cascade processes, microcanonical multiscale formalism, phase reconstruction, wavelets.