Theoretical analysis of adaptive optics system based on stochastic parallel gradient descent algorithm

Abstract

The adaptive optics (AO) technology without a wave-front sensor is simple and has more application fields than conventional AO technologies. The theory basis of the AO system based on stochastic parallel gradient descent (SPGD) from the convergence, the stability, and the averaged convergence rate is analyzed, where SPGD is used to control the AO system. The results show that the AO system based on SPGD can obtain good convergence and stability, and the fast convergence rate, which is in inverse proportion to n (n is the number of control parameters). C Adaptive optics (AO) technologies are often used to compensate different wave-front distortions. The classical AO technologies have been implemented in astronomy successfully [1] and retina imaging [2,3] . A significant drawback of classical AO technologies is that the information of phase modulation can not be measured directly and must be reconstructed from intensity information gathered from wave-front sensors. There exists an alternative method, which does not require determining phase from intensity. The system usually considers a "sharpness" criterion as a function of the control parameters and then uses certain optimization algorithm to find the optimum. Among mode-free optimization techniques, the stochastic parallel gradient descent (SPGD) [4] is perhaps the most promising control algorithm for AO applications [5] .Researchers have studied applications of AO technology based on SPGD in different fields and have obtained some valuable results, such as retina imaging [6] , direct energy and laser communication applications [7] , astronomy imaging [8] and extended object imaging [9] . M.A. Vorontsov [4] preliminarily deduced the convergence and the stability of AO system based on SPGD. In this paper, we will generalize the convergence and the stability and analyze the convergence rate of AO system based on SPGD.It is assumed that the system performance metric is J = J(u), the control parameter is u = {u 1 , u 2 , u n }, and the *

Research on a New Singularity-Free Controller for Uncertain Lorenz System

“…, γ n }, and the change of the system performance is δ J , where n is the number of control parameters. The SPGD performs an incremental adjustment of control parameter {γ j } using a realtime estimation for the gradient {J j = ∂J /∂γ j } with the replacement ofJ = δ J δ γ j in real applications [33], where δ is defined as a perturbation. In this paper, to compute Eqs.…”