Model Predictive Control of Time-Varying Aberrations for Sensorless Adaptive Optics

Abstract

We propose a model predictive control (MPC) 1 method to compensate for the time-varying phase aberrations 2 in a sensorless adaptive optics (AO) system. The approximate 3 model for the point spread function (PSF) of the imaging system 4 with phase diversity is mathematically derived, and its validity 5 is verified. The proposed MPC, which considers the operating 6 limits of the deformable mirror (DM), computes the optimal 7 applied voltage of each actuator over a prediction horizon, and 8 the receding horizon scheme is applied as feedback control. 9 Numerical case studies with the time-varying phase aberrations 10 generated by an atmospheric turbulence simulator are presented 11 to demonstrate the correction performance of the MPC strat-12 egy. The proposed method caused a 50% improvement in the 13 reduction in residual aberration, making it competitive with a 14 saturation linear quadratic regulator (LQR). The computational 15 feasibility of the proposed method is validated using fast MPC, 16 which approximates the primal barrier method. 17 Index Terms-Model identification, model predictive control 18 (MPC), phase diversity, phase retrieval method, point spread 19 function (PSF), sensorless adaptive optics (AO). 20 I. INTRODUCTION 21 A TMOSPHERIC turbulence or nonuniform refractive 22 index distribution of a specimen can cause optical aber-23 rations, which degrade the axial resolution and contrast of 24 the image and limit the depth of focus. To eliminate these 25 aberrations, adaptive optics (AO) has been introduced to 26 generate a conjugated wavefront corresponding to the opposite 27 component of the distorted wavefront. The AO system uses an 28 adaptive element, such as a deformable mirror (DM) or spatial 29 light modulator to correct aberrations and a control system that 30 generates a signal to drive the adaptive element.

Optimized Approach for Image Design Processing in Optical Networks: A Comparative Study

“…According to different control algorithms, WFSless AO systems can be roughly divided into modelfree optimization systems [37]- [39] and model-based optimization systems [40]- [41]. Model-free optimization systems directly use various blind optimization algorithms as system control algorithms, such as stochastic parallel gradient descent (SPGD) [42], simulated annealing [43], genetic algorithm (GA) [44], etc.…”