Optimal control, observers and integrators in adaptive optics

Abstract

The fundamental issue of residual phase variance minimization in adaptive optics (AO) loops is addressed here from a control engineering perspective. This problem, when suitably modeled using a state-space approach, can be broken down into an optimal deterministic control problem and an optimal estimation problem, the solution of which are a linear quadratic (LQ) control and a Kalman filter. This approach provides a convenient framework for analyzing existing AO controllers, which are shown to contain an implicit phase turbulent model. In particular, standard integrator-based AO controllers assume a constant turbulent phase, which renders them prone to the notorious wind-up effect.

Kalman Filter Based Optimal Controllers in Free Space Optics Communication

“…However, atmospheric turbulence in this system will bring phase disturbances along propagation paths that result in intensity fluctuation (scintillation), beam wandering and beam broadening at the receiver leading to significant decrease of coupling efficiency at the receiving terminal, which influences the stability and reliability of the FSO communication systems. Adaptive optics (AO) systems are used to compensate time-varying wavefront distortions by using noise and measurement delay [1]. The objective of AO system in astronomy or satellite-to-ground free space laser communication is to minimize the effects of atmospheric aberrations of received signals [2,3].…”

“…However, in our study, we focus on the various Kalman filters in an AO system with the models more conveniently given in [1,[20][21][22][23][24]. A closedloop control law resulting from a global optimization is proposed in [20] to demonstrate the efficiency in the context of multi-conjugate adaptive optics (MCAO).…”

“…Under the same frame, the issue of residual phase variance minimization in AO loops from control perspective is addressed in [1]. This study indicates that a suitably modeled AO system can be divided into an optimal deterministic control problem and an optimal estimation problem.…”

“…The solution of this problem is a linear quadratic (LG) control with a Kalman filter. Actually, a convenient framework for the analysis of AO controllers is provided in [1] with an implicit phase turbulence model. Based on the framework, some interesting experimental studies are also given in [21][22][23][24], for example, vibrations, windshake, and tracking are considered in [21,22,24] which illustrate the experimental validation of the control law that LQG can provide an optimal correction of the vibrations in the case of residual phase minimal variance.…”

“…Based on the framework, some interesting experimental studies are also given in [21][22][23][24], for example, vibrations, windshake, and tracking are considered in [21,22,24] which illustrate the experimental validation of the control law that LQG can provide an optimal correction of the vibrations in the case of residual phase minimal variance. The method with experimental proof in [23] is fundamentally the same as that in [1]. In addition, basically by following Caroline Kulcsár's model [1], an improvement for bad performance of Kalman gain from some unrealistic assumptions is presented in [25].…”